Properties

Label 731.2.e.a.681.8
Level 731
Weight 2
Character 731.681
Analytic conductor 5.837
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 681.8
Character \(\chi\) = 731.681
Dual form 731.2.e.a.307.8

$q$-expansion

\(f(q)\) \(=\) \(q-1.79000 q^{2} +(0.128663 + 0.222852i) q^{3} +1.20411 q^{4} +(-1.10204 - 1.90879i) q^{5} +(-0.230308 - 0.398905i) q^{6} +(1.71488 - 2.97026i) q^{7} +1.42464 q^{8} +(1.46689 - 2.54073i) q^{9} +O(q^{10})\) \(q-1.79000 q^{2} +(0.128663 + 0.222852i) q^{3} +1.20411 q^{4} +(-1.10204 - 1.90879i) q^{5} +(-0.230308 - 0.398905i) q^{6} +(1.71488 - 2.97026i) q^{7} +1.42464 q^{8} +(1.46689 - 2.54073i) q^{9} +(1.97265 + 3.41674i) q^{10} -5.96131 q^{11} +(0.154926 + 0.268339i) q^{12} +(1.79991 - 3.11754i) q^{13} +(-3.06964 + 5.31677i) q^{14} +(0.283584 - 0.491182i) q^{15} -4.95834 q^{16} +(0.500000 - 0.866025i) q^{17} +(-2.62574 + 4.54792i) q^{18} +(-0.138506 - 0.239899i) q^{19} +(-1.32698 - 2.29840i) q^{20} +0.882569 q^{21} +10.6708 q^{22} +(2.74128 + 4.74803i) q^{23} +(0.183299 + 0.317483i) q^{24} +(0.0710215 - 0.123013i) q^{25} +(-3.22185 + 5.58042i) q^{26} +1.52692 q^{27} +(2.06491 - 3.57653i) q^{28} +(-2.44223 + 4.23007i) q^{29} +(-0.507617 + 0.879218i) q^{30} +(1.48371 + 2.56986i) q^{31} +6.02617 q^{32} +(-0.767003 - 1.32849i) q^{33} +(-0.895002 + 1.55019i) q^{34} -7.55945 q^{35} +(1.76631 - 3.05933i) q^{36} +(-3.22207 - 5.58079i) q^{37} +(0.247926 + 0.429420i) q^{38} +0.926333 q^{39} +(-1.57001 - 2.71933i) q^{40} -9.04143 q^{41} -1.57980 q^{42} +(-5.22616 + 3.96071i) q^{43} -7.17810 q^{44} -6.46628 q^{45} +(-4.90690 - 8.49900i) q^{46} +9.75435 q^{47} +(-0.637957 - 1.10497i) q^{48} +(-2.38162 - 4.12508i) q^{49} +(-0.127129 + 0.220193i) q^{50} +0.257327 q^{51} +(2.16730 - 3.75388i) q^{52} +(-1.89056 - 3.27454i) q^{53} -2.73320 q^{54} +(6.56959 + 11.3789i) q^{55} +(2.44308 - 4.23154i) q^{56} +(0.0356413 - 0.0617325i) q^{57} +(4.37161 - 7.57185i) q^{58} -3.55194 q^{59} +(0.341468 - 0.591440i) q^{60} +(3.11029 - 5.38718i) q^{61} +(-2.65585 - 4.60007i) q^{62} +(-5.03108 - 8.71409i) q^{63} -0.870188 q^{64} -7.93430 q^{65} +(1.37294 + 2.37800i) q^{66} +(-5.60312 - 9.70488i) q^{67} +(0.602057 - 1.04279i) q^{68} +(-0.705405 + 1.22180i) q^{69} +13.5314 q^{70} +(-4.74674 + 8.22160i) q^{71} +(2.08979 - 3.61962i) q^{72} +(-4.76251 + 8.24892i) q^{73} +(5.76752 + 9.98964i) q^{74} +0.0365515 q^{75} +(-0.166777 - 0.288866i) q^{76} +(-10.2229 + 17.7066i) q^{77} -1.65814 q^{78} +(6.80018 - 11.7783i) q^{79} +(5.46428 + 9.46441i) q^{80} +(-4.20422 - 7.28191i) q^{81} +16.1842 q^{82} +(-1.77690 - 3.07768i) q^{83} +1.06271 q^{84} -2.20408 q^{85} +(9.35485 - 7.08969i) q^{86} -1.25690 q^{87} -8.49271 q^{88} +(-0.0943611 - 0.163438i) q^{89} +11.5747 q^{90} +(-6.17327 - 10.6924i) q^{91} +(3.30081 + 5.71718i) q^{92} +(-0.381799 + 0.661295i) q^{93} -17.4603 q^{94} +(-0.305277 + 0.528756i) q^{95} +(0.775348 + 1.34294i) q^{96} -16.6653 q^{97} +(4.26310 + 7.38391i) q^{98} +(-8.74460 + 15.1461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + O(q^{10}) \) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + 4q^{10} + 16q^{11} + 12q^{12} + 2q^{13} - 11q^{14} + 7q^{15} + 30q^{16} + 29q^{17} + 8q^{18} + 8q^{19} - 33q^{20} - 26q^{21} - 22q^{22} - 5q^{23} + 12q^{24} - 36q^{25} - 12q^{27} + 15q^{28} + 2q^{29} + 11q^{30} + 3q^{31} - 40q^{32} + 17q^{33} - 3q^{34} + 38q^{35} - 7q^{36} + 2q^{37} + q^{38} - 54q^{39} + 5q^{40} + 14q^{41} - 112q^{42} + 31q^{43} - 24q^{44} - 46q^{45} - 13q^{46} - 28q^{47} - 28q^{49} - 13q^{50} + 6q^{51} + 85q^{52} - 10q^{53} + 34q^{54} + 36q^{55} - 54q^{56} - 23q^{57} + 3q^{58} + 12q^{59} + 2q^{60} - q^{61} - q^{62} - 14q^{63} + 28q^{64} + 80q^{65} - 74q^{66} + 11q^{67} + 27q^{68} - 11q^{69} + 2q^{70} + 16q^{71} + 21q^{72} + 14q^{73} + 21q^{74} - 54q^{75} + 44q^{76} + 25q^{77} + 88q^{78} - 4q^{79} - 112q^{80} + 11q^{81} - 176q^{82} - 3q^{83} + 100q^{84} - 2q^{85} + 44q^{86} + 8q^{87} - 106q^{88} + 82q^{89} + 54q^{90} - 15q^{91} + 42q^{92} + 88q^{94} + 29q^{95} + 20q^{96} + 20q^{97} + 44q^{98} - 54q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.79000 −1.26572 −0.632862 0.774265i \(-0.718120\pi\)
−0.632862 + 0.774265i \(0.718120\pi\)
\(3\) 0.128663 + 0.222852i 0.0742839 + 0.128663i 0.900775 0.434287i \(-0.143000\pi\)
−0.826491 + 0.562950i \(0.809666\pi\)
\(4\) 1.20411 0.602057
\(5\) −1.10204 1.90879i −0.492847 0.853635i 0.507119 0.861876i \(-0.330710\pi\)
−0.999966 + 0.00824034i \(0.997377\pi\)
\(6\) −0.230308 0.398905i −0.0940229 0.162852i
\(7\) 1.71488 2.97026i 0.648163 1.12265i −0.335398 0.942076i \(-0.608871\pi\)
0.983561 0.180575i \(-0.0577958\pi\)
\(8\) 1.42464 0.503686
\(9\) 1.46689 2.54073i 0.488964 0.846910i
\(10\) 1.97265 + 3.41674i 0.623808 + 1.08047i
\(11\) −5.96131 −1.79740 −0.898701 0.438561i \(-0.855488\pi\)
−0.898701 + 0.438561i \(0.855488\pi\)
\(12\) 0.154926 + 0.268339i 0.0447231 + 0.0774628i
\(13\) 1.79991 3.11754i 0.499207 0.864651i −0.500793 0.865567i \(-0.666958\pi\)
1.00000 0.000915945i \(0.000291554\pi\)
\(14\) −3.06964 + 5.31677i −0.820396 + 1.42097i
\(15\) 0.283584 0.491182i 0.0732211 0.126823i
\(16\) −4.95834 −1.23958
\(17\) 0.500000 0.866025i 0.121268 0.210042i
\(18\) −2.62574 + 4.54792i −0.618893 + 1.07195i
\(19\) −0.138506 0.239899i −0.0317754 0.0550366i 0.849700 0.527266i \(-0.176783\pi\)
−0.881476 + 0.472229i \(0.843449\pi\)
\(20\) −1.32698 2.29840i −0.296722 0.513937i
\(21\) 0.882569 0.192592
\(22\) 10.6708 2.27502
\(23\) 2.74128 + 4.74803i 0.571596 + 0.990034i 0.996402 + 0.0847493i \(0.0270089\pi\)
−0.424806 + 0.905284i \(0.639658\pi\)
\(24\) 0.183299 + 0.317483i 0.0374157 + 0.0648060i
\(25\) 0.0710215 0.123013i 0.0142043 0.0246026i
\(26\) −3.22185 + 5.58042i −0.631858 + 1.09441i
\(27\) 1.52692 0.293856
\(28\) 2.06491 3.57653i 0.390231 0.675900i
\(29\) −2.44223 + 4.23007i −0.453511 + 0.785505i −0.998601 0.0528730i \(-0.983162\pi\)
0.545090 + 0.838378i \(0.316495\pi\)
\(30\) −0.507617 + 0.879218i −0.0926777 + 0.160523i
\(31\) 1.48371 + 2.56986i 0.266483 + 0.461561i 0.967951 0.251139i \(-0.0808052\pi\)
−0.701468 + 0.712701i \(0.747472\pi\)
\(32\) 6.02617 1.06529
\(33\) −0.767003 1.32849i −0.133518 0.231260i
\(34\) −0.895002 + 1.55019i −0.153492 + 0.265855i
\(35\) −7.55945 −1.27778
\(36\) 1.76631 3.05933i 0.294384 0.509888i
\(37\) −3.22207 5.58079i −0.529705 0.917476i −0.999400 0.0346472i \(-0.988969\pi\)
0.469694 0.882829i \(-0.344364\pi\)
\(38\) 0.247926 + 0.429420i 0.0402189 + 0.0696612i
\(39\) 0.926333 0.148332
\(40\) −1.57001 2.71933i −0.248240 0.429964i
\(41\) −9.04143 −1.41203 −0.706017 0.708195i \(-0.749510\pi\)
−0.706017 + 0.708195i \(0.749510\pi\)
\(42\) −1.57980 −0.243769
\(43\) −5.22616 + 3.96071i −0.796982 + 0.604003i
\(44\) −7.17810 −1.08214
\(45\) −6.46628 −0.963937
\(46\) −4.90690 8.49900i −0.723483 1.25311i
\(47\) 9.75435 1.42282 0.711409 0.702778i \(-0.248057\pi\)
0.711409 + 0.702778i \(0.248057\pi\)
\(48\) −0.637957 1.10497i −0.0920811 0.159489i
\(49\) −2.38162 4.12508i −0.340231 0.589297i
\(50\) −0.127129 + 0.220193i −0.0179787 + 0.0311401i
\(51\) 0.257327 0.0360330
\(52\) 2.16730 3.75388i 0.300551 0.520569i
\(53\) −1.89056 3.27454i −0.259688 0.449792i 0.706470 0.707743i \(-0.250286\pi\)
−0.966158 + 0.257950i \(0.916953\pi\)
\(54\) −2.73320 −0.371941
\(55\) 6.56959 + 11.3789i 0.885844 + 1.53433i
\(56\) 2.44308 4.23154i 0.326471 0.565464i
\(57\) 0.0356413 0.0617325i 0.00472080 0.00817667i
\(58\) 4.37161 7.57185i 0.574020 0.994232i
\(59\) −3.55194 −0.462423 −0.231211 0.972904i \(-0.574269\pi\)
−0.231211 + 0.972904i \(0.574269\pi\)
\(60\) 0.341468 0.591440i 0.0440833 0.0763545i
\(61\) 3.11029 5.38718i 0.398232 0.689758i −0.595276 0.803521i \(-0.702957\pi\)
0.993508 + 0.113763i \(0.0362906\pi\)
\(62\) −2.65585 4.60007i −0.337293 0.584209i
\(63\) −5.03108 8.71409i −0.633857 1.09787i
\(64\) −0.870188 −0.108774
\(65\) −7.93430 −0.984129
\(66\) 1.37294 + 2.37800i 0.168997 + 0.292711i
\(67\) −5.60312 9.70488i −0.684530 1.18564i −0.973584 0.228328i \(-0.926674\pi\)
0.289055 0.957313i \(-0.406659\pi\)
\(68\) 0.602057 1.04279i 0.0730102 0.126457i
\(69\) −0.705405 + 1.22180i −0.0849208 + 0.147087i
\(70\) 13.5314 1.61732
\(71\) −4.74674 + 8.22160i −0.563335 + 0.975724i 0.433868 + 0.900977i \(0.357149\pi\)
−0.997202 + 0.0747478i \(0.976185\pi\)
\(72\) 2.08979 3.61962i 0.246284 0.426577i
\(73\) −4.76251 + 8.24892i −0.557410 + 0.965463i 0.440301 + 0.897850i \(0.354872\pi\)
−0.997712 + 0.0676128i \(0.978462\pi\)
\(74\) 5.76752 + 9.98964i 0.670461 + 1.16127i
\(75\) 0.0365515 0.00422060
\(76\) −0.166777 0.288866i −0.0191306 0.0331352i
\(77\) −10.2229 + 17.7066i −1.16501 + 2.01786i
\(78\) −1.65814 −0.187747
\(79\) 6.80018 11.7783i 0.765080 1.32516i −0.175124 0.984546i \(-0.556033\pi\)
0.940204 0.340612i \(-0.110634\pi\)
\(80\) 5.46428 + 9.46441i 0.610925 + 1.05815i
\(81\) −4.20422 7.28191i −0.467135 0.809102i
\(82\) 16.1842 1.78725
\(83\) −1.77690 3.07768i −0.195040 0.337819i 0.751874 0.659307i \(-0.229150\pi\)
−0.946914 + 0.321488i \(0.895817\pi\)
\(84\) 1.06271 0.115952
\(85\) −2.20408 −0.239066
\(86\) 9.35485 7.08969i 1.00876 0.764501i
\(87\) −1.25690 −0.134754
\(88\) −8.49271 −0.905326
\(89\) −0.0943611 0.163438i −0.0100023 0.0173244i 0.860981 0.508637i \(-0.169851\pi\)
−0.870983 + 0.491313i \(0.836517\pi\)
\(90\) 11.5747 1.22008
\(91\) −6.17327 10.6924i −0.647135 1.12087i
\(92\) 3.30081 + 5.71718i 0.344134 + 0.596057i
\(93\) −0.381799 + 0.661295i −0.0395907 + 0.0685731i
\(94\) −17.4603 −1.80089
\(95\) −0.305277 + 0.528756i −0.0313208 + 0.0542492i
\(96\) 0.775348 + 1.34294i 0.0791336 + 0.137063i
\(97\) −16.6653 −1.69211 −0.846053 0.533099i \(-0.821027\pi\)
−0.846053 + 0.533099i \(0.821027\pi\)
\(98\) 4.26310 + 7.38391i 0.430638 + 0.745888i
\(99\) −8.74460 + 15.1461i −0.878865 + 1.52224i
\(100\) 0.0855180 0.148121i 0.00855180 0.0148121i
\(101\) 6.70119 11.6068i 0.666793 1.15492i −0.312002 0.950081i \(-0.601000\pi\)
0.978796 0.204839i \(-0.0656670\pi\)
\(102\) −0.460616 −0.0456078
\(103\) −6.39494 + 11.0764i −0.630112 + 1.09139i 0.357416 + 0.933945i \(0.383658\pi\)
−0.987528 + 0.157441i \(0.949676\pi\)
\(104\) 2.56423 4.44137i 0.251443 0.435512i
\(105\) −0.972625 1.68464i −0.0949185 0.164404i
\(106\) 3.38410 + 5.86144i 0.328693 + 0.569313i
\(107\) −5.29217 −0.511614 −0.255807 0.966728i \(-0.582341\pi\)
−0.255807 + 0.966728i \(0.582341\pi\)
\(108\) 1.83859 0.176918
\(109\) 2.46133 + 4.26315i 0.235753 + 0.408335i 0.959491 0.281739i \(-0.0909112\pi\)
−0.723739 + 0.690074i \(0.757578\pi\)
\(110\) −11.7596 20.3682i −1.12123 1.94203i
\(111\) 0.829126 1.43609i 0.0786971 0.136307i
\(112\) −8.50295 + 14.7275i −0.803453 + 1.39162i
\(113\) 15.8972 1.49548 0.747741 0.663990i \(-0.231138\pi\)
0.747741 + 0.663990i \(0.231138\pi\)
\(114\) −0.0637980 + 0.110501i −0.00597523 + 0.0103494i
\(115\) 6.04199 10.4650i 0.563419 0.975870i
\(116\) −2.94073 + 5.09349i −0.273040 + 0.472919i
\(117\) −5.28056 9.14620i −0.488188 0.845566i
\(118\) 6.35798 0.585300
\(119\) −1.71488 2.97026i −0.157203 0.272283i
\(120\) 0.404005 0.699757i 0.0368804 0.0638788i
\(121\) 24.5372 2.23066
\(122\) −5.56743 + 9.64308i −0.504052 + 0.873043i
\(123\) −1.16330 2.01490i −0.104891 0.181677i
\(124\) 1.78656 + 3.09441i 0.160438 + 0.277886i
\(125\) −11.3335 −1.01370
\(126\) 9.00566 + 15.5983i 0.802288 + 1.38960i
\(127\) 11.3260 1.00502 0.502511 0.864571i \(-0.332410\pi\)
0.502511 + 0.864571i \(0.332410\pi\)
\(128\) −10.4947 −0.927609
\(129\) −1.55507 0.655059i −0.136916 0.0576748i
\(130\) 14.2024 1.24564
\(131\) −7.14682 −0.624421 −0.312210 0.950013i \(-0.601069\pi\)
−0.312210 + 0.950013i \(0.601069\pi\)
\(132\) −0.923559 1.59965i −0.0803855 0.139232i
\(133\) −0.950082 −0.0823826
\(134\) 10.0296 + 17.3718i 0.866426 + 1.50069i
\(135\) −1.68273 2.91457i −0.144826 0.250846i
\(136\) 0.712319 1.23377i 0.0610809 0.105795i
\(137\) −2.21993 −0.189662 −0.0948308 0.995493i \(-0.530231\pi\)
−0.0948308 + 0.995493i \(0.530231\pi\)
\(138\) 1.26268 2.18702i 0.107486 0.186172i
\(139\) 9.16672 + 15.8772i 0.777511 + 1.34669i 0.933372 + 0.358910i \(0.116851\pi\)
−0.155861 + 0.987779i \(0.549815\pi\)
\(140\) −9.10244 −0.769297
\(141\) 1.25503 + 2.17377i 0.105692 + 0.183065i
\(142\) 8.49669 14.7167i 0.713026 1.23500i
\(143\) −10.7299 + 18.5846i −0.897275 + 1.55413i
\(144\) −7.27334 + 12.5978i −0.606112 + 1.04982i
\(145\) 10.7657 0.894046
\(146\) 8.52492 14.7656i 0.705527 1.22201i
\(147\) 0.612854 1.06149i 0.0505473 0.0875506i
\(148\) −3.87974 6.71991i −0.318913 0.552373i
\(149\) −5.36497 9.29240i −0.439516 0.761263i 0.558136 0.829749i \(-0.311517\pi\)
−0.997652 + 0.0684858i \(0.978183\pi\)
\(150\) −0.0654273 −0.00534212
\(151\) −5.64830 −0.459652 −0.229826 0.973232i \(-0.573816\pi\)
−0.229826 + 0.973232i \(0.573816\pi\)
\(152\) −0.197321 0.341769i −0.0160048 0.0277212i
\(153\) −1.46689 2.54073i −0.118591 0.205406i
\(154\) 18.2991 31.6949i 1.47458 2.55405i
\(155\) 3.27022 5.66418i 0.262670 0.454958i
\(156\) 1.11541 0.0893044
\(157\) 0.462871 0.801716i 0.0369411 0.0639839i −0.846964 0.531651i \(-0.821572\pi\)
0.883905 + 0.467667i \(0.154905\pi\)
\(158\) −12.1724 + 21.0831i −0.968381 + 1.67728i
\(159\) 0.486491 0.842627i 0.0385812 0.0668247i
\(160\) −6.64107 11.5027i −0.525023 0.909366i
\(161\) 18.8038 1.48195
\(162\) 7.52556 + 13.0347i 0.591264 + 1.02410i
\(163\) 6.75447 11.6991i 0.529051 0.916344i −0.470375 0.882467i \(-0.655881\pi\)
0.999426 0.0338769i \(-0.0107854\pi\)
\(164\) −10.8869 −0.850125
\(165\) −1.69053 + 2.92809i −0.131608 + 0.227952i
\(166\) 3.18065 + 5.50905i 0.246867 + 0.427585i
\(167\) 4.78116 + 8.28121i 0.369977 + 0.640819i 0.989562 0.144111i \(-0.0460322\pi\)
−0.619585 + 0.784930i \(0.712699\pi\)
\(168\) 1.25734 0.0970060
\(169\) 0.0206131 + 0.0357029i 0.00158562 + 0.00274638i
\(170\) 3.94531 0.302591
\(171\) −0.812692 −0.0621481
\(172\) −6.29289 + 4.76915i −0.479829 + 0.363644i
\(173\) 5.54269 0.421403 0.210701 0.977550i \(-0.432425\pi\)
0.210701 + 0.977550i \(0.432425\pi\)
\(174\) 2.24986 0.170562
\(175\) −0.243586 0.421904i −0.0184134 0.0318929i
\(176\) 29.5582 2.22803
\(177\) −0.457004 0.791555i −0.0343506 0.0594969i
\(178\) 0.168907 + 0.292555i 0.0126601 + 0.0219279i
\(179\) 3.83923 6.64974i 0.286958 0.497025i −0.686124 0.727484i \(-0.740689\pi\)
0.973082 + 0.230459i \(0.0740228\pi\)
\(180\) −7.78615 −0.580345
\(181\) −2.07910 + 3.60111i −0.154539 + 0.267669i −0.932891 0.360159i \(-0.882722\pi\)
0.778352 + 0.627828i \(0.216056\pi\)
\(182\) 11.0502 + 19.1395i 0.819094 + 1.41871i
\(183\) 1.60072 0.118329
\(184\) 3.90533 + 6.76423i 0.287905 + 0.498666i
\(185\) −7.10169 + 12.3005i −0.522127 + 0.904350i
\(186\) 0.683422 1.18372i 0.0501109 0.0867947i
\(187\) −2.98066 + 5.16265i −0.217967 + 0.377530i
\(188\) 11.7454 0.856618
\(189\) 2.61849 4.53535i 0.190467 0.329898i
\(190\) 0.546448 0.946475i 0.0396435 0.0686645i
\(191\) −5.97365 10.3467i −0.432238 0.748658i 0.564828 0.825209i \(-0.308943\pi\)
−0.997066 + 0.0765505i \(0.975609\pi\)
\(192\) −0.111961 0.193923i −0.00808012 0.0139952i
\(193\) 27.6627 1.99120 0.995601 0.0936945i \(-0.0298677\pi\)
0.995601 + 0.0936945i \(0.0298677\pi\)
\(194\) 29.8310 2.14174
\(195\) −1.02085 1.76817i −0.0731049 0.126621i
\(196\) −2.86774 4.96707i −0.204838 0.354791i
\(197\) −5.06571 + 8.77406i −0.360917 + 0.625126i −0.988112 0.153736i \(-0.950869\pi\)
0.627195 + 0.778862i \(0.284203\pi\)
\(198\) 15.6529 27.1116i 1.11240 1.92673i
\(199\) −0.391001 −0.0277173 −0.0138586 0.999904i \(-0.504411\pi\)
−0.0138586 + 0.999904i \(0.504411\pi\)
\(200\) 0.101180 0.175249i 0.00715450 0.0123920i
\(201\) 1.44183 2.49733i 0.101699 0.176148i
\(202\) −11.9952 + 20.7762i −0.843976 + 1.46181i
\(203\) 8.37627 + 14.5081i 0.587899 + 1.01827i
\(204\) 0.309851 0.0216939
\(205\) 9.96400 + 17.2582i 0.695916 + 1.20536i
\(206\) 11.4470 19.8267i 0.797548 1.38139i
\(207\) 16.0846 1.11796
\(208\) −8.92458 + 15.4578i −0.618809 + 1.07181i
\(209\) 0.825676 + 1.43011i 0.0571132 + 0.0989230i
\(210\) 1.74100 + 3.01551i 0.120141 + 0.208090i
\(211\) 15.3111 1.05406 0.527030 0.849847i \(-0.323305\pi\)
0.527030 + 0.849847i \(0.323305\pi\)
\(212\) −2.27645 3.94292i −0.156347 0.270801i
\(213\) −2.44293 −0.167387
\(214\) 9.47301 0.647561
\(215\) 13.3196 + 5.61077i 0.908388 + 0.382651i
\(216\) 2.17531 0.148011
\(217\) 10.1775 0.690897
\(218\) −4.40579 7.63105i −0.298398 0.516840i
\(219\) −2.45105 −0.165626
\(220\) 7.91054 + 13.7015i 0.533329 + 0.923753i
\(221\) −1.79991 3.11754i −0.121075 0.209709i
\(222\) −1.48414 + 2.57060i −0.0996088 + 0.172528i
\(223\) 1.01291 0.0678298 0.0339149 0.999425i \(-0.489202\pi\)
0.0339149 + 0.999425i \(0.489202\pi\)
\(224\) 10.3341 17.8993i 0.690479 1.19594i
\(225\) −0.208362 0.360893i −0.0138908 0.0240595i
\(226\) −28.4560 −1.89287
\(227\) −3.25044 5.62992i −0.215739 0.373671i 0.737762 0.675061i \(-0.235883\pi\)
−0.953501 + 0.301390i \(0.902549\pi\)
\(228\) 0.0429162 0.0743330i 0.00284219 0.00492282i
\(229\) −1.74663 + 3.02524i −0.115420 + 0.199914i −0.917948 0.396701i \(-0.870155\pi\)
0.802527 + 0.596615i \(0.203488\pi\)
\(230\) −10.8152 + 18.7325i −0.713132 + 1.23518i
\(231\) −5.26127 −0.346166
\(232\) −3.47930 + 6.02632i −0.228427 + 0.395647i
\(233\) −13.3216 + 23.0738i −0.872730 + 1.51161i −0.0135678 + 0.999908i \(0.504319\pi\)
−0.859162 + 0.511704i \(0.829014\pi\)
\(234\) 9.45222 + 16.3717i 0.617911 + 1.07025i
\(235\) −10.7497 18.6190i −0.701231 1.21457i
\(236\) −4.27694 −0.278405
\(237\) 3.49974 0.227333
\(238\) 3.06964 + 5.31677i 0.198975 + 0.344635i
\(239\) −1.46616 2.53946i −0.0948380 0.164264i 0.814703 0.579878i \(-0.196900\pi\)
−0.909541 + 0.415614i \(0.863567\pi\)
\(240\) −1.40611 + 2.43545i −0.0907638 + 0.157207i
\(241\) 6.47443 11.2140i 0.417054 0.722360i −0.578587 0.815621i \(-0.696396\pi\)
0.995642 + 0.0932610i \(0.0297291\pi\)
\(242\) −43.9217 −2.82340
\(243\) 3.37224 5.84089i 0.216329 0.374693i
\(244\) 3.74515 6.48678i 0.239758 0.415274i
\(245\) −5.24927 + 9.09200i −0.335363 + 0.580866i
\(246\) 2.08231 + 3.60667i 0.132764 + 0.229953i
\(247\) −0.997194 −0.0634500
\(248\) 2.11375 + 3.66113i 0.134223 + 0.232482i
\(249\) 0.457243 0.791969i 0.0289766 0.0501890i
\(250\) 20.2869 1.28306
\(251\) 12.0870 20.9353i 0.762926 1.32143i −0.178410 0.983956i \(-0.557095\pi\)
0.941336 0.337470i \(-0.109571\pi\)
\(252\) −6.05800 10.4928i −0.381618 0.660982i
\(253\) −16.3416 28.3045i −1.02739 1.77949i
\(254\) −20.2736 −1.27208
\(255\) −0.283584 0.491182i −0.0177587 0.0307590i
\(256\) 20.5259 1.28287
\(257\) −17.9242 −1.11808 −0.559039 0.829141i \(-0.688830\pi\)
−0.559039 + 0.829141i \(0.688830\pi\)
\(258\) 2.78358 + 1.17256i 0.173298 + 0.0730003i
\(259\) −22.1018 −1.37334
\(260\) −9.55381 −0.592502
\(261\) 7.16498 + 12.4101i 0.443501 + 0.768167i
\(262\) 12.7928 0.790344
\(263\) −10.2694 17.7871i −0.633238 1.09680i −0.986886 0.161421i \(-0.948392\pi\)
0.353648 0.935379i \(-0.384941\pi\)
\(264\) −1.09270 1.89262i −0.0672511 0.116482i
\(265\) −4.16693 + 7.21734i −0.255973 + 0.443357i
\(266\) 1.70065 0.104274
\(267\) 0.0242817 0.0420571i 0.00148601 0.00257385i
\(268\) −6.74679 11.6858i −0.412126 0.713823i
\(269\) −4.64672 −0.283316 −0.141658 0.989916i \(-0.545243\pi\)
−0.141658 + 0.989916i \(0.545243\pi\)
\(270\) 3.01209 + 5.21709i 0.183310 + 0.317502i
\(271\) −5.23478 + 9.06690i −0.317990 + 0.550775i −0.980069 0.198659i \(-0.936341\pi\)
0.662078 + 0.749435i \(0.269675\pi\)
\(272\) −2.47917 + 4.29405i −0.150322 + 0.260365i
\(273\) 1.58855 2.75145i 0.0961433 0.166525i
\(274\) 3.97369 0.240059
\(275\) −0.423381 + 0.733318i −0.0255308 + 0.0442207i
\(276\) −0.849388 + 1.47118i −0.0511272 + 0.0885549i
\(277\) −14.5074 25.1276i −0.871668 1.50977i −0.860270 0.509838i \(-0.829705\pi\)
−0.0113979 0.999935i \(-0.503628\pi\)
\(278\) −16.4085 28.4203i −0.984114 1.70454i
\(279\) 8.70578 0.521201
\(280\) −10.7695 −0.643600
\(281\) −7.15139 12.3866i −0.426616 0.738921i 0.569954 0.821677i \(-0.306961\pi\)
−0.996570 + 0.0827560i \(0.973628\pi\)
\(282\) −2.24651 3.89106i −0.133777 0.231709i
\(283\) 0.0952753 0.165022i 0.00566353 0.00980952i −0.863180 0.504897i \(-0.831531\pi\)
0.868843 + 0.495087i \(0.164864\pi\)
\(284\) −5.71562 + 9.89975i −0.339160 + 0.587442i
\(285\) −0.157112 −0.00930652
\(286\) 19.2065 33.2666i 1.13570 1.96709i
\(287\) −15.5049 + 26.8554i −0.915228 + 1.58522i
\(288\) 8.83973 15.3109i 0.520886 0.902201i
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) −19.2707 −1.13162
\(291\) −2.14422 3.71389i −0.125696 0.217712i
\(292\) −5.73461 + 9.93264i −0.335593 + 0.581264i
\(293\) 23.1638 1.35324 0.676620 0.736332i \(-0.263444\pi\)
0.676620 + 0.736332i \(0.263444\pi\)
\(294\) −1.09701 + 1.90008i −0.0639790 + 0.110815i
\(295\) 3.91437 + 6.77989i 0.227904 + 0.394740i
\(296\) −4.59029 7.95061i −0.266805 0.462120i
\(297\) −9.10246 −0.528178
\(298\) 9.60332 + 16.6334i 0.556305 + 0.963549i
\(299\) 19.7363 1.14138
\(300\) 0.0440122 0.00254104
\(301\) 2.80210 + 22.3152i 0.161511 + 1.28623i
\(302\) 10.1105 0.581793
\(303\) 3.44879 0.198128
\(304\) 0.686758 + 1.18950i 0.0393883 + 0.0682225i
\(305\) −13.7106 −0.785069
\(306\) 2.62574 + 4.54792i 0.150104 + 0.259987i
\(307\) −3.25299 5.63434i −0.185658 0.321569i 0.758140 0.652092i \(-0.226108\pi\)
−0.943798 + 0.330523i \(0.892775\pi\)
\(308\) −12.3096 + 21.3208i −0.701403 + 1.21487i
\(309\) −3.29118 −0.187229
\(310\) −5.85370 + 10.1389i −0.332468 + 0.575851i
\(311\) 5.09951 + 8.83262i 0.289167 + 0.500852i 0.973611 0.228214i \(-0.0732884\pi\)
−0.684444 + 0.729065i \(0.739955\pi\)
\(312\) 1.31969 0.0747127
\(313\) −12.6223 21.8625i −0.713455 1.23574i −0.963552 0.267519i \(-0.913796\pi\)
0.250098 0.968221i \(-0.419537\pi\)
\(314\) −0.828541 + 1.43507i −0.0467572 + 0.0809859i
\(315\) −11.0889 + 19.2065i −0.624788 + 1.08217i
\(316\) 8.18820 14.1824i 0.460622 0.797821i
\(317\) −6.66686 −0.374448 −0.187224 0.982317i \(-0.559949\pi\)
−0.187224 + 0.982317i \(0.559949\pi\)
\(318\) −0.870821 + 1.50831i −0.0488332 + 0.0845816i
\(319\) 14.5589 25.2168i 0.815142 1.41187i
\(320\) 0.958981 + 1.66100i 0.0536087 + 0.0928529i
\(321\) −0.680909 1.17937i −0.0380046 0.0658260i
\(322\) −33.6590 −1.87574
\(323\) −0.277012 −0.0154133
\(324\) −5.06236 8.76826i −0.281242 0.487125i
\(325\) −0.255665 0.442825i −0.0141818 0.0245635i
\(326\) −12.0905 + 20.9414i −0.669633 + 1.15984i
\(327\) −0.633366 + 1.09702i −0.0350252 + 0.0606655i
\(328\) −12.8808 −0.711221
\(329\) 16.7275 28.9729i 0.922218 1.59733i
\(330\) 3.02606 5.24129i 0.166579 0.288524i
\(331\) −5.08184 + 8.80200i −0.279323 + 0.483801i −0.971217 0.238198i \(-0.923443\pi\)
0.691894 + 0.721999i \(0.256777\pi\)
\(332\) −2.13959 3.70587i −0.117425 0.203386i
\(333\) −18.9057 −1.03603
\(334\) −8.55829 14.8234i −0.468289 0.811100i
\(335\) −12.3497 + 21.3903i −0.674736 + 1.16868i
\(336\) −4.37607 −0.238734
\(337\) −8.33151 + 14.4306i −0.453846 + 0.786085i −0.998621 0.0524975i \(-0.983282\pi\)
0.544775 + 0.838582i \(0.316615\pi\)
\(338\) −0.0368975 0.0639084i −0.00200696 0.00347616i
\(339\) 2.04539 + 3.54272i 0.111090 + 0.192414i
\(340\) −2.65396 −0.143931
\(341\) −8.84487 15.3198i −0.478976 0.829612i
\(342\) 1.45472 0.0786623
\(343\) 7.67157 0.414226
\(344\) −7.44539 + 5.64258i −0.401428 + 0.304228i
\(345\) 3.10953 0.167412
\(346\) −9.92144 −0.533380
\(347\) −6.32850 10.9613i −0.339731 0.588432i 0.644651 0.764477i \(-0.277003\pi\)
−0.984382 + 0.176045i \(0.943670\pi\)
\(348\) −1.51346 −0.0811298
\(349\) −7.83631 13.5729i −0.419468 0.726540i 0.576418 0.817155i \(-0.304450\pi\)
−0.995886 + 0.0906153i \(0.971117\pi\)
\(350\) 0.436021 + 0.755210i 0.0233063 + 0.0403677i
\(351\) 2.74833 4.76025i 0.146695 0.254083i
\(352\) −35.9239 −1.91475
\(353\) 0.653966 1.13270i 0.0348071 0.0602876i −0.848097 0.529841i \(-0.822252\pi\)
0.882904 + 0.469553i \(0.155585\pi\)
\(354\) 0.818040 + 1.41689i 0.0434783 + 0.0753067i
\(355\) 20.9244 1.11055
\(356\) −0.113622 0.196798i −0.00602193 0.0104303i
\(357\) 0.441284 0.764327i 0.0233552 0.0404525i
\(358\) −6.87224 + 11.9031i −0.363209 + 0.629096i
\(359\) −1.93693 + 3.35485i −0.102227 + 0.177062i −0.912602 0.408849i \(-0.865930\pi\)
0.810375 + 0.585912i \(0.199263\pi\)
\(360\) −9.21212 −0.485521
\(361\) 9.46163 16.3880i 0.497981 0.862528i
\(362\) 3.72160 6.44601i 0.195603 0.338795i
\(363\) 3.15704 + 5.46816i 0.165702 + 0.287004i
\(364\) −7.43332 12.8749i −0.389612 0.674828i
\(365\) 20.9939 1.09887
\(366\) −2.86530 −0.149772
\(367\) 18.4980 + 32.0394i 0.965586 + 1.67244i 0.708031 + 0.706181i \(0.249584\pi\)
0.257555 + 0.966264i \(0.417083\pi\)
\(368\) −13.5922 23.5424i −0.708542 1.22723i
\(369\) −13.2628 + 22.9718i −0.690433 + 1.19587i
\(370\) 12.7121 22.0179i 0.660868 1.14466i
\(371\) −12.9683 −0.673280
\(372\) −0.459730 + 0.796275i −0.0238359 + 0.0412849i
\(373\) −10.1052 + 17.5027i −0.523228 + 0.906257i 0.476407 + 0.879225i \(0.341939\pi\)
−0.999635 + 0.0270322i \(0.991394\pi\)
\(374\) 5.33539 9.24116i 0.275886 0.477849i
\(375\) −1.45820 2.52568i −0.0753012 0.130426i
\(376\) 13.8964 0.716653
\(377\) 8.79162 + 15.2275i 0.452792 + 0.784258i
\(378\) −4.68710 + 8.11830i −0.241078 + 0.417560i
\(379\) 25.2529 1.29715 0.648576 0.761150i \(-0.275365\pi\)
0.648576 + 0.761150i \(0.275365\pi\)
\(380\) −0.367589 + 0.636683i −0.0188569 + 0.0326611i
\(381\) 1.45724 + 2.52402i 0.0746569 + 0.129310i
\(382\) 10.6929 + 18.5206i 0.547094 + 0.947595i
\(383\) −18.4448 −0.942486 −0.471243 0.882003i \(-0.656194\pi\)
−0.471243 + 0.882003i \(0.656194\pi\)
\(384\) −1.35028 2.33876i −0.0689064 0.119349i
\(385\) 45.0642 2.29669
\(386\) −49.5163 −2.52031
\(387\) 2.39689 + 19.0882i 0.121841 + 0.970308i
\(388\) −20.0669 −1.01874
\(389\) 22.4870 1.14013 0.570067 0.821598i \(-0.306917\pi\)
0.570067 + 0.821598i \(0.306917\pi\)
\(390\) 1.82733 + 3.16504i 0.0925307 + 0.160268i
\(391\) 5.48256 0.277265
\(392\) −3.39294 5.87675i −0.171369 0.296821i
\(393\) −0.919535 1.59268i −0.0463844 0.0803401i
\(394\) 9.06764 15.7056i 0.456821 0.791237i
\(395\) −29.9763 −1.50827
\(396\) −10.5295 + 18.2376i −0.529127 + 0.916475i
\(397\) −16.8433 29.1735i −0.845342 1.46418i −0.885323 0.464976i \(-0.846063\pi\)
0.0399810 0.999200i \(-0.487270\pi\)
\(398\) 0.699893 0.0350824
\(399\) −0.122241 0.211727i −0.00611970 0.0105996i
\(400\) −0.352148 + 0.609939i −0.0176074 + 0.0304969i
\(401\) 7.82142 13.5471i 0.390583 0.676510i −0.601943 0.798539i \(-0.705607\pi\)
0.992527 + 0.122029i \(0.0389401\pi\)
\(402\) −2.58089 + 4.47023i −0.128723 + 0.222955i
\(403\) 10.6822 0.532119
\(404\) 8.06900 13.9759i 0.401448 0.695328i
\(405\) −9.26642 + 16.0499i −0.460452 + 0.797526i
\(406\) −14.9935 25.9696i −0.744117 1.28885i
\(407\) 19.2078 + 33.2688i 0.952094 + 1.64907i
\(408\) 0.366598 0.0181493
\(409\) −9.90458 −0.489750 −0.244875 0.969555i \(-0.578747\pi\)
−0.244875 + 0.969555i \(0.578747\pi\)
\(410\) −17.8356 30.8922i −0.880838 1.52566i
\(411\) −0.285624 0.494715i −0.0140888 0.0244025i
\(412\) −7.70024 + 13.3372i −0.379364 + 0.657077i
\(413\) −6.09114 + 10.5502i −0.299725 + 0.519140i
\(414\) −28.7916 −1.41503
\(415\) −3.91642 + 6.78344i −0.192249 + 0.332986i
\(416\) 10.8466 18.7868i 0.531798 0.921101i
\(417\) −2.35884 + 4.08564i −0.115513 + 0.200075i
\(418\) −1.47796 2.55991i −0.0722895 0.125209i
\(419\) 28.7642 1.40522 0.702611 0.711574i \(-0.252017\pi\)
0.702611 + 0.711574i \(0.252017\pi\)
\(420\) −1.17115 2.02849i −0.0571464 0.0989804i
\(421\) 5.71266 9.89463i 0.278418 0.482235i −0.692574 0.721347i \(-0.743523\pi\)
0.970992 + 0.239113i \(0.0768565\pi\)
\(422\) −27.4069 −1.33415
\(423\) 14.3086 24.7832i 0.695707 1.20500i
\(424\) −2.69336 4.66503i −0.130801 0.226554i
\(425\) −0.0710215 0.123013i −0.00344505 0.00596700i
\(426\) 4.37285 0.211865
\(427\) −10.6675 18.4767i −0.516239 0.894152i
\(428\) −6.37238 −0.308021
\(429\) −5.52216 −0.266612
\(430\) −23.8421 10.0433i −1.14977 0.484331i
\(431\) 16.1131 0.776139 0.388069 0.921630i \(-0.373142\pi\)
0.388069 + 0.921630i \(0.373142\pi\)
\(432\) −7.57100 −0.364260
\(433\) 12.5095 + 21.6671i 0.601169 + 1.04126i 0.992644 + 0.121066i \(0.0386314\pi\)
−0.391476 + 0.920189i \(0.628035\pi\)
\(434\) −18.2178 −0.874484
\(435\) 1.38516 + 2.39916i 0.0664132 + 0.115031i
\(436\) 2.96372 + 5.13332i 0.141937 + 0.245841i
\(437\) 0.759366 1.31526i 0.0363254 0.0629174i
\(438\) 4.38738 0.209637
\(439\) −2.24621 + 3.89055i −0.107206 + 0.185686i −0.914637 0.404275i \(-0.867524\pi\)
0.807431 + 0.589961i \(0.200857\pi\)
\(440\) 9.35930 + 16.2108i 0.446187 + 0.772819i
\(441\) −13.9743 −0.665442
\(442\) 3.22185 + 5.58042i 0.153248 + 0.265433i
\(443\) 11.5300 19.9705i 0.547805 0.948826i −0.450620 0.892716i \(-0.648797\pi\)
0.998425 0.0561099i \(-0.0178697\pi\)
\(444\) 0.998362 1.72921i 0.0473802 0.0820649i
\(445\) −0.207979 + 0.360230i −0.00985916 + 0.0170766i
\(446\) −1.81312 −0.0858538
\(447\) 1.38055 2.39119i 0.0652979 0.113099i
\(448\) −1.49227 + 2.58468i −0.0705030 + 0.122115i
\(449\) −0.726640 1.25858i −0.0342922 0.0593959i 0.848370 0.529404i \(-0.177584\pi\)
−0.882662 + 0.470008i \(0.844251\pi\)
\(450\) 0.372968 + 0.646000i 0.0175819 + 0.0304527i
\(451\) 53.8988 2.53799
\(452\) 19.1420 0.900366
\(453\) −0.726730 1.25873i −0.0341448 0.0591405i
\(454\) 5.81830 + 10.0776i 0.273066 + 0.472964i
\(455\) −13.6064 + 23.5669i −0.637876 + 1.10483i
\(456\) 0.0507759 0.0879465i 0.00237780 0.00411847i
\(457\) −19.2248 −0.899299 −0.449649 0.893205i \(-0.648451\pi\)
−0.449649 + 0.893205i \(0.648451\pi\)
\(458\) 3.12647 5.41520i 0.146090 0.253036i
\(459\) 0.763461 1.32235i 0.0356353 0.0617222i
\(460\) 7.27525 12.6011i 0.339210 0.587529i
\(461\) −2.59155 4.48869i −0.120700 0.209059i 0.799344 0.600874i \(-0.205181\pi\)
−0.920044 + 0.391815i \(0.871847\pi\)
\(462\) 9.41769 0.438151
\(463\) 10.8768 + 18.8391i 0.505486 + 0.875528i 0.999980 + 0.00634678i \(0.00202026\pi\)
−0.494493 + 0.869181i \(0.664646\pi\)
\(464\) 12.1094 20.9741i 0.562165 0.973699i
\(465\) 1.68303 0.0780486
\(466\) 23.8458 41.3021i 1.10463 1.91328i
\(467\) −8.74578 15.1481i −0.404706 0.700972i 0.589581 0.807709i \(-0.299293\pi\)
−0.994287 + 0.106737i \(0.965960\pi\)
\(468\) −6.35840 11.0131i −0.293917 0.509079i
\(469\) −38.4347 −1.77475
\(470\) 19.2420 + 33.3280i 0.887565 + 1.53731i
\(471\) 0.238218 0.0109765
\(472\) −5.06023 −0.232916
\(473\) 31.1548 23.6110i 1.43250 1.08564i
\(474\) −6.26455 −0.287740
\(475\) −0.0393475 −0.00180539
\(476\) −2.06491 3.57653i −0.0946450 0.163930i
\(477\) −11.0930 −0.507912
\(478\) 2.62443 + 4.54565i 0.120039 + 0.207913i
\(479\) −15.2132 26.3501i −0.695110 1.20397i −0.970144 0.242531i \(-0.922022\pi\)
0.275034 0.961434i \(-0.411311\pi\)
\(480\) 1.70893 2.95995i 0.0780014 0.135102i
\(481\) −23.1978 −1.05773
\(482\) −11.5893 + 20.0732i −0.527876 + 0.914308i
\(483\) 2.41937 + 4.19047i 0.110085 + 0.190673i
\(484\) 29.5456 1.34298
\(485\) 18.3658 + 31.8105i 0.833949 + 1.44444i
\(486\) −6.03633 + 10.4552i −0.273813 + 0.474258i
\(487\) 13.7910 23.8867i 0.624928 1.08241i −0.363626 0.931545i \(-0.618462\pi\)
0.988555 0.150863i \(-0.0482051\pi\)
\(488\) 4.43104 7.67479i 0.200584 0.347421i
\(489\) 3.47622 0.157200
\(490\) 9.39621 16.2747i 0.424477 0.735216i
\(491\) 7.68483 13.3105i 0.346811 0.600695i −0.638870 0.769315i \(-0.720598\pi\)
0.985681 + 0.168620i \(0.0539310\pi\)
\(492\) −1.40075 2.42617i −0.0631506 0.109380i
\(493\) 2.44223 + 4.23007i 0.109993 + 0.190513i
\(494\) 1.78498 0.0803101
\(495\) 38.5475 1.73258
\(496\) −7.35674 12.7423i −0.330328 0.572144i
\(497\) 16.2802 + 28.1981i 0.730266 + 1.26486i
\(498\) −0.818468 + 1.41763i −0.0366764 + 0.0635254i
\(499\) −20.0347 + 34.7010i −0.896874 + 1.55343i −0.0654065 + 0.997859i \(0.520834\pi\)
−0.831468 + 0.555573i \(0.812499\pi\)
\(500\) −13.6468 −0.610303
\(501\) −1.23032 + 2.13098i −0.0549667 + 0.0952050i
\(502\) −21.6358 + 37.4743i −0.965653 + 1.67256i
\(503\) 17.2831 29.9352i 0.770614 1.33474i −0.166613 0.986022i \(-0.553283\pi\)
0.937227 0.348720i \(-0.113384\pi\)
\(504\) −7.16747 12.4144i −0.319265 0.552982i
\(505\) −29.5399 −1.31451
\(506\) 29.2516 + 50.6652i 1.30039 + 2.25234i
\(507\) −0.00530431 + 0.00918733i −0.000235572 + 0.000408023i
\(508\) 13.6378 0.605080
\(509\) 10.6524 18.4504i 0.472158 0.817802i −0.527334 0.849658i \(-0.676808\pi\)
0.999492 + 0.0318561i \(0.0101418\pi\)
\(510\) 0.507617 + 0.879218i 0.0224777 + 0.0389324i
\(511\) 16.3343 + 28.2918i 0.722585 + 1.25155i
\(512\) −15.7521 −0.696151
\(513\) −0.211488 0.366307i −0.00933740 0.0161729i
\(514\) 32.0843 1.41518
\(515\) 28.1899 1.24219
\(516\) −1.87248 0.788767i −0.0824313 0.0347235i
\(517\) −58.1487 −2.55738
\(518\) 39.5624 1.73827
\(519\) 0.713142 + 1.23520i 0.0313034 + 0.0542192i
\(520\) −11.3035 −0.495692
\(521\) −10.9820 19.0214i −0.481130 0.833342i 0.518635 0.854996i \(-0.326440\pi\)
−0.999766 + 0.0216536i \(0.993107\pi\)
\(522\) −12.8253 22.2142i −0.561350 0.972287i
\(523\) 7.14182 12.3700i 0.312290 0.540902i −0.666568 0.745445i \(-0.732237\pi\)
0.978858 + 0.204542i \(0.0655706\pi\)
\(524\) −8.60559 −0.375937
\(525\) 0.0626813 0.108567i 0.00273564 0.00473826i
\(526\) 18.3822 + 31.8390i 0.801504 + 1.38825i
\(527\) 2.96742 0.129263
\(528\) 3.80306 + 6.58709i 0.165507 + 0.286666i
\(529\) −3.52922 + 6.11279i −0.153445 + 0.265774i
\(530\) 7.45882 12.9191i 0.323991 0.561168i
\(531\) −5.21030 + 9.02451i −0.226108 + 0.391631i
\(532\) −1.14401 −0.0495990
\(533\) −16.2738 + 28.1870i −0.704897 + 1.22092i
\(534\) −0.0434643 + 0.0752823i −0.00188088 + 0.00325778i
\(535\) 5.83218 + 10.1016i 0.252147 + 0.436731i
\(536\) −7.98242 13.8260i −0.344788 0.597190i
\(537\) 1.97587 0.0852653
\(538\) 8.31765 0.358599
\(539\) 14.1976 + 24.5909i 0.611532 + 1.05920i
\(540\) −2.02620 3.50947i −0.0871936 0.151024i
\(541\) −10.9296 + 18.9305i −0.469898 + 0.813888i −0.999408 0.0344165i \(-0.989043\pi\)
0.529509 + 0.848304i \(0.322376\pi\)
\(542\) 9.37028 16.2298i 0.402488 0.697129i
\(543\) −1.07002 −0.0459189
\(544\) 3.01308 5.21881i 0.129185 0.223755i
\(545\) 5.42496 9.39631i 0.232380 0.402494i
\(546\) −2.84351 + 4.92510i −0.121691 + 0.210775i
\(547\) 8.82300 + 15.2819i 0.377244 + 0.653406i 0.990660 0.136354i \(-0.0435384\pi\)
−0.613416 + 0.789760i \(0.710205\pi\)
\(548\) −2.67305 −0.114187
\(549\) −9.12492 15.8048i −0.389442 0.674533i
\(550\) 0.757854 1.31264i 0.0323150 0.0559712i
\(551\) 1.35305 0.0576420
\(552\) −1.00495 + 1.74062i −0.0427734 + 0.0740857i
\(553\) −23.3230 40.3966i −0.991794 1.71784i
\(554\) 25.9684 + 44.9786i 1.10329 + 1.91096i
\(555\) −3.65491 −0.155142
\(556\) 11.0378 + 19.1180i 0.468106 + 0.810784i
\(557\) −34.4813 −1.46102 −0.730509 0.682903i \(-0.760717\pi\)
−0.730509 + 0.682903i \(0.760717\pi\)
\(558\) −15.5834 −0.659697
\(559\) 2.94105 + 23.4217i 0.124393 + 0.990634i
\(560\) 37.4823 1.58392
\(561\) −1.53401 −0.0647658
\(562\) 12.8010 + 22.1720i 0.539978 + 0.935270i
\(563\) 18.0282 0.759799 0.379900 0.925028i \(-0.375959\pi\)
0.379900 + 0.925028i \(0.375959\pi\)
\(564\) 1.51120 + 2.61747i 0.0636329 + 0.110215i
\(565\) −17.5193 30.3444i −0.737044 1.27660i
\(566\) −0.170543 + 0.295390i −0.00716847 + 0.0124162i
\(567\) −28.8389 −1.21112
\(568\) −6.76239 + 11.7128i −0.283744 + 0.491458i
\(569\) 6.83004 + 11.8300i 0.286330 + 0.495939i 0.972931 0.231096i \(-0.0742312\pi\)
−0.686601 + 0.727035i \(0.740898\pi\)
\(570\) 0.281231 0.0117795
\(571\) −5.75628 9.97017i −0.240893 0.417239i 0.720076 0.693895i \(-0.244107\pi\)
−0.960969 + 0.276657i \(0.910774\pi\)
\(572\) −12.9200 + 22.3780i −0.540211 + 0.935673i
\(573\) 1.53718 2.66248i 0.0642167 0.111227i
\(574\) 27.7539 48.0712i 1.15843 2.00645i
\(575\) 0.778759 0.0324765
\(576\) −1.27647 + 2.21091i −0.0531863 + 0.0921214i
\(577\) 14.2254 24.6391i 0.592210 1.02574i −0.401724 0.915761i \(-0.631589\pi\)
0.993934 0.109977i \(-0.0350778\pi\)
\(578\) 0.895002 + 1.55019i 0.0372272 + 0.0644794i
\(579\) 3.55917 + 6.16467i 0.147914 + 0.256195i
\(580\) 12.9632 0.538267
\(581\) −12.1886 −0.505670
\(582\) 3.83816 + 6.64788i 0.159097 + 0.275564i
\(583\) 11.2702 + 19.5205i 0.466764 + 0.808458i
\(584\) −6.78486 + 11.7517i −0.280760 + 0.486290i
\(585\) −11.6388 + 20.1589i −0.481204 + 0.833469i
\(586\) −41.4632 −1.71283
\(587\) −8.31840 + 14.4079i −0.343337 + 0.594677i −0.985050 0.172268i \(-0.944891\pi\)
0.641713 + 0.766945i \(0.278224\pi\)
\(588\) 0.737946 1.27816i 0.0304324 0.0527105i
\(589\) 0.411005 0.711882i 0.0169352 0.0293326i
\(590\) −7.00674 12.1360i −0.288463 0.499632i
\(591\) −2.60709 −0.107241
\(592\) 15.9761 + 27.6714i 0.656614 + 1.13729i
\(593\) 16.6531 28.8440i 0.683860 1.18448i −0.289934 0.957047i \(-0.593633\pi\)
0.973794 0.227434i \(-0.0730335\pi\)
\(594\) 16.2934 0.668528
\(595\) −3.77972 + 6.54668i −0.154954 + 0.268388i
\(596\) −6.46004 11.1891i −0.264614 0.458324i
\(597\) −0.0503075 0.0871351i −0.00205895 0.00356620i
\(598\) −35.3280 −1.44467
\(599\) 17.8293 + 30.8812i 0.728485 + 1.26177i 0.957523 + 0.288355i \(0.0931084\pi\)
−0.229039 + 0.973417i \(0.573558\pi\)
\(600\) 0.0520726 0.00212586
\(601\) 27.2436 1.11129 0.555644 0.831420i \(-0.312472\pi\)
0.555644 + 0.831420i \(0.312472\pi\)
\(602\) −5.01578 39.9443i −0.204428 1.62801i
\(603\) −32.8767 −1.33884
\(604\) −6.80120 −0.276737
\(605\) −27.0410 46.8363i −1.09937 1.90417i
\(606\) −6.17336 −0.250775
\(607\) −18.7478 32.4722i −0.760951 1.31801i −0.942361 0.334598i \(-0.891400\pi\)
0.181410 0.983407i \(-0.441934\pi\)
\(608\) −0.834659 1.44567i −0.0338499 0.0586297i
\(609\) −2.15544 + 3.73333i −0.0873428 + 0.151282i
\(610\) 24.5421 0.993681
\(611\) 17.5570 30.4096i 0.710280 1.23024i
\(612\) −1.76631 3.05933i −0.0713987 0.123666i
\(613\) −12.1160 −0.489361 −0.244681 0.969604i \(-0.578683\pi\)
−0.244681 + 0.969604i \(0.578683\pi\)
\(614\) 5.82286 + 10.0855i 0.234991 + 0.407017i
\(615\) −2.56401 + 4.44099i −0.103391 + 0.179078i
\(616\) −14.5640 + 25.2255i −0.586799 + 1.01637i
\(617\) 20.6611 35.7861i 0.831786 1.44069i −0.0648353 0.997896i \(-0.520652\pi\)
0.896621 0.442799i \(-0.146014\pi\)
\(618\) 5.89123 0.236980
\(619\) −2.26740 + 3.92725i −0.0911344 + 0.157849i −0.907989 0.418995i \(-0.862383\pi\)
0.816854 + 0.576844i \(0.195716\pi\)
\(620\) 3.93771 6.82032i 0.158142 0.273911i
\(621\) 4.18572 + 7.24988i 0.167967 + 0.290928i
\(622\) −9.12815 15.8104i −0.366005 0.633940i
\(623\) −0.647271 −0.0259324
\(624\) −4.59307 −0.183870
\(625\) 12.1348 + 21.0181i 0.485392 + 0.840724i
\(626\) 22.5940 + 39.1339i 0.903037 + 1.56411i
\(627\) −0.212469 + 0.368006i −0.00848518 + 0.0146968i
\(628\) 0.557349 0.965357i 0.0222407 0.0385220i
\(629\) −6.44414 −0.256945
\(630\) 19.8492 34.3798i 0.790809 1.36972i
\(631\) 19.7873 34.2727i 0.787722 1.36437i −0.139638 0.990203i \(-0.544594\pi\)
0.927360 0.374171i \(-0.122073\pi\)
\(632\) 9.68780 16.7798i 0.385360 0.667463i
\(633\) 1.96998 + 3.41211i 0.0782997 + 0.135619i
\(634\) 11.9337 0.473948
\(635\) −12.4817 21.6190i −0.495321 0.857922i
\(636\) 0.585791 1.01462i 0.0232281 0.0402323i
\(637\) −17.1468 −0.679382
\(638\) −26.0605 + 45.1381i −1.03175 + 1.78704i
\(639\) 13.9259 + 24.1204i 0.550901 + 0.954188i
\(640\) 11.5656 + 20.0321i 0.457169 + 0.791840i
\(641\) −17.1250 −0.676396 −0.338198 0.941075i \(-0.609817\pi\)
−0.338198 + 0.941075i \(0.609817\pi\)
\(642\) 1.21883 + 2.11108i 0.0481034 + 0.0833175i
\(643\) 42.7166 1.68458 0.842290 0.539025i \(-0.181207\pi\)
0.842290 + 0.539025i \(0.181207\pi\)
\(644\) 22.6420 0.892219
\(645\) 0.463375 + 3.69019i 0.0182454 + 0.145301i
\(646\) 0.495852 0.0195090
\(647\) 45.4761 1.78785 0.893926 0.448215i \(-0.147940\pi\)
0.893926 + 0.448215i \(0.147940\pi\)
\(648\) −5.98949 10.3741i −0.235289 0.407533i
\(649\) 21.1742 0.831160
\(650\) 0.457642 + 0.792659i 0.0179502 + 0.0310906i
\(651\) 1.30948 + 2.26808i 0.0513225 + 0.0888932i
\(652\) 8.13316 14.0870i 0.318519 0.551691i
\(653\) 46.4798 1.81890 0.909448 0.415818i \(-0.136505\pi\)
0.909448 + 0.415818i \(0.136505\pi\)
\(654\) 1.13373 1.96367i 0.0443323 0.0767858i
\(655\) 7.87607 + 13.6418i 0.307744 + 0.533028i
\(656\) 44.8304 1.75033
\(657\) 13.9722 + 24.2005i 0.545107 + 0.944153i
\(658\) −29.9423 + 51.8616i −1.16727 + 2.02178i
\(659\) 15.9907 27.6966i 0.622908 1.07891i −0.366034 0.930602i \(-0.619284\pi\)
0.988941 0.148306i \(-0.0473822\pi\)
\(660\) −2.03560 + 3.52576i −0.0792355 + 0.137240i
\(661\) 2.51336 0.0977586 0.0488793 0.998805i \(-0.484435\pi\)
0.0488793 + 0.998805i \(0.484435\pi\)
\(662\) 9.09651 15.7556i 0.353546 0.612359i
\(663\) 0.463167 0.802228i 0.0179879 0.0311560i
\(664\) −2.53144 4.38458i −0.0982388 0.170155i
\(665\) 1.04703 + 1.81350i 0.0406020 + 0.0703247i
\(666\) 33.8413 1.31132
\(667\) −26.7794 −1.03690
\(668\) 5.75706 + 9.97152i 0.222747 + 0.385810i
\(669\) 0.130325 + 0.225730i 0.00503866 + 0.00872721i
\(670\) 22.1060 38.2888i 0.854030 1.47922i
\(671\) −18.5414 + 32.1147i −0.715783 + 1.23977i
\(672\) 5.31851 0.205166
\(673\) −12.8784 + 22.3061i −0.496427 + 0.859836i −0.999992 0.00412104i \(-0.998688\pi\)
0.503565 + 0.863958i \(0.332022\pi\)
\(674\) 14.9134 25.8308i 0.574444 0.994967i
\(675\) 0.108444 0.187831i 0.00417402 0.00722962i
\(676\) 0.0248205 + 0.0429904i 0.000954636 + 0.00165348i
\(677\) −2.09134 −0.0803767 −0.0401884 0.999192i \(-0.512796\pi\)
−0.0401884 + 0.999192i \(0.512796\pi\)
\(678\) −3.66125 6.34148i −0.140610 0.243543i
\(679\) −28.5790 + 49.5002i −1.09676 + 1.89965i
\(680\) −3.14001 −0.120414
\(681\) 0.836425 1.44873i 0.0320519 0.0555155i
\(682\) 15.8323 + 27.4224i 0.606252 + 1.05006i
\(683\) 11.1206 + 19.2614i 0.425517 + 0.737018i 0.996469 0.0839663i \(-0.0267588\pi\)
−0.570951 + 0.820984i \(0.693425\pi\)
\(684\) −0.978574 −0.0374167
\(685\) 2.44645 + 4.23738i 0.0934741 + 0.161902i
\(686\) −13.7321 −0.524295
\(687\) −0.898908 −0.0342955
\(688\) 25.9131 19.6386i 0.987926 0.748713i
\(689\) −13.6114 −0.518551
\(690\) −5.56608 −0.211897
\(691\) 2.60475 + 4.51156i 0.0990894 + 0.171628i 0.911308 0.411725i \(-0.135074\pi\)
−0.812219 + 0.583353i \(0.801740\pi\)
\(692\) 6.67403 0.253709
\(693\) 29.9918 + 51.9474i 1.13930 + 1.97332i
\(694\) 11.3280 + 19.6207i 0.430006 + 0.744793i
\(695\) 20.2042 34.9946i 0.766387 1.32742i
\(696\) −1.79063 −0.0678738
\(697\) −4.52071 + 7.83011i −0.171234 + 0.296586i
\(698\) 14.0270 + 24.2955i 0.530930 + 0.919599i
\(699\) −6.85603 −0.259319
\(700\) −0.293306 0.508021i −0.0110859 0.0192014i
\(701\) 5.55145 9.61539i 0.209675 0.363168i −0.741937 0.670470i \(-0.766093\pi\)
0.951612 + 0.307302i \(0.0994260\pi\)
\(702\) −4.91952 + 8.52086i −0.185675 + 0.321599i
\(703\) −0.892551 + 1.54594i −0.0336632 + 0.0583063i
\(704\) 5.18746 0.195510
\(705\) 2.76618 4.79116i 0.104180 0.180446i
\(706\) −1.17060 + 2.02754i −0.0440562 + 0.0763075i
\(707\) −22.9835 39.8085i −0.864382 1.49715i
\(708\) −0.550286 0.953123i −0.0206810 0.0358205i
\(709\) −30.3304 −1.13908 −0.569541 0.821963i \(-0.692879\pi\)
−0.569541 + 0.821963i \(0.692879\pi\)
\(710\) −37.4547 −1.40565
\(711\) −19.9503 34.5549i −0.748193 1.29591i
\(712\) −0.134430 0.232840i −0.00503799 0.00872606i
\(713\) −8.13454 + 14.0894i −0.304641 + 0.527653i
\(714\) −0.789901 + 1.36815i −0.0295613 + 0.0512017i
\(715\) 47.2988 1.76888
\(716\) 4.62287 8.00705i 0.172765 0.299237i
\(717\) 0.377283 0.653472i 0.0140899 0.0244044i
\(718\) 3.46710 6.00520i 0.129391 0.224112i
\(719\) 1.42220 + 2.46332i 0.0530391 + 0.0918664i 0.891326 0.453363i \(-0.149776\pi\)
−0.838287 + 0.545229i \(0.816443\pi\)
\(720\) 32.0620 1.19488
\(721\) 21.9331 + 37.9892i 0.816831 + 1.41479i
\(722\) −16.9364 + 29.3346i −0.630306 + 1.09172i
\(723\) 3.33209 0.123922
\(724\) −2.50348 + 4.33615i −0.0930410 + 0.161152i
\(725\) 0.346902 + 0.600852i 0.0128836 + 0.0223151i
\(726\) −5.65112 9.78803i −0.209733 0.363268i
\(727\) −41.7704 −1.54918 −0.774589 0.632465i \(-0.782043\pi\)
−0.774589 + 0.632465i \(0.782043\pi\)
\(728\) −8.79468 15.2328i −0.325952 0.564566i
\(729\) −23.4898 −0.869991
\(730\) −37.5792 −1.39087
\(731\) 0.816998 + 6.50634i 0.0302178 + 0.240646i
\(732\) 1.92745 0.0712408
\(733\) 28.0260 1.03516 0.517581 0.855634i \(-0.326833\pi\)
0.517581 + 0.855634i \(0.326833\pi\)
\(734\) −33.1115 57.3507i −1.22217 2.11685i
\(735\) −2.70156 −0.0996484
\(736\) 16.5194 + 28.6125i 0.608913 + 1.05467i
\(737\) 33.4019 + 57.8538i 1.23038 + 2.13107i
\(738\) 23.7405 41.1197i 0.873898 1.51364i
\(739\) −27.5086 −1.01192 −0.505959 0.862557i \(-0.668861\pi\)
−0.505959 + 0.862557i \(0.668861\pi\)
\(740\) −8.55125 + 14.8112i −0.314350 + 0.544471i
\(741\) −0.128302 0.222226i −0.00471331 0.00816369i
\(742\) 23.2133 0.852187
\(743\) −2.03829 3.53043i −0.0747778 0.129519i 0.826212 0.563360i \(-0.190491\pi\)
−0.900990 + 0.433841i \(0.857158\pi\)
\(744\) −0.543926 + 0.942107i −0.0199413 + 0.0345393i
\(745\) −11.8248 + 20.4812i −0.433228 + 0.750372i
\(746\) 18.0884 31.3300i 0.662262 1.14707i
\(747\) −10.4261 −0.381470
\(748\) −3.58905 + 6.21642i −0.131229 + 0.227295i
\(749\) −9.07543 + 15.7191i −0.331609 + 0.574364i
\(750\) 2.61019 + 4.52098i 0.0953106 + 0.165083i
\(751\) −3.60661 6.24682i −0.131607 0.227950i 0.792689 0.609626i \(-0.208680\pi\)
−0.924296 + 0.381676i \(0.875347\pi\)
\(752\) −48.3654 −1.76370
\(753\) 6.22063 0.226692
\(754\) −15.7370 27.2574i −0.573109 0.992654i
\(755\) 6.22465 + 10.7814i 0.226538 + 0.392376i
\(756\) 3.15296 5.46108i 0.114672 0.198618i
\(757\) −9.48129 + 16.4221i −0.344603 + 0.596870i −0.985282 0.170939i \(-0.945320\pi\)
0.640678 + 0.767809i \(0.278653\pi\)
\(758\) −45.2027 −1.64184
\(759\) 4.20514 7.28351i 0.152637 0.264375i
\(760\) −0.434910 + 0.753286i −0.0157758 + 0.0273246i
\(761\) 17.2156 29.8183i 0.624064 1.08091i −0.364657 0.931142i \(-0.618814\pi\)
0.988721 0.149769i \(-0.0478530\pi\)
\(762\) −2.60847 4.51801i −0.0944950 0.163670i
\(763\) 16.8835 0.611225
\(764\) −7.19296 12.4586i −0.260232 0.450735i
\(765\) −3.23314 + 5.59997i −0.116895 + 0.202467i
\(766\) 33.0163 1.19293
\(767\) −6.39318 + 11.0733i