Properties

Label 731.2.m.c.87.3
Level 731
Weight 2
Character 731.87
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.m (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(32\) over \(\Q(\zeta_{8})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 87.3
Character \(\chi\) = 731.87
Dual form 731.2.m.c.689.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.73249 - 1.73249i) q^{2} +(2.93607 - 1.21616i) q^{3} +4.00305i q^{4} +(0.137451 + 0.331835i) q^{5} +(-7.19370 - 2.97973i) q^{6} +(-0.639449 + 1.54377i) q^{7} +(3.47026 - 3.47026i) q^{8} +(5.02014 - 5.02014i) q^{9} +O(q^{10})\) \(q+(-1.73249 - 1.73249i) q^{2} +(2.93607 - 1.21616i) q^{3} +4.00305i q^{4} +(0.137451 + 0.331835i) q^{5} +(-7.19370 - 2.97973i) q^{6} +(-0.639449 + 1.54377i) q^{7} +(3.47026 - 3.47026i) q^{8} +(5.02014 - 5.02014i) q^{9} +(0.336769 - 0.813033i) q^{10} +(-4.27974 - 1.77273i) q^{11} +(4.86834 + 11.7532i) q^{12} -4.60128i q^{13} +(3.78240 - 1.56672i) q^{14} +(0.807129 + 0.807129i) q^{15} -4.01830 q^{16} +(3.41504 - 2.31031i) q^{17} -17.3947 q^{18} +(2.56658 + 2.56658i) q^{19} +(-1.32835 + 0.550221i) q^{20} +5.31028i q^{21} +(4.34338 + 10.4858i) q^{22} +(-1.45643 - 0.603271i) q^{23} +(5.96854 - 14.4093i) q^{24} +(3.44431 - 3.44431i) q^{25} +(-7.97168 + 7.97168i) q^{26} +(4.98570 - 12.0365i) q^{27} +(-6.17978 - 2.55975i) q^{28} +(-1.54114 - 3.72065i) q^{29} -2.79669i q^{30} +(2.01425 - 0.834328i) q^{31} +(0.0211394 + 0.0211394i) q^{32} -14.7215 q^{33} +(-9.91911 - 1.91393i) q^{34} -0.600169 q^{35} +(20.0958 + 20.0958i) q^{36} +(-3.93237 + 1.62884i) q^{37} -8.89315i q^{38} +(-5.59589 - 13.5097i) q^{39} +(1.62854 + 0.674565i) q^{40} +(-0.381172 + 0.920231i) q^{41} +(9.20001 - 9.20001i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(7.09631 - 17.1320i) q^{44} +(2.35588 + 0.975837i) q^{45} +(1.47808 + 3.56840i) q^{46} -12.1145i q^{47} +(-11.7980 + 4.88689i) q^{48} +(2.97543 + 2.97543i) q^{49} -11.9345 q^{50} +(7.21708 - 10.9365i) q^{51} +18.4192 q^{52} +(5.65186 + 5.65186i) q^{53} +(-29.4909 + 12.2155i) q^{54} -1.66383i q^{55} +(3.13822 + 7.57633i) q^{56} +(10.6570 + 4.41428i) q^{57} +(-3.77597 + 9.11600i) q^{58} +(6.05376 - 6.05376i) q^{59} +(-3.23098 + 3.23098i) q^{60} +(-1.72990 + 4.17634i) q^{61} +(-4.93513 - 2.04420i) q^{62} +(4.53980 + 10.9600i) q^{63} +7.96335i q^{64} +(1.52687 - 0.632449i) q^{65} +(25.5049 + 25.5049i) q^{66} +2.08192 q^{67} +(9.24827 + 13.6706i) q^{68} -5.00984 q^{69} +(1.03979 + 1.03979i) q^{70} +(-7.30247 + 3.02478i) q^{71} -34.8424i q^{72} +(2.66629 + 6.43700i) q^{73} +(9.63475 + 3.99084i) q^{74} +(5.92390 - 14.3016i) q^{75} +(-10.2741 + 10.2741i) q^{76} +(5.47336 - 5.47336i) q^{77} +(-13.7106 + 33.1002i) q^{78} +(-6.09528 - 2.52475i) q^{79} +(-0.552318 - 1.33341i) q^{80} -20.1049i q^{81} +(2.25467 - 0.933914i) q^{82} +(-6.67871 - 6.67871i) q^{83} -21.2573 q^{84} +(1.23604 + 0.815676i) q^{85} +2.45011 q^{86} +(-9.04980 - 9.04980i) q^{87} +(-21.0037 + 8.70000i) q^{88} +11.2275i q^{89} +(-2.39091 - 5.77216i) q^{90} +(7.10331 + 2.94229i) q^{91} +(2.41492 - 5.83014i) q^{92} +(4.89929 - 4.89929i) q^{93} +(-20.9882 + 20.9882i) q^{94} +(-0.498903 + 1.20446i) q^{95} +(0.0877757 + 0.0363579i) q^{96} +(4.60112 + 11.1081i) q^{97} -10.3098i q^{98} +(-30.3842 + 12.5856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} + O(q^{10}) \) \( 128q + 4q^{2} + 4q^{3} + 8q^{5} - 12q^{6} + 4q^{7} - 4q^{8} + 8q^{9} - 8q^{10} - 4q^{11} + 12q^{12} + 12q^{14} - 12q^{15} - 144q^{16} - 12q^{17} + 64q^{18} - 28q^{19} - 8q^{20} - 12q^{22} + 16q^{23} - 16q^{24} - 20q^{25} + 16q^{26} - 8q^{27} + 20q^{28} + 12q^{31} - 4q^{32} - 104q^{33} + 20q^{34} + 32q^{35} - 96q^{36} - 12q^{37} + 8q^{39} + 216q^{40} + 24q^{41} - 4q^{42} + 24q^{44} - 28q^{45} - 48q^{46} + 28q^{48} - 80q^{50} - 20q^{51} + 56q^{52} - 36q^{53} - 12q^{54} - 8q^{56} + 72q^{57} - 32q^{58} + 48q^{59} - 40q^{60} - 76q^{61} - 44q^{62} + 36q^{65} - 68q^{66} - 48q^{67} + 32q^{68} + 216q^{69} - 196q^{70} + 4q^{71} + 20q^{73} + 88q^{74} + 80q^{75} + 72q^{76} + 28q^{77} - 120q^{78} + 68q^{79} - 68q^{80} + 28q^{82} - 36q^{83} - 152q^{84} + 28q^{85} - 24q^{86} - 56q^{87} + 20q^{88} - 112q^{90} + 96q^{91} - 28q^{92} + 24q^{93} - 36q^{94} - 108q^{95} + 272q^{96} + 8q^{97} - 20q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(173\) \(562\)
\(\chi(n)\) \(e\left(\frac{7}{8}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73249 1.73249i −1.22506 1.22506i −0.965812 0.259244i \(-0.916527\pi\)
−0.259244 0.965812i \(-0.583473\pi\)
\(3\) 2.93607 1.21616i 1.69514 0.702150i 0.695278 0.718741i \(-0.255281\pi\)
0.999862 + 0.0165912i \(0.00528139\pi\)
\(4\) 4.00305i 2.00152i
\(5\) 0.137451 + 0.331835i 0.0614698 + 0.148401i 0.951630 0.307247i \(-0.0994076\pi\)
−0.890160 + 0.455648i \(0.849408\pi\)
\(6\) −7.19370 2.97973i −2.93681 1.21647i
\(7\) −0.639449 + 1.54377i −0.241689 + 0.583489i −0.997451 0.0713576i \(-0.977267\pi\)
0.755762 + 0.654847i \(0.227267\pi\)
\(8\) 3.47026 3.47026i 1.22692 1.22692i
\(9\) 5.02014 5.02014i 1.67338 1.67338i
\(10\) 0.336769 0.813033i 0.106496 0.257104i
\(11\) −4.27974 1.77273i −1.29039 0.534497i −0.371289 0.928517i \(-0.621084\pi\)
−0.919102 + 0.394020i \(0.871084\pi\)
\(12\) 4.86834 + 11.7532i 1.40537 + 3.39286i
\(13\) 4.60128i 1.27617i −0.769967 0.638083i \(-0.779728\pi\)
0.769967 0.638083i \(-0.220272\pi\)
\(14\) 3.78240 1.56672i 1.01089 0.418724i
\(15\) 0.807129 + 0.807129i 0.208400 + 0.208400i
\(16\) −4.01830 −1.00457
\(17\) 3.41504 2.31031i 0.828268 0.560332i
\(18\) −17.3947 −4.09996
\(19\) 2.56658 + 2.56658i 0.588814 + 0.588814i 0.937310 0.348497i \(-0.113308\pi\)
−0.348497 + 0.937310i \(0.613308\pi\)
\(20\) −1.32835 + 0.550221i −0.297029 + 0.123033i
\(21\) 5.31028i 1.15880i
\(22\) 4.34338 + 10.4858i 0.926012 + 2.23559i
\(23\) −1.45643 0.603271i −0.303686 0.125791i 0.225637 0.974212i \(-0.427554\pi\)
−0.529322 + 0.848421i \(0.677554\pi\)
\(24\) 5.96854 14.4093i 1.21832 2.94129i
\(25\) 3.44431 3.44431i 0.688862 0.688862i
\(26\) −7.97168 + 7.97168i −1.56338 + 1.56338i
\(27\) 4.98570 12.0365i 0.959498 2.31643i
\(28\) −6.17978 2.55975i −1.16787 0.483747i
\(29\) −1.54114 3.72065i −0.286183 0.690907i 0.713772 0.700378i \(-0.246985\pi\)
−0.999955 + 0.00947112i \(0.996985\pi\)
\(30\) 2.79669i 0.510603i
\(31\) 2.01425 0.834328i 0.361769 0.149850i −0.194392 0.980924i \(-0.562274\pi\)
0.556162 + 0.831074i \(0.312274\pi\)
\(32\) 0.0211394 + 0.0211394i 0.00373696 + 0.00373696i
\(33\) −14.7215 −2.56269
\(34\) −9.91911 1.91393i −1.70111 0.328237i
\(35\) −0.600169 −0.101447
\(36\) 20.0958 + 20.0958i 3.34931 + 3.34931i
\(37\) −3.93237 + 1.62884i −0.646478 + 0.267780i −0.681736 0.731598i \(-0.738775\pi\)
0.0352580 + 0.999378i \(0.488775\pi\)
\(38\) 8.89315i 1.44266i
\(39\) −5.59589 13.5097i −0.896060 2.16328i
\(40\) 1.62854 + 0.674565i 0.257496 + 0.106658i
\(41\) −0.381172 + 0.920231i −0.0595291 + 0.143716i −0.950845 0.309666i \(-0.899783\pi\)
0.891316 + 0.453382i \(0.149783\pi\)
\(42\) 9.20001 9.20001i 1.41959 1.41959i
\(43\) −0.707107 + 0.707107i −0.107833 + 0.107833i
\(44\) 7.09631 17.1320i 1.06981 2.58275i
\(45\) 2.35588 + 0.975837i 0.351194 + 0.145469i
\(46\) 1.47808 + 3.56840i 0.217931 + 0.526133i
\(47\) 12.1145i 1.76708i −0.468355 0.883540i \(-0.655153\pi\)
0.468355 0.883540i \(-0.344847\pi\)
\(48\) −11.7980 + 4.88689i −1.70289 + 0.705362i
\(49\) 2.97543 + 2.97543i 0.425061 + 0.425061i
\(50\) −11.9345 −1.68779
\(51\) 7.21708 10.9365i 1.01059 1.53141i
\(52\) 18.4192 2.55428
\(53\) 5.65186 + 5.65186i 0.776342 + 0.776342i 0.979207 0.202865i \(-0.0650251\pi\)
−0.202865 + 0.979207i \(0.565025\pi\)
\(54\) −29.4909 + 12.2155i −4.01320 + 1.66232i
\(55\) 1.66383i 0.224351i
\(56\) 3.13822 + 7.57633i 0.419362 + 1.01243i
\(57\) 10.6570 + 4.41428i 1.41156 + 0.584686i
\(58\) −3.77597 + 9.11600i −0.495809 + 1.19699i
\(59\) 6.05376 6.05376i 0.788133 0.788133i −0.193055 0.981188i \(-0.561840\pi\)
0.981188 + 0.193055i \(0.0618396\pi\)
\(60\) −3.23098 + 3.23098i −0.417117 + 0.417117i
\(61\) −1.72990 + 4.17634i −0.221491 + 0.534726i −0.995093 0.0989457i \(-0.968453\pi\)
0.773602 + 0.633672i \(0.218453\pi\)
\(62\) −4.93513 2.04420i −0.626762 0.259613i
\(63\) 4.53980 + 10.9600i 0.571961 + 1.38084i
\(64\) 7.96335i 0.995419i
\(65\) 1.52687 0.632449i 0.189385 0.0784457i
\(66\) 25.5049 + 25.5049i 3.13944 + 3.13944i
\(67\) 2.08192 0.254347 0.127174 0.991880i \(-0.459409\pi\)
0.127174 + 0.991880i \(0.459409\pi\)
\(68\) 9.24827 + 13.6706i 1.12152 + 1.65780i
\(69\) −5.00984 −0.603114
\(70\) 1.03979 + 1.03979i 0.124278 + 0.124278i
\(71\) −7.30247 + 3.02478i −0.866643 + 0.358975i −0.771302 0.636469i \(-0.780394\pi\)
−0.0953413 + 0.995445i \(0.530394\pi\)
\(72\) 34.8424i 4.10621i
\(73\) 2.66629 + 6.43700i 0.312066 + 0.753394i 0.999628 + 0.0272683i \(0.00868084\pi\)
−0.687562 + 0.726125i \(0.741319\pi\)
\(74\) 9.63475 + 3.99084i 1.12002 + 0.463926i
\(75\) 5.92390 14.3016i 0.684034 1.65140i
\(76\) −10.2741 + 10.2741i −1.17852 + 1.17852i
\(77\) 5.47336 5.47336i 0.623747 0.623747i
\(78\) −13.7106 + 33.1002i −1.55242 + 3.74786i
\(79\) −6.09528 2.52475i −0.685773 0.284056i 0.0124649 0.999922i \(-0.496032\pi\)
−0.698238 + 0.715866i \(0.746032\pi\)
\(80\) −0.552318 1.33341i −0.0617510 0.149080i
\(81\) 20.1049i 2.23388i
\(82\) 2.25467 0.933914i 0.248986 0.103134i
\(83\) −6.67871 6.67871i −0.733084 0.733084i 0.238146 0.971229i \(-0.423460\pi\)
−0.971229 + 0.238146i \(0.923460\pi\)
\(84\) −21.2573 −2.31936
\(85\) 1.23604 + 0.815676i 0.134067 + 0.0884725i
\(86\) 2.45011 0.264202
\(87\) −9.04980 9.04980i −0.970240 0.970240i
\(88\) −21.0037 + 8.70000i −2.23900 + 0.927423i
\(89\) 11.2275i 1.19011i 0.803686 + 0.595054i \(0.202869\pi\)
−0.803686 + 0.595054i \(0.797131\pi\)
\(90\) −2.39091 5.77216i −0.252024 0.608440i
\(91\) 7.10331 + 2.94229i 0.744629 + 0.308436i
\(92\) 2.41492 5.83014i 0.251773 0.607834i
\(93\) 4.89929 4.89929i 0.508033 0.508033i
\(94\) −20.9882 + 20.9882i −2.16477 + 2.16477i
\(95\) −0.498903 + 1.20446i −0.0511864 + 0.123575i
\(96\) 0.0877757 + 0.0363579i 0.00895857 + 0.00371076i
\(97\) 4.60112 + 11.1081i 0.467173 + 1.12786i 0.965392 + 0.260805i \(0.0839879\pi\)
−0.498218 + 0.867052i \(0.666012\pi\)
\(98\) 10.3098i 1.04145i
\(99\) −30.3842 + 12.5856i −3.05373 + 1.26490i
\(100\) 13.7877 + 13.7877i 1.37877 + 1.37877i
\(101\) −13.3944 −1.33279 −0.666397 0.745597i \(-0.732165\pi\)
−0.666397 + 0.745597i \(0.732165\pi\)
\(102\) −31.4508 + 6.44377i −3.11410 + 0.638029i
\(103\) −0.681348 −0.0671352 −0.0335676 0.999436i \(-0.510687\pi\)
−0.0335676 + 0.999436i \(0.510687\pi\)
\(104\) −15.9677 15.9677i −1.56576 1.56576i
\(105\) −1.76214 + 0.729901i −0.171967 + 0.0712311i
\(106\) 19.5836i 1.90213i
\(107\) 7.02754 + 16.9660i 0.679378 + 1.64016i 0.765153 + 0.643849i \(0.222663\pi\)
−0.0857751 + 0.996315i \(0.527337\pi\)
\(108\) 48.1829 + 19.9580i 4.63640 + 1.92046i
\(109\) −6.26783 + 15.1319i −0.600349 + 1.44937i 0.272873 + 0.962050i \(0.412026\pi\)
−0.873222 + 0.487322i \(0.837974\pi\)
\(110\) −2.88257 + 2.88257i −0.274843 + 0.274843i
\(111\) −9.56478 + 9.56478i −0.907849 + 0.907849i
\(112\) 2.56950 6.20332i 0.242795 0.586158i
\(113\) 6.22400 + 2.57807i 0.585505 + 0.242524i 0.655715 0.755008i \(-0.272367\pi\)
−0.0702107 + 0.997532i \(0.522367\pi\)
\(114\) −10.8155 26.1109i −1.01296 2.44551i
\(115\) 0.566213i 0.0527996i
\(116\) 14.8939 6.16927i 1.38287 0.572802i
\(117\) −23.0991 23.0991i −2.13551 2.13551i
\(118\) −20.9762 −1.93101
\(119\) 1.38283 + 6.74935i 0.126764 + 0.618712i
\(120\) 5.60190 0.511381
\(121\) 7.39546 + 7.39546i 0.672314 + 0.672314i
\(122\) 10.2325 4.23844i 0.926408 0.383731i
\(123\) 3.16543i 0.285417i
\(124\) 3.33986 + 8.06312i 0.299928 + 0.724090i
\(125\) 3.27554 + 1.35677i 0.292973 + 0.121354i
\(126\) 11.1230 26.8533i 0.990917 2.39228i
\(127\) 15.5456 15.5456i 1.37945 1.37945i 0.533897 0.845549i \(-0.320727\pi\)
0.845549 0.533897i \(-0.179273\pi\)
\(128\) 13.8387 13.8387i 1.22318 1.22318i
\(129\) −1.21616 + 2.93607i −0.107077 + 0.258506i
\(130\) −3.74100 1.54957i −0.328107 0.135906i
\(131\) 6.10267 + 14.7332i 0.533193 + 1.28724i 0.929398 + 0.369080i \(0.120327\pi\)
−0.396205 + 0.918162i \(0.629673\pi\)
\(132\) 58.9310i 5.12929i
\(133\) −5.60340 + 2.32100i −0.485876 + 0.201256i
\(134\) −3.60691 3.60691i −0.311590 0.311590i
\(135\) 4.67943 0.402742
\(136\) 3.83370 19.8684i 0.328737 1.70371i
\(137\) 15.4739 1.32203 0.661014 0.750374i \(-0.270126\pi\)
0.661014 + 0.750374i \(0.270126\pi\)
\(138\) 8.67950 + 8.67950i 0.738848 + 0.738848i
\(139\) −2.29638 + 0.951193i −0.194777 + 0.0806791i −0.477940 0.878393i \(-0.658616\pi\)
0.283163 + 0.959072i \(0.408616\pi\)
\(140\) 2.40251i 0.203049i
\(141\) −14.7332 35.5690i −1.24076 2.99545i
\(142\) 17.8919 + 7.41105i 1.50145 + 0.621922i
\(143\) −8.15682 + 19.6923i −0.682108 + 1.64675i
\(144\) −20.1724 + 20.1724i −1.68103 + 1.68103i
\(145\) 1.02281 1.02281i 0.0849398 0.0849398i
\(146\) 6.53271 15.7714i 0.540651 1.30525i
\(147\) 12.3546 + 5.11746i 1.01899 + 0.422081i
\(148\) −6.52033 15.7415i −0.535968 1.29394i
\(149\) 1.73929i 0.142488i −0.997459 0.0712441i \(-0.977303\pi\)
0.997459 0.0712441i \(-0.0226969\pi\)
\(150\) −35.0404 + 14.5142i −2.86104 + 1.18508i
\(151\) −13.7432 13.7432i −1.11840 1.11840i −0.991976 0.126426i \(-0.959649\pi\)
−0.126426 0.991976i \(-0.540351\pi\)
\(152\) 17.8134 1.44486
\(153\) 5.54589 28.7420i 0.448359 2.32365i
\(154\) −18.9651 −1.52825
\(155\) 0.553719 + 0.553719i 0.0444758 + 0.0444758i
\(156\) 54.0799 22.4006i 4.32986 1.79349i
\(157\) 20.3358i 1.62297i 0.584372 + 0.811486i \(0.301341\pi\)
−0.584372 + 0.811486i \(0.698659\pi\)
\(158\) 6.18592 + 14.9341i 0.492125 + 1.18810i
\(159\) 23.4678 + 9.72068i 1.86112 + 0.770900i
\(160\) −0.00410918 + 0.00992043i −0.000324859 + 0.000784279i
\(161\) 1.86262 1.86262i 0.146795 0.146795i
\(162\) −34.8315 + 34.8315i −2.73662 + 2.73662i
\(163\) −1.51967 + 3.66881i −0.119030 + 0.287363i −0.972153 0.234346i \(-0.924705\pi\)
0.853124 + 0.521709i \(0.174705\pi\)
\(164\) −3.68373 1.52585i −0.287651 0.119149i
\(165\) −2.02348 4.88512i −0.157528 0.380306i
\(166\) 23.1416i 1.79614i
\(167\) −0.683976 + 0.283312i −0.0529277 + 0.0219234i −0.408990 0.912539i \(-0.634119\pi\)
0.356063 + 0.934462i \(0.384119\pi\)
\(168\) 18.4281 + 18.4281i 1.42176 + 1.42176i
\(169\) −8.17181 −0.628601
\(170\) −0.728277 3.55458i −0.0558563 0.272624i
\(171\) 25.7691 1.97062
\(172\) −2.83058 2.83058i −0.215830 0.215830i
\(173\) 18.3456 7.59901i 1.39479 0.577742i 0.446398 0.894835i \(-0.352707\pi\)
0.948395 + 0.317093i \(0.102707\pi\)
\(174\) 31.3574i 2.37720i
\(175\) 3.11475 + 7.51968i 0.235453 + 0.568434i
\(176\) 17.1973 + 7.12335i 1.29629 + 0.536942i
\(177\) 10.4119 25.1366i 0.782608 1.88938i
\(178\) 19.4515 19.4515i 1.45795 1.45795i
\(179\) 7.03958 7.03958i 0.526163 0.526163i −0.393263 0.919426i \(-0.628654\pi\)
0.919426 + 0.393263i \(0.128654\pi\)
\(180\) −3.90632 + 9.43069i −0.291160 + 0.702922i
\(181\) 21.1522 + 8.76154i 1.57223 + 0.651240i 0.987159 0.159740i \(-0.0510656\pi\)
0.585074 + 0.810980i \(0.301066\pi\)
\(182\) −7.20893 17.4039i −0.534362 1.29006i
\(183\) 14.3659i 1.06196i
\(184\) −7.14769 + 2.96067i −0.526934 + 0.218263i
\(185\) −1.08101 1.08101i −0.0794777 0.0794777i
\(186\) −16.9759 −1.24474
\(187\) −18.7110 + 3.83359i −1.36829 + 0.280340i
\(188\) 48.4949 3.53685
\(189\) 15.3935 + 15.3935i 1.11971 + 1.11971i
\(190\) 2.95106 1.22237i 0.214092 0.0886799i
\(191\) 13.0708i 0.945773i 0.881123 + 0.472886i \(0.156788\pi\)
−0.881123 + 0.472886i \(0.843212\pi\)
\(192\) 9.68470 + 23.3809i 0.698933 + 1.68737i
\(193\) −9.29480 3.85003i −0.669055 0.277132i 0.0221884 0.999754i \(-0.492937\pi\)
−0.691243 + 0.722622i \(0.742937\pi\)
\(194\) 11.2733 27.2161i 0.809374 1.95400i
\(195\) 3.71383 3.71383i 0.265953 0.265953i
\(196\) −11.9108 + 11.9108i −0.850769 + 0.850769i
\(197\) −7.13544 + 17.2265i −0.508379 + 1.22734i 0.436437 + 0.899735i \(0.356240\pi\)
−0.944816 + 0.327601i \(0.893760\pi\)
\(198\) 74.4447 + 30.8360i 5.29056 + 2.19142i
\(199\) −4.23600 10.2266i −0.300282 0.724944i −0.999945 0.0104717i \(-0.996667\pi\)
0.699663 0.714473i \(-0.253333\pi\)
\(200\) 23.9053i 1.69036i
\(201\) 6.11267 2.53195i 0.431154 0.178590i
\(202\) 23.2057 + 23.2057i 1.63275 + 1.63275i
\(203\) 6.72930 0.472304
\(204\) 43.7791 + 28.8903i 3.06515 + 2.02273i
\(205\) −0.357757 −0.0249868
\(206\) 1.18043 + 1.18043i 0.0822444 + 0.0822444i
\(207\) −10.3400 + 4.28295i −0.718676 + 0.297686i
\(208\) 18.4893i 1.28200i
\(209\) −6.43445 15.5341i −0.445080 1.07452i
\(210\) 4.31743 + 1.78834i 0.297931 + 0.123407i
\(211\) −6.83523 + 16.5017i −0.470557 + 1.13602i 0.493361 + 0.869824i \(0.335768\pi\)
−0.963918 + 0.266200i \(0.914232\pi\)
\(212\) −22.6247 + 22.6247i −1.55387 + 1.55387i
\(213\) −17.7619 + 17.7619i −1.21703 + 1.21703i
\(214\) 17.2183 41.5685i 1.17702 2.84157i
\(215\) −0.331835 0.137451i −0.0226310 0.00937405i
\(216\) −24.4683 59.0716i −1.66486 4.01932i
\(217\) 3.64304i 0.247306i
\(218\) 37.0748 15.3569i 2.51102 1.04010i
\(219\) 15.6568 + 15.6568i 1.05799 + 1.05799i
\(220\) 6.66040 0.449044
\(221\) −10.6304 15.7136i −0.715077 1.05701i
\(222\) 33.1418 2.22433
\(223\) 3.85642 + 3.85642i 0.258245 + 0.258245i 0.824340 0.566095i \(-0.191547\pi\)
−0.566095 + 0.824340i \(0.691547\pi\)
\(224\) −0.0461519 + 0.0191168i −0.00308366 + 0.00127729i
\(225\) 34.5818i 2.30545i
\(226\) −6.31655 15.2495i −0.420171 1.01438i
\(227\) −5.17959 2.14546i −0.343781 0.142399i 0.204111 0.978948i \(-0.434570\pi\)
−0.547892 + 0.836549i \(0.684570\pi\)
\(228\) −17.6706 + 42.6606i −1.17026 + 2.82526i
\(229\) −1.63233 + 1.63233i −0.107868 + 0.107868i −0.758981 0.651113i \(-0.774302\pi\)
0.651113 + 0.758981i \(0.274302\pi\)
\(230\) −0.980959 + 0.980959i −0.0646825 + 0.0646825i
\(231\) 9.41368 22.7266i 0.619374 1.49530i
\(232\) −18.2598 7.56345i −1.19881 0.496565i
\(233\) −9.71089 23.4442i −0.636181 1.53588i −0.831728 0.555183i \(-0.812648\pi\)
0.195547 0.980694i \(-0.437352\pi\)
\(234\) 80.0378i 5.23224i
\(235\) 4.02001 1.66514i 0.262237 0.108622i
\(236\) 24.2335 + 24.2335i 1.57747 + 1.57747i
\(237\) −20.9667 −1.36193
\(238\) 9.29744 14.0889i 0.602663 0.913250i
\(239\) −11.8765 −0.768225 −0.384113 0.923286i \(-0.625493\pi\)
−0.384113 + 0.923286i \(0.625493\pi\)
\(240\) −3.24328 3.24328i −0.209353 0.209353i
\(241\) 8.26055 3.42163i 0.532109 0.220407i −0.100418 0.994945i \(-0.532018\pi\)
0.632527 + 0.774539i \(0.282018\pi\)
\(242\) 25.6251i 1.64725i
\(243\) −9.49365 22.9197i −0.609018 1.47030i
\(244\) −16.7181 6.92486i −1.07027 0.443319i
\(245\) −0.578377 + 1.39632i −0.0369511 + 0.0892079i
\(246\) 5.48407 5.48407i 0.349652 0.349652i
\(247\) 11.8096 11.8096i 0.751424 0.751424i
\(248\) 4.09463 9.88530i 0.260009 0.627717i
\(249\) −27.7315 11.4868i −1.75741 0.727945i
\(250\) −3.32425 8.02545i −0.210244 0.507574i
\(251\) 7.65242i 0.483016i −0.970399 0.241508i \(-0.922358\pi\)
0.970399 0.241508i \(-0.0776421\pi\)
\(252\) −43.8736 + 18.1730i −2.76378 + 1.14479i
\(253\) 5.16369 + 5.16369i 0.324638 + 0.324638i
\(254\) −53.8651 −3.37980
\(255\) 4.62109 + 0.891659i 0.289384 + 0.0558379i
\(256\) −32.0242 −2.00151
\(257\) 0.232300 + 0.232300i 0.0144905 + 0.0144905i 0.714315 0.699824i \(-0.246738\pi\)
−0.699824 + 0.714315i \(0.746738\pi\)
\(258\) 7.19370 2.97973i 0.447860 0.185510i
\(259\) 7.11223i 0.441932i
\(260\) 2.53173 + 6.11213i 0.157011 + 0.379058i
\(261\) −26.4149 10.9414i −1.63504 0.677256i
\(262\) 14.9522 36.0979i 0.923752 2.23013i
\(263\) −10.1427 + 10.1427i −0.625426 + 0.625426i −0.946914 0.321487i \(-0.895817\pi\)
0.321487 + 0.946914i \(0.395817\pi\)
\(264\) −51.0876 + 51.0876i −3.14422 + 3.14422i
\(265\) −1.09863 + 2.65234i −0.0674885 + 0.162932i
\(266\) 13.7290 + 5.68672i 0.841776 + 0.348675i
\(267\) 13.6544 + 32.9646i 0.835634 + 2.01740i
\(268\) 8.33404i 0.509082i
\(269\) −2.16338 + 0.896100i −0.131903 + 0.0546362i −0.447659 0.894204i \(-0.647742\pi\)
0.315755 + 0.948841i \(0.397742\pi\)
\(270\) −8.10708 8.10708i −0.493381 0.493381i
\(271\) 13.9447 0.847079 0.423540 0.905878i \(-0.360787\pi\)
0.423540 + 0.905878i \(0.360787\pi\)
\(272\) −13.7226 + 9.28350i −0.832057 + 0.562895i
\(273\) 24.4341 1.47882
\(274\) −26.8085 26.8085i −1.61956 1.61956i
\(275\) −20.8466 + 8.63494i −1.25710 + 0.520707i
\(276\) 20.0546i 1.20715i
\(277\) −1.64216 3.96452i −0.0986676 0.238205i 0.866836 0.498593i \(-0.166150\pi\)
−0.965504 + 0.260388i \(0.916150\pi\)
\(278\) 5.62639 + 2.33053i 0.337449 + 0.139776i
\(279\) 5.92335 14.3002i 0.354622 0.856132i
\(280\) −2.08274 + 2.08274i −0.124468 + 0.124468i
\(281\) 15.0109 15.0109i 0.895472 0.895472i −0.0995594 0.995032i \(-0.531743\pi\)
0.995032 + 0.0995594i \(0.0317433\pi\)
\(282\) −36.0979 + 87.1480i −2.14960 + 5.18959i
\(283\) −16.8696 6.98761i −1.00279 0.415370i −0.179972 0.983672i \(-0.557601\pi\)
−0.822820 + 0.568301i \(0.807601\pi\)
\(284\) −12.1083 29.2321i −0.718498 1.73461i
\(285\) 4.14312i 0.245417i
\(286\) 48.2484 19.9851i 2.85299 1.18175i
\(287\) −1.17688 1.17688i −0.0694691 0.0694691i
\(288\) 0.212245 0.0125067
\(289\) 6.32496 15.7796i 0.372056 0.928210i
\(290\) −3.54402 −0.208112
\(291\) 27.0184 + 27.0184i 1.58385 + 1.58385i
\(292\) −25.7676 + 10.6733i −1.50794 + 0.624607i
\(293\) 5.66868i 0.331168i −0.986196 0.165584i \(-0.947049\pi\)
0.986196 0.165584i \(-0.0529508\pi\)
\(294\) −12.5384 30.2703i −0.731252 1.76540i
\(295\) 2.84094 + 1.17676i 0.165406 + 0.0685135i
\(296\) −7.99385 + 19.2989i −0.464633 + 1.12172i
\(297\) −42.6750 + 42.6750i −2.47626 + 2.47626i
\(298\) −3.01330 + 3.01330i −0.174556 + 0.174556i
\(299\) −2.77582 + 6.70143i −0.160530 + 0.387553i
\(300\) 57.2499 + 23.7137i 3.30532 + 1.36911i
\(301\) −0.639449 1.54377i −0.0368572 0.0889813i
\(302\) 47.6198i 2.74021i
\(303\) −39.3269 + 16.2898i −2.25927 + 0.935822i
\(304\) −10.3133 10.3133i −0.591507 0.591507i
\(305\) −1.62363 −0.0929690
\(306\) −59.4035 + 40.1870i −3.39587 + 2.29734i
\(307\) −21.3068 −1.21605 −0.608023 0.793920i \(-0.708037\pi\)
−0.608023 + 0.793920i \(0.708037\pi\)
\(308\) 21.9101 + 21.9101i 1.24844 + 1.24844i
\(309\) −2.00049 + 0.828628i −0.113804 + 0.0471390i
\(310\) 1.91863i 0.108971i
\(311\) −11.8155 28.5251i −0.669994 1.61751i −0.781618 0.623757i \(-0.785605\pi\)
0.111625 0.993750i \(-0.464395\pi\)
\(312\) −66.3014 27.4629i −3.75358 1.55478i
\(313\) 7.68068 18.5428i 0.434138 1.04810i −0.543802 0.839214i \(-0.683016\pi\)
0.977940 0.208888i \(-0.0669843\pi\)
\(314\) 35.2315 35.2315i 1.98823 1.98823i
\(315\) −3.01293 + 3.01293i −0.169759 + 0.169759i
\(316\) 10.1067 24.3997i 0.568546 1.37259i
\(317\) 16.4095 + 6.79705i 0.921651 + 0.381760i 0.792505 0.609865i \(-0.208777\pi\)
0.129146 + 0.991626i \(0.458777\pi\)
\(318\) −23.8168 57.4987i −1.33558 3.22437i
\(319\) 18.6554i 1.04450i
\(320\) −2.64252 + 1.09457i −0.147721 + 0.0611882i
\(321\) 41.2667 + 41.2667i 2.30328 + 2.30328i
\(322\) −6.45394 −0.359664
\(323\) 14.6945 + 2.83538i 0.817626 + 0.157765i
\(324\) 80.4808 4.47116
\(325\) −15.8483 15.8483i −0.879103 0.879103i
\(326\) 8.98899 3.72336i 0.497854 0.206218i
\(327\) 52.0509i 2.87842i
\(328\) 1.87067 + 4.51621i 0.103291 + 0.249366i
\(329\) 18.7020 + 7.74660i 1.03107 + 0.427084i
\(330\) −4.95776 + 11.9691i −0.272916 + 0.658877i
\(331\) 23.6989 23.6989i 1.30261 1.30261i 0.375981 0.926628i \(-0.377306\pi\)
0.926628 0.375981i \(-0.122694\pi\)
\(332\) 26.7352 26.7352i 1.46728 1.46728i
\(333\) −11.5640 + 27.9180i −0.633705 + 1.52990i
\(334\) 1.67582 + 0.694147i 0.0916967 + 0.0379820i
\(335\) 0.286162 + 0.690855i 0.0156347 + 0.0377454i
\(336\) 21.3383i 1.16410i
\(337\) 12.5546 5.20028i 0.683892 0.283277i −0.0135606 0.999908i \(-0.504317\pi\)
0.697453 + 0.716631i \(0.254317\pi\)
\(338\) 14.1576 + 14.1576i 0.770071 + 0.770071i
\(339\) 21.4094 1.16280
\(340\) −3.26519 + 4.94793i −0.177080 + 0.268339i
\(341\) −10.0995 −0.546918
\(342\) −44.6448 44.6448i −2.41411 2.41411i
\(343\) −17.3024 + 7.16688i −0.934240 + 0.386975i
\(344\) 4.90769i 0.264605i
\(345\) −0.688605 1.66244i −0.0370733 0.0895028i
\(346\) −44.9488 18.6184i −2.41646 1.00093i
\(347\) −7.56148 + 18.2550i −0.405921 + 0.979981i 0.580278 + 0.814418i \(0.302944\pi\)
−0.986199 + 0.165562i \(0.947056\pi\)
\(348\) 36.2268 36.2268i 1.94196 1.94196i
\(349\) −10.8223 + 10.8223i −0.579302 + 0.579302i −0.934711 0.355409i \(-0.884342\pi\)
0.355409 + 0.934711i \(0.384342\pi\)
\(350\) 7.63149 18.4241i 0.407921 0.984807i
\(351\) −55.3835 22.9406i −2.95615 1.22448i
\(352\) −0.0529968 0.127946i −0.00282474 0.00681953i
\(353\) 34.3374i 1.82760i 0.406167 + 0.913799i \(0.366865\pi\)
−0.406167 + 0.913799i \(0.633135\pi\)
\(354\) −61.5875 + 25.5104i −3.27334 + 1.35586i
\(355\) −2.00746 2.00746i −0.106545 0.106545i
\(356\) −44.9441 −2.38203
\(357\) 12.2684 + 18.1348i 0.649311 + 0.959796i
\(358\) −24.3920 −1.28916
\(359\) 1.72341 + 1.72341i 0.0909580 + 0.0909580i 0.751122 0.660164i \(-0.229513\pi\)
−0.660164 + 0.751122i \(0.729513\pi\)
\(360\) 11.5619 4.78911i 0.609367 0.252408i
\(361\) 5.82535i 0.306597i
\(362\) −21.4668 51.8253i −1.12827 2.72388i
\(363\) 30.7076 + 12.7195i 1.61173 + 0.667601i
\(364\) −11.7781 + 28.4349i −0.617341 + 1.49039i
\(365\) −1.76954 + 1.76954i −0.0926219 + 0.0926219i
\(366\) 24.8887 24.8887i 1.30095 1.30095i
\(367\) −11.8763 + 28.6719i −0.619937 + 1.49666i 0.231840 + 0.972754i \(0.425526\pi\)
−0.851776 + 0.523905i \(0.824474\pi\)
\(368\) 5.85235 + 2.42412i 0.305075 + 0.126366i
\(369\) 2.70615 + 6.53322i 0.140876 + 0.340106i
\(370\) 3.74569i 0.194729i
\(371\) −12.3392 + 5.11108i −0.640621 + 0.265354i
\(372\) 19.6121 + 19.6121i 1.01684 + 1.01684i
\(373\) 16.1022 0.833739 0.416870 0.908966i \(-0.363127\pi\)
0.416870 + 0.908966i \(0.363127\pi\)
\(374\) 39.0583 + 25.7750i 2.01966 + 1.33279i
\(375\) 11.2673 0.581839
\(376\) −42.0405 42.0405i −2.16807 2.16807i
\(377\) −17.1198 + 7.09123i −0.881712 + 0.365217i
\(378\) 53.3383i 2.74342i
\(379\) −0.304093 0.734147i −0.0156202 0.0377106i 0.915877 0.401459i \(-0.131497\pi\)
−0.931497 + 0.363748i \(0.881497\pi\)
\(380\) −4.82151 1.99713i −0.247338 0.102451i
\(381\) 26.7370 64.5488i 1.36978 3.30693i
\(382\) 22.6451 22.6451i 1.15862 1.15862i
\(383\) 2.54759 2.54759i 0.130176 0.130176i −0.639017 0.769193i \(-0.720659\pi\)
0.769193 + 0.639017i \(0.220659\pi\)
\(384\) 23.8013 57.4615i 1.21461 2.93232i
\(385\) 2.56857 + 1.06394i 0.130906 + 0.0542232i
\(386\) 9.43301 + 22.7733i 0.480128 + 1.15913i
\(387\) 7.09954i 0.360890i
\(388\) −44.4662 + 18.4185i −2.25743 + 0.935059i
\(389\) −3.77256 3.77256i −0.191276 0.191276i 0.604971 0.796247i \(-0.293185\pi\)
−0.796247 + 0.604971i \(0.793185\pi\)
\(390\) −12.8683 −0.651614
\(391\) −6.36749 + 1.30460i −0.322018 + 0.0659763i
\(392\) 20.6510 1.04303
\(393\) 35.8357 + 35.8357i 1.80767 + 1.80767i
\(394\) 42.2068 17.4826i 2.12635 0.880763i
\(395\) 2.36966i 0.119230i
\(396\) −50.3806 121.629i −2.53172 6.11211i
\(397\) 24.2019 + 10.0248i 1.21466 + 0.503128i 0.895708 0.444643i \(-0.146669\pi\)
0.318951 + 0.947771i \(0.396669\pi\)
\(398\) −10.3787 + 25.0563i −0.520235 + 1.25596i
\(399\) −13.6292 + 13.6292i −0.682316 + 0.682316i
\(400\) −13.8403 + 13.8403i −0.692014 + 0.692014i
\(401\) 7.83386 18.9126i 0.391204 0.944450i −0.598474 0.801142i \(-0.704226\pi\)
0.989678 0.143308i \(-0.0457740\pi\)
\(402\) −14.9767 6.20356i −0.746971 0.309405i
\(403\) −3.83898 9.26812i −0.191233 0.461678i
\(404\) 53.6185i 2.66762i
\(405\) 6.67151 2.76343i 0.331510 0.137316i
\(406\) −11.6584 11.6584i −0.578599 0.578599i
\(407\) 19.7170 0.977337
\(408\) −12.9072 62.9975i −0.639001 3.11884i
\(409\) −17.8123 −0.880761 −0.440381 0.897811i \(-0.645157\pi\)
−0.440381 + 0.897811i \(0.645157\pi\)
\(410\) 0.619811 + 0.619811i 0.0306103 + 0.0306103i
\(411\) 45.4326 18.8188i 2.24102 0.928262i
\(412\) 2.72747i 0.134373i
\(413\) 5.47453 + 13.2167i 0.269384 + 0.650350i
\(414\) 25.3340 + 10.4937i 1.24510 + 0.515737i
\(415\) 1.29824 3.13422i 0.0637280 0.153853i
\(416\) 0.0972685 0.0972685i 0.00476898 0.00476898i
\(417\) −5.58553 + 5.58553i −0.273525 + 0.273525i
\(418\) −15.7651 + 38.0604i −0.771097 + 1.86159i
\(419\) −6.21631 2.57488i −0.303687 0.125791i 0.225636 0.974212i \(-0.427554\pi\)
−0.529323 + 0.848421i \(0.677554\pi\)
\(420\) −2.92183 7.05392i −0.142571 0.344196i
\(421\) 11.3071i 0.551072i 0.961291 + 0.275536i \(0.0888554\pi\)
−0.961291 + 0.275536i \(0.911145\pi\)
\(422\) 40.4310 16.7471i 1.96815 0.815235i
\(423\) −60.8164 60.8164i −2.95699 2.95699i
\(424\) 39.2269 1.90502
\(425\) 3.80503 19.7199i 0.184571 0.956554i
\(426\) 61.5448 2.98185
\(427\) −5.34112 5.34112i −0.258475 0.258475i
\(428\) −67.9156 + 28.1316i −3.28283 + 1.35979i
\(429\) 67.7380i 3.27042i
\(430\) 0.336769 + 0.813033i 0.0162405 + 0.0392079i
\(431\) −3.60177 1.49190i −0.173491 0.0718625i 0.294247 0.955729i \(-0.404931\pi\)
−0.467739 + 0.883867i \(0.654931\pi\)
\(432\) −20.0340 + 48.3664i −0.963887 + 2.32703i
\(433\) −6.26661 + 6.26661i −0.301154 + 0.301154i −0.841465 0.540311i \(-0.818307\pi\)
0.540311 + 0.841465i \(0.318307\pi\)
\(434\) 6.31153 6.31153i 0.302963 0.302963i
\(435\) 1.75914 4.24694i 0.0843444 0.203625i
\(436\) −60.5737 25.0904i −2.90095 1.20161i
\(437\) −2.18969 5.28637i −0.104747 0.252881i
\(438\) 54.2506i 2.59220i
\(439\) 15.8395 6.56095i 0.755980 0.313137i 0.0288011 0.999585i \(-0.490831\pi\)
0.727179 + 0.686448i \(0.240831\pi\)
\(440\) −5.77393 5.77393i −0.275261 0.275261i
\(441\) 29.8741 1.42257
\(442\) −8.80655 + 45.6406i −0.418885 + 2.17090i
\(443\) −18.1614 −0.862876 −0.431438 0.902143i \(-0.641994\pi\)
−0.431438 + 0.902143i \(0.641994\pi\)
\(444\) −38.2883 38.2883i −1.81708 1.81708i
\(445\) −3.72567 + 1.54322i −0.176613 + 0.0731557i
\(446\) 13.3624i 0.632728i
\(447\) −2.11525 5.10667i −0.100048 0.241537i
\(448\) −12.2936 5.09216i −0.580816 0.240582i
\(449\) −7.75874 + 18.7312i −0.366157 + 0.883982i 0.628215 + 0.778040i \(0.283786\pi\)
−0.994372 + 0.105942i \(0.966214\pi\)
\(450\) −59.9127 + 59.9127i −2.82431 + 2.82431i
\(451\) 3.26264 3.26264i 0.153632 0.153632i
\(452\) −10.3201 + 24.9150i −0.485418 + 1.17190i
\(453\) −57.0647 23.6370i −2.68113 1.11056i
\(454\) 5.25661 + 12.6906i 0.246705 + 0.595598i
\(455\) 2.76155i 0.129463i
\(456\) 52.3014 21.6639i 2.44924 1.01451i
\(457\) −20.1211 20.1211i −0.941223 0.941223i 0.0571428 0.998366i \(-0.481801\pi\)
−0.998366 + 0.0571428i \(0.981801\pi\)
\(458\) 5.65600 0.264288
\(459\) −10.7818 52.6237i −0.503250 2.45627i
\(460\) 2.26658 0.105680
\(461\) −0.326653 0.326653i −0.0152137 0.0152137i 0.699459 0.714673i \(-0.253424\pi\)
−0.714673 + 0.699459i \(0.753424\pi\)
\(462\) −55.6828 + 23.0646i −2.59060 + 1.07306i
\(463\) 29.6467i 1.37780i 0.724857 + 0.688899i \(0.241906\pi\)
−0.724857 + 0.688899i \(0.758094\pi\)
\(464\) 6.19277 + 14.9507i 0.287492 + 0.694067i
\(465\) 2.29917 + 0.952346i 0.106621 + 0.0441640i
\(466\) −23.7928 + 57.4408i −1.10218 + 2.66089i
\(467\) −8.70060 + 8.70060i −0.402616 + 0.402616i −0.879154 0.476538i \(-0.841891\pi\)
0.476538 + 0.879154i \(0.341891\pi\)
\(468\) 92.4667 92.4667i 4.27427 4.27427i
\(469\) −1.33128 + 3.21400i −0.0614730 + 0.148409i
\(470\) −9.84949 4.07979i −0.454323 0.188187i
\(471\) 24.7316 + 59.7072i 1.13957 + 2.75116i
\(472\) 42.0163i 1.93396i
\(473\) 4.27974 1.77273i 0.196783 0.0815101i
\(474\) 36.3246 + 36.3246i 1.66844 + 1.66844i
\(475\) 17.6802 0.811223
\(476\) −27.0180 + 5.53555i −1.23837 + 0.253722i
\(477\) 56.7462 2.59823
\(478\) 20.5759 + 20.5759i 0.941119 + 0.941119i
\(479\) −36.5080 + 15.1221i −1.66809 + 0.690946i −0.998651 0.0519196i \(-0.983466\pi\)
−0.669440 + 0.742866i \(0.733466\pi\)
\(480\) 0.0341245i 0.00155756i
\(481\) 7.49476 + 18.0940i 0.341732 + 0.825014i
\(482\) −20.2393 8.38338i −0.921874 0.381853i
\(483\) 3.20354 7.73402i 0.145766 0.351910i
\(484\) −29.6044 + 29.6044i −1.34565 + 1.34565i
\(485\) −3.05363 + 3.05363i −0.138658 + 0.138658i
\(486\) −23.2605 + 56.1558i −1.05512 + 2.54728i
\(487\) −7.46746 3.09312i −0.338383 0.140163i 0.207020 0.978337i \(-0.433623\pi\)
−0.545403 + 0.838174i \(0.683623\pi\)
\(488\) 8.48981 + 20.4962i 0.384315 + 0.927820i
\(489\) 12.6200i 0.570698i
\(490\) 3.42115 1.41709i 0.154552 0.0640175i
\(491\) 27.0678 + 27.0678i 1.22155 + 1.22155i 0.967081 + 0.254470i \(0.0819012\pi\)
0.254470 + 0.967081i \(0.418099\pi\)
\(492\) −12.6714 −0.571269
\(493\) −13.8589 9.14564i −0.624173 0.411899i
\(494\) −40.9199 −1.84107
\(495\) −8.35266 8.35266i −0.375424 0.375424i
\(496\) −8.09384 + 3.35258i −0.363424 + 0.150535i
\(497\) 13.2075i 0.592438i
\(498\) 28.1439 + 67.9454i 1.26116 + 3.04470i
\(499\) 15.9607 + 6.61114i 0.714500 + 0.295955i 0.710165 0.704035i \(-0.248620\pi\)
0.00433457 + 0.999991i \(0.498620\pi\)
\(500\) −5.43123 + 13.1122i −0.242892 + 0.586393i
\(501\) −1.66365 + 1.66365i −0.0743263 + 0.0743263i
\(502\) −13.2577 + 13.2577i −0.591722 + 0.591722i
\(503\) 13.3204 32.1582i 0.593926 1.43387i −0.285755 0.958303i \(-0.592244\pi\)
0.879682 0.475563i \(-0.157756\pi\)
\(504\) 53.7885 + 22.2799i 2.39593 + 0.992427i
\(505\) −1.84107 4.44474i −0.0819266 0.197788i
\(506\) 17.8921i 0.795400i
\(507\) −23.9930 + 9.93823i −1.06557 + 0.441372i
\(508\) 62.2297 + 62.2297i 2.76100 + 2.76100i
\(509\) −5.61443 −0.248855 −0.124428 0.992229i \(-0.539709\pi\)
−0.124428 + 0.992229i \(0.539709\pi\)
\(510\) −6.46121 9.55079i −0.286107 0.422916i
\(511\) −11.6422 −0.515020
\(512\) 27.8042 + 27.8042i 1.22878 + 1.22878i
\(513\) 43.6889 18.0965i 1.92891 0.798982i
\(514\) 0.804917i 0.0355034i
\(515\) −0.0936517 0.226095i −0.00412679 0.00996295i
\(516\) −11.7532 4.86834i −0.517407 0.214317i
\(517\) −21.4757 + 51.8469i −0.944500 + 2.28022i
\(518\) −12.3219 + 12.3219i −0.541392 + 0.541392i
\(519\) 44.6224 44.6224i 1.95871 1.95871i
\(520\) 3.10387 7.49340i 0.136114 0.328607i
\(521\) −17.1671 7.11087i −0.752106 0.311533i −0.0265057 0.999649i \(-0.508438\pi\)
−0.725601 + 0.688116i \(0.758438\pi\)
\(522\) 26.8077 + 64.7195i 1.17334 + 2.83269i
\(523\) 16.2866i 0.712163i −0.934455 0.356082i \(-0.884113\pi\)
0.934455 0.356082i \(-0.115887\pi\)
\(524\) −58.9775 + 24.4293i −2.57645 + 1.06720i
\(525\) 18.2903 + 18.2903i 0.798252 + 0.798252i
\(526\) 35.1443 1.53236
\(527\) 4.95117 7.50279i 0.215676 0.326827i
\(528\) 59.1555 2.57441
\(529\) −14.5062 14.5062i −0.630705 0.630705i
\(530\) 6.49852 2.69178i 0.282278 0.116923i
\(531\) 60.7814i 2.63769i
\(532\) −9.29109 22.4307i −0.402820 0.972493i
\(533\) 4.23424 + 1.75388i 0.183405 + 0.0759690i
\(534\) 33.4548 80.7669i 1.44773 3.49513i
\(535\) −4.66397 + 4.66397i −0.201641 + 0.201641i
\(536\) 7.22482 7.22482i 0.312065 0.312065i
\(537\) 12.1074 29.2299i 0.522474 1.26136i
\(538\) 5.30052 + 2.19555i 0.228521 + 0.0946567i
\(539\) −7.45944 18.0087i −0.321301 0.775688i
\(540\) 18.7320i 0.806097i
\(541\) 35.4985 14.7040i 1.52620 0.632173i 0.547378 0.836886i \(-0.315626\pi\)
0.978822 + 0.204713i \(0.0656261\pi\)
\(542\) −24.1590 24.1590i −1.03772 1.03772i
\(543\) 72.7598 3.12242
\(544\) 0.121030 + 0.0233533i 0.00518914 + 0.00100127i
\(545\) −5.88281 −0.251992
\(546\) −42.3319 42.3319i −1.81164 1.81164i
\(547\) 33.5004 13.8763i 1.43237 0.593309i 0.474437 0.880289i \(-0.342652\pi\)
0.957936 + 0.286981i \(0.0926516\pi\)
\(548\) 61.9429i 2.64607i
\(549\) 12.2815 + 29.6501i 0.524161 + 1.26544i
\(550\) 51.0765 + 21.1566i 2.17791 + 0.902119i
\(551\) 5.59387 13.5048i 0.238307 0.575324i
\(552\) −17.3855 + 17.3855i −0.739974 + 0.739974i
\(553\) 7.79525 7.79525i 0.331488 0.331488i
\(554\) −4.02347 + 9.71351i −0.170941 + 0.412687i
\(555\) −4.48862 1.85925i −0.190531 0.0789206i
\(556\) −3.80767 9.19253i −0.161481 0.389850i
\(557\) 11.0520i 0.468288i 0.972202 + 0.234144i \(0.0752287\pi\)
−0.972202 + 0.234144i \(0.924771\pi\)
\(558\) −35.0372 + 14.5129i −1.48324 + 0.614379i
\(559\) 3.25360 + 3.25360i 0.137613 + 0.137613i
\(560\) 2.41166 0.101911
\(561\) −50.2746 + 34.0113i −2.12260 + 1.43596i
\(562\) −52.0123 −2.19401
\(563\) −5.28365 5.28365i −0.222679 0.222679i 0.586946 0.809626i \(-0.300330\pi\)
−0.809626 + 0.586946i \(0.800330\pi\)
\(564\) 142.384 58.9775i 5.99546 2.48340i
\(565\) 2.41970i 0.101797i
\(566\) 17.1204 + 41.3324i 0.719625 + 1.73733i
\(567\) 31.0373 + 12.8561i 1.30344 + 0.539904i
\(568\) −14.8447 + 35.8383i −0.622869 + 1.50374i
\(569\) −29.6943 + 29.6943i −1.24485 + 1.24485i −0.286882 + 0.957966i \(0.592619\pi\)
−0.957966 + 0.286882i \(0.907381\pi\)
\(570\) 7.17792 7.17792i 0.300650 0.300650i
\(571\) 2.05137 4.95245i 0.0858473 0.207254i −0.875126 0.483895i \(-0.839222\pi\)
0.960973 + 0.276642i \(0.0892215\pi\)
\(572\) −78.8293 32.6521i −3.29602 1.36525i
\(573\) 15.8962 + 38.3769i 0.664074 + 1.60322i
\(574\) 4.07787i 0.170207i
\(575\) −7.09424 + 2.93853i −0.295850 + 0.122545i
\(576\) 39.9771 + 39.9771i 1.66571 + 1.66571i
\(577\) 29.6355 1.23374 0.616871 0.787064i \(-0.288400\pi\)
0.616871 + 0.787064i \(0.288400\pi\)
\(578\) −38.2959 + 16.3800i −1.59290 + 0.681319i
\(579\) −31.9724 −1.32873
\(580\) 4.09436 + 4.09436i 0.170009 + 0.170009i
\(581\) 14.5811 6.03968i 0.604925 0.250568i
\(582\) 93.6184i 3.88061i
\(583\) −14.1693 34.2077i −0.586832 1.41674i
\(584\) 31.5908 + 13.0853i 1.30724 + 0.541475i
\(585\) 4.49010 10.8401i 0.185643 0.448181i
\(586\) −9.82093 + 9.82093i −0.405699 + 0.405699i
\(587\) −20.9035 + 20.9035i −0.862781 + 0.862781i −0.991660 0.128879i \(-0.958862\pi\)
0.128879 + 0.991660i \(0.458862\pi\)
\(588\) −20.4854 + 49.4562i −0.844805 + 2.03954i
\(589\) 7.31109 + 3.02835i 0.301248 + 0.124781i
\(590\) −2.88319 6.96063i −0.118699 0.286565i
\(591\) 59.2560i 2.43747i
\(592\) 15.8014 6.54517i 0.649435 0.269005i
\(593\) 26.8548 + 26.8548i 1.10279 + 1.10279i 0.994072 + 0.108720i \(0.0346752\pi\)
0.108720 + 0.994072i \(0.465325\pi\)
\(594\) 147.868 6.06710
\(595\) −2.04960 + 1.38657i −0.0840254 + 0.0568440i
\(596\) 6.96246 0.285193
\(597\) −24.8743 24.8743i −1.01804 1.01804i
\(598\) 16.4192 6.80107i 0.671433 0.278117i
\(599\) 0.763279i 0.0311868i 0.999878 + 0.0155934i \(0.00496373\pi\)
−0.999878 + 0.0155934i \(0.995036\pi\)
\(600\) −29.0727 70.1877i −1.18689 2.86540i
\(601\) 12.7972 + 5.30078i 0.522009 + 0.216223i 0.628099 0.778133i \(-0.283833\pi\)
−0.106090 + 0.994357i \(0.533833\pi\)
\(602\) −1.56672 + 3.78240i −0.0638548 + 0.154159i
\(603\) 10.4515 10.4515i 0.425619 0.425619i
\(604\) 55.0145 55.0145i 2.23851 2.23851i
\(605\) −1.43756 + 3.47058i −0.0584452 + 0.141099i
\(606\) 96.3554 + 39.9117i 3.91417 + 1.62130i
\(607\) 6.25840 + 15.1091i 0.254021 + 0.613260i 0.998521 0.0543616i \(-0.0173124\pi\)
−0.744501 + 0.667622i \(0.767312\pi\)
\(608\) 0.108512i 0.00440074i
\(609\) 19.7577 8.18390i 0.800621 0.331628i
\(610\) 2.81293 + 2.81293i 0.113892 + 0.113892i
\(611\) −55.7422 −2.25509
\(612\) 115.056 + 22.2005i 4.65085 + 0.897401i
\(613\) 25.0812 1.01302 0.506511 0.862233i \(-0.330935\pi\)
0.506511 + 0.862233i \(0.330935\pi\)
\(614\) 36.9139 + 36.9139i 1.48972 + 1.48972i
\(615\) −1.05040 + 0.435090i −0.0423562 + 0.0175445i
\(616\) 37.9880i 1.53058i
\(617\) −11.7052 28.2589i −0.471235 1.13766i −0.963618 0.267283i \(-0.913874\pi\)
0.492383 0.870379i \(-0.336126\pi\)
\(618\) 4.90141 + 2.03023i 0.197164 + 0.0816679i
\(619\) 6.88838 16.6300i 0.276867 0.668417i −0.722878 0.690975i \(-0.757181\pi\)
0.999746 + 0.0225587i \(0.00718127\pi\)
\(620\) −2.21656 + 2.21656i −0.0890193 + 0.0890193i
\(621\) −14.5226 + 14.5226i −0.582772 + 0.582772i
\(622\) −28.9492 + 69.8896i −1.16076 + 2.80232i
\(623\) −17.3326 7.17939i −0.694415 0.287636i
\(624\) 22.4860 + 54.2859i 0.900159 + 2.17318i
\(625\) 23.0815i 0.923261i
\(626\) −45.4319 + 18.8185i −1.81583 + 0.752140i
\(627\) −37.7840 37.7840i −1.50895 1.50895i
\(628\) −81.4051 −3.24842
\(629\) −9.66607 + 14.6475i −0.385411 + 0.584036i
\(630\) 10.4397 0.415929
\(631\) −22.8510 22.8510i −0.909685 0.909685i 0.0865617 0.996246i \(-0.472412\pi\)
−0.996246 + 0.0865617i \(0.972412\pi\)
\(632\) −29.9138 + 12.3907i −1.18991 + 0.492875i
\(633\) 56.7629i 2.25612i
\(634\) −16.6535 40.2052i −0.661396 1.59675i
\(635\) 7.29532 + 3.02182i 0.289506 + 0.119917i
\(636\) −38.9124 + 93.9427i −1.54298 + 3.72507i
\(637\) 13.6908 13.6908i 0.542448 0.542448i
\(638\) 32.3204 32.3204i 1.27958 1.27958i
\(639\) −21.4746 + 51.8442i −0.849521 + 2.05092i
\(640\) 6.49431 + 2.69003i 0.256710 + 0.106333i
\(641\) 1.69486 + 4.09174i 0.0669428 + 0.161614i 0.953810 0.300410i \(-0.0971234\pi\)
−0.886867 + 0.462024i \(0.847123\pi\)
\(642\) 142.988i 5.64330i
\(643\) −20.2537 + 8.38937i −0.798729 + 0.330844i −0.744447 0.667681i \(-0.767287\pi\)
−0.0542819 + 0.998526i \(0.517287\pi\)
\(644\) 7.45616 + 7.45616i 0.293814 + 0.293814i
\(645\) −1.14145 −0.0449447
\(646\) −20.5459 30.3704i −0.808368 1.19491i
\(647\) −19.3776 −0.761812 −0.380906 0.924614i \(-0.624388\pi\)
−0.380906 + 0.924614i \(0.624388\pi\)
\(648\) −69.7692 69.7692i −2.74079 2.74079i
\(649\) −36.6402 + 15.1769i −1.43825 + 0.595744i
\(650\) 54.9139i 2.15390i
\(651\) 4.43052 + 10.6962i 0.173646 + 0.419218i
\(652\) −14.6864 6.08331i −0.575165 0.238241i
\(653\) 2.77334 6.69544i 0.108529 0.262013i −0.860279 0.509823i \(-0.829711\pi\)
0.968809 + 0.247810i \(0.0797109\pi\)
\(654\) 90.1778 90.1778i 3.52623 3.52623i
\(655\) −4.05016 + 4.05016i −0.158253 + 0.158253i
\(656\) 1.53166 3.69776i 0.0598014 0.144373i
\(657\) 45.6998 + 18.9295i 1.78292 + 0.738508i
\(658\) −18.9800 45.8219i −0.739919 1.78632i
\(659\) 13.7567i 0.535885i 0.963435 + 0.267942i \(0.0863437\pi\)
−0.963435 + 0.267942i \(0.913656\pi\)
\(660\) 19.5554 8.10011i 0.761192 0.315296i
\(661\) 6.55171 + 6.55171i 0.254832 + 0.254832i 0.822948 0.568116i \(-0.192328\pi\)
−0.568116 + 0.822948i \(0.692328\pi\)
\(662\) −82.1162 −3.19154
\(663\) −50.3217 33.2078i −1.95433 1.28969i
\(664\) −46.3538 −1.79887
\(665\) −1.54038 1.54038i −0.0597334 0.0597334i
\(666\) 68.4023 28.3332i 2.65054 1.09789i
\(667\) 6.34857i 0.245818i
\(668\) −1.13411 2.73799i −0.0438801 0.105936i
\(669\) 16.0127 + 6.63269i 0.619088 + 0.256434i
\(670\) 0.701128 1.69267i 0.0270869 0.0653936i
\(671\) 14.8070 14.8070i 0.571619 0.571619i
\(672\) −0.112256 + 0.112256i −0.00433038 + 0.00433038i
\(673\) −8.98828 + 21.6996i −0.346473 + 0.836459i 0.650558 + 0.759457i \(0.274535\pi\)
−0.997031 + 0.0770029i \(0.975465\pi\)
\(674\) −30.7602 12.7413i −1.18484 0.490776i
\(675\) −24.2853 58.6299i −0.934742 2.25667i
\(676\) 32.7122i 1.25816i
\(677\) 10.2495 4.24549i 0.393921 0.163167i −0.176926 0.984224i \(-0.556615\pi\)
0.570846 + 0.821057i \(0.306615\pi\)
\(678\) −37.0916 37.0916i −1.42450 1.42450i
\(679\) −20.0905 −0.771003
\(680\) 7.11999 1.45877i 0.273039 0.0559414i
\(681\) −17.8169 −0.682743
\(682\) 17.4973 + 17.4973i 0.670005 + 0.670005i
\(683\) 6.67963 2.76679i 0.255589 0.105868i −0.251210 0.967933i \(-0.580829\pi\)
0.506799 + 0.862064i \(0.330829\pi\)
\(684\) 103.155i 3.94423i
\(685\) 2.12690 + 5.13480i 0.0812648 + 0.196191i
\(686\) 42.3927 + 17.5596i 1.61856 + 0.670430i
\(687\) −2.80746 + 6.77782i −0.107111 + 0.258590i
\(688\) 2.84137 2.84137i 0.108326 0.108326i
\(689\) 26.0058 26.0058i 0.990742 0.990742i
\(690\) −1.68716 + 4.07316i −0.0642291 + 0.155063i
\(691\) 24.6904 + 10.2271i 0.939267 + 0.389057i 0.799187 0.601083i \(-0.205264\pi\)
0.140081 + 0.990140i \(0.455264\pi\)
\(692\) 30.4192 + 73.4384i 1.15636 + 2.79171i
\(693\) 54.9540i 2.08753i
\(694\) 44.7268 18.5265i 1.69781 0.703255i
\(695\) −0.631278 0.631278i −0.0239457 0.0239457i
\(696\) −62.8104 −2.38082
\(697\) 0.824299 + 4.02325i 0.0312226 + 0.152391i
\(698\) 37.4989 1.41935
\(699\) −57.0237 57.0237i −2.15683 2.15683i
\(700\) −30.1016 + 12.4685i −1.13774 + 0.471265i
\(701\) 31.4077i 1.18625i −0.805110 0.593126i \(-0.797894\pi\)
0.805110 0.593126i \(-0.202106\pi\)
\(702\) 56.2071 + 135.696i 2.12140 + 5.12151i
\(703\) −14.2733 5.91219i −0.538327 0.222983i
\(704\) 14.1168 34.0811i 0.532049 1.28448i
\(705\) 9.77796 9.77796i 0.368259 0.368259i
\(706\) 59.4893 59.4893i 2.23891 2.23891i
\(707\) 8.56506 20.6779i 0.322122 0.777671i
\(708\) 100.623 + 41.6794i 3.78165 + 1.56641i
\(709\) 9.28446 + 22.4147i 0.348685 + 0.841801i 0.996776 + 0.0802374i \(0.0255678\pi\)
−0.648091 + 0.761563i \(0.724432\pi\)
\(710\) 6.95580i 0.261047i
\(711\) −43.2737 + 17.9246i −1.62289 + 0.672224i
\(712\) 38.9622 + 38.9622i 1.46017 + 1.46017i
\(713\) −3.43692 −0.128714
\(714\) 10.1635 52.6732i 0.380360 1.97125i
\(715\) −7.65576 −0.286309
\(716\) 28.1798 + 28.1798i 1.05313 + 1.05313i
\(717\) −34.8701 + 14.4437i −1.30225 + 0.539409i
\(718\) 5.97158i 0.222857i
\(719\) −3.37646 8.15149i −0.125921 0.303999i 0.848330 0.529468i \(-0.177609\pi\)
−0.974250 + 0.225469i \(0.927609\pi\)
\(720\) −9.46662 3.92120i −0.352800 0.146135i
\(721\) 0.435688 1.05184i 0.0162259 0.0391727i
\(722\) −10.0924 + 10.0924i −0.375599 + 0.375599i
\(723\) 20.0923 20.0923i 0.747240 0.747240i
\(724\) −35.0729 + 84.6734i −1.30347 + 3.14686i
\(725\) −18.1232 7.50689i −0.673080 0.278799i
\(726\) −31.1642 75.2371i −1.15661 2.79231i
\(727\) 11.9093i 0.441690i −0.975309 0.220845i \(-0.929119\pi\)
0.975309 0.220845i \(-0.0708815\pi\)
\(728\) 34.8609 14.4398i 1.29203 0.535176i
\(729\) −13.0991 13.0991i −0.485153 0.485153i
\(730\) 6.13142 0.226934
\(731\) −0.781162 + 4.04843i −0.0288923 + 0.149737i
\(732\) −57.5072 −2.12553
\(733\) 24.5751 + 24.5751i 0.907702 + 0.907702i 0.996086 0.0883849i \(-0.0281705\pi\)
−0.0883849 + 0.996086i \(0.528171\pi\)
\(734\) 70.2493 29.0982i 2.59295 1.07403i
\(735\) 4.80310i 0.177165i
\(736\) −0.0180352 0.0435408i −0.000664786 0.00160493i
\(737\) −8.91009 3.69068i −0.328207 0.135948i
\(738\) 6.63036 16.0071i 0.244067 0.589230i
\(739\) 23.7769 23.7769i 0.874648 0.874648i −0.118327 0.992975i \(-0.537753\pi\)
0.992975 + 0.118327i \(0.0377531\pi\)
\(740\) 4.32735 4.32735i 0.159077 0.159077i
\(741\) 20.3114 49.0360i 0.746157 1.80138i
\(742\) 30.2325 + 12.5227i 1.10987 + 0.459723i
\(743\) 5.73786 + 13.8524i 0.210502 + 0.508196i 0.993501 0.113827i \(-0.0363110\pi\)
−0.782999 + 0.622023i \(0.786311\pi\)
\(744\) 34.0036i 1.24663i
\(745\) 0.577157 0.239066i 0.0211454 0.00875871i
\(746\) −27.8969 27.8969i −1.02138 1.02138i
\(747\) −67.0561 −2.45345
\(748\) −15.3460 74.9011i −0.561107 2.73866i
\(749\) −30.6853 −1.12122
\(750\) −19.5204 19.5204i −0.712786 0.712786i
\(751\) −0.796333 + 0.329852i −0.0290586 + 0.0120365i −0.397165 0.917747i \(-0.630006\pi\)
0.368107 + 0.929784i \(0.380006\pi\)
\(752\) 48.6796i 1.77516i
\(753\) −9.30656 22.4680i −0.339150 0.818780i
\(754\) 41.9453 + 17.3743i 1.52756 + 0.632735i
\(755\) 2.67146 6.44947i 0.0972243 0.234720i
\(756\) −61.6210 + 61.6210i −2.24113 + 2.24113i
\(757\) 20.0327 20.0327i 0.728102 0.728102i −0.242140 0.970241i \(-0.577849\pi\)
0.970241 + 0.242140i \(0.0778492\pi\)
\(758\) −0.745063 + 1.79874i −0.0270619 + 0.0653332i
\(759\) 21.4408 + 8.88108i 0.778252 + 0.322363i
\(760\) 2.44846 + 5.91111i 0.0888151 + 0.214419i
\(761\) 31.5235i 1.14273i 0.820697 + 0.571363i