Properties

Label 43.2.c.b.6.1
Level 43
Weight 2
Character 43.6
Analytic conductor 0.343
Analytic rank 0
Dimension 4
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(0.343356728692\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 6.1
Root \(-0.309017 + 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 43.6
Dual form 43.2.c.b.36.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.61803 q^{2} +(0.190983 - 0.330792i) q^{3} +4.85410 q^{4} +(1.61803 - 2.80252i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.118034 - 0.204441i) q^{7} -7.47214 q^{8} +(1.42705 + 2.47172i) q^{9} +O(q^{10})\) \(q-2.61803 q^{2} +(0.190983 - 0.330792i) q^{3} +4.85410 q^{4} +(1.61803 - 2.80252i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-0.118034 - 0.204441i) q^{7} -7.47214 q^{8} +(1.42705 + 2.47172i) q^{9} +(-4.23607 + 7.33708i) q^{10} -1.38197 q^{11} +(0.927051 - 1.60570i) q^{12} +(-1.80902 - 3.13331i) q^{13} +(0.309017 + 0.535233i) q^{14} +(-0.618034 - 1.07047i) q^{15} +9.85410 q^{16} +(2.54508 + 4.40822i) q^{17} +(-3.73607 - 6.47106i) q^{18} +(-1.61803 + 2.80252i) q^{19} +(7.85410 - 13.6037i) q^{20} -0.0901699 q^{21} +3.61803 q^{22} +(-3.30902 + 5.73139i) q^{23} +(-1.42705 + 2.47172i) q^{24} +(-2.73607 - 4.73901i) q^{25} +(4.73607 + 8.20311i) q^{26} +2.23607 q^{27} +(-0.572949 - 0.992377i) q^{28} +(-1.50000 - 2.59808i) q^{29} +(1.61803 + 2.80252i) q^{30} -10.8541 q^{32} +(-0.263932 + 0.457144i) q^{33} +(-6.66312 - 11.5409i) q^{34} -0.763932 q^{35} +(6.92705 + 11.9980i) q^{36} +(-0.927051 + 1.60570i) q^{37} +(4.23607 - 7.33708i) q^{38} -1.38197 q^{39} +(-12.0902 + 20.9408i) q^{40} +0.527864 q^{41} +0.236068 q^{42} +(-6.50000 + 0.866025i) q^{43} -6.70820 q^{44} +9.23607 q^{45} +(8.66312 - 15.0050i) q^{46} +7.85410 q^{47} +(1.88197 - 3.25966i) q^{48} +(3.47214 - 6.01392i) q^{49} +(7.16312 + 12.4069i) q^{50} +1.94427 q^{51} +(-8.78115 - 15.2094i) q^{52} +(1.80902 - 3.13331i) q^{53} -5.85410 q^{54} +(-2.23607 + 3.87298i) q^{55} +(0.881966 + 1.52761i) q^{56} +(0.618034 + 1.07047i) q^{57} +(3.92705 + 6.80185i) q^{58} -6.09017 q^{59} +(-3.00000 - 5.19615i) q^{60} +(1.92705 + 3.33775i) q^{61} +(0.336881 - 0.583495i) q^{63} +8.70820 q^{64} -11.7082 q^{65} +(0.690983 - 1.19682i) q^{66} +(-1.42705 + 2.47172i) q^{67} +(12.3541 + 21.3979i) q^{68} +(1.26393 + 2.18919i) q^{69} +2.00000 q^{70} +(-6.89919 - 11.9497i) q^{71} +(-10.6631 - 18.4691i) q^{72} +(2.42705 + 4.20378i) q^{73} +(2.42705 - 4.20378i) q^{74} -2.09017 q^{75} +(-7.85410 + 13.6037i) q^{76} +(0.163119 + 0.282530i) q^{77} +3.61803 q^{78} +(1.80902 + 3.13331i) q^{79} +(15.9443 - 27.6163i) q^{80} +(-3.85410 + 6.67550i) q^{81} -1.38197 q^{82} +(6.51722 - 11.2882i) q^{83} -0.437694 q^{84} +16.4721 q^{85} +(17.0172 - 2.26728i) q^{86} -1.14590 q^{87} +10.3262 q^{88} +(-2.42705 + 4.20378i) q^{89} -24.1803 q^{90} +(-0.427051 + 0.739674i) q^{91} +(-16.0623 + 27.8207i) q^{92} -20.5623 q^{94} +(5.23607 + 9.06914i) q^{95} +(-2.07295 + 3.59045i) q^{96} -4.76393 q^{97} +(-9.09017 + 15.7446i) q^{98} +(-1.97214 - 3.41584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 6q^{2} + 3q^{3} + 6q^{4} + 2q^{5} - 2q^{6} + 4q^{7} - 12q^{8} - q^{9} + O(q^{10}) \) \( 4q - 6q^{2} + 3q^{3} + 6q^{4} + 2q^{5} - 2q^{6} + 4q^{7} - 12q^{8} - q^{9} - 8q^{10} - 10q^{11} - 3q^{12} - 5q^{13} - q^{14} + 2q^{15} + 26q^{16} - q^{17} - 6q^{18} - 2q^{19} + 18q^{20} + 22q^{21} + 10q^{22} - 11q^{23} + q^{24} - 2q^{25} + 10q^{26} - 9q^{28} - 6q^{29} + 2q^{30} - 30q^{32} - 10q^{33} - 11q^{34} - 12q^{35} + 21q^{36} + 3q^{37} + 8q^{38} - 10q^{39} - 26q^{40} + 20q^{41} - 8q^{42} - 26q^{43} + 28q^{45} + 19q^{46} + 18q^{47} + 12q^{48} - 4q^{49} + 13q^{50} - 28q^{51} - 15q^{52} + 5q^{53} - 10q^{54} + 8q^{56} - 2q^{57} + 9q^{58} - 2q^{59} - 12q^{60} + q^{61} + 17q^{63} + 8q^{64} - 20q^{65} + 5q^{66} + q^{67} + 36q^{68} + 14q^{69} + 8q^{70} - 3q^{71} - 27q^{72} + 3q^{73} + 3q^{74} + 14q^{75} - 18q^{76} - 15q^{77} + 10q^{78} + 5q^{79} + 28q^{80} - 2q^{81} - 10q^{82} - 3q^{83} - 42q^{84} + 48q^{85} + 39q^{86} - 18q^{87} + 10q^{88} - 3q^{89} - 52q^{90} + 5q^{91} - 24q^{92} - 42q^{94} + 12q^{95} - 15q^{96} - 28q^{97} - 14q^{98} + 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.61803 −1.85123 −0.925615 0.378467i \(-0.876451\pi\)
−0.925615 + 0.378467i \(0.876451\pi\)
\(3\) 0.190983 0.330792i 0.110264 0.190983i −0.805613 0.592443i \(-0.798164\pi\)
0.915877 + 0.401460i \(0.131497\pi\)
\(4\) 4.85410 2.42705
\(5\) 1.61803 2.80252i 0.723607 1.25332i −0.235938 0.971768i \(-0.575816\pi\)
0.959545 0.281556i \(-0.0908504\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) −0.118034 0.204441i −0.0446127 0.0772714i 0.842857 0.538138i \(-0.180872\pi\)
−0.887469 + 0.460866i \(0.847539\pi\)
\(8\) −7.47214 −2.64180
\(9\) 1.42705 + 2.47172i 0.475684 + 0.823908i
\(10\) −4.23607 + 7.33708i −1.33956 + 2.32019i
\(11\) −1.38197 −0.416678 −0.208339 0.978057i \(-0.566806\pi\)
−0.208339 + 0.978057i \(0.566806\pi\)
\(12\) 0.927051 1.60570i 0.267617 0.463525i
\(13\) −1.80902 3.13331i −0.501731 0.869024i −0.999998 0.00199999i \(-0.999363\pi\)
0.498267 0.867024i \(-0.333970\pi\)
\(14\) 0.309017 + 0.535233i 0.0825883 + 0.143047i
\(15\) −0.618034 1.07047i −0.159576 0.276393i
\(16\) 9.85410 2.46353
\(17\) 2.54508 + 4.40822i 0.617274 + 1.06915i 0.989981 + 0.141201i \(0.0450962\pi\)
−0.372707 + 0.927949i \(0.621570\pi\)
\(18\) −3.73607 6.47106i −0.880600 1.52524i
\(19\) −1.61803 + 2.80252i −0.371202 + 0.642942i −0.989751 0.142805i \(-0.954388\pi\)
0.618548 + 0.785747i \(0.287721\pi\)
\(20\) 7.85410 13.6037i 1.75623 3.04188i
\(21\) −0.0901699 −0.0196767
\(22\) 3.61803 0.771367
\(23\) −3.30902 + 5.73139i −0.689978 + 1.19508i 0.281867 + 0.959454i \(0.409046\pi\)
−0.971845 + 0.235623i \(0.924287\pi\)
\(24\) −1.42705 + 2.47172i −0.291296 + 0.504539i
\(25\) −2.73607 4.73901i −0.547214 0.947802i
\(26\) 4.73607 + 8.20311i 0.928819 + 1.60876i
\(27\) 2.23607 0.430331
\(28\) −0.572949 0.992377i −0.108277 0.187542i
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 1.61803 + 2.80252i 0.295411 + 0.511667i
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) −10.8541 −1.91875
\(33\) −0.263932 + 0.457144i −0.0459447 + 0.0795785i
\(34\) −6.66312 11.5409i −1.14272 1.97924i
\(35\) −0.763932 −0.129128
\(36\) 6.92705 + 11.9980i 1.15451 + 1.99967i
\(37\) −0.927051 + 1.60570i −0.152406 + 0.263975i −0.932112 0.362171i \(-0.882036\pi\)
0.779705 + 0.626147i \(0.215369\pi\)
\(38\) 4.23607 7.33708i 0.687181 1.19023i
\(39\) −1.38197 −0.221292
\(40\) −12.0902 + 20.9408i −1.91162 + 3.31103i
\(41\) 0.527864 0.0824385 0.0412193 0.999150i \(-0.486876\pi\)
0.0412193 + 0.999150i \(0.486876\pi\)
\(42\) 0.236068 0.0364261
\(43\) −6.50000 + 0.866025i −0.991241 + 0.132068i
\(44\) −6.70820 −1.01130
\(45\) 9.23607 1.37683
\(46\) 8.66312 15.0050i 1.27731 2.21236i
\(47\) 7.85410 1.14564 0.572819 0.819682i \(-0.305850\pi\)
0.572819 + 0.819682i \(0.305850\pi\)
\(48\) 1.88197 3.25966i 0.271638 0.470492i
\(49\) 3.47214 6.01392i 0.496019 0.859131i
\(50\) 7.16312 + 12.4069i 1.01302 + 1.75460i
\(51\) 1.94427 0.272253
\(52\) −8.78115 15.2094i −1.21773 2.10916i
\(53\) 1.80902 3.13331i 0.248488 0.430393i −0.714619 0.699514i \(-0.753400\pi\)
0.963106 + 0.269121i \(0.0867331\pi\)
\(54\) −5.85410 −0.796642
\(55\) −2.23607 + 3.87298i −0.301511 + 0.522233i
\(56\) 0.881966 + 1.52761i 0.117858 + 0.204135i
\(57\) 0.618034 + 1.07047i 0.0818606 + 0.141787i
\(58\) 3.92705 + 6.80185i 0.515647 + 0.893127i
\(59\) −6.09017 −0.792873 −0.396436 0.918062i \(-0.629753\pi\)
−0.396436 + 0.918062i \(0.629753\pi\)
\(60\) −3.00000 5.19615i −0.387298 0.670820i
\(61\) 1.92705 + 3.33775i 0.246734 + 0.427355i 0.962618 0.270864i \(-0.0873094\pi\)
−0.715884 + 0.698219i \(0.753976\pi\)
\(62\) 0 0
\(63\) 0.336881 0.583495i 0.0424430 0.0735135i
\(64\) 8.70820 1.08853
\(65\) −11.7082 −1.45222
\(66\) 0.690983 1.19682i 0.0850541 0.147318i
\(67\) −1.42705 + 2.47172i −0.174342 + 0.301969i −0.939933 0.341358i \(-0.889113\pi\)
0.765591 + 0.643327i \(0.222447\pi\)
\(68\) 12.3541 + 21.3979i 1.49815 + 2.59488i
\(69\) 1.26393 + 2.18919i 0.152160 + 0.263548i
\(70\) 2.00000 0.239046
\(71\) −6.89919 11.9497i −0.818783 1.41817i −0.906580 0.422035i \(-0.861316\pi\)
0.0877966 0.996138i \(-0.472017\pi\)
\(72\) −10.6631 18.4691i −1.25666 2.17660i
\(73\) 2.42705 + 4.20378i 0.284065 + 0.492015i 0.972382 0.233395i \(-0.0749836\pi\)
−0.688317 + 0.725410i \(0.741650\pi\)
\(74\) 2.42705 4.20378i 0.282139 0.488679i
\(75\) −2.09017 −0.241352
\(76\) −7.85410 + 13.6037i −0.900927 + 1.56045i
\(77\) 0.163119 + 0.282530i 0.0185891 + 0.0321973i
\(78\) 3.61803 0.409662
\(79\) 1.80902 + 3.13331i 0.203530 + 0.352525i 0.949663 0.313272i \(-0.101425\pi\)
−0.746133 + 0.665797i \(0.768092\pi\)
\(80\) 15.9443 27.6163i 1.78262 3.08759i
\(81\) −3.85410 + 6.67550i −0.428234 + 0.741722i
\(82\) −1.38197 −0.152613
\(83\) 6.51722 11.2882i 0.715358 1.23904i −0.247463 0.968897i \(-0.579597\pi\)
0.962821 0.270139i \(-0.0870697\pi\)
\(84\) −0.437694 −0.0477563
\(85\) 16.4721 1.78665
\(86\) 17.0172 2.26728i 1.83501 0.244488i
\(87\) −1.14590 −0.122853
\(88\) 10.3262 1.10078
\(89\) −2.42705 + 4.20378i −0.257267 + 0.445599i −0.965509 0.260371i \(-0.916155\pi\)
0.708242 + 0.705970i \(0.249489\pi\)
\(90\) −24.1803 −2.54883
\(91\) −0.427051 + 0.739674i −0.0447671 + 0.0775389i
\(92\) −16.0623 + 27.8207i −1.67461 + 2.90051i
\(93\) 0 0
\(94\) −20.5623 −2.12084
\(95\) 5.23607 + 9.06914i 0.537209 + 0.930474i
\(96\) −2.07295 + 3.59045i −0.211569 + 0.366449i
\(97\) −4.76393 −0.483704 −0.241852 0.970313i \(-0.577755\pi\)
−0.241852 + 0.970313i \(0.577755\pi\)
\(98\) −9.09017 + 15.7446i −0.918246 + 1.59045i
\(99\) −1.97214 3.41584i −0.198207 0.343305i
\(100\) −13.2812 23.0036i −1.32812 2.30036i
\(101\) −4.11803 7.13264i −0.409760 0.709725i 0.585103 0.810959i \(-0.301054\pi\)
−0.994863 + 0.101234i \(0.967721\pi\)
\(102\) −5.09017 −0.504002
\(103\) −5.20820 9.02087i −0.513180 0.888853i −0.999883 0.0152859i \(-0.995134\pi\)
0.486704 0.873567i \(-0.338199\pi\)
\(104\) 13.5172 + 23.4125i 1.32547 + 2.29579i
\(105\) −0.145898 + 0.252703i −0.0142382 + 0.0246613i
\(106\) −4.73607 + 8.20311i −0.460008 + 0.796757i
\(107\) 16.4721 1.59242 0.796211 0.605019i \(-0.206835\pi\)
0.796211 + 0.605019i \(0.206835\pi\)
\(108\) 10.8541 1.04444
\(109\) 3.57295 6.18853i 0.342226 0.592754i −0.642619 0.766186i \(-0.722152\pi\)
0.984846 + 0.173432i \(0.0554857\pi\)
\(110\) 5.85410 10.1396i 0.558167 0.966773i
\(111\) 0.354102 + 0.613323i 0.0336099 + 0.0582140i
\(112\) −1.16312 2.01458i −0.109904 0.190360i
\(113\) −13.3820 −1.25887 −0.629435 0.777053i \(-0.716714\pi\)
−0.629435 + 0.777053i \(0.716714\pi\)
\(114\) −1.61803 2.80252i −0.151543 0.262480i
\(115\) 10.7082 + 18.5472i 0.998545 + 1.72953i
\(116\) −7.28115 12.6113i −0.676038 1.17093i
\(117\) 5.16312 8.94278i 0.477331 0.826761i
\(118\) 15.9443 1.46779
\(119\) 0.600813 1.04064i 0.0550764 0.0953952i
\(120\) 4.61803 + 7.99867i 0.421567 + 0.730175i
\(121\) −9.09017 −0.826379
\(122\) −5.04508 8.73834i −0.456761 0.791132i
\(123\) 0.100813 0.174613i 0.00909001 0.0157444i
\(124\) 0 0
\(125\) −1.52786 −0.136656
\(126\) −0.881966 + 1.52761i −0.0785718 + 0.136090i
\(127\) 16.6525 1.47767 0.738834 0.673887i \(-0.235377\pi\)
0.738834 + 0.673887i \(0.235377\pi\)
\(128\) −1.09017 −0.0963583
\(129\) −0.954915 + 2.31555i −0.0840756 + 0.203872i
\(130\) 30.6525 2.68840
\(131\) −7.94427 −0.694094 −0.347047 0.937848i \(-0.612816\pi\)
−0.347047 + 0.937848i \(0.612816\pi\)
\(132\) −1.28115 + 2.21902i −0.111510 + 0.193141i
\(133\) 0.763932 0.0662413
\(134\) 3.73607 6.47106i 0.322747 0.559014i
\(135\) 3.61803 6.26662i 0.311391 0.539345i
\(136\) −19.0172 32.9388i −1.63071 2.82448i
\(137\) −9.70820 −0.829428 −0.414714 0.909952i \(-0.636118\pi\)
−0.414714 + 0.909952i \(0.636118\pi\)
\(138\) −3.30902 5.73139i −0.281682 0.487888i
\(139\) 9.35410 16.2018i 0.793405 1.37422i −0.130443 0.991456i \(-0.541640\pi\)
0.923847 0.382761i \(-0.125027\pi\)
\(140\) −3.70820 −0.313400
\(141\) 1.50000 2.59808i 0.126323 0.218797i
\(142\) 18.0623 + 31.2848i 1.51576 + 2.62536i
\(143\) 2.50000 + 4.33013i 0.209061 + 0.362103i
\(144\) 14.0623 + 24.3566i 1.17186 + 2.02972i
\(145\) −9.70820 −0.806222
\(146\) −6.35410 11.0056i −0.525869 0.910832i
\(147\) −1.32624 2.29711i −0.109386 0.189463i
\(148\) −4.50000 + 7.79423i −0.369898 + 0.640682i
\(149\) −4.50000 + 7.79423i −0.368654 + 0.638528i −0.989355 0.145519i \(-0.953515\pi\)
0.620701 + 0.784047i \(0.286848\pi\)
\(150\) 5.47214 0.446798
\(151\) −2.14590 −0.174631 −0.0873154 0.996181i \(-0.527829\pi\)
−0.0873154 + 0.996181i \(0.527829\pi\)
\(152\) 12.0902 20.9408i 0.980642 1.69852i
\(153\) −7.26393 + 12.5815i −0.587254 + 1.01715i
\(154\) −0.427051 0.739674i −0.0344127 0.0596046i
\(155\) 0 0
\(156\) −6.70820 −0.537086
\(157\) 5.92705 + 10.2660i 0.473030 + 0.819312i 0.999524 0.0308670i \(-0.00982682\pi\)
−0.526493 + 0.850179i \(0.676493\pi\)
\(158\) −4.73607 8.20311i −0.376781 0.652604i
\(159\) −0.690983 1.19682i −0.0547985 0.0949138i
\(160\) −17.5623 + 30.4188i −1.38842 + 2.40482i
\(161\) 1.56231 0.123127
\(162\) 10.0902 17.4767i 0.792759 1.37310i
\(163\) −7.00000 12.1244i −0.548282 0.949653i −0.998392 0.0566798i \(-0.981949\pi\)
0.450110 0.892973i \(-0.351385\pi\)
\(164\) 2.56231 0.200082
\(165\) 0.854102 + 1.47935i 0.0664917 + 0.115167i
\(166\) −17.0623 + 29.5528i −1.32429 + 2.29374i
\(167\) −4.88197 + 8.45581i −0.377778 + 0.654330i −0.990739 0.135783i \(-0.956645\pi\)
0.612961 + 0.790113i \(0.289978\pi\)
\(168\) 0.673762 0.0519819
\(169\) −0.0450850 + 0.0780895i −0.00346807 + 0.00600688i
\(170\) −43.1246 −3.30751
\(171\) −9.23607 −0.706300
\(172\) −31.5517 + 4.20378i −2.40579 + 0.320535i
\(173\) −8.23607 −0.626177 −0.313088 0.949724i \(-0.601364\pi\)
−0.313088 + 0.949724i \(0.601364\pi\)
\(174\) 3.00000 0.227429
\(175\) −0.645898 + 1.11873i −0.0488253 + 0.0845679i
\(176\) −13.6180 −1.02650
\(177\) −1.16312 + 2.01458i −0.0874254 + 0.151425i
\(178\) 6.35410 11.0056i 0.476260 0.824907i
\(179\) 10.8262 + 18.7516i 0.809191 + 1.40156i 0.913425 + 0.407007i \(0.133428\pi\)
−0.104234 + 0.994553i \(0.533239\pi\)
\(180\) 44.8328 3.34164
\(181\) 10.8090 + 18.7218i 0.803428 + 1.39158i 0.917347 + 0.398088i \(0.130326\pi\)
−0.113919 + 0.993490i \(0.536341\pi\)
\(182\) 1.11803 1.93649i 0.0828742 0.143542i
\(183\) 1.47214 0.108823
\(184\) 24.7254 42.8257i 1.82278 3.15715i
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) 0 0
\(187\) −3.51722 6.09201i −0.257205 0.445492i
\(188\) 38.1246 2.78052
\(189\) −0.263932 0.457144i −0.0191982 0.0332523i
\(190\) −13.7082 23.7433i −0.994498 1.72252i
\(191\) 11.7361 20.3275i 0.849192 1.47084i −0.0327382 0.999464i \(-0.510423\pi\)
0.881930 0.471380i \(-0.156244\pi\)
\(192\) 1.66312 2.88061i 0.120025 0.207890i
\(193\) −10.7082 −0.770793 −0.385397 0.922751i \(-0.625935\pi\)
−0.385397 + 0.922751i \(0.625935\pi\)
\(194\) 12.4721 0.895447
\(195\) −2.23607 + 3.87298i −0.160128 + 0.277350i
\(196\) 16.8541 29.1922i 1.20386 2.08515i
\(197\) −7.47214 12.9421i −0.532368 0.922088i −0.999286 0.0377873i \(-0.987969\pi\)
0.466918 0.884301i \(-0.345364\pi\)
\(198\) 5.16312 + 8.94278i 0.366927 + 0.635536i
\(199\) −15.9443 −1.13026 −0.565130 0.825002i \(-0.691174\pi\)
−0.565130 + 0.825002i \(0.691174\pi\)
\(200\) 20.4443 + 35.4105i 1.44563 + 2.50390i
\(201\) 0.545085 + 0.944115i 0.0384473 + 0.0665927i
\(202\) 10.7812 + 18.6735i 0.758559 + 1.31386i
\(203\) −0.354102 + 0.613323i −0.0248531 + 0.0430468i
\(204\) 9.43769 0.660771
\(205\) 0.854102 1.47935i 0.0596531 0.103322i
\(206\) 13.6353 + 23.6170i 0.950013 + 1.64547i
\(207\) −18.8885 −1.31284
\(208\) −17.8262 30.8759i −1.23603 2.14086i
\(209\) 2.23607 3.87298i 0.154672 0.267900i
\(210\) 0.381966 0.661585i 0.0263582 0.0456537i
\(211\) −4.76393 −0.327963 −0.163981 0.986463i \(-0.552434\pi\)
−0.163981 + 0.986463i \(0.552434\pi\)
\(212\) 8.78115 15.2094i 0.603092 1.04459i
\(213\) −5.27051 −0.361129
\(214\) −43.1246 −2.94794
\(215\) −8.09017 + 19.6176i −0.551745 + 1.33791i
\(216\) −16.7082 −1.13685
\(217\) 0 0
\(218\) −9.35410 + 16.2018i −0.633540 + 1.09732i
\(219\) 1.85410 0.125289
\(220\) −10.8541 + 18.7999i −0.731783 + 1.26749i
\(221\) 9.20820 15.9491i 0.619411 1.07285i
\(222\) −0.927051 1.60570i −0.0622196 0.107767i
\(223\) 7.23607 0.484563 0.242281 0.970206i \(-0.422104\pi\)
0.242281 + 0.970206i \(0.422104\pi\)
\(224\) 1.28115 + 2.21902i 0.0856006 + 0.148265i
\(225\) 7.80902 13.5256i 0.520601 0.901708i
\(226\) 35.0344 2.33046
\(227\) −3.73607 + 6.47106i −0.247972 + 0.429499i −0.962963 0.269634i \(-0.913097\pi\)
0.714991 + 0.699133i \(0.246431\pi\)
\(228\) 3.00000 + 5.19615i 0.198680 + 0.344124i
\(229\) 7.85410 + 13.6037i 0.519014 + 0.898958i 0.999756 + 0.0220961i \(0.00703396\pi\)
−0.480742 + 0.876862i \(0.659633\pi\)
\(230\) −28.0344 48.5571i −1.84854 3.20176i
\(231\) 0.124612 0.00819885
\(232\) 11.2082 + 19.4132i 0.735855 + 1.27454i
\(233\) 5.51722 + 9.55611i 0.361445 + 0.626041i 0.988199 0.153176i \(-0.0489501\pi\)
−0.626754 + 0.779217i \(0.715617\pi\)
\(234\) −13.5172 + 23.4125i −0.883648 + 1.53052i
\(235\) 12.7082 22.0113i 0.828992 1.43586i
\(236\) −29.5623 −1.92434
\(237\) 1.38197 0.0897683
\(238\) −1.57295 + 2.72443i −0.101959 + 0.176598i
\(239\) 10.8541 18.7999i 0.702093 1.21606i −0.265637 0.964073i \(-0.585582\pi\)
0.967730 0.251988i \(-0.0810845\pi\)
\(240\) −6.09017 10.5485i −0.393119 0.680902i
\(241\) 14.6353 + 25.3490i 0.942740 + 1.63287i 0.760215 + 0.649672i \(0.225094\pi\)
0.182525 + 0.983201i \(0.441573\pi\)
\(242\) 23.7984 1.52982
\(243\) 4.82624 + 8.35929i 0.309603 + 0.536249i
\(244\) 9.35410 + 16.2018i 0.598835 + 1.03721i
\(245\) −11.2361 19.4614i −0.717846 1.24335i
\(246\) −0.263932 + 0.457144i −0.0168277 + 0.0291464i
\(247\) 11.7082 0.744975
\(248\) 0 0
\(249\) −2.48936 4.31169i −0.157757 0.273242i
\(250\) 4.00000 0.252982
\(251\) 3.40983 + 5.90600i 0.215227 + 0.372783i 0.953343 0.301890i \(-0.0976177\pi\)
−0.738116 + 0.674674i \(0.764284\pi\)
\(252\) 1.63525 2.83234i 0.103011 0.178421i
\(253\) 4.57295 7.92058i 0.287499 0.497963i
\(254\) −43.5967 −2.73550
\(255\) 3.14590 5.44886i 0.197004 0.341221i
\(256\) −14.5623 −0.910144
\(257\) 23.5623 1.46978 0.734888 0.678188i \(-0.237235\pi\)
0.734888 + 0.678188i \(0.237235\pi\)
\(258\) 2.50000 6.06218i 0.155643 0.377415i
\(259\) 0.437694 0.0271970
\(260\) −56.8328 −3.52462
\(261\) 4.28115 7.41517i 0.264997 0.458988i
\(262\) 20.7984 1.28493
\(263\) 5.25329 9.09896i 0.323932 0.561066i −0.657364 0.753573i \(-0.728329\pi\)
0.981296 + 0.192507i \(0.0616619\pi\)
\(264\) 1.97214 3.41584i 0.121377 0.210230i
\(265\) −5.85410 10.1396i −0.359615 0.622871i
\(266\) −2.00000 −0.122628
\(267\) 0.927051 + 1.60570i 0.0567346 + 0.0982672i
\(268\) −6.92705 + 11.9980i −0.423137 + 0.732895i
\(269\) −8.56231 −0.522053 −0.261027 0.965332i \(-0.584061\pi\)
−0.261027 + 0.965332i \(0.584061\pi\)
\(270\) −9.47214 + 16.4062i −0.576456 + 0.998451i
\(271\) −3.57295 6.18853i −0.217041 0.375926i 0.736861 0.676044i \(-0.236307\pi\)
−0.953902 + 0.300118i \(0.902974\pi\)
\(272\) 25.0795 + 43.4390i 1.52067 + 2.63388i
\(273\) 0.163119 + 0.282530i 0.00987241 + 0.0170995i
\(274\) 25.4164 1.53546
\(275\) 3.78115 + 6.54915i 0.228012 + 0.394929i
\(276\) 6.13525 + 10.6266i 0.369299 + 0.639645i
\(277\) 1.76393 3.05522i 0.105984 0.183570i −0.808156 0.588969i \(-0.799534\pi\)
0.914140 + 0.405399i \(0.132867\pi\)
\(278\) −24.4894 + 42.4168i −1.46877 + 2.54399i
\(279\) 0 0
\(280\) 5.70820 0.341130
\(281\) 0.736068 1.27491i 0.0439101 0.0760546i −0.843235 0.537545i \(-0.819352\pi\)
0.887145 + 0.461490i \(0.152685\pi\)
\(282\) −3.92705 + 6.80185i −0.233852 + 0.405044i
\(283\) −7.61803 13.1948i −0.452845 0.784351i 0.545716 0.837970i \(-0.316258\pi\)
−0.998561 + 0.0536192i \(0.982924\pi\)
\(284\) −33.4894 58.0053i −1.98723 3.44198i
\(285\) 4.00000 0.236940
\(286\) −6.54508 11.3364i −0.387019 0.670337i
\(287\) −0.0623059 0.107917i −0.00367780 0.00637014i
\(288\) −15.4894 26.8284i −0.912719 1.58088i
\(289\) −4.45492 + 7.71614i −0.262054 + 0.453891i
\(290\) 25.4164 1.49250
\(291\) −0.909830 + 1.57587i −0.0533352 + 0.0923792i
\(292\) 11.7812 + 20.4056i 0.689440 + 1.19414i
\(293\) −0.909830 −0.0531528 −0.0265764 0.999647i \(-0.508461\pi\)
−0.0265764 + 0.999647i \(0.508461\pi\)
\(294\) 3.47214 + 6.01392i 0.202499 + 0.350739i
\(295\) −9.85410 + 17.0678i −0.573728 + 0.993726i
\(296\) 6.92705 11.9980i 0.402627 0.697370i
\(297\) −3.09017 −0.179310
\(298\) 11.7812 20.4056i 0.682464 1.18206i
\(299\) 23.9443 1.38473
\(300\) −10.1459 −0.585774
\(301\) 0.944272 + 1.22665i 0.0544269 + 0.0707027i
\(302\) 5.61803 0.323282
\(303\) −3.14590 −0.180727
\(304\) −15.9443 + 27.6163i −0.914467 + 1.58390i
\(305\) 12.4721 0.714152
\(306\) 19.0172 32.9388i 1.08714 1.88299i
\(307\) −14.1074 + 24.4347i −0.805151 + 1.39456i 0.111038 + 0.993816i \(0.464583\pi\)
−0.916189 + 0.400747i \(0.868751\pi\)
\(308\) 0.791796 + 1.37143i 0.0451168 + 0.0781445i
\(309\) −3.97871 −0.226341
\(310\) 0 0
\(311\) −11.9164 + 20.6398i −0.675717 + 1.17038i 0.300541 + 0.953769i \(0.402833\pi\)
−0.976259 + 0.216608i \(0.930501\pi\)
\(312\) 10.3262 0.584608
\(313\) 13.5623 23.4906i 0.766587 1.32777i −0.172817 0.984954i \(-0.555287\pi\)
0.939404 0.342813i \(-0.111380\pi\)
\(314\) −15.5172 26.8766i −0.875687 1.51674i
\(315\) −1.09017 1.88823i −0.0614241 0.106390i
\(316\) 8.78115 + 15.2094i 0.493978 + 0.855596i
\(317\) −29.3050 −1.64593 −0.822965 0.568092i \(-0.807682\pi\)
−0.822965 + 0.568092i \(0.807682\pi\)
\(318\) 1.80902 + 3.13331i 0.101445 + 0.175707i
\(319\) 2.07295 + 3.59045i 0.116063 + 0.201027i
\(320\) 14.0902 24.4049i 0.787664 1.36427i
\(321\) 3.14590 5.44886i 0.175587 0.304125i
\(322\) −4.09017 −0.227936
\(323\) −16.4721 −0.916534
\(324\) −18.7082 + 32.4036i −1.03934 + 1.80020i
\(325\) −9.89919 + 17.1459i −0.549108 + 0.951083i
\(326\) 18.3262 + 31.7420i 1.01500 + 1.75803i
\(327\) −1.36475 2.36381i −0.0754706 0.130719i
\(328\) −3.94427 −0.217786
\(329\) −0.927051 1.60570i −0.0511100 0.0885251i
\(330\) −2.23607 3.87298i −0.123091 0.213201i
\(331\) −1.73607 3.00696i −0.0954229 0.165277i 0.814362 0.580357i \(-0.197087\pi\)
−0.909785 + 0.415080i \(0.863754\pi\)
\(332\) 31.6353 54.7939i 1.73621 3.00720i
\(333\) −5.29180 −0.289989
\(334\) 12.7812 22.1376i 0.699354 1.21132i
\(335\) 4.61803 + 7.99867i 0.252310 + 0.437014i
\(336\) −0.888544 −0.0484740
\(337\) −14.0000 24.2487i −0.762629 1.32091i −0.941491 0.337037i \(-0.890575\pi\)
0.178863 0.983874i \(-0.442758\pi\)
\(338\) 0.118034 0.204441i 0.00642020 0.0111201i
\(339\) −2.55573 + 4.42665i −0.138808 + 0.240423i
\(340\) 79.9574 4.33630
\(341\) 0 0
\(342\) 24.1803 1.30752
\(343\) −3.29180 −0.177740
\(344\) 48.5689 6.47106i 2.61866 0.348896i
\(345\) 8.18034 0.440415
\(346\) 21.5623 1.15920
\(347\) 0.545085 0.944115i 0.0292617 0.0506827i −0.851024 0.525127i \(-0.824018\pi\)
0.880285 + 0.474445i \(0.157351\pi\)
\(348\) −5.56231 −0.298171
\(349\) −3.64590 + 6.31488i −0.195160 + 0.338028i −0.946953 0.321372i \(-0.895856\pi\)
0.751793 + 0.659400i \(0.229189\pi\)
\(350\) 1.69098 2.92887i 0.0903868 0.156555i
\(351\) −4.04508 7.00629i −0.215911 0.373968i
\(352\) 15.0000 0.799503
\(353\) 6.38197 + 11.0539i 0.339678 + 0.588339i 0.984372 0.176101i \(-0.0563486\pi\)
−0.644694 + 0.764441i \(0.723015\pi\)
\(354\) 3.04508 5.27424i 0.161844 0.280323i
\(355\) −44.6525 −2.36991
\(356\) −11.7812 + 20.4056i −0.624400 + 1.08149i
\(357\) −0.229490 0.397489i −0.0121459 0.0210373i
\(358\) −28.3435 49.0923i −1.49800 2.59461i
\(359\) 18.3262 + 31.7420i 0.967222 + 1.67528i 0.703523 + 0.710672i \(0.251609\pi\)
0.263699 + 0.964605i \(0.415058\pi\)
\(360\) −69.0132 −3.63731
\(361\) 4.26393 + 7.38535i 0.224417 + 0.388702i
\(362\) −28.2984 49.0142i −1.48733 2.57613i
\(363\) −1.73607 + 3.00696i −0.0911199 + 0.157824i
\(364\) −2.07295 + 3.59045i −0.108652 + 0.188191i
\(365\) 15.7082 0.822205
\(366\) −3.85410 −0.201457
\(367\) 1.59017 2.75426i 0.0830062 0.143771i −0.821534 0.570160i \(-0.806881\pi\)
0.904540 + 0.426389i \(0.140215\pi\)
\(368\) −32.6074 + 56.4777i −1.69978 + 2.94410i
\(369\) 0.753289 + 1.30473i 0.0392147 + 0.0679218i
\(370\) −7.85410 13.6037i −0.408315 0.707223i
\(371\) −0.854102 −0.0443428
\(372\) 0 0
\(373\) −3.00000 5.19615i −0.155334 0.269047i 0.777847 0.628454i \(-0.216312\pi\)
−0.933181 + 0.359408i \(0.882979\pi\)
\(374\) 9.20820 + 15.9491i 0.476145 + 0.824707i
\(375\) −0.291796 + 0.505406i −0.0150683 + 0.0260990i
\(376\) −58.6869 −3.02655
\(377\) −5.42705 + 9.39993i −0.279507 + 0.484121i
\(378\) 0.690983 + 1.19682i 0.0355403 + 0.0615577i
\(379\) 17.3607 0.891758 0.445879 0.895093i \(-0.352891\pi\)
0.445879 + 0.895093i \(0.352891\pi\)
\(380\) 25.4164 + 44.0225i 1.30383 + 2.25831i
\(381\) 3.18034 5.50851i 0.162934 0.282210i
\(382\) −30.7254 + 53.2180i −1.57205 + 2.72287i
\(383\) −2.12461 −0.108563 −0.0542813 0.998526i \(-0.517287\pi\)
−0.0542813 + 0.998526i \(0.517287\pi\)
\(384\) −0.208204 + 0.360620i −0.0106249 + 0.0184028i
\(385\) 1.05573 0.0538049
\(386\) 28.0344 1.42692
\(387\) −11.4164 14.8303i −0.580329 0.753869i
\(388\) −23.1246 −1.17397
\(389\) 23.0689 1.16964 0.584819 0.811164i \(-0.301165\pi\)
0.584819 + 0.811164i \(0.301165\pi\)
\(390\) 5.85410 10.1396i 0.296434 0.513439i
\(391\) −33.6869 −1.70362
\(392\) −25.9443 + 44.9368i −1.31038 + 2.26965i
\(393\) −1.51722 + 2.62790i −0.0765337 + 0.132560i
\(394\) 19.5623 + 33.8829i 0.985535 + 1.70700i
\(395\) 11.7082 0.589104
\(396\) −9.57295 16.5808i −0.481059 0.833218i
\(397\) −2.79180 + 4.83553i −0.140116 + 0.242688i −0.927540 0.373723i \(-0.878081\pi\)
0.787424 + 0.616412i \(0.211414\pi\)
\(398\) 41.7426 2.09237
\(399\) 0.145898 0.252703i 0.00730404 0.0126510i
\(400\) −26.9615 46.6987i −1.34807 2.33493i
\(401\) −0.708204 1.22665i −0.0353660 0.0612557i 0.847801 0.530315i \(-0.177926\pi\)
−0.883167 + 0.469059i \(0.844593\pi\)
\(402\) −1.42705 2.47172i −0.0711748 0.123278i
\(403\) 0 0
\(404\) −19.9894 34.6226i −0.994508 1.72254i
\(405\) 12.4721 + 21.6024i 0.619745 + 1.07343i
\(406\) 0.927051 1.60570i 0.0460088 0.0796895i
\(407\) 1.28115 2.21902i 0.0635044 0.109993i
\(408\) −14.5279 −0.719236
\(409\) 20.0902 0.993395 0.496697 0.867924i \(-0.334546\pi\)
0.496697 + 0.867924i \(0.334546\pi\)
\(410\) −2.23607 + 3.87298i −0.110432 + 0.191273i
\(411\) −1.85410 + 3.21140i −0.0914561 + 0.158407i
\(412\) −25.2812 43.7882i −1.24551 2.15729i
\(413\) 0.718847 + 1.24508i 0.0353722 + 0.0612664i
\(414\) 49.4508 2.43038
\(415\) −21.0902 36.5292i −1.03528 1.79315i
\(416\) 19.6353 + 34.0093i 0.962698 + 1.66744i
\(417\) −3.57295 6.18853i −0.174968 0.303054i
\(418\) −5.85410 + 10.1396i −0.286333 + 0.495944i
\(419\) −5.76393 −0.281587 −0.140793 0.990039i \(-0.544965\pi\)
−0.140793 + 0.990039i \(0.544965\pi\)
\(420\) −0.708204 + 1.22665i −0.0345568 + 0.0598542i
\(421\) −11.8262 20.4836i −0.576376 0.998312i −0.995891 0.0905634i \(-0.971133\pi\)
0.419515 0.907748i \(-0.362200\pi\)
\(422\) 12.4721 0.607134
\(423\) 11.2082 + 19.4132i 0.544962 + 0.943901i
\(424\) −13.5172 + 23.4125i −0.656454 + 1.13701i
\(425\) 13.9271 24.1224i 0.675561 1.17011i
\(426\) 13.7984 0.668533
\(427\) 0.454915 0.787936i 0.0220149 0.0381309i
\(428\) 79.9574 3.86489
\(429\) 1.90983 0.0922075
\(430\) 21.1803 51.3596i 1.02141 2.47678i
\(431\) −0.201626 −0.00971199 −0.00485599 0.999988i \(-0.501546\pi\)
−0.00485599 + 0.999988i \(0.501546\pi\)
\(432\) 22.0344 1.06013
\(433\) 10.6459 18.4392i 0.511609 0.886133i −0.488300 0.872676i \(-0.662383\pi\)
0.999909 0.0134574i \(-0.00428377\pi\)
\(434\) 0 0
\(435\) −1.85410 + 3.21140i −0.0888974 + 0.153975i
\(436\) 17.3435 30.0398i 0.830601 1.43864i
\(437\) −10.7082 18.5472i −0.512243 0.887231i
\(438\) −4.85410 −0.231938
\(439\) −3.92705 6.80185i −0.187428 0.324635i 0.756964 0.653457i \(-0.226682\pi\)
−0.944392 + 0.328822i \(0.893348\pi\)
\(440\) 16.7082 28.9395i 0.796532 1.37963i
\(441\) 19.8197 0.943793
\(442\) −24.1074 + 41.7552i −1.14667 + 1.98609i
\(443\) 3.23607 + 5.60503i 0.153750 + 0.266303i 0.932603 0.360903i \(-0.117532\pi\)
−0.778853 + 0.627206i \(0.784198\pi\)
\(444\) 1.71885 + 2.97713i 0.0815729 + 0.141288i
\(445\) 7.85410 + 13.6037i 0.372320 + 0.644877i
\(446\) −18.9443 −0.897037
\(447\) 1.71885 + 2.97713i 0.0812987 + 0.140813i
\(448\) −1.02786 1.78031i −0.0485620 0.0841119i
\(449\) −10.4164 + 18.0417i −0.491581 + 0.851443i −0.999953 0.00969466i \(-0.996914\pi\)
0.508372 + 0.861137i \(0.330247\pi\)
\(450\) −20.4443 + 35.4105i −0.963752 + 1.66927i
\(451\) −0.729490 −0.0343504
\(452\) −64.9574 −3.05534
\(453\) −0.409830 + 0.709846i −0.0192555 + 0.0333515i
\(454\) 9.78115 16.9415i 0.459052 0.795102i
\(455\) 1.38197 + 2.39364i 0.0647876 + 0.112215i
\(456\) −4.61803 7.99867i −0.216259 0.374572i
\(457\) −2.29180 −0.107206 −0.0536028 0.998562i \(-0.517070\pi\)
−0.0536028 + 0.998562i \(0.517070\pi\)
\(458\) −20.5623 35.6150i −0.960813 1.66418i
\(459\) 5.69098 + 9.85707i 0.265632 + 0.460089i
\(460\) 51.9787 + 90.0298i 2.42352 + 4.19766i
\(461\) −8.79837 + 15.2392i −0.409781 + 0.709762i −0.994865 0.101211i \(-0.967728\pi\)
0.585084 + 0.810973i \(0.301062\pi\)
\(462\) −0.326238 −0.0151780
\(463\) −11.9164 + 20.6398i −0.553802 + 0.959214i 0.444193 + 0.895931i \(0.353490\pi\)
−0.997996 + 0.0632829i \(0.979843\pi\)
\(464\) −14.7812 25.6017i −0.686198 1.18853i
\(465\) 0 0
\(466\) −14.4443 25.0182i −0.669118 1.15895i
\(467\) 16.4721 28.5306i 0.762240 1.32024i −0.179454 0.983766i \(-0.557433\pi\)
0.941694 0.336471i \(-0.109234\pi\)
\(468\) 25.0623 43.4092i 1.15851 2.00659i
\(469\) 0.673762 0.0311114
\(470\) −33.2705 + 57.6262i −1.53465 + 2.65810i
\(471\) 4.52786 0.208633
\(472\) 45.5066 2.09461
\(473\) 8.98278 1.19682i 0.413029 0.0550297i
\(474\) −3.61803 −0.166182
\(475\) 17.7082 0.812508
\(476\) 2.91641 5.05137i 0.133673 0.231529i
\(477\) 10.3262 0.472806
\(478\) −28.4164 + 49.2187i −1.29974 + 2.25121i
\(479\) 18.0902 31.3331i 0.826561 1.43165i −0.0741595 0.997246i \(-0.523627\pi\)
0.900720 0.434399i \(-0.143039\pi\)
\(480\) 6.70820 + 11.6190i 0.306186 + 0.530330i
\(481\) 6.70820 0.305868
\(482\) −38.3156 66.3646i −1.74523 3.02282i
\(483\) 0.298374 0.516799i 0.0135765 0.0235152i
\(484\) −44.1246 −2.00566
\(485\) −7.70820 + 13.3510i −0.350012 + 0.606238i
\(486\) −12.6353 21.8849i −0.573147 0.992719i
\(487\) 7.16312 + 12.4069i 0.324592 + 0.562210i 0.981430 0.191822i \(-0.0614397\pi\)
−0.656838 + 0.754032i \(0.728106\pi\)
\(488\) −14.3992 24.9401i −0.651821 1.12899i
\(489\) −5.34752 −0.241823
\(490\) 29.4164 + 50.9507i 1.32890 + 2.30172i
\(491\) 4.82624 + 8.35929i 0.217805 + 0.377249i 0.954137 0.299371i \(-0.0967770\pi\)
−0.736332 + 0.676621i \(0.763444\pi\)
\(492\) 0.489357 0.847591i 0.0220619 0.0382124i
\(493\) 7.63525 13.2246i 0.343875 0.595608i
\(494\) −30.6525 −1.37912
\(495\) −12.7639 −0.573696
\(496\) 0 0
\(497\) −1.62868 + 2.82095i −0.0730562 + 0.126537i
\(498\) 6.51722 + 11.2882i 0.292044 + 0.505834i
\(499\) −3.57295 6.18853i −0.159947 0.277037i 0.774902 0.632081i \(-0.217799\pi\)
−0.934849 + 0.355044i \(0.884466\pi\)
\(500\) −7.41641 −0.331672
\(501\) 1.86475 + 3.22983i 0.0833107 + 0.144298i
\(502\) −8.92705 15.4621i −0.398434 0.690108i
\(503\) 2.26393 + 3.92125i 0.100944 + 0.174840i 0.912074 0.410026i \(-0.134480\pi\)
−0.811130 + 0.584866i \(0.801147\pi\)
\(504\) −2.51722 + 4.35995i −0.112126 + 0.194208i
\(505\) −26.6525 −1.18602
\(506\) −11.9721 + 20.7363i −0.532226 + 0.921843i
\(507\) 0.0172209 + 0.0298275i 0.000764808 + 0.00132469i
\(508\) 80.8328 3.58638
\(509\) −2.64590 4.58283i −0.117277 0.203130i 0.801410 0.598115i \(-0.204083\pi\)
−0.918688 + 0.394984i \(0.870750\pi\)
\(510\) −8.23607 + 14.2653i −0.364699 + 0.631678i
\(511\) 0.572949 0.992377i 0.0253458 0.0439002i
\(512\) 40.3050 1.78124
\(513\) −3.61803 + 6.26662i −0.159740 + 0.276678i
\(514\) −61.6869 −2.72089
\(515\) −33.7082 −1.48536
\(516\) −4.63525 + 11.2399i −0.204056 + 0.494809i
\(517\) −10.8541 −0.477363
\(518\) −1.14590 −0.0503479
\(519\) −1.57295 + 2.72443i −0.0690448 + 0.119589i
\(520\) 87.4853 3.83648
\(521\) −3.51722 + 6.09201i −0.154092 + 0.266896i −0.932728 0.360580i \(-0.882579\pi\)
0.778636 + 0.627476i \(0.215912\pi\)
\(522\) −11.2082 + 19.4132i −0.490570 + 0.849692i
\(523\) 8.91641 + 15.4437i 0.389887 + 0.675305i 0.992434 0.122779i \(-0.0391806\pi\)
−0.602547 + 0.798084i \(0.705847\pi\)
\(524\) −38.5623 −1.68460
\(525\) 0.246711 + 0.427316i 0.0107674 + 0.0186496i
\(526\) −13.7533 + 23.8214i −0.599672 + 1.03866i
\(527\) 0 0
\(528\) −2.60081 + 4.50474i −0.113186 + 0.196044i
\(529\) −10.3992 18.0119i −0.452139 0.783127i
\(530\) 15.3262 + 26.5458i 0.665729 + 1.15308i
\(531\) −8.69098 15.0532i −0.377157 0.653254i
\(532\) 3.70820 0.160771
\(533\) −0.954915 1.65396i −0.0413620 0.0716410i
\(534\) −2.42705 4.20378i −0.105029 0.181915i
\(535\) 26.6525 46.1634i 1.15229 1.99582i
\(536\) 10.6631 18.4691i 0.460577 0.797742i
\(537\) 8.27051 0.356899
\(538\) 22.4164 0.966440
\(539\) −4.79837 + 8.31103i −0.206681 + 0.357981i
\(540\) 17.5623 30.4188i 0.755761 1.30902i
\(541\) 10.0279 + 17.3688i 0.431132 + 0.746742i 0.996971 0.0777737i \(-0.0247812\pi\)
−0.565839 + 0.824515i \(0.691448\pi\)
\(542\) 9.35410 + 16.2018i 0.401793 + 0.695926i
\(543\) 8.25735 0.354357
\(544\) −27.6246 47.8472i −1.18440 2.05143i
\(545\) −11.5623 20.0265i −0.495275 0.857841i
\(546\) −0.427051 0.739674i −0.0182761 0.0316551i
\(547\) −10.5000 + 18.1865i −0.448948 + 0.777600i −0.998318 0.0579790i \(-0.981534\pi\)
0.549370 + 0.835579i \(0.314868\pi\)
\(548\) −47.1246 −2.01306
\(549\) −5.50000 + 9.52628i −0.234734 + 0.406572i
\(550\) −9.89919 17.1459i −0.422103 0.731103i
\(551\) 9.70820 0.413583
\(552\) −9.44427 16.3580i −0.401975 0.696241i
\(553\) 0.427051 0.739674i 0.0181601 0.0314541i
\(554\) −4.61803 + 7.99867i −0.196201 + 0.339831i
\(555\) 2.29180 0.0972813
\(556\) 45.4058 78.6451i 1.92563 3.33529i
\(557\) −18.4377 −0.781230 −0.390615 0.920554i \(-0.627738\pi\)
−0.390615 + 0.920554i \(0.627738\pi\)
\(558\) 0 0
\(559\) 14.4721 + 18.7999i 0.612106 + 0.795149i
\(560\) −7.52786 −0.318110
\(561\) −2.68692 −0.113442
\(562\) −1.92705 + 3.33775i −0.0812877 + 0.140794i
\(563\) 14.3262 0.603779 0.301889 0.953343i \(-0.402383\pi\)
0.301889 + 0.953343i \(0.402383\pi\)
\(564\) 7.28115 12.6113i 0.306592 0.531033i
\(565\) −21.6525 + 37.5032i −0.910927 + 1.57777i
\(566\) 19.9443 + 34.5445i 0.838320 + 1.45201i
\(567\) 1.81966 0.0764185
\(568\) 51.5517 + 89.2901i 2.16306 + 3.74653i
\(569\) 4.02786 6.97647i 0.168857 0.292469i −0.769161 0.639055i \(-0.779326\pi\)
0.938018 + 0.346586i \(0.112659\pi\)
\(570\) −10.4721 −0.438630
\(571\) 10.4098 18.0304i 0.435638 0.754547i −0.561710 0.827334i \(-0.689856\pi\)
0.997347 + 0.0727876i \(0.0231895\pi\)
\(572\) 12.1353 + 21.0189i 0.507400 + 0.878843i
\(573\) −4.48278 7.76440i −0.187271 0.324363i
\(574\) 0.163119 + 0.282530i 0.00680845 + 0.0117926i
\(575\) 36.2148 1.51026
\(576\) 12.4271 + 21.5243i 0.517794 + 0.896845i
\(577\) −11.6074 20.1046i −0.483222 0.836965i 0.516592 0.856231i \(-0.327200\pi\)
−0.999814 + 0.0192664i \(0.993867\pi\)
\(578\) 11.6631 20.2011i 0.485122 0.840256i
\(579\) −2.04508 + 3.54219i −0.0849908 + 0.147208i
\(580\) −47.1246 −1.95674
\(581\) −3.07701 −0.127656
\(582\) 2.38197 4.12569i 0.0987357 0.171015i
\(583\) −2.50000 + 4.33013i −0.103539 + 0.179336i
\(584\) −18.1353 31.4112i −0.750442 1.29980i
\(585\) −16.7082 28.9395i −0.690799 1.19650i
\(586\) 2.38197 0.0983981
\(587\) 13.3713 + 23.1598i 0.551894 + 0.955908i 0.998138 + 0.0609966i \(0.0194279\pi\)
−0.446244 + 0.894911i \(0.647239\pi\)
\(588\) −6.43769 11.1504i −0.265486 0.459835i
\(589\) 0 0
\(590\) 25.7984 44.6841i 1.06210 1.83962i
\(591\) −5.70820 −0.234804
\(592\) −9.13525 + 15.8227i −0.375457 + 0.650310i
\(593\) 10.7639 + 18.6437i 0.442022 + 0.765604i 0.997839 0.0657001i \(-0.0209281\pi\)
−0.555818 + 0.831304i \(0.687595\pi\)
\(594\) 8.09017 0.331944
\(595\) −1.94427 3.36758i −0.0797074 0.138057i
\(596\) −21.8435 + 37.8340i −0.894743 + 1.54974i
\(597\) −3.04508 + 5.27424i −0.124627 + 0.215860i
\(598\) −62.6869 −2.56346
\(599\) −15.8820 + 27.5084i −0.648920 + 1.12396i 0.334462 + 0.942409i \(0.391445\pi\)
−0.983381 + 0.181552i \(0.941888\pi\)
\(600\) 15.6180 0.637604
\(601\) 2.58359 0.105387 0.0526935 0.998611i \(-0.483219\pi\)
0.0526935 + 0.998611i \(0.483219\pi\)
\(602\) −2.47214 3.21140i −0.100757 0.130887i
\(603\) −8.14590 −0.331727
\(604\) −10.4164 −0.423838
\(605\) −14.7082 + 25.4754i −0.597974 + 1.03572i
\(606\) 8.23607 0.334567
\(607\) 8.57295 14.8488i 0.347965 0.602694i −0.637923 0.770100i \(-0.720206\pi\)
0.985888 + 0.167407i \(0.0535394\pi\)
\(608\) 17.5623 30.4188i 0.712246 1.23365i
\(609\) 0.135255 + 0.234268i 0.00548081 + 0.00949303i
\(610\) −32.6525 −1.32206
\(611\) −14.2082 24.6093i −0.574802 0.995587i
\(612\) −35.2599 + 61.0719i −1.42530 + 2.46868i
\(613\) 29.7984 1.20354 0.601772 0.798668i \(-0.294461\pi\)
0.601772 + 0.798668i \(0.294461\pi\)
\(614\) 36.9336 63.9709i 1.49052 2.58166i
\(615\) −0.326238 0.565061i −0.0131552 0.0227854i
\(616\) −1.21885 2.11111i −0.0491087 0.0850588i
\(617\) 1.85410 + 3.21140i 0.0746433 + 0.129286i 0.900931 0.433962i \(-0.142885\pi\)
−0.826288 + 0.563248i \(0.809552\pi\)
\(618\) 10.4164 0.419009
\(619\) −1.63525 2.83234i −0.0657264 0.113842i 0.831290 0.555840i \(-0.187603\pi\)
−0.897016 + 0.441998i \(0.854270\pi\)
\(620\) 0 0
\(621\) −7.39919 + 12.8158i −0.296919 + 0.514279i
\(622\) 31.1976 54.0358i 1.25091 2.16664i
\(623\) 1.14590 0.0459094
\(624\) −13.6180 −0.545158
\(625\) 11.2082 19.4132i 0.448328 0.776527i
\(626\) −35.5066 + 61.4992i −1.41913 + 2.45800i
\(627\) −0.854102 1.47935i −0.0341095 0.0590795i
\(628\) 28.7705 + 49.8320i 1.14807 + 1.98851i
\(629\) −9.43769 −0.376306
\(630\) 2.85410 + 4.94345i 0.113710 + 0.196952i
\(631\) 7.95492 + 13.7783i 0.316680 + 0.548506i 0.979793 0.200013i \(-0.0640985\pi\)
−0.663113 + 0.748519i \(0.730765\pi\)
\(632\) −13.5172 23.4125i −0.537686 0.931300i
\(633\) −0.909830 + 1.57587i −0.0361625 + 0.0626353i
\(634\) 76.7214 3.04699
\(635\) 26.9443 46.6688i 1.06925 1.85200i
\(636\) −3.35410 5.80948i −0.132999 0.230361i
\(637\) −25.1246 −0.995473
\(638\) −5.42705 9.39993i −0.214859 0.372147i
\(639\) 19.6910 34.1058i 0.778963 1.34920i
\(640\) −1.76393 + 3.05522i −0.0697255 + 0.120768i
\(641\) 33.1803 1.31054 0.655272 0.755393i \(-0.272554\pi\)
0.655272 + 0.755393i \(0.272554\pi\)
\(642\) −8.23607 + 14.2653i −0.325052 + 0.563006i
\(643\) 29.5623 1.16582 0.582912 0.812535i \(-0.301913\pi\)
0.582912 + 0.812535i \(0.301913\pi\)
\(644\) 7.58359 0.298835
\(645\) 4.94427 + 6.42280i 0.194681 + 0.252897i
\(646\) 43.1246 1.69672
\(647\) −37.3262 −1.46745 −0.733723 0.679449i \(-0.762219\pi\)
−0.733723 + 0.679449i \(0.762219\pi\)
\(648\) 28.7984 49.8802i 1.13131 1.95948i
\(649\) 8.41641 0.330373
\(650\) 25.9164 44.8885i 1.01653 1.76067i
\(651\) 0 0
\(652\) −33.9787 58.8529i −1.33071 2.30486i
\(653\) 2.88854 0.113037 0.0565187 0.998402i \(-0.482000\pi\)
0.0565187 + 0.998402i \(0.482000\pi\)
\(654\) 3.57295 + 6.18853i 0.139713 + 0.241991i
\(655\) −12.8541 + 22.2640i −0.502251 + 0.869925i
\(656\) 5.20163 0.203089
\(657\) −6.92705 + 11.9980i −0.270250 + 0.468087i
\(658\) 2.42705 + 4.20378i 0.0946163 + 0.163880i
\(659\) −7.68034 13.3027i −0.299184 0.518201i 0.676766 0.736198i \(-0.263381\pi\)
−0.975949 + 0.217997i \(0.930048\pi\)
\(660\) 4.14590 + 7.18091i 0.161379 + 0.279516i
\(661\) 30.3951 1.18223 0.591117 0.806586i \(-0.298687\pi\)
0.591117 + 0.806586i \(0.298687\pi\)
\(662\) 4.54508 + 7.87232i 0.176650 + 0.305966i
\(663\) −3.51722 6.09201i −0.136598 0.236594i
\(664\) −48.6976 + 84.3466i −1.88983 + 3.27328i
\(665\) 1.23607 2.14093i 0.0479327 0.0830218i
\(666\) 13.8541 0.536836
\(667\) 19.8541 0.768754
\(668\) −23.6976 + 41.0454i −0.916886 + 1.58809i
\(669\) 1.38197 2.39364i 0.0534299 0.0925433i
\(670\) −12.0902 20.9408i −0.467084 0.809013i
\(671\) −2.66312 4.61266i −0.102809 0.178070i
\(672\) 0.978714 0.0377547
\(673\) 19.9164 + 34.4962i 0.767721 + 1.32973i 0.938796 + 0.344474i \(0.111943\pi\)
−0.171075 + 0.985258i \(0.554724\pi\)
\(674\) 36.6525 + 63.4840i 1.41180 + 2.44531i
\(675\) −6.11803 10.5967i −0.235483 0.407869i
\(676\) −0.218847 + 0.379054i −0.00841719 + 0.0145790i
\(677\) −36.2361 −1.39267 −0.696333 0.717719i \(-0.745186\pi\)
−0.696333 + 0.717719i \(0.745186\pi\)
\(678\) 6.69098 11.5891i 0.256966 0.445078i
\(679\) 0.562306 + 0.973942i 0.0215793 + 0.0373765i
\(680\) −123.082 −4.71998
\(681\) 1.42705 + 2.47172i 0.0546847 + 0.0947167i
\(682\) 0 0
\(683\) −14.5623 + 25.2227i −0.557211 + 0.965118i 0.440517 + 0.897744i \(0.354795\pi\)
−0.997728 + 0.0673736i \(0.978538\pi\)
\(684\) −44.8328 −1.71423
\(685\) −15.7082 + 27.2074i −0.600180 + 1.03954i
\(686\) 8.61803 0.329038
\(687\) 6.00000 0.228914
\(688\) −64.0517 + 8.53390i −2.44195 + 0.325352i
\(689\) −13.0902 −0.498696
\(690\) −21.4164 −0.815309
\(691\) −24.6353 + 42.6695i −0.937169 + 1.62322i −0.166450 + 0.986050i \(0.553230\pi\)
−0.770719 + 0.637175i \(0.780103\pi\)
\(692\) −39.9787 −1.51976
\(693\) −0.465558 + 0.806370i −0.0176851 + 0.0306315i
\(694\) −1.42705 + 2.47172i −0.0541701 + 0.0938254i
\(695\) −30.2705 52.4301i −1.14823 1.98879i
\(696\) 8.56231 0.324553
\(697\) 1.34346 + 2.32694i 0.0508871 + 0.0881391i
\(698\) 9.54508 16.5326i 0.361287 0.625767i
\(699\) 4.21478 0.159418
\(700\) −3.13525 + 5.43042i −0.118501 + 0.205251i
\(701\) −11.7533 20.3573i −0.443916 0.768884i 0.554060 0.832476i \(-0.313078\pi\)
−0.997976 + 0.0635921i \(0.979744\pi\)
\(702\) 10.5902 + 18.3427i 0.399700 + 0.692301i
\(703\) −3.00000 5.19615i −0.113147 0.195977i
\(704\) −12.0344 −0.453565
\(705\) −4.85410 8.40755i −0.182816 0.316647i
\(706\) −16.7082 28.9395i −0.628822 1.08915i
\(707\) −0.972136 + 1.68379i −0.0365609 + 0.0633254i
\(708\) −5.64590 + 9.77898i −0.212186 + 0.367517i
\(709\) −6.88854 −0.258705 −0.129352 0.991599i \(-0.541290\pi\)
−0.129352 + 0.991599i \(0.541290\pi\)
\(710\) 116.902 4.38724
\(711\) −5.16312 + 8.94278i −0.193632 + 0.335381i
\(712\) 18.1353 31.4112i 0.679647 1.17718i
\(713\) 0 0
\(714\) 0.600813 + 1.04064i 0.0224849 + 0.0389449i
\(715\) 16.1803 0.605110
\(716\) 52.5517 + 91.0221i 1.96395 + 3.40166i
\(717\) −4.14590 7.18091i −0.154831 0.268176i
\(718\) −47.9787 83.1016i −1.79055 3.10132i
\(719\) −6.89919 + 11.9497i −0.257296 + 0.445650i −0.965517 0.260341i \(-0.916165\pi\)
0.708220 + 0.705991i \(0.249498\pi\)
\(720\) 91.0132 3.39186
\(721\) −1.22949 + 2.12954i −0.0457886 + 0.0793082i
\(722\) −11.1631 19.3351i −0.415448 0.719578i
\(723\) 11.1803 0.415801
\(724\) 52.4681 + 90.8774i 1.94996 + 3.37743i
\(725\) −8.20820 + 14.2170i −0.304845 + 0.528007i
\(726\) 4.54508 7.87232i 0.168684 0.292169i
\(727\) 28.9787 1.07476 0.537381 0.843340i \(-0.319414\pi\)
0.537381 + 0.843340i \(0.319414\pi\)
\(728\) 3.19098 5.52694i 0.118266 0.204842i
\(729\) −19.4377 −0.719915
\(730\) −41.1246 −1.52209
\(731\) −20.3607 26.4493i −0.753067 0.978263i
\(732\) 7.14590 0.264120
\(733\) −42.5410 −1.57129 −0.785644 0.618679i \(-0.787668\pi\)
−0.785644 + 0.618679i \(0.787668\pi\)
\(734\) −4.16312 + 7.21073i −0.153664 + 0.266153i
\(735\) −8.58359 −0.316611
\(736\) 35.9164 62.2090i 1.32390 2.29306i
\(737\) 1.97214 3.41584i 0.0726446 0.125824i
\(738\) −1.97214 3.41584i −0.0725953 0.125739i
\(739\) −17.5410 −0.645257 −0.322628 0.946526i \(-0.604566\pi\)
−0.322628 + 0.946526i \(0.604566\pi\)
\(740\) 14.5623 + 25.2227i 0.535321 + 0.927203i
\(741\) 2.23607 3.87298i 0.0821440 0.142278i
\(742\) 2.23607 0.0820886
\(743\) 5.68034 9.83864i 0.208391 0.360945i −0.742817 0.669495i \(-0.766511\pi\)
0.951208 + 0.308550i \(0.0998439\pi\)
\(744\) 0 0
\(745\) 14.5623 + 25.2227i 0.533522 + 0.924087i
\(746\) 7.85410 + 13.6037i 0.287559 + 0.498067i
\(747\) 37.2016 1.36114
\(748\) −17.0729 29.5712i −0.624249 1.08123i
\(749\) −1.94427 3.36758i −0.0710421 0.123049i
\(750\) 0.763932 1.32317i 0.0278949 0.0483153i
\(751\) −4.48936 + 7.77579i −0.163819 + 0.283743i −0.936235 0.351374i \(-0.885715\pi\)
0.772416 + 0.635117i \(0.219048\pi\)
\(752\) 77.3951 2.82231
\(753\) 2.60488 0.0949270
\(754\) 14.2082 24.6093i 0.517432 0.896219i
\(755\) −3.47214 + 6.01392i −0.126364 + 0.218869i
\(756\) −1.28115 2.21902i −0.0465951 0.0807050i
\(757\) −7.98936 13.8380i −0.290378 0.502950i 0.683521 0.729931i \(-0.260448\pi\)
−0.973899 + 0.226981i \(0.927114\pi\)
\(758\) −45.4508 −1.65085
\(759\) −1.74671 3.02539i −0.0634016 0.109815i
\(760\) −39.1246 67.7658i −1.41920 2.45812i
\(761\) 5.04508 + 8.73834i 0.182884 + 0.316765i 0.942862 0.333185i \(-0.108123\pi\)
−0.759977 + 0.649950i \(0.774790\pi\)
\(762\) −8.32624 + 14.4215i −0.301628 + 0.522435i
\(763\) −1.68692 −0.0610705
\(764\) 56.9681 98.6716i 2.06103 3.56981i
\(765\) 23.5066 + 40.7146i 0.849882 + 1.47204i
\(766\) 5.56231 0.200974
\(767\) 11.0172 + 19.0824i 0.397809 + 0.689025i
\(768\) −2.78115 + 4.81710i −0.100356 + 0.173822i
\(769\) 7.94427 13.7599i 0.286478 0.496194i −0.686489 0.727140i \(-0.740849\pi\)
0.972966 + 0.230946i \(0.0741822\pi\)
\(770\) −2.76393 −0.0996052
\(771\) 4.50000 7.79423i 0.162064 0.280702i
\(772\) −51.9787 −1.87075
\(773\) −33.5967 −1.20839 −0.604196 0.796836i \(-0.706505\pi\)
−0.604196 + 0.796836i \(0.706505\pi\)
\(774\) 29.8885 + 38.8264i 1.07432 + 1.39558i
\(775\) 0 0
\(776\) 35.5967 1.27785
\(777\) 0.0835921 0.144786i 0.00299885 0.00519416i
\(778\) −60.3951 −2.16527
\(779\) −0.854102 + 1.47935i −0.0306014 + 0.0530031i
\(780\) −10.8541 + 18.7999i −0.388639 + 0.673143i
\(781\) 9.53444 + 16.5141i 0.341169 + 0.590922i
\(782\) 88.1935 3.15379
\(783\) −3.35410 5.80948i −0.119866 0.207614i
\(784\) 34.2148 59.2617i 1.22196 2.11649i
\(785\) 38.3607 1.36915