Properties

Label 403.2.v.a.36.18
Level 403
Weight 2
Character 403.36
Analytic conductor 3.218
Analytic rank 0
Dimension 70
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.v (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(70\)
Relative dimension: \(35\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 36.18
Character \(\chi\) \(=\) 403.36
Dual form 403.2.v.a.56.18

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0898111 + 0.0518525i) q^{2} -0.467545 q^{3} +(-0.994623 + 1.72274i) q^{4} +(1.88817 - 1.09014i) q^{5} +(0.0419908 - 0.0242434i) q^{6} +(-2.42419 + 1.39960i) q^{7} -0.413704i q^{8} -2.78140 q^{9} +O(q^{10})\) \(q+(-0.0898111 + 0.0518525i) q^{2} -0.467545 q^{3} +(-0.994623 + 1.72274i) q^{4} +(1.88817 - 1.09014i) q^{5} +(0.0419908 - 0.0242434i) q^{6} +(-2.42419 + 1.39960i) q^{7} -0.413704i q^{8} -2.78140 q^{9} +(-0.113053 + 0.195813i) q^{10} +(2.24155 + 1.29416i) q^{11} +(0.465031 - 0.805457i) q^{12} +(-0.248332 + 3.59699i) q^{13} +(0.145146 - 0.251400i) q^{14} +(-0.882807 + 0.509689i) q^{15} +(-1.96779 - 3.40832i) q^{16} +(1.32604 + 2.29677i) q^{17} +(0.249801 - 0.144223i) q^{18} +(-6.58957 + 3.80449i) q^{19} +4.33710i q^{20} +(1.13342 - 0.654379i) q^{21} -0.268422 q^{22} +(-3.60890 - 6.25080i) q^{23} +0.193426i q^{24} +(-0.123198 + 0.213385i) q^{25} +(-0.164210 - 0.335926i) q^{26} +2.70307 q^{27} -5.56831i q^{28} +(4.67329 + 8.09438i) q^{29} +(0.0528573 - 0.0915514i) q^{30} +(-5.23399 - 1.89878i) q^{31} +(1.07002 + 0.617774i) q^{32} +(-1.04803 - 0.605079i) q^{33} +(-0.238186 - 0.137517i) q^{34} +(-3.05153 + 5.28540i) q^{35} +(2.76644 - 4.79162i) q^{36} +1.96464i q^{37} +(0.394544 - 0.683371i) q^{38} +(0.116106 - 1.68176i) q^{39} +(-0.450995 - 0.781146i) q^{40} +(-0.383246 - 0.221267i) q^{41} +(-0.0678623 + 0.117541i) q^{42} +(3.17167 + 5.49349i) q^{43} +(-4.45900 + 2.57441i) q^{44} +(-5.25177 + 3.03211i) q^{45} +(0.648239 + 0.374261i) q^{46} +1.47978i q^{47} +(0.920032 + 1.59354i) q^{48} +(0.417788 - 0.723630i) q^{49} -0.0255524i q^{50} +(-0.619983 - 1.07384i) q^{51} +(-5.94967 - 4.00546i) q^{52} +(-0.238168 - 0.412519i) q^{53} +(-0.242765 + 0.140161i) q^{54} +5.64326 q^{55} +(0.579023 + 1.00290i) q^{56} +(3.08092 - 1.77877i) q^{57} +(-0.839427 - 0.484643i) q^{58} +(7.19608 - 4.15466i) q^{59} -2.02779i q^{60} +(0.841967 - 1.45833i) q^{61} +(0.568527 - 0.100864i) q^{62} +(6.74264 - 3.89286i) q^{63} +7.74304 q^{64} +(3.45232 + 7.06246i) q^{65} +0.125499 q^{66} +(4.58340 + 2.64623i) q^{67} -5.27564 q^{68} +(1.68733 + 2.92253i) q^{69} -0.632917i q^{70} -14.2493i q^{71} +1.15068i q^{72} +(6.54975 - 3.78150i) q^{73} +(-0.101871 - 0.176446i) q^{74} +(0.0576005 - 0.0997670i) q^{75} -15.1361i q^{76} -7.24526 q^{77} +(0.0767755 + 0.157061i) q^{78} +(2.92619 - 5.06831i) q^{79} +(-7.43108 - 4.29033i) q^{80} +7.08040 q^{81} +0.0458930 q^{82} +(-1.39500 + 0.805406i) q^{83} +2.60344i q^{84} +(5.00759 + 2.89113i) q^{85} +(-0.569702 - 0.328918i) q^{86} +(-2.18497 - 3.78449i) q^{87} +(0.535401 - 0.927341i) q^{88} +(7.89148 - 4.55615i) q^{89} +(0.314445 - 0.544635i) q^{90} +(-4.43236 - 9.06734i) q^{91} +14.3580 q^{92} +(2.44713 + 0.887765i) q^{93} +(-0.0767301 - 0.132901i) q^{94} +(-8.29483 + 14.3671i) q^{95} +(-0.500281 - 0.288837i) q^{96} +(-0.625592 - 0.361186i) q^{97} +0.0866533i q^{98} +(-6.23466 - 3.59958i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 70q - 6q^{2} + 4q^{3} + 30q^{4} + 6q^{6} - 12q^{7} + 58q^{9} + O(q^{10}) \) \( 70q - 6q^{2} + 4q^{3} + 30q^{4} + 6q^{6} - 12q^{7} + 58q^{9} - q^{10} - 6q^{11} + 13q^{12} - 14q^{13} - 14q^{14} - 15q^{15} - 28q^{16} + 6q^{17} + 12q^{19} + 9q^{21} - 8q^{22} + 10q^{23} + 19q^{25} + 34q^{27} - 18q^{29} - 31q^{30} + 2q^{31} + 36q^{32} - 12q^{33} - 9q^{34} - 12q^{35} + 8q^{36} - 21q^{38} - 30q^{39} + 5q^{40} + 18q^{41} - 49q^{42} + 19q^{43} - 42q^{44} - 63q^{45} - 6q^{46} - 27q^{48} + 9q^{49} - 7q^{51} - 43q^{52} - 22q^{53} + 18q^{54} + 30q^{55} + 25q^{56} - 15q^{57} - 12q^{58} + 33q^{59} - 13q^{61} - 17q^{62} - 6q^{63} - 38q^{64} + 9q^{65} - 52q^{66} + 30q^{67} + 88q^{68} - 16q^{69} + 9q^{73} - 19q^{74} + 25q^{75} + 34q^{77} + 14q^{78} + 6q^{79} + 6q^{80} + 22q^{81} - 78q^{82} + 54q^{83} - 33q^{85} + 24q^{86} - 14q^{87} + 16q^{88} - 6q^{89} - 11q^{90} - 70q^{91} - 6q^{92} + 7q^{93} - 43q^{94} + 25q^{95} - 36q^{96} - 75q^{97} - 93q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0898111 + 0.0518525i −0.0635060 + 0.0366652i −0.531417 0.847110i \(-0.678340\pi\)
0.467911 + 0.883776i \(0.345007\pi\)
\(3\) −0.467545 −0.269937 −0.134969 0.990850i \(-0.543093\pi\)
−0.134969 + 0.990850i \(0.543093\pi\)
\(4\) −0.994623 + 1.72274i −0.497311 + 0.861368i
\(5\) 1.88817 1.09014i 0.844417 0.487525i −0.0143459 0.999897i \(-0.504567\pi\)
0.858763 + 0.512372i \(0.171233\pi\)
\(6\) 0.0419908 0.0242434i 0.0171427 0.00989732i
\(7\) −2.42419 + 1.39960i −0.916256 + 0.529001i −0.882439 0.470427i \(-0.844100\pi\)
−0.0338176 + 0.999428i \(0.510767\pi\)
\(8\) 0.413704i 0.146267i
\(9\) −2.78140 −0.927134
\(10\) −0.113053 + 0.195813i −0.0357504 + 0.0619215i
\(11\) 2.24155 + 1.29416i 0.675854 + 0.390205i 0.798291 0.602272i \(-0.205738\pi\)
−0.122437 + 0.992476i \(0.539071\pi\)
\(12\) 0.465031 0.805457i 0.134243 0.232516i
\(13\) −0.248332 + 3.59699i −0.0688749 + 0.997625i
\(14\) 0.145146 0.251400i 0.0387919 0.0671895i
\(15\) −0.882807 + 0.509689i −0.227940 + 0.131601i
\(16\) −1.96779 3.40832i −0.491948 0.852080i
\(17\) 1.32604 + 2.29677i 0.321612 + 0.557048i 0.980821 0.194912i \(-0.0624420\pi\)
−0.659209 + 0.751960i \(0.729109\pi\)
\(18\) 0.249801 0.144223i 0.0588786 0.0339936i
\(19\) −6.58957 + 3.80449i −1.51175 + 0.872809i −0.511845 + 0.859078i \(0.671038\pi\)
−0.999906 + 0.0137313i \(0.995629\pi\)
\(20\) 4.33710i 0.969806i
\(21\) 1.13342 0.654379i 0.247332 0.142797i
\(22\) −0.268422 −0.0572278
\(23\) −3.60890 6.25080i −0.752508 1.30338i −0.946603 0.322400i \(-0.895510\pi\)
0.194095 0.980983i \(-0.437823\pi\)
\(24\) 0.193426i 0.0394828i
\(25\) −0.123198 + 0.213385i −0.0246395 + 0.0426769i
\(26\) −0.164210 0.335926i −0.0322042 0.0658806i
\(27\) 2.70307 0.520205
\(28\) 5.56831i 1.05231i
\(29\) 4.67329 + 8.09438i 0.867808 + 1.50309i 0.864232 + 0.503094i \(0.167805\pi\)
0.00357667 + 0.999994i \(0.498862\pi\)
\(30\) 0.0528573 0.0915514i 0.00965037 0.0167149i
\(31\) −5.23399 1.89878i −0.940052 0.341031i
\(32\) 1.07002 + 0.617774i 0.189154 + 0.109208i
\(33\) −1.04803 0.605079i −0.182438 0.105331i
\(34\) −0.238186 0.137517i −0.0408486 0.0235839i
\(35\) −3.05153 + 5.28540i −0.515802 + 0.893395i
\(36\) 2.76644 4.79162i 0.461074 0.798604i
\(37\) 1.96464i 0.322984i 0.986874 + 0.161492i \(0.0516306\pi\)
−0.986874 + 0.161492i \(0.948369\pi\)
\(38\) 0.394544 0.683371i 0.0640035 0.110857i
\(39\) 0.116106 1.68176i 0.0185919 0.269296i
\(40\) −0.450995 0.781146i −0.0713086 0.123510i
\(41\) −0.383246 0.221267i −0.0598530 0.0345561i 0.469775 0.882786i \(-0.344335\pi\)
−0.529628 + 0.848230i \(0.677668\pi\)
\(42\) −0.0678623 + 0.117541i −0.0104714 + 0.0181370i
\(43\) 3.17167 + 5.49349i 0.483675 + 0.837749i 0.999824 0.0187494i \(-0.00596847\pi\)
−0.516150 + 0.856498i \(0.672635\pi\)
\(44\) −4.45900 + 2.57441i −0.672220 + 0.388106i
\(45\) −5.25177 + 3.03211i −0.782888 + 0.452001i
\(46\) 0.648239 + 0.374261i 0.0955777 + 0.0551818i
\(47\) 1.47978i 0.215848i 0.994159 + 0.107924i \(0.0344203\pi\)
−0.994159 + 0.107924i \(0.965580\pi\)
\(48\) 0.920032 + 1.59354i 0.132795 + 0.230008i
\(49\) 0.417788 0.723630i 0.0596840 0.103376i
\(50\) 0.0255524i 0.00361366i
\(51\) −0.619983 1.07384i −0.0868151 0.150368i
\(52\) −5.94967 4.00546i −0.825071 0.555457i
\(53\) −0.238168 0.412519i −0.0327149 0.0566639i 0.849204 0.528064i \(-0.177082\pi\)
−0.881919 + 0.471400i \(0.843749\pi\)
\(54\) −0.242765 + 0.140161i −0.0330362 + 0.0190735i
\(55\) 5.64326 0.760937
\(56\) 0.579023 + 1.00290i 0.0773752 + 0.134018i
\(57\) 3.08092 1.77877i 0.408078 0.235604i
\(58\) −0.839427 0.484643i −0.110222 0.0636368i
\(59\) 7.19608 4.15466i 0.936850 0.540891i 0.0478787 0.998853i \(-0.484754\pi\)
0.888972 + 0.457962i \(0.151421\pi\)
\(60\) 2.02779i 0.261787i
\(61\) 0.841967 1.45833i 0.107803 0.186720i −0.807077 0.590446i \(-0.798952\pi\)
0.914880 + 0.403726i \(0.132285\pi\)
\(62\) 0.568527 0.100864i 0.0722030 0.0128097i
\(63\) 6.74264 3.89286i 0.849492 0.490455i
\(64\) 7.74304 0.967880
\(65\) 3.45232 + 7.06246i 0.428208 + 0.875990i
\(66\) 0.125499 0.0154479
\(67\) 4.58340 + 2.64623i 0.559952 + 0.323288i 0.753126 0.657876i \(-0.228545\pi\)
−0.193174 + 0.981164i \(0.561878\pi\)
\(68\) −5.27564 −0.639765
\(69\) 1.68733 + 2.92253i 0.203130 + 0.351832i
\(70\) 0.632917i 0.0756480i
\(71\) 14.2493i 1.69108i −0.533913 0.845539i \(-0.679279\pi\)
0.533913 0.845539i \(-0.320721\pi\)
\(72\) 1.15068i 0.135609i
\(73\) 6.54975 3.78150i 0.766590 0.442591i −0.0650665 0.997881i \(-0.520726\pi\)
0.831657 + 0.555290i \(0.187393\pi\)
\(74\) −0.101871 0.176446i −0.0118423 0.0205114i
\(75\) 0.0576005 0.0997670i 0.00665113 0.0115201i
\(76\) 15.1361i 1.73623i
\(77\) −7.24526 −0.825674
\(78\) 0.0767755 + 0.157061i 0.00869311 + 0.0177836i
\(79\) 2.92619 5.06831i 0.329222 0.570229i −0.653136 0.757241i \(-0.726547\pi\)
0.982358 + 0.187012i \(0.0598802\pi\)
\(80\) −7.43108 4.29033i −0.830820 0.479674i
\(81\) 7.08040 0.786711
\(82\) 0.0458930 0.00506804
\(83\) −1.39500 + 0.805406i −0.153122 + 0.0884048i −0.574603 0.818432i \(-0.694844\pi\)
0.421482 + 0.906837i \(0.361510\pi\)
\(84\) 2.60344i 0.284058i
\(85\) 5.00759 + 2.89113i 0.543149 + 0.313587i
\(86\) −0.569702 0.328918i −0.0614325 0.0354681i
\(87\) −2.18497 3.78449i −0.234254 0.405740i
\(88\) 0.535401 0.927341i 0.0570739 0.0988549i
\(89\) 7.89148 4.55615i 0.836495 0.482951i −0.0195761 0.999808i \(-0.506232\pi\)
0.856071 + 0.516858i \(0.172898\pi\)
\(90\) 0.314445 0.544635i 0.0331454 0.0574095i
\(91\) −4.43236 9.06734i −0.464638 0.950516i
\(92\) 14.3580 1.49692
\(93\) 2.44713 + 0.887765i 0.253755 + 0.0920569i
\(94\) −0.0767301 0.132901i −0.00791411 0.0137076i
\(95\) −8.29483 + 14.3671i −0.851032 + 1.47403i
\(96\) −0.500281 0.288837i −0.0510597 0.0294793i
\(97\) −0.625592 0.361186i −0.0635192 0.0366728i 0.467904 0.883779i \(-0.345009\pi\)
−0.531423 + 0.847106i \(0.678343\pi\)
\(98\) 0.0866533i 0.00875331i
\(99\) −6.23466 3.59958i −0.626607 0.361772i
\(100\) −0.245070 0.424474i −0.0245070 0.0424474i
\(101\) 2.05050 + 3.55157i 0.204033 + 0.353395i 0.949824 0.312785i \(-0.101262\pi\)
−0.745792 + 0.666179i \(0.767928\pi\)
\(102\) 0.111363 + 0.0642954i 0.0110266 + 0.00636619i
\(103\) 4.96396 + 8.59783i 0.489113 + 0.847169i 0.999922 0.0125256i \(-0.00398714\pi\)
−0.510808 + 0.859695i \(0.670654\pi\)
\(104\) 1.48809 + 0.102736i 0.145919 + 0.0100741i
\(105\) 1.42673 2.47116i 0.139234 0.241161i
\(106\) 0.0427803 + 0.0246992i 0.00415519 + 0.00239900i
\(107\) −10.6631 −1.03084 −0.515419 0.856939i \(-0.672364\pi\)
−0.515419 + 0.856939i \(0.672364\pi\)
\(108\) −2.68853 + 4.65667i −0.258704 + 0.448089i
\(109\) 8.55112i 0.819049i 0.912299 + 0.409524i \(0.134305\pi\)
−0.912299 + 0.409524i \(0.865695\pi\)
\(110\) −0.506828 + 0.292617i −0.0483241 + 0.0278999i
\(111\) 0.918556i 0.0871855i
\(112\) 9.54060 + 5.50827i 0.901502 + 0.520482i
\(113\) 5.98570 0.563087 0.281543 0.959548i \(-0.409154\pi\)
0.281543 + 0.959548i \(0.409154\pi\)
\(114\) −0.184467 + 0.319507i −0.0172769 + 0.0299245i
\(115\) −13.6285 7.86841i −1.27086 0.733733i
\(116\) −18.5926 −1.72628
\(117\) 0.690711 10.0047i 0.0638563 0.924932i
\(118\) −0.430859 + 0.746269i −0.0396638 + 0.0686997i
\(119\) −6.42914 3.71186i −0.589358 0.340266i
\(120\) 0.210861 + 0.365221i 0.0192488 + 0.0333400i
\(121\) −2.15029 3.72441i −0.195481 0.338583i
\(122\) 0.174632i 0.0158105i
\(123\) 0.179185 + 0.103452i 0.0161566 + 0.00932799i
\(124\) 8.47694 7.12822i 0.761252 0.640133i
\(125\) 11.4386i 1.02310i
\(126\) −0.403709 + 0.699245i −0.0359653 + 0.0622937i
\(127\) −3.97793 −0.352985 −0.176492 0.984302i \(-0.556475\pi\)
−0.176492 + 0.984302i \(0.556475\pi\)
\(128\) −2.83544 + 1.63704i −0.250620 + 0.144696i
\(129\) −1.48290 2.56845i −0.130562 0.226140i
\(130\) −0.676263 0.455276i −0.0593122 0.0399304i
\(131\) −1.93144 + 3.34535i −0.168751 + 0.292285i −0.937981 0.346687i \(-0.887307\pi\)
0.769230 + 0.638972i \(0.220640\pi\)
\(132\) 2.08478 1.20365i 0.181457 0.104764i
\(133\) 10.6496 18.4456i 0.923434 1.59943i
\(134\) −0.548854 −0.0474138
\(135\) 5.10386 2.94672i 0.439270 0.253613i
\(136\) 0.950183 0.548589i 0.0814775 0.0470411i
\(137\) 1.13091i 0.0966201i 0.998832 + 0.0483100i \(0.0153836\pi\)
−0.998832 + 0.0483100i \(0.984616\pi\)
\(138\) −0.303081 0.174984i −0.0258000 0.0148956i
\(139\) −4.10740 + 7.11422i −0.348385 + 0.603420i −0.985963 0.166966i \(-0.946603\pi\)
0.637578 + 0.770386i \(0.279936\pi\)
\(140\) −6.07023 10.5140i −0.513028 0.888591i
\(141\) 0.691863i 0.0582654i
\(142\) 0.738860 + 1.27974i 0.0620038 + 0.107394i
\(143\) −5.21174 + 7.74147i −0.435827 + 0.647374i
\(144\) 5.47322 + 9.47990i 0.456102 + 0.789992i
\(145\) 17.6480 + 10.1891i 1.46558 + 0.846156i
\(146\) −0.392160 + 0.679242i −0.0324554 + 0.0562144i
\(147\) −0.195335 + 0.338330i −0.0161109 + 0.0279050i
\(148\) −3.38455 1.95407i −0.278208 0.160624i
\(149\) −2.59359 + 1.49741i −0.212475 + 0.122673i −0.602461 0.798148i \(-0.705813\pi\)
0.389986 + 0.920821i \(0.372480\pi\)
\(150\) 0.0119469i 0.000975461i
\(151\) 2.07619i 0.168958i 0.996425 + 0.0844791i \(0.0269226\pi\)
−0.996425 + 0.0844791i \(0.973077\pi\)
\(152\) 1.57393 + 2.72613i 0.127663 + 0.221119i
\(153\) −3.68825 6.38823i −0.298177 0.516458i
\(154\) 0.650705 0.375685i 0.0524353 0.0302735i
\(155\) −11.9526 + 2.12054i −0.960057 + 0.170326i
\(156\) 2.78174 + 1.87273i 0.222717 + 0.149939i
\(157\) 22.9115 1.82854 0.914269 0.405107i \(-0.132766\pi\)
0.914269 + 0.405107i \(0.132766\pi\)
\(158\) 0.606921i 0.0482840i
\(159\) 0.111354 + 0.192871i 0.00883098 + 0.0152957i
\(160\) 2.69384 0.212967
\(161\) 17.4973 + 10.1021i 1.37898 + 0.796155i
\(162\) −0.635898 + 0.367136i −0.0499609 + 0.0288449i
\(163\) 19.4002 + 11.2007i 1.51954 + 0.877307i 0.999735 + 0.0230216i \(0.00732866\pi\)
0.519805 + 0.854285i \(0.326005\pi\)
\(164\) 0.762371 0.440155i 0.0595311 0.0343703i
\(165\) −2.63848 −0.205405
\(166\) 0.0835245 0.144669i 0.00648276 0.0112285i
\(167\) 14.0524i 1.08740i 0.839278 + 0.543702i \(0.182978\pi\)
−0.839278 + 0.543702i \(0.817022\pi\)
\(168\) −0.270719 0.468900i −0.0208864 0.0361764i
\(169\) −12.8767 1.78650i −0.990512 0.137423i
\(170\) −0.599650 −0.0459910
\(171\) 18.3282 10.5818i 1.40159 0.809211i
\(172\) −12.6184 −0.962148
\(173\) −9.12665 −0.693886 −0.346943 0.937886i \(-0.612780\pi\)
−0.346943 + 0.937886i \(0.612780\pi\)
\(174\) 0.392470 + 0.226593i 0.0297531 + 0.0171779i
\(175\) 0.689712i 0.0521373i
\(176\) 10.1866i 0.767842i
\(177\) −3.36449 + 1.94249i −0.252891 + 0.146007i
\(178\) −0.472495 + 0.818385i −0.0354150 + 0.0613406i
\(179\) −21.9819 −1.64300 −0.821502 0.570206i \(-0.806863\pi\)
−0.821502 + 0.570206i \(0.806863\pi\)
\(180\) 12.0632i 0.899140i
\(181\) −4.10222 7.10525i −0.304916 0.528129i 0.672327 0.740254i \(-0.265295\pi\)
−0.977243 + 0.212125i \(0.931962\pi\)
\(182\) 0.868239 + 0.584519i 0.0643582 + 0.0433274i
\(183\) −0.393658 + 0.681835i −0.0291000 + 0.0504027i
\(184\) −2.58599 + 1.49302i −0.190641 + 0.110067i
\(185\) 2.14172 + 3.70958i 0.157463 + 0.272733i
\(186\) −0.265812 + 0.0471584i −0.0194903 + 0.00345782i
\(187\) 6.86444i 0.501978i
\(188\) −2.54927 1.47182i −0.185924 0.107344i
\(189\) −6.55274 + 3.78323i −0.476642 + 0.275189i
\(190\) 1.72043i 0.124813i
\(191\) −4.68493 −0.338990 −0.169495 0.985531i \(-0.554214\pi\)
−0.169495 + 0.985531i \(0.554214\pi\)
\(192\) −3.62022 −0.261267
\(193\) 22.8543i 1.64509i 0.568702 + 0.822544i \(0.307446\pi\)
−0.568702 + 0.822544i \(0.692554\pi\)
\(194\) 0.0749134 0.00537847
\(195\) −1.61412 3.30202i −0.115589 0.236463i
\(196\) 0.831083 + 1.43948i 0.0593630 + 0.102820i
\(197\) 11.7868 + 6.80512i 0.839775 + 0.484844i 0.857188 0.515004i \(-0.172210\pi\)
−0.0174127 + 0.999848i \(0.505543\pi\)
\(198\) 0.746589 0.0530578
\(199\) −5.71576 −0.405179 −0.202590 0.979264i \(-0.564936\pi\)
−0.202590 + 0.979264i \(0.564936\pi\)
\(200\) 0.0882782 + 0.0509674i 0.00624221 + 0.00360394i
\(201\) −2.14295 1.23723i −0.151152 0.0872676i
\(202\) −0.368316 0.212647i −0.0259146 0.0149618i
\(203\) −22.6579 13.0815i −1.59027 0.918143i
\(204\) 2.46660 0.172696
\(205\) −0.964847 −0.0673879
\(206\) −0.891637 0.514787i −0.0621233 0.0358669i
\(207\) 10.0378 + 17.3860i 0.697676 + 1.20841i
\(208\) 12.7484 6.23174i 0.883939 0.432093i
\(209\) −19.6945 −1.36230
\(210\) 0.295917i 0.0204202i
\(211\) −14.1177 −0.971904 −0.485952 0.873986i \(-0.661527\pi\)
−0.485952 + 0.873986i \(0.661527\pi\)
\(212\) 0.947550 0.0650780
\(213\) 6.66218i 0.456485i
\(214\) 0.957662 0.552906i 0.0654644 0.0377959i
\(215\) 11.9773 + 6.91511i 0.816847 + 0.471607i
\(216\) 1.11827i 0.0760887i
\(217\) 15.3457 2.72252i 1.04173 0.184817i
\(218\) −0.443397 0.767986i −0.0300306 0.0520145i
\(219\) −3.06231 + 1.76802i −0.206931 + 0.119472i
\(220\) −5.61292 + 9.72186i −0.378423 + 0.655447i
\(221\) −8.59075 + 4.19939i −0.577876 + 0.282481i
\(222\) 0.0476294 + 0.0824965i 0.00319668 + 0.00553680i
\(223\) 18.3161i 1.22653i −0.789876 0.613267i \(-0.789855\pi\)
0.789876 0.613267i \(-0.210145\pi\)
\(224\) −3.45856 −0.231085
\(225\) 0.342662 0.593508i 0.0228441 0.0395672i
\(226\) −0.537582 + 0.310373i −0.0357594 + 0.0206457i
\(227\) 9.06698i 0.601797i −0.953656 0.300898i \(-0.902714\pi\)
0.953656 0.300898i \(-0.0972865\pi\)
\(228\) 7.07682i 0.468674i
\(229\) −22.9448 13.2472i −1.51624 0.875400i −0.999818 0.0190631i \(-0.993932\pi\)
−0.516418 0.856337i \(-0.672735\pi\)
\(230\) 1.63199 0.107610
\(231\) 3.38749 0.222880
\(232\) 3.34868 1.93336i 0.219852 0.126931i
\(233\) −6.83119 −0.447526 −0.223763 0.974644i \(-0.571834\pi\)
−0.223763 + 0.974644i \(0.571834\pi\)
\(234\) 0.456733 + 0.934346i 0.0298576 + 0.0610801i
\(235\) 1.61316 + 2.79408i 0.105231 + 0.182266i
\(236\) 16.5293i 1.07596i
\(237\) −1.36813 + 2.36966i −0.0888693 + 0.153926i
\(238\) 0.769877 0.0499037
\(239\) −20.5168 + 11.8454i −1.32712 + 0.766215i −0.984854 0.173387i \(-0.944529\pi\)
−0.342269 + 0.939602i \(0.611195\pi\)
\(240\) 3.47436 + 2.00592i 0.224269 + 0.129482i
\(241\) 1.56891 0.905812i 0.101063 0.0583485i −0.448617 0.893724i \(-0.648083\pi\)
0.549679 + 0.835376i \(0.314750\pi\)
\(242\) 0.386240 + 0.222996i 0.0248284 + 0.0143347i
\(243\) −11.4196 −0.732568
\(244\) 1.67488 + 2.90098i 0.107223 + 0.185716i
\(245\) 1.82179i 0.116390i
\(246\) −0.0214571 −0.00136805
\(247\) −12.0483 24.6474i −0.766615 1.56827i
\(248\) −0.785533 + 2.16532i −0.0498814 + 0.137498i
\(249\) 0.652227 0.376564i 0.0413332 0.0238637i
\(250\) −0.593119 1.02731i −0.0375122 0.0649730i
\(251\) 12.5396 + 21.7192i 0.791493 + 1.37091i 0.925042 + 0.379864i \(0.124029\pi\)
−0.133549 + 0.991042i \(0.542637\pi\)
\(252\) 15.4877i 0.975635i
\(253\) 18.6820i 1.17453i
\(254\) 0.357263 0.206266i 0.0224167 0.0129423i
\(255\) −2.34127 1.35174i −0.146616 0.0846489i
\(256\) −7.57327 + 13.1173i −0.473330 + 0.819831i
\(257\) −7.87380 + 13.6378i −0.491154 + 0.850704i −0.999948 0.0101843i \(-0.996758\pi\)
0.508794 + 0.860888i \(0.330092\pi\)
\(258\) 0.266361 + 0.153784i 0.0165829 + 0.00957416i
\(259\) −2.74971 4.76264i −0.170859 0.295936i
\(260\) −15.6005 1.07704i −0.967503 0.0667953i
\(261\) −12.9983 22.5137i −0.804574 1.39356i
\(262\) 0.400599i 0.0247491i
\(263\) 5.76508 + 9.98541i 0.355490 + 0.615727i 0.987202 0.159477i \(-0.0509807\pi\)
−0.631712 + 0.775203i \(0.717647\pi\)
\(264\) −0.250324 + 0.433574i −0.0154064 + 0.0266846i
\(265\) −0.899406 0.519272i −0.0552501 0.0318987i
\(266\) 2.20882i 0.135432i
\(267\) −3.68962 + 2.13021i −0.225801 + 0.130366i
\(268\) −9.11751 + 5.26400i −0.556941 + 0.321550i
\(269\) 16.2051 0.988042 0.494021 0.869450i \(-0.335527\pi\)
0.494021 + 0.869450i \(0.335527\pi\)
\(270\) −0.305589 + 0.529296i −0.0185976 + 0.0322119i
\(271\) 18.4205 10.6351i 1.11896 0.646035i 0.177828 0.984061i \(-0.443093\pi\)
0.941137 + 0.338027i \(0.109759\pi\)
\(272\) 5.21875 9.03913i 0.316433 0.548078i
\(273\) 2.07233 + 4.23939i 0.125423 + 0.256580i
\(274\) −0.0586404 0.101568i −0.00354260 0.00613596i
\(275\) −0.552309 + 0.318876i −0.0333055 + 0.0192289i
\(276\) −6.71301 −0.404076
\(277\) −13.7122 + 23.7503i −0.823889 + 1.42702i 0.0788762 + 0.996884i \(0.474867\pi\)
−0.902765 + 0.430133i \(0.858467\pi\)
\(278\) 0.851915i 0.0510945i
\(279\) 14.5578 + 5.28127i 0.871554 + 0.316181i
\(280\) 2.18659 + 1.26243i 0.130674 + 0.0754446i
\(281\) 27.1552i 1.61994i −0.586468 0.809972i \(-0.699482\pi\)
0.586468 0.809972i \(-0.300518\pi\)
\(282\) 0.0358748 + 0.0621370i 0.00213631 + 0.00370020i
\(283\) 12.6713 + 21.9473i 0.753228 + 1.30463i 0.946250 + 0.323436i \(0.104838\pi\)
−0.193022 + 0.981194i \(0.561829\pi\)
\(284\) 24.5478 + 14.1727i 1.45664 + 0.840992i
\(285\) 3.87821 6.71726i 0.229725 0.397896i
\(286\) 0.0666578 0.965511i 0.00394156 0.0570919i
\(287\) 1.23875 0.0731209
\(288\) −2.97615 1.71828i −0.175371 0.101251i
\(289\) 4.98324 8.63122i 0.293132 0.507719i
\(290\) −2.11331 −0.124098
\(291\) 0.292492 + 0.168871i 0.0171462 + 0.00989937i
\(292\) 15.0447i 0.880423i
\(293\) 24.9323 14.3947i 1.45656 0.840946i 0.457720 0.889096i \(-0.348666\pi\)
0.998840 + 0.0481508i \(0.0153328\pi\)
\(294\) 0.0405143i 0.00236284i
\(295\) 9.05831 15.6894i 0.527395 0.913475i
\(296\) 0.812778 0.0472418
\(297\) 6.05907 + 3.49821i 0.351583 + 0.202987i
\(298\) 0.155289 0.268968i 0.00899565 0.0155809i
\(299\) 23.3803 11.4289i 1.35212 0.660951i
\(300\) 0.114581 + 0.198461i 0.00661537 + 0.0114581i
\(301\) −15.3774 8.87816i −0.886340 0.511729i
\(302\) −0.107656 0.186465i −0.00619489 0.0107299i
\(303\) −0.958702 1.66052i −0.0550760 0.0953944i
\(304\) 25.9338 + 14.9729i 1.48741 + 0.858754i
\(305\) 3.67144i 0.210226i
\(306\) 0.662491 + 0.382490i 0.0378721 + 0.0218655i
\(307\) 6.10713 + 3.52595i 0.348552 + 0.201237i 0.664047 0.747690i \(-0.268837\pi\)
−0.315495 + 0.948927i \(0.602171\pi\)
\(308\) 7.20630 12.4817i 0.410617 0.711210i
\(309\) −2.32087 4.01987i −0.132030 0.228683i
\(310\) 0.963522 0.810221i 0.0547244 0.0460175i
\(311\) −15.9658 −0.905335 −0.452668 0.891679i \(-0.649528\pi\)
−0.452668 + 0.891679i \(0.649528\pi\)
\(312\) −0.695750 0.0480338i −0.0393891 0.00271938i
\(313\) 5.47484 9.48271i 0.309456 0.535994i −0.668787 0.743454i \(-0.733186\pi\)
0.978244 + 0.207460i \(0.0665196\pi\)
\(314\) −2.05771 + 1.18802i −0.116123 + 0.0670438i
\(315\) 8.48752 14.7008i 0.478217 0.828297i
\(316\) 5.82091 + 10.0821i 0.327452 + 0.567163i
\(317\) 15.2919 + 8.82876i 0.858877 + 0.495873i 0.863636 0.504116i \(-0.168182\pi\)
−0.00475939 + 0.999989i \(0.501515\pi\)
\(318\) −0.0200017 0.0115480i −0.00112164 0.000647580i
\(319\) 24.1920i 1.35449i
\(320\) 14.6202 8.44099i 0.817295 0.471865i
\(321\) 4.98546 0.278261
\(322\) −2.09527 −0.116765
\(323\) −17.4761 10.0898i −0.972394 0.561412i
\(324\) −7.04232 + 12.1977i −0.391240 + 0.677648i
\(325\) −0.736948 0.496131i −0.0408785 0.0275204i
\(326\) −2.32314 −0.128667
\(327\) 3.99803i 0.221092i
\(328\) −0.0915392 + 0.158551i −0.00505441 + 0.00875449i
\(329\) −2.07110 3.58726i −0.114184 0.197772i
\(330\) 0.236965 0.136812i 0.0130445 0.00753124i
\(331\) 6.27388i 0.344844i −0.985023 0.172422i \(-0.944841\pi\)
0.985023 0.172422i \(-0.0551592\pi\)
\(332\) 3.20430i 0.175859i
\(333\) 5.46444i 0.299449i
\(334\) −0.728650 1.26206i −0.0398699 0.0690567i
\(335\) 11.5390 0.630444
\(336\) −4.46066 2.57536i −0.243349 0.140498i
\(337\) −15.1703 −0.826381 −0.413190 0.910645i \(-0.635586\pi\)
−0.413190 + 0.910645i \(0.635586\pi\)
\(338\) 1.24910 0.507240i 0.0679422 0.0275902i
\(339\) −2.79858 −0.151998
\(340\) −9.96132 + 5.75117i −0.540229 + 0.311901i
\(341\) −9.27494 11.0298i −0.502266 0.597300i
\(342\) −1.09739 + 1.90073i −0.0593398 + 0.102780i
\(343\) 17.2555i 0.931710i
\(344\) 2.27268 1.31213i 0.122535 0.0707455i
\(345\) 6.37193 + 3.67884i 0.343053 + 0.198062i
\(346\) 0.819675 0.473239i 0.0440660 0.0254415i
\(347\) −5.61177 9.71987i −0.301256 0.521790i 0.675165 0.737667i \(-0.264072\pi\)
−0.976421 + 0.215877i \(0.930739\pi\)
\(348\) 8.69290 0.465988
\(349\) −1.33978 + 0.773523i −0.0717168 + 0.0414057i −0.535430 0.844580i \(-0.679850\pi\)
0.463713 + 0.885986i \(0.346517\pi\)
\(350\) 0.0357633 + 0.0619438i 0.00191163 + 0.00331104i
\(351\) −0.671258 + 9.72290i −0.0358291 + 0.518970i
\(352\) 1.59900 + 2.76955i 0.0852270 + 0.147618i
\(353\) 18.4041i 0.979550i −0.871849 0.489775i \(-0.837079\pi\)
0.871849 0.489775i \(-0.162921\pi\)
\(354\) 0.201446 0.348915i 0.0107067 0.0185446i
\(355\) −15.5337 26.9051i −0.824442 1.42798i
\(356\) 18.1266i 0.960707i
\(357\) 3.00591 + 1.73546i 0.159090 + 0.0918505i
\(358\) 1.97422 1.13982i 0.104341 0.0602411i
\(359\) 25.8896 14.9473i 1.36640 0.788890i 0.375932 0.926647i \(-0.377323\pi\)
0.990466 + 0.137757i \(0.0439892\pi\)
\(360\) 1.25440 + 2.17268i 0.0661126 + 0.114510i
\(361\) 19.4483 33.6854i 1.02359 1.77291i
\(362\) 0.736850 + 0.425420i 0.0387280 + 0.0223596i
\(363\) 1.00536 + 1.74133i 0.0527676 + 0.0913961i
\(364\) 20.0292 + 1.38279i 1.04981 + 0.0724780i
\(365\) 8.24472 14.2803i 0.431548 0.747463i
\(366\) 0.0816485i 0.00426784i
\(367\) −18.0857 + 31.3254i −0.944068 + 1.63517i −0.186462 + 0.982462i \(0.559702\pi\)
−0.757606 + 0.652712i \(0.773631\pi\)
\(368\) −14.2032 + 24.6006i −0.740391 + 1.28239i
\(369\) 1.06596 + 0.615433i 0.0554917 + 0.0320382i
\(370\) −0.384701 0.222107i −0.0199997 0.0115468i
\(371\) 1.15473 + 0.666683i 0.0599505 + 0.0346124i
\(372\) −3.96335 + 3.33276i −0.205490 + 0.172796i
\(373\) −18.9713 + 32.8593i −0.982299 + 1.70139i −0.328924 + 0.944356i \(0.606686\pi\)
−0.653374 + 0.757035i \(0.726647\pi\)
\(374\) −0.355938 0.616503i −0.0184051 0.0318786i
\(375\) 5.34806i 0.276173i
\(376\) 0.612191 0.0315713
\(377\) −30.2759 + 14.7997i −1.55929 + 0.762222i
\(378\) 0.392339 0.679551i 0.0201797 0.0349523i
\(379\) 3.14272i 0.161430i −0.996737 0.0807152i \(-0.974280\pi\)
0.996737 0.0807152i \(-0.0257204\pi\)
\(380\) −16.5005 28.5796i −0.846456 1.46610i
\(381\) 1.85986 0.0952837
\(382\) 0.420759 0.242925i 0.0215279 0.0124291i
\(383\) 19.2381i 0.983022i 0.870871 + 0.491511i \(0.163555\pi\)
−0.870871 + 0.491511i \(0.836445\pi\)
\(384\) 1.32570 0.765392i 0.0676518 0.0390588i
\(385\) −13.6803 + 7.89834i −0.697214 + 0.402537i
\(386\) −1.18505 2.05257i −0.0603175 0.104473i
\(387\) −8.82168 15.2796i −0.448431 0.776706i
\(388\) 1.24446 0.718487i 0.0631776 0.0364756i
\(389\) 18.4669 31.9855i 0.936307 1.62173i 0.164019 0.986457i \(-0.447554\pi\)
0.772287 0.635273i \(-0.219113\pi\)
\(390\) 0.316183 + 0.212862i 0.0160106 + 0.0107787i
\(391\) 9.57110 16.5776i 0.484031 0.838367i
\(392\) −0.299369 0.172841i −0.0151204 0.00872977i
\(393\) 0.903035 1.56410i 0.0455521 0.0788985i
\(394\) −1.41145 −0.0711077
\(395\) 12.7598i 0.642015i
\(396\) 12.4023 7.16046i 0.623238 0.359826i
\(397\) 2.54433 1.46897i 0.127696 0.0737254i −0.434791 0.900531i \(-0.643178\pi\)
0.562487 + 0.826806i \(0.309845\pi\)
\(398\) 0.513339 0.296376i 0.0257313 0.0148560i
\(399\) −4.97915 + 8.62414i −0.249269 + 0.431747i
\(400\) 0.969710 0.0484855
\(401\) −0.530530 + 0.306302i −0.0264934 + 0.0152960i −0.513188 0.858276i \(-0.671536\pi\)
0.486695 + 0.873572i \(0.338202\pi\)
\(402\) 0.256614 0.0127987
\(403\) 8.12965 18.3551i 0.404967 0.914331i
\(404\) −8.15790 −0.405871
\(405\) 13.3690 7.71861i 0.664312 0.383541i
\(406\) 2.71324 0.134656
\(407\) −2.54256 + 4.40384i −0.126030 + 0.218290i
\(408\) −0.444254 + 0.256490i −0.0219938 + 0.0126981i
\(409\) −20.4261 + 11.7930i −1.01001 + 0.583128i −0.911194 0.411978i \(-0.864838\pi\)
−0.0988140 + 0.995106i \(0.531505\pi\)
\(410\) 0.0866540 0.0500297i 0.00427954 0.00247079i
\(411\) 0.528751i 0.0260814i
\(412\) −19.7491 −0.972966
\(413\) −11.6298 + 20.1433i −0.572263 + 0.991189i
\(414\) −1.80301 1.04097i −0.0886133 0.0511609i
\(415\) −1.75601 + 3.04149i −0.0861990 + 0.149301i
\(416\) −2.48785 + 3.69542i −0.121977 + 0.181183i
\(417\) 1.92039 3.32622i 0.0940421 0.162886i
\(418\) 1.76878 1.02121i 0.0865141 0.0499489i
\(419\) 17.4783 + 30.2732i 0.853869 + 1.47894i 0.877690 + 0.479228i \(0.159083\pi\)
−0.0238216 + 0.999716i \(0.507583\pi\)
\(420\) 2.83811 + 4.91575i 0.138485 + 0.239864i
\(421\) −4.35059 + 2.51181i −0.212035 + 0.122418i −0.602257 0.798303i \(-0.705732\pi\)
0.390222 + 0.920721i \(0.372398\pi\)
\(422\) 1.26793 0.732039i 0.0617218 0.0356351i
\(423\) 4.11586i 0.200120i
\(424\) −0.170661 + 0.0985312i −0.00828804 + 0.00478510i
\(425\) −0.653460 −0.0316975
\(426\) −0.345451 0.598338i −0.0167371 0.0289896i
\(427\) 4.71369i 0.228111i
\(428\) 10.6057 18.3697i 0.512647 0.887931i
\(429\) 2.43672 3.61949i 0.117646 0.174750i
\(430\) −1.43426 −0.0691663
\(431\) 8.65847i 0.417064i −0.978016 0.208532i \(-0.933131\pi\)
0.978016 0.208532i \(-0.0668685\pi\)
\(432\) −5.31908 9.21291i −0.255914 0.443256i
\(433\) 7.58986 13.1460i 0.364746 0.631758i −0.623990 0.781433i \(-0.714489\pi\)
0.988735 + 0.149675i \(0.0478226\pi\)
\(434\) −1.23705 + 1.04023i −0.0593801 + 0.0499324i
\(435\) −8.25123 4.76385i −0.395616 0.228409i
\(436\) −14.7313 8.50514i −0.705503 0.407322i
\(437\) 47.5622 + 27.4601i 2.27521 + 1.31359i
\(438\) 0.183353 0.317576i 0.00876093 0.0151744i
\(439\) 8.60356 14.9018i 0.410625 0.711224i −0.584333 0.811514i \(-0.698644\pi\)
0.994958 + 0.100290i \(0.0319771\pi\)
\(440\) 2.33464i 0.111300i
\(441\) −1.16204 + 2.01271i −0.0553350 + 0.0958431i
\(442\) 0.553796 0.822603i 0.0263414 0.0391273i
\(443\) 15.5018 + 26.8499i 0.736513 + 1.27568i 0.954057 + 0.299627i \(0.0968621\pi\)
−0.217544 + 0.976051i \(0.569805\pi\)
\(444\) 1.58243 + 0.913617i 0.0750988 + 0.0433583i
\(445\) 9.93366 17.2056i 0.470901 0.815624i
\(446\) 0.949733 + 1.64499i 0.0449711 + 0.0778923i
\(447\) 1.21262 0.700107i 0.0573550 0.0331139i
\(448\) −18.7706 + 10.8372i −0.886827 + 0.512010i
\(449\) 29.3791 + 16.9620i 1.38648 + 0.800487i 0.992917 0.118809i \(-0.0379077\pi\)
0.393567 + 0.919296i \(0.371241\pi\)
\(450\) 0.0710715i 0.00335034i
\(451\) −0.572711 0.991965i −0.0269679 0.0467098i
\(452\) −5.95351 + 10.3118i −0.280029 + 0.485025i
\(453\) 0.970714i 0.0456081i
\(454\) 0.470145 + 0.814316i 0.0220650 + 0.0382177i
\(455\) −18.2537 12.2888i −0.855748 0.576110i
\(456\) −0.735885 1.27459i −0.0344610 0.0596882i
\(457\) 15.9304 9.19741i 0.745192 0.430237i −0.0787622 0.996893i \(-0.525097\pi\)
0.823954 + 0.566657i \(0.191763\pi\)
\(458\) 2.74760 0.128387
\(459\) 3.58437 + 6.20832i 0.167304 + 0.289779i
\(460\) 27.1104 15.6522i 1.26403 0.729787i
\(461\) 6.32830 + 3.65365i 0.294738 + 0.170167i 0.640077 0.768311i \(-0.278903\pi\)
−0.345338 + 0.938478i \(0.612236\pi\)
\(462\) −0.304234 + 0.175650i −0.0141542 + 0.00817196i
\(463\) 29.9774i 1.39317i −0.717475 0.696584i \(-0.754702\pi\)
0.717475 0.696584i \(-0.245298\pi\)
\(464\) 18.3921 31.8561i 0.853834 1.47888i
\(465\) 5.58839 0.991451i 0.259155 0.0459774i
\(466\) 0.613517 0.354214i 0.0284206 0.0164087i
\(467\) −16.9517 −0.784432 −0.392216 0.919873i \(-0.628291\pi\)
−0.392216 + 0.919873i \(0.628291\pi\)
\(468\) 16.5484 + 11.1408i 0.764951 + 0.514983i
\(469\) −14.8147 −0.684079
\(470\) −0.289760 0.167293i −0.0133656 0.00771665i
\(471\) −10.7122 −0.493591
\(472\) −1.71880 2.97705i −0.0791143 0.137030i
\(473\) 16.4186i 0.754928i
\(474\) 0.283763i 0.0130337i
\(475\) 1.87482i 0.0860225i
\(476\) 12.7891 7.38381i 0.586189 0.338436i
\(477\) 0.662441 + 1.14738i 0.0303311 + 0.0525350i
\(478\) 1.22843 2.12770i 0.0561869 0.0973185i
\(479\) 22.7292i 1.03852i −0.854615 0.519262i \(-0.826207\pi\)
0.854615 0.519262i \(-0.173793\pi\)
\(480\) −1.25949 −0.0574876
\(481\) −7.06677 0.487882i −0.322217 0.0222455i
\(482\) −0.0939372 + 0.162704i −0.00427872 + 0.00741096i
\(483\) −8.18079 4.72318i −0.372239 0.214912i
\(484\) 8.55490 0.388859
\(485\) −1.57497 −0.0715156
\(486\) 1.02561 0.592135i 0.0465225 0.0268598i
\(487\) 5.80554i 0.263074i −0.991311 0.131537i \(-0.958009\pi\)
0.991311 0.131537i \(-0.0419913\pi\)
\(488\) −0.603318 0.348326i −0.0273109 0.0157680i
\(489\) −9.07046 5.23683i −0.410181 0.236818i
\(490\) 0.0944641 + 0.163617i 0.00426745 + 0.00739145i
\(491\) −3.07021 + 5.31776i −0.138557 + 0.239987i −0.926951 0.375184i \(-0.877580\pi\)
0.788394 + 0.615171i \(0.210913\pi\)
\(492\) −0.356443 + 0.205792i −0.0160697 + 0.00927783i
\(493\) −12.3939 + 21.4669i −0.558195 + 0.966822i
\(494\) 2.36010 + 1.58887i 0.106186 + 0.0714868i
\(495\) −15.6962 −0.705491
\(496\) 3.82777 + 21.5755i 0.171872 + 0.968769i
\(497\) 19.9434 + 34.5429i 0.894582 + 1.54946i
\(498\) −0.0390515 + 0.0676392i −0.00174994 + 0.00303098i
\(499\) −10.9066 6.29691i −0.488245 0.281889i 0.235601 0.971850i \(-0.424294\pi\)
−0.723846 + 0.689961i \(0.757628\pi\)
\(500\) −19.7057 11.3771i −0.881265 0.508799i
\(501\) 6.57011i 0.293531i
\(502\) −2.25239 1.30042i −0.100529 0.0580405i
\(503\) 8.60682 + 14.9075i 0.383759 + 0.664690i 0.991596 0.129371i \(-0.0412959\pi\)
−0.607837 + 0.794062i \(0.707963\pi\)
\(504\) −1.61049 2.78946i −0.0717371 0.124252i
\(505\) 7.74341 + 4.47066i 0.344577 + 0.198942i
\(506\) 0.968709 + 1.67785i 0.0430644 + 0.0745897i
\(507\) 6.02042 + 0.835268i 0.267376 + 0.0370955i
\(508\) 3.95654 6.85293i 0.175543 0.304050i
\(509\) −11.6945 6.75181i −0.518349 0.299269i 0.217910 0.975969i \(-0.430076\pi\)
−0.736259 + 0.676700i \(0.763409\pi\)
\(510\) 0.280363 0.0124147
\(511\) −10.5852 + 18.3341i −0.468262 + 0.811054i
\(512\) 8.11895i 0.358810i
\(513\) −17.8120 + 10.2838i −0.786421 + 0.454040i
\(514\) 1.63310i 0.0720331i
\(515\) 18.7456 + 10.8228i 0.826031 + 0.476909i
\(516\) 5.89969 0.259720
\(517\) −1.91507 + 3.31700i −0.0842248 + 0.145882i
\(518\) 0.493910 + 0.285159i 0.0217011 + 0.0125292i
\(519\) 4.26712 0.187306
\(520\) 2.92177 1.42824i 0.128128 0.0626325i
\(521\) −17.6142 + 30.5087i −0.771692 + 1.33661i 0.164943 + 0.986303i \(0.447256\pi\)
−0.936635 + 0.350307i \(0.886077\pi\)
\(522\) 2.33478 + 1.34799i 0.102191 + 0.0589998i
\(523\) −0.930339 1.61139i −0.0406809 0.0704613i 0.844968 0.534817i \(-0.179619\pi\)
−0.885649 + 0.464355i \(0.846286\pi\)
\(524\) −3.84211 6.65472i −0.167843 0.290713i
\(525\) 0.322472i 0.0140738i
\(526\) −1.03554 0.597867i −0.0451515 0.0260682i
\(527\) −2.57942 14.5391i −0.112361 0.633334i
\(528\) 4.76268i 0.207269i
\(529\) −14.5484 + 25.1985i −0.632538 + 1.09559i
\(530\) 0.107702 0.00467829
\(531\) −20.0152 + 11.5558i −0.868586 + 0.501478i
\(532\) 21.1846 + 36.6928i 0.918468 + 1.59083i
\(533\) 0.891068 1.32358i 0.0385964 0.0573308i
\(534\) 0.220913 0.382632i 0.00955983 0.0165581i
\(535\) −20.1337 + 11.6242i −0.870457 + 0.502559i
\(536\) 1.09476 1.89617i 0.0472863 0.0819022i
\(537\) 10.2775 0.443508
\(538\) −1.45540 + 0.840274i −0.0627466 + 0.0362268i
\(539\) 1.87299 1.08137i 0.0806753 0.0465779i
\(540\) 11.7235i 0.504498i
\(541\) 10.4785 + 6.04975i 0.450505 + 0.260099i 0.708043 0.706169i \(-0.249578\pi\)
−0.257538 + 0.966268i \(0.582911\pi\)
\(542\) −1.10291 + 1.91030i −0.0473740 + 0.0820542i
\(543\) 1.91797 + 3.32203i 0.0823081 + 0.142562i
\(544\) 3.27677i 0.140490i
\(545\) 9.32190 + 16.1460i 0.399306 + 0.691619i
\(546\) −0.405941 0.273289i −0.0173727 0.0116957i
\(547\) 11.7886 + 20.4185i 0.504045 + 0.873032i 0.999989 + 0.00467729i \(0.00148883\pi\)
−0.495944 + 0.868355i \(0.665178\pi\)
\(548\) −1.94826 1.12483i −0.0832255 0.0480503i
\(549\) −2.34185 + 4.05620i −0.0999477 + 0.173114i
\(550\) 0.0330690 0.0572771i 0.00141007 0.00244231i
\(551\) −61.5899 35.5590i −2.62382 1.51486i
\(552\) 1.20907 0.698054i 0.0514612 0.0297112i
\(553\) 16.3820i 0.696635i
\(554\) 2.84406i 0.120832i
\(555\) −1.00135 1.73439i −0.0425051 0.0736209i
\(556\) −8.17062 14.1519i −0.346512 0.600176i
\(557\) 29.7725 17.1891i 1.26150 0.728327i 0.288135 0.957590i \(-0.406965\pi\)
0.973365 + 0.229263i \(0.0736315\pi\)
\(558\) −1.58130 + 0.280543i −0.0669418 + 0.0118763i
\(559\) −20.5476 + 10.0442i −0.869073 + 0.424826i
\(560\) 24.0191 1.01499
\(561\) 3.20944i 0.135503i
\(562\) 1.40807 + 2.43884i 0.0593956 + 0.102876i
\(563\) 17.4321 0.734676 0.367338 0.930087i \(-0.380269\pi\)
0.367338 + 0.930087i \(0.380269\pi\)
\(564\) 1.19190 + 0.688143i 0.0501880 + 0.0289760i
\(565\) 11.3020 6.52523i 0.475480 0.274519i
\(566\) −2.27604 1.31407i −0.0956691 0.0552346i
\(567\) −17.1642 + 9.90976i −0.720829 + 0.416171i
\(568\) −5.89499 −0.247348
\(569\) −6.50800 + 11.2722i −0.272829 + 0.472554i −0.969585 0.244754i \(-0.921293\pi\)
0.696756 + 0.717308i \(0.254626\pi\)
\(570\) 0.804379i 0.0336917i
\(571\) −13.1084 22.7045i −0.548571 0.950152i −0.998373 0.0570239i \(-0.981839\pi\)
0.449802 0.893128i \(-0.351494\pi\)
\(572\) −8.15280 16.6783i −0.340886 0.697354i
\(573\) 2.19042 0.0915060
\(574\) −0.111253 + 0.0642321i −0.00464362 + 0.00268100i
\(575\) 1.77843 0.0741658
\(576\) −21.5365 −0.897355
\(577\) −1.77482 1.02469i −0.0738866 0.0426585i 0.462602 0.886566i \(-0.346916\pi\)
−0.536488 + 0.843908i \(0.680249\pi\)
\(578\) 1.03357i 0.0429910i
\(579\) 10.6854i 0.444070i
\(580\) −35.1062 + 20.2685i −1.45770 + 0.841606i
\(581\) 2.25450 3.90491i 0.0935324 0.162003i
\(582\) −0.0350254 −0.00145185
\(583\) 1.23291i 0.0510620i
\(584\) −1.56442 2.70966i −0.0647363 0.112127i
\(585\) −9.60229 19.6435i −0.397006 0.812160i
\(586\) −1.49280 + 2.58560i −0.0616669 + 0.106810i
\(587\) 10.7148 6.18621i 0.442248 0.255332i −0.262303 0.964986i \(-0.584482\pi\)
0.704551 + 0.709654i \(0.251149\pi\)
\(588\) −0.388569 0.673021i −0.0160243 0.0277549i
\(589\) 41.7136 7.40052i 1.71878 0.304933i
\(590\) 1.87878i 0.0773483i
\(591\) −5.51086 3.18170i −0.226687 0.130878i
\(592\) 6.69610 3.86600i 0.275208 0.158892i
\(593\) 4.14808i 0.170341i −0.996366 0.0851705i \(-0.972856\pi\)
0.996366 0.0851705i \(-0.0271435\pi\)
\(594\) −0.725563 −0.0297702
\(595\) −16.1858 −0.663552
\(596\) 5.95744i 0.244026i
\(597\) 2.67238 0.109373
\(598\) −1.50719 + 2.23877i −0.0616337 + 0.0915501i
\(599\) −7.66485 13.2759i −0.313177 0.542439i 0.665871 0.746067i \(-0.268060\pi\)
−0.979048 + 0.203628i \(0.934727\pi\)
\(600\) −0.0412740 0.0238296i −0.00168501 0.000972838i
\(601\) 15.1788 0.619156 0.309578 0.950874i \(-0.399812\pi\)
0.309578 + 0.950874i \(0.399812\pi\)
\(602\) 1.84142 0.0750506
\(603\) −12.7483 7.36022i −0.519150 0.299732i
\(604\) −3.57674 2.06503i −0.145535 0.0840248i
\(605\) −8.12024 4.68822i −0.330135 0.190603i
\(606\) 0.172204 + 0.0994222i 0.00699532 + 0.00403875i
\(607\) −18.4662 −0.749519 −0.374760 0.927122i \(-0.622275\pi\)
−0.374760 + 0.927122i \(0.622275\pi\)
\(608\) −9.40126 −0.381271
\(609\) 10.5936 + 6.11620i 0.429273 + 0.247841i
\(610\) 0.190373 + 0.329736i 0.00770799 + 0.0133506i
\(611\) −5.32275 0.367476i −0.215335 0.0148665i
\(612\) 14.6737 0.593148
\(613\) 21.4990i 0.868336i 0.900832 + 0.434168i \(0.142958\pi\)
−0.900832 + 0.434168i \(0.857042\pi\)
\(614\) −0.731317 −0.0295136
\(615\) 0.451110 0.0181905
\(616\) 2.99740i 0.120769i
\(617\) −18.3888 + 10.6168i −0.740304 + 0.427415i −0.822180 0.569228i \(-0.807242\pi\)
0.0818761 + 0.996643i \(0.473909\pi\)
\(618\) 0.416881 + 0.240686i 0.0167694 + 0.00968182i
\(619\) 23.8119i 0.957080i 0.878066 + 0.478540i \(0.158834\pi\)
−0.878066 + 0.478540i \(0.841166\pi\)
\(620\) 8.23520 22.7004i 0.330734 0.911668i
\(621\) −9.75511 16.8963i −0.391459 0.678027i
\(622\) 1.43390 0.827864i 0.0574943 0.0331943i
\(623\) −12.7536 + 22.0899i −0.510963 + 0.885014i
\(624\) −5.96043 + 2.91362i −0.238608 + 0.116638i
\(625\) 11.8537 + 20.5311i 0.474146 + 0.821245i
\(626\) 1.13554i 0.0453852i
\(627\) 9.20807 0.367735
\(628\) −22.7883 + 39.4705i −0.909353 + 1.57505i
\(629\) −4.51231 + 2.60518i −0.179918 + 0.103876i
\(630\) 1.76039i 0.0701358i
\(631\) 15.0376i 0.598636i −0.954153 0.299318i \(-0.903241\pi\)
0.954153 0.299318i \(-0.0967592\pi\)
\(632\) −2.09678 1.21058i −0.0834055 0.0481542i
\(633\) 6.60067 0.262353
\(634\) −1.83117 −0.0727251
\(635\) −7.51103 + 4.33650i −0.298066 + 0.172089i
\(636\) −0.443022 −0.0175670
\(637\) 2.49914 + 1.68248i 0.0990195 + 0.0666622i
\(638\) −1.25441 2.17271i −0.0496627 0.0860184i
\(639\) 39.6330i 1.56786i
\(640\) −3.56921 + 6.18205i −0.141085 + 0.244367i
\(641\) −2.91588 −0.115170 −0.0575852 0.998341i \(-0.518340\pi\)
−0.0575852 + 0.998341i \(0.518340\pi\)
\(642\) −0.447750 + 0.258509i −0.0176713 + 0.0102025i
\(643\) 21.2276 + 12.2557i 0.837133 + 0.483319i 0.856289 0.516497i \(-0.172764\pi\)
−0.0191555 + 0.999817i \(0.506098\pi\)
\(644\) −34.8065 + 20.0955i −1.37157 + 0.791874i
\(645\) −5.59994 3.23313i −0.220497 0.127304i
\(646\) 2.09273 0.0823372
\(647\) 5.89770 + 10.2151i 0.231862 + 0.401598i 0.958356 0.285576i \(-0.0921847\pi\)
−0.726494 + 0.687173i \(0.758851\pi\)
\(648\) 2.92919i 0.115070i
\(649\) 21.5072 0.844232
\(650\) 0.0919118 + 0.00634549i 0.00360508 + 0.000248890i
\(651\) −7.17481 + 1.27290i −0.281203 + 0.0498890i
\(652\) −38.5917 + 22.2809i −1.51137 + 0.872589i
\(653\) −15.3868 26.6507i −0.602131 1.04292i −0.992498 0.122262i \(-0.960985\pi\)
0.390367 0.920659i \(-0.372348\pi\)
\(654\) 0.207308 + 0.359068i 0.00810638 + 0.0140407i
\(655\) 8.42214i 0.329080i
\(656\) 1.74163i 0.0679993i
\(657\) −18.2175 + 10.5179i −0.710732 + 0.410341i
\(658\) 0.372016 + 0.214784i 0.0145027 + 0.00837314i
\(659\) 9.30223 16.1119i 0.362364 0.627632i −0.625986 0.779834i \(-0.715303\pi\)
0.988349 + 0.152202i \(0.0486365\pi\)
\(660\) 2.62429 4.54541i 0.102150 0.176930i
\(661\) −23.9085 13.8036i −0.929934 0.536898i −0.0431435 0.999069i \(-0.513737\pi\)
−0.886791 + 0.462171i \(0.847071\pi\)
\(662\) 0.325316 + 0.563464i 0.0126438 + 0.0218997i
\(663\) 4.01656 1.96340i 0.155990 0.0762523i
\(664\) 0.333200 + 0.577119i 0.0129307 + 0.0223966i
\(665\) 46.4380i 1.80079i
\(666\) 0.283345 + 0.490767i 0.0109794 + 0.0190169i
\(667\) 33.7309 58.4237i 1.30607 2.26217i
\(668\) −24.2085 13.9768i −0.936656 0.540778i
\(669\) 8.56358i 0.331087i
\(670\) −1.03633 + 0.598327i −0.0400370 + 0.0231154i
\(671\) 3.77463 2.17928i 0.145718 0.0841303i
\(672\) 1.61703 0.0623784
\(673\) −12.0777 + 20.9192i −0.465562 + 0.806377i −0.999227 0.0393194i \(-0.987481\pi\)
0.533665 + 0.845696i \(0.320814\pi\)
\(674\) 1.36246 0.786619i 0.0524802 0.0302994i
\(675\) −0.333012 + 0.576793i −0.0128176 + 0.0222008i
\(676\) 15.8851 20.4062i 0.610965 0.784854i
\(677\) 19.0345 + 32.9687i 0.731554 + 1.26709i 0.956219 + 0.292653i \(0.0945379\pi\)
−0.224665 + 0.974436i \(0.572129\pi\)
\(678\) 0.251344 0.145113i 0.00965280 0.00557305i
\(679\) 2.02207 0.0775999
\(680\) 1.19607 2.07166i 0.0458674 0.0794446i
\(681\) 4.23922i 0.162447i
\(682\) 1.40492 + 0.509674i 0.0537971 + 0.0195164i
\(683\) −9.71900 5.61127i −0.371887 0.214709i 0.302395 0.953183i \(-0.402214\pi\)
−0.674283 + 0.738473i \(0.735547\pi\)
\(684\) 42.0996i 1.60972i
\(685\) 1.23285 + 2.13535i 0.0471047 + 0.0815877i
\(686\) 0.894741 + 1.54974i 0.0341614 + 0.0591692i
\(687\) 10.7277 + 6.19366i 0.409289 + 0.236303i
\(688\) 12.4824 21.6201i 0.475886 0.824259i
\(689\) 1.54297 0.754247i 0.0587826 0.0287345i
\(690\) −0.763027 −0.0290479
\(691\) 18.3109 + 10.5718i 0.696579 + 0.402170i 0.806072 0.591817i \(-0.201589\pi\)
−0.109493 + 0.993988i \(0.534923\pi\)
\(692\) 9.07757 15.7228i 0.345078 0.597692i
\(693\) 20.1520 0.765511
\(694\) 1.00800 + 0.581968i 0.0382631 + 0.0220912i
\(695\) 17.9105i 0.679385i
\(696\) −1.56566 + 0.903934i −0.0593461 + 0.0342635i
\(697\) 1.17364i 0.0444547i
\(698\) 0.0802181 0.138942i 0.00303630 0.00525903i
\(699\) 3.19389 0.120804
\(700\) 1.18819 + 0.686003i 0.0449095 + 0.0259285i
\(701\) 23.9382 41.4621i 0.904132 1.56600i 0.0820542 0.996628i \(-0.473852\pi\)
0.822078 0.569375i \(-0.192815\pi\)
\(702\) −0.443870 0.908031i −0.0167528 0.0342714i
\(703\) −7.47443 12.9461i −0.281904 0.488271i
\(704\) 17.3565 + 10.0208i 0.654146 + 0.377671i
\(705\) −0.754226 1.30636i −0.0284058 0.0492003i
\(706\) 0.954297 + 1.65289i 0.0359154 + 0.0622074i
\(707\) −9.94160 5.73978i −0.373892 0.215867i
\(708\) 7.72818i 0.290443i
\(709\) −32.9655 19.0326i −1.23804 0.714785i −0.269350 0.963042i \(-0.586809\pi\)
−0.968694 + 0.248257i \(0.920142\pi\)
\(710\) 2.79019 + 1.61092i 0.104714 + 0.0604567i
\(711\) −8.13891 + 14.0970i −0.305233 + 0.528679i
\(712\) −1.88490 3.26474i −0.0706396 0.122351i
\(713\) 7.02007 + 39.5692i 0.262904 + 1.48188i
\(714\) −0.359952 −0.0134709
\(715\) −1.40140 + 20.2988i −0.0524095 + 0.759130i
\(716\) 21.8637 37.8690i 0.817084 1.41523i
\(717\) 9.59254 5.53826i 0.358240 0.206830i
\(718\) −1.55011 + 2.68487i −0.0578497 + 0.100199i
\(719\) 11.6617 + 20.1987i 0.434908 + 0.753283i 0.997288 0.0735958i \(-0.0234475\pi\)
−0.562380 + 0.826879i \(0.690114\pi\)
\(720\) 20.6688 + 11.9331i 0.770281 + 0.444722i
\(721\) −24.0671 13.8952i −0.896306 0.517483i
\(722\) 4.03376i 0.150121i
\(723\) −0.733537 + 0.423508i −0.0272805 + 0.0157504i
\(724\) 16.3206 0.606552
\(725\) −2.30295 −0.0855296
\(726\) −0.180584 0.104260i −0.00670212 0.00386947i
\(727\) −10.9626 + 18.9878i −0.406580 + 0.704218i −0.994504 0.104698i \(-0.966612\pi\)
0.587924 + 0.808917i \(0.299946\pi\)
\(728\) −3.75120 + 1.83369i −0.139029 + 0.0679610i
\(729\) −15.9020 −0.588963
\(730\) 1.71004i 0.0632913i
\(731\) −8.41151 + 14.5692i −0.311111 + 0.538860i
\(732\) −0.783082 1.35634i −0.0289435 0.0501317i
\(733\) 9.42650 5.44239i 0.348176 0.201019i −0.315706 0.948857i \(-0.602241\pi\)
0.663881 + 0.747838i \(0.268908\pi\)
\(734\) 3.75116i 0.138458i
\(735\) 0.851767i 0.0314179i
\(736\) 8.91795i 0.328720i
\(737\) 6.84930 + 11.8633i 0.252297 + 0.436991i
\(738\) −0.127647 −0.00469875
\(739\) −3.12715 1.80546i −0.115034 0.0664149i 0.441379 0.897321i \(-0.354489\pi\)
−0.556413 + 0.830906i \(0.687823\pi\)
\(740\) −8.52083 −0.313232
\(741\) 5.63313 + 11.5238i 0.206938 + 0.423336i
\(742\) −0.138277 −0.00507629
\(743\) −14.0619 + 8.11867i −0.515883 + 0.297845i −0.735248 0.677798i \(-0.762935\pi\)
0.219366 + 0.975643i \(0.429601\pi\)
\(744\) 0.367272 1.01239i 0.0134649 0.0371159i
\(745\) −3.26477 + 5.65475i −0.119612 + 0.207174i
\(746\) 3.93484i 0.144065i
\(747\) 3.88006 2.24016i 0.141964 0.0819630i
\(748\) −11.8256 6.82753i −0.432388 0.249639i
\(749\) 25.8493 14.9241i 0.944511 0.545314i
\(750\) 0.277310 + 0.480315i 0.0101259 + 0.0175386i
\(751\) 42.6465 1.55619 0.778097 0.628144i \(-0.216185\pi\)
0.778097 + 0.628144i \(0.216185\pi\)
\(752\) 5.04356 2.91190i 0.183920 0.106186i
\(753\) −5.86283 10.1547i −0.213654 0.370059i
\(754\) 1.95171 2.89906i 0.0710772 0.105577i
\(755\) 2.26334 + 3.92022i 0.0823713 + 0.142671i
\(756\) 15.0515i 0.547419i
\(757\) 15.5666 26.9622i 0.565779 0.979958i −0.431198 0.902257i \(-0.641909\pi\)
0.996977 0.0777003i \(-0.0247577\pi\)
\(758\) 0.162958 + 0.282251i 0.00591889 + 0.0102518i
\(759\) 8.73469i 0.317049i
\(760\) 5.94372 + 3.43161i 0.215601 + 0.124478i
\(761\) −20.2526 + 11.6929i −0.734157 + 0.423866i −0.819941 0.572448i \(-0.805994\pi\)
0.0857837 + 0.996314i \(0.472661\pi\)
\(762\) −0.167036 + 0.0964385i −0.00605109 + 0.00349360i
\(763\) −11.9682 20.7295i −0.433278 0.750459i
\(764\) 4.65974 8.07091i 0.168583 0.291995i
\(765\)