Properties

Label 403.2.h.b.118.14
Level 403
Weight 2
Character 403.118
Analytic conductor 3.218
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 403 = 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 403.h (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(34\)
Relative dimension: \(17\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 118.14
Character \(\chi\) \(=\) 403.118
Dual form 403.2.h.b.222.14

$q$-expansion

\(f(q)\) \(=\) \(q+2.14110 q^{2} +(-0.301124 - 0.521562i) q^{3} +2.58432 q^{4} +(0.249792 - 0.432653i) q^{5} +(-0.644738 - 1.11672i) q^{6} +(2.01488 + 3.48987i) q^{7} +1.25109 q^{8} +(1.31865 - 2.28397i) q^{9} +O(q^{10})\) \(q+2.14110 q^{2} +(-0.301124 - 0.521562i) q^{3} +2.58432 q^{4} +(0.249792 - 0.432653i) q^{5} +(-0.644738 - 1.11672i) q^{6} +(2.01488 + 3.48987i) q^{7} +1.25109 q^{8} +(1.31865 - 2.28397i) q^{9} +(0.534831 - 0.926355i) q^{10} +(1.14955 - 1.99108i) q^{11} +(-0.778201 - 1.34788i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(4.31405 + 7.47216i) q^{14} -0.300874 q^{15} -2.48993 q^{16} +(0.938003 + 1.62467i) q^{17} +(2.82336 - 4.89021i) q^{18} +(-2.05191 - 3.55401i) q^{19} +(0.645543 - 1.11811i) q^{20} +(1.21346 - 2.10177i) q^{21} +(2.46131 - 4.26311i) q^{22} -4.23857 q^{23} +(-0.376733 - 0.652520i) q^{24} +(2.37521 + 4.11398i) q^{25} +(-1.07055 + 1.85425i) q^{26} -3.39505 q^{27} +(5.20708 + 9.01893i) q^{28} +6.47268 q^{29} -0.644202 q^{30} +(-4.97197 + 2.50589i) q^{31} -7.83337 q^{32} -1.38463 q^{33} +(2.00836 + 3.47858i) q^{34} +2.01320 q^{35} +(3.40781 - 5.90250i) q^{36} +(-4.34525 - 7.52619i) q^{37} +(-4.39334 - 7.60949i) q^{38} +0.602248 q^{39} +(0.312512 - 0.541287i) q^{40} +(-5.02057 + 8.69589i) q^{41} +(2.59813 - 4.50010i) q^{42} +(-5.16322 - 8.94295i) q^{43} +(2.97081 - 5.14559i) q^{44} +(-0.658777 - 1.14103i) q^{45} -9.07522 q^{46} +5.34751 q^{47} +(0.749779 + 1.29865i) q^{48} +(-4.61944 + 8.00111i) q^{49} +(5.08556 + 8.80845i) q^{50} +(0.564911 - 0.978454i) q^{51} +(-1.29216 + 2.23809i) q^{52} +(-4.26962 + 7.39519i) q^{53} -7.26915 q^{54} +(-0.574298 - 0.994713i) q^{55} +(2.52079 + 4.36613i) q^{56} +(-1.23576 + 2.14039i) q^{57} +13.8587 q^{58} +(5.60232 + 9.70350i) q^{59} -0.777555 q^{60} -8.92279 q^{61} +(-10.6455 + 5.36537i) q^{62} +10.6276 q^{63} -11.7922 q^{64} +(0.249792 + 0.432653i) q^{65} -2.96463 q^{66} +(3.45028 - 5.97606i) q^{67} +(2.42410 + 4.19866i) q^{68} +(1.27634 + 2.21068i) q^{69} +4.31047 q^{70} +(-5.69504 + 9.86409i) q^{71} +(1.64974 - 2.85744i) q^{72} +(5.64714 - 9.78114i) q^{73} +(-9.30362 - 16.1143i) q^{74} +(1.43046 - 2.47764i) q^{75} +(-5.30278 - 9.18468i) q^{76} +9.26480 q^{77} +1.28948 q^{78} +(0.487117 + 0.843712i) q^{79} +(-0.621966 + 1.07728i) q^{80} +(-2.93361 - 5.08117i) q^{81} +(-10.7496 + 18.6188i) q^{82} +(0.735814 - 1.27447i) q^{83} +(3.13596 - 5.43163i) q^{84} +0.937224 q^{85} +(-11.0550 - 19.1478i) q^{86} +(-1.94908 - 3.37591i) q^{87} +(1.43819 - 2.49102i) q^{88} +0.499561 q^{89} +(-1.41051 - 2.44307i) q^{90} -4.02975 q^{91} -10.9538 q^{92} +(2.80416 + 1.83861i) q^{93} +11.4496 q^{94} -2.05020 q^{95} +(2.35882 + 4.08559i) q^{96} +8.56900 q^{97} +(-9.89070 + 17.1312i) q^{98} +(-3.03171 - 5.25107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} + O(q^{10}) \) \( 34q + 6q^{2} - 2q^{3} + 34q^{4} - 5q^{5} - 2q^{7} + 36q^{8} - 23q^{9} - 7q^{10} - 5q^{11} - 28q^{12} - 17q^{13} - 7q^{14} + 8q^{15} + 18q^{16} - 8q^{17} + 6q^{18} + 3q^{19} - 8q^{20} + 13q^{21} + 12q^{22} - 14q^{23} - 6q^{24} - 26q^{25} - 3q^{26} + 28q^{27} - 7q^{28} - 18q^{29} - 60q^{30} - 9q^{31} + 58q^{32} - 14q^{33} - 15q^{34} + 50q^{35} - 49q^{36} - 6q^{37} + 2q^{38} + 4q^{39} - 29q^{40} - 5q^{41} + 8q^{42} - q^{43} - 22q^{44} + 13q^{45} + 34q^{46} + 16q^{47} - 49q^{48} + 3q^{49} - 35q^{51} - 17q^{52} + 30q^{53} - 2q^{54} + 21q^{55} - 7q^{56} + 34q^{58} - 9q^{59} - 38q^{60} - 28q^{61} - 62q^{62} + 88q^{63} + 56q^{64} - 5q^{65} + 140q^{66} - 31q^{67} - 39q^{68} + 5q^{69} + 56q^{70} + q^{71} - 32q^{72} - 10q^{73} - 39q^{74} - 2q^{75} - 16q^{76} + 76q^{77} - 23q^{79} - 22q^{80} - 29q^{81} - 10q^{82} + 3q^{83} + 52q^{84} - 32q^{85} + 4q^{86} + 18q^{87} - 10q^{88} + 26q^{89} + 35q^{90} + 4q^{91} - 94q^{92} - 41q^{93} + 70q^{94} + 28q^{95} - 23q^{96} + 32q^{97} - 38q^{98} - 70q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(249\) \(313\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.14110 1.51399 0.756994 0.653422i \(-0.226667\pi\)
0.756994 + 0.653422i \(0.226667\pi\)
\(3\) −0.301124 0.521562i −0.173854 0.301124i 0.765910 0.642948i \(-0.222289\pi\)
−0.939764 + 0.341824i \(0.888955\pi\)
\(4\) 2.58432 1.29216
\(5\) 0.249792 0.432653i 0.111711 0.193488i −0.804749 0.593615i \(-0.797700\pi\)
0.916460 + 0.400126i \(0.131034\pi\)
\(6\) −0.644738 1.11672i −0.263213 0.455898i
\(7\) 2.01488 + 3.48987i 0.761551 + 1.31905i 0.942051 + 0.335470i \(0.108895\pi\)
−0.180499 + 0.983575i \(0.557771\pi\)
\(8\) 1.25109 0.442326
\(9\) 1.31865 2.28397i 0.439549 0.761322i
\(10\) 0.534831 0.926355i 0.169128 0.292939i
\(11\) 1.14955 1.99108i 0.346603 0.600333i −0.639041 0.769173i \(-0.720669\pi\)
0.985644 + 0.168839i \(0.0540019\pi\)
\(12\) −0.778201 1.34788i −0.224647 0.389100i
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i
\(14\) 4.31405 + 7.47216i 1.15298 + 1.99702i
\(15\) −0.300874 −0.0776854
\(16\) −2.48993 −0.622483
\(17\) 0.938003 + 1.62467i 0.227499 + 0.394040i 0.957066 0.289869i \(-0.0936118\pi\)
−0.729567 + 0.683909i \(0.760278\pi\)
\(18\) 2.82336 4.89021i 0.665473 1.15263i
\(19\) −2.05191 3.55401i −0.470739 0.815345i 0.528700 0.848808i \(-0.322679\pi\)
−0.999440 + 0.0334638i \(0.989346\pi\)
\(20\) 0.645543 1.11811i 0.144348 0.250018i
\(21\) 1.21346 2.10177i 0.264798 0.458643i
\(22\) 2.46131 4.26311i 0.524752 0.908897i
\(23\) −4.23857 −0.883804 −0.441902 0.897063i \(-0.645696\pi\)
−0.441902 + 0.897063i \(0.645696\pi\)
\(24\) −0.376733 0.652520i −0.0769002 0.133195i
\(25\) 2.37521 + 4.11398i 0.475042 + 0.822796i
\(26\) −1.07055 + 1.85425i −0.209952 + 0.363648i
\(27\) −3.39505 −0.653378
\(28\) 5.20708 + 9.01893i 0.984046 + 1.70442i
\(29\) 6.47268 1.20195 0.600973 0.799269i \(-0.294780\pi\)
0.600973 + 0.799269i \(0.294780\pi\)
\(30\) −0.644202 −0.117615
\(31\) −4.97197 + 2.50589i −0.892993 + 0.450071i
\(32\) −7.83337 −1.38476
\(33\) −1.38463 −0.241033
\(34\) 2.00836 + 3.47858i 0.344431 + 0.596572i
\(35\) 2.01320 0.340293
\(36\) 3.40781 5.90250i 0.567968 0.983750i
\(37\) −4.34525 7.52619i −0.714354 1.23730i −0.963208 0.268757i \(-0.913387\pi\)
0.248854 0.968541i \(-0.419946\pi\)
\(38\) −4.39334 7.60949i −0.712694 1.23442i
\(39\) 0.602248 0.0964369
\(40\) 0.312512 0.541287i 0.0494125 0.0855850i
\(41\) −5.02057 + 8.69589i −0.784082 + 1.35807i 0.145464 + 0.989363i \(0.453532\pi\)
−0.929546 + 0.368706i \(0.879801\pi\)
\(42\) 2.59813 4.50010i 0.400900 0.694380i
\(43\) −5.16322 8.94295i −0.787383 1.36379i −0.927565 0.373662i \(-0.878102\pi\)
0.140182 0.990126i \(-0.455231\pi\)
\(44\) 2.97081 5.14559i 0.447866 0.775726i
\(45\) −0.658777 1.14103i −0.0982046 0.170095i
\(46\) −9.07522 −1.33807
\(47\) 5.34751 0.780015 0.390007 0.920812i \(-0.372472\pi\)
0.390007 + 0.920812i \(0.372472\pi\)
\(48\) 0.749779 + 1.29865i 0.108221 + 0.187445i
\(49\) −4.61944 + 8.00111i −0.659921 + 1.14302i
\(50\) 5.08556 + 8.80845i 0.719207 + 1.24570i
\(51\) 0.564911 0.978454i 0.0791033 0.137011i
\(52\) −1.29216 + 2.23809i −0.179190 + 0.310367i
\(53\) −4.26962 + 7.39519i −0.586477 + 1.01581i 0.408213 + 0.912887i \(0.366152\pi\)
−0.994690 + 0.102921i \(0.967181\pi\)
\(54\) −7.26915 −0.989207
\(55\) −0.574298 0.994713i −0.0774383 0.134127i
\(56\) 2.52079 + 4.36613i 0.336854 + 0.583448i
\(57\) −1.23576 + 2.14039i −0.163680 + 0.283502i
\(58\) 13.8587 1.81973
\(59\) 5.60232 + 9.70350i 0.729359 + 1.26329i 0.957154 + 0.289578i \(0.0935151\pi\)
−0.227795 + 0.973709i \(0.573152\pi\)
\(60\) −0.777555 −0.100382
\(61\) −8.92279 −1.14245 −0.571223 0.820795i \(-0.693531\pi\)
−0.571223 + 0.820795i \(0.693531\pi\)
\(62\) −10.6455 + 5.36537i −1.35198 + 0.681402i
\(63\) 10.6276 1.33896
\(64\) −11.7922 −1.47402
\(65\) 0.249792 + 0.432653i 0.0309829 + 0.0536640i
\(66\) −2.96463 −0.364921
\(67\) 3.45028 5.97606i 0.421519 0.730092i −0.574569 0.818456i \(-0.694830\pi\)
0.996088 + 0.0883635i \(0.0281637\pi\)
\(68\) 2.42410 + 4.19866i 0.293965 + 0.509163i
\(69\) 1.27634 + 2.21068i 0.153653 + 0.266135i
\(70\) 4.31047 0.515200
\(71\) −5.69504 + 9.86409i −0.675876 + 1.17065i 0.300336 + 0.953834i \(0.402901\pi\)
−0.976212 + 0.216819i \(0.930432\pi\)
\(72\) 1.64974 2.85744i 0.194424 0.336753i
\(73\) 5.64714 9.78114i 0.660948 1.14480i −0.319419 0.947614i \(-0.603488\pi\)
0.980367 0.197182i \(-0.0631789\pi\)
\(74\) −9.30362 16.1143i −1.08152 1.87325i
\(75\) 1.43046 2.47764i 0.165176 0.286093i
\(76\) −5.30278 9.18468i −0.608271 1.05356i
\(77\) 9.26480 1.05582
\(78\) 1.28948 0.146004
\(79\) 0.487117 + 0.843712i 0.0548050 + 0.0949250i 0.892126 0.451786i \(-0.149213\pi\)
−0.837321 + 0.546711i \(0.815880\pi\)
\(80\) −0.621966 + 1.07728i −0.0695379 + 0.120443i
\(81\) −2.93361 5.08117i −0.325957 0.564574i
\(82\) −10.7496 + 18.6188i −1.18709 + 2.05610i
\(83\) 0.735814 1.27447i 0.0807661 0.139891i −0.822813 0.568312i \(-0.807597\pi\)
0.903579 + 0.428421i \(0.140930\pi\)
\(84\) 3.13596 5.43163i 0.342161 0.592640i
\(85\) 0.937224 0.101656
\(86\) −11.0550 19.1478i −1.19209 2.06476i
\(87\) −1.94908 3.37591i −0.208963 0.361935i
\(88\) 1.43819 2.49102i 0.153311 0.265543i
\(89\) 0.499561 0.0529533 0.0264767 0.999649i \(-0.491571\pi\)
0.0264767 + 0.999649i \(0.491571\pi\)
\(90\) −1.41051 2.44307i −0.148681 0.257522i
\(91\) −4.02975 −0.422433
\(92\) −10.9538 −1.14202
\(93\) 2.80416 + 1.83861i 0.290778 + 0.190655i
\(94\) 11.4496 1.18093
\(95\) −2.05020 −0.210346
\(96\) 2.35882 + 4.08559i 0.240746 + 0.416984i
\(97\) 8.56900 0.870050 0.435025 0.900418i \(-0.356739\pi\)
0.435025 + 0.900418i \(0.356739\pi\)
\(98\) −9.89070 + 17.1312i −0.999112 + 1.73051i
\(99\) −3.03171 5.25107i −0.304698 0.527752i
\(100\) 6.13829 + 10.6318i 0.613829 + 1.06318i
\(101\) 5.68573 0.565751 0.282876 0.959157i \(-0.408712\pi\)
0.282876 + 0.959157i \(0.408712\pi\)
\(102\) 1.20953 2.09497i 0.119761 0.207433i
\(103\) −1.33511 + 2.31248i −0.131552 + 0.227855i −0.924275 0.381727i \(-0.875329\pi\)
0.792723 + 0.609582i \(0.208663\pi\)
\(104\) −0.625544 + 1.08347i −0.0613396 + 0.106243i
\(105\) −0.606224 1.05001i −0.0591614 0.102471i
\(106\) −9.14169 + 15.8339i −0.887919 + 1.53792i
\(107\) −6.48159 11.2264i −0.626599 1.08530i −0.988229 0.152980i \(-0.951113\pi\)
0.361630 0.932322i \(-0.382220\pi\)
\(108\) −8.77390 −0.844269
\(109\) 18.2487 1.74791 0.873956 0.486006i \(-0.161547\pi\)
0.873956 + 0.486006i \(0.161547\pi\)
\(110\) −1.22963 2.12978i −0.117241 0.203067i
\(111\) −2.61692 + 4.53263i −0.248387 + 0.430219i
\(112\) −5.01690 8.68953i −0.474053 0.821084i
\(113\) 6.60383 11.4382i 0.621236 1.07601i −0.368020 0.929818i \(-0.619964\pi\)
0.989256 0.146194i \(-0.0467024\pi\)
\(114\) −2.64588 + 4.58280i −0.247810 + 0.429219i
\(115\) −1.05876 + 1.83383i −0.0987302 + 0.171006i
\(116\) 16.7275 1.55311
\(117\) 1.31865 + 2.28397i 0.121909 + 0.211153i
\(118\) 11.9951 + 20.7762i 1.10424 + 1.91260i
\(119\) −3.77992 + 6.54701i −0.346504 + 0.600163i
\(120\) −0.376420 −0.0343623
\(121\) 2.85707 + 4.94859i 0.259733 + 0.449871i
\(122\) −19.1046 −1.72965
\(123\) 6.04726 0.545263
\(124\) −12.8492 + 6.47602i −1.15389 + 0.581564i
\(125\) 4.87116 0.435690
\(126\) 22.7549 2.02717
\(127\) −3.13031 5.42185i −0.277770 0.481111i 0.693060 0.720879i \(-0.256262\pi\)
−0.970830 + 0.239768i \(0.922929\pi\)
\(128\) −9.58154 −0.846897
\(129\) −3.10954 + 5.38588i −0.273780 + 0.474200i
\(130\) 0.534831 + 0.926355i 0.0469078 + 0.0812467i
\(131\) −5.87697 10.1792i −0.513473 0.889361i −0.999878 0.0156278i \(-0.995025\pi\)
0.486405 0.873734i \(-0.338308\pi\)
\(132\) −3.57833 −0.311453
\(133\) 8.26867 14.3218i 0.716984 1.24185i
\(134\) 7.38741 12.7954i 0.638175 1.10535i
\(135\) −0.848058 + 1.46888i −0.0729892 + 0.126421i
\(136\) 1.17352 + 2.03260i 0.100629 + 0.174294i
\(137\) 9.92619 17.1927i 0.848052 1.46887i −0.0348924 0.999391i \(-0.511109\pi\)
0.882944 0.469478i \(-0.155558\pi\)
\(138\) 2.73277 + 4.73329i 0.232629 + 0.402925i
\(139\) −0.264089 −0.0223998 −0.0111999 0.999937i \(-0.503565\pi\)
−0.0111999 + 0.999937i \(0.503565\pi\)
\(140\) 5.20276 0.439713
\(141\) −1.61027 2.78906i −0.135609 0.234881i
\(142\) −12.1937 + 21.1200i −1.02327 + 1.77235i
\(143\) 1.14955 + 1.99108i 0.0961302 + 0.166502i
\(144\) −3.28335 + 5.68692i −0.273612 + 0.473910i
\(145\) 1.61683 2.80042i 0.134270 0.232563i
\(146\) 12.0911 20.9424i 1.00067 1.73321i
\(147\) 5.56411 0.458920
\(148\) −11.2295 19.4501i −0.923060 1.59879i
\(149\) 7.58800 + 13.1428i 0.621634 + 1.07670i 0.989182 + 0.146696i \(0.0468640\pi\)
−0.367548 + 0.930005i \(0.619803\pi\)
\(150\) 3.06277 5.30488i 0.250074 0.433141i
\(151\) 4.28970 0.349091 0.174546 0.984649i \(-0.444154\pi\)
0.174546 + 0.984649i \(0.444154\pi\)
\(152\) −2.56711 4.44637i −0.208220 0.360648i
\(153\) 4.94758 0.399988
\(154\) 19.8369 1.59850
\(155\) −0.157780 + 2.77709i −0.0126732 + 0.223061i
\(156\) 1.55640 0.124612
\(157\) 21.0273 1.67816 0.839080 0.544009i \(-0.183094\pi\)
0.839080 + 0.544009i \(0.183094\pi\)
\(158\) 1.04297 + 1.80647i 0.0829741 + 0.143715i
\(159\) 5.14274 0.407846
\(160\) −1.95672 + 3.38913i −0.154692 + 0.267935i
\(161\) −8.54020 14.7921i −0.673062 1.16578i
\(162\) −6.28117 10.8793i −0.493495 0.854758i
\(163\) −3.33996 −0.261606 −0.130803 0.991408i \(-0.541755\pi\)
−0.130803 + 0.991408i \(0.541755\pi\)
\(164\) −12.9748 + 22.4729i −1.01316 + 1.75484i
\(165\) −0.345870 + 0.599064i −0.0269259 + 0.0466371i
\(166\) 1.57545 2.72876i 0.122279 0.211793i
\(167\) 0.372394 + 0.645006i 0.0288167 + 0.0499120i 0.880074 0.474836i \(-0.157493\pi\)
−0.851257 + 0.524748i \(0.824159\pi\)
\(168\) 1.51814 2.62949i 0.117127 0.202870i
\(169\) −0.500000 0.866025i −0.0384615 0.0666173i
\(170\) 2.00669 0.153906
\(171\) −10.8230 −0.827653
\(172\) −13.3434 23.1114i −1.01742 1.76223i
\(173\) −11.3449 + 19.6499i −0.862536 + 1.49396i 0.00693745 + 0.999976i \(0.497792\pi\)
−0.869473 + 0.493980i \(0.835542\pi\)
\(174\) −4.17318 7.22816i −0.316368 0.547965i
\(175\) −9.57149 + 16.5783i −0.723537 + 1.25320i
\(176\) −2.86230 + 4.95765i −0.215754 + 0.373697i
\(177\) 3.37399 5.84391i 0.253604 0.439255i
\(178\) 1.06961 0.0801707
\(179\) 5.83113 + 10.0998i 0.435839 + 0.754895i 0.997364 0.0725647i \(-0.0231184\pi\)
−0.561525 + 0.827460i \(0.689785\pi\)
\(180\) −1.70249 2.94880i −0.126896 0.219790i
\(181\) 1.74861 3.02868i 0.129973 0.225120i −0.793693 0.608319i \(-0.791844\pi\)
0.923666 + 0.383199i \(0.125178\pi\)
\(182\) −8.62811 −0.639558
\(183\) 2.68687 + 4.65379i 0.198619 + 0.344018i
\(184\) −5.30283 −0.390930
\(185\) −4.34164 −0.319204
\(186\) 6.00399 + 3.93665i 0.440234 + 0.288649i
\(187\) 4.31313 0.315407
\(188\) 13.8197 1.00790
\(189\) −6.84061 11.8483i −0.497581 0.861836i
\(190\) −4.38969 −0.318462
\(191\) −2.07410 + 3.59245i −0.150077 + 0.259941i −0.931255 0.364367i \(-0.881285\pi\)
0.781179 + 0.624307i \(0.214619\pi\)
\(192\) 3.55091 + 6.15036i 0.256265 + 0.443864i
\(193\) −9.16800 15.8794i −0.659927 1.14303i −0.980634 0.195849i \(-0.937254\pi\)
0.320707 0.947178i \(-0.396079\pi\)
\(194\) 18.3471 1.31725
\(195\) 0.150437 0.260565i 0.0107730 0.0186594i
\(196\) −11.9381 + 20.6774i −0.852723 + 1.47696i
\(197\) 8.98604 15.5643i 0.640229 1.10891i −0.345153 0.938546i \(-0.612173\pi\)
0.985382 0.170362i \(-0.0544937\pi\)
\(198\) −6.49119 11.2431i −0.461309 0.799011i
\(199\) −10.4843 + 18.1593i −0.743210 + 1.28728i 0.207816 + 0.978168i \(0.433365\pi\)
−0.951026 + 0.309110i \(0.899969\pi\)
\(200\) 2.97159 + 5.14695i 0.210123 + 0.363944i
\(201\) −4.15585 −0.293131
\(202\) 12.1737 0.856541
\(203\) 13.0416 + 22.5888i 0.915344 + 1.58542i
\(204\) 1.45991 2.52864i 0.102214 0.177040i
\(205\) 2.50820 + 4.34433i 0.175180 + 0.303421i
\(206\) −2.85860 + 4.95125i −0.199168 + 0.344970i
\(207\) −5.58919 + 9.68076i −0.388476 + 0.672859i
\(208\) 1.24497 2.15634i 0.0863229 0.149516i
\(209\) −9.43508 −0.652638
\(210\) −1.29799 2.24818i −0.0895696 0.155139i
\(211\) −1.14184 1.97773i −0.0786076 0.136152i 0.824042 0.566529i \(-0.191714\pi\)
−0.902649 + 0.430377i \(0.858381\pi\)
\(212\) −11.0341 + 19.1115i −0.757822 + 1.31259i
\(213\) 6.85965 0.470016
\(214\) −13.8778 24.0370i −0.948664 1.64313i
\(215\) −5.15893 −0.351836
\(216\) −4.24751 −0.289006
\(217\) −18.7631 12.3025i −1.27372 0.835146i
\(218\) 39.0724 2.64632
\(219\) −6.80196 −0.459634
\(220\) −1.48417 2.57066i −0.100063 0.173314i
\(221\) −1.87601 −0.126194
\(222\) −5.60309 + 9.70483i −0.376055 + 0.651346i
\(223\) −3.12789 5.41767i −0.209459 0.362794i 0.742085 0.670306i \(-0.233837\pi\)
−0.951544 + 0.307512i \(0.900504\pi\)
\(224\) −15.7833 27.3374i −1.05456 1.82656i
\(225\) 12.5283 0.835217
\(226\) 14.1395 24.4903i 0.940544 1.62907i
\(227\) −5.67796 + 9.83452i −0.376859 + 0.652740i −0.990603 0.136765i \(-0.956329\pi\)
0.613744 + 0.789505i \(0.289663\pi\)
\(228\) −3.19359 + 5.53146i −0.211501 + 0.366330i
\(229\) 5.57406 + 9.65456i 0.368344 + 0.637991i 0.989307 0.145849i \(-0.0465914\pi\)
−0.620962 + 0.783840i \(0.713258\pi\)
\(230\) −2.26692 + 3.92642i −0.149476 + 0.258901i
\(231\) −2.78986 4.83217i −0.183559 0.317934i
\(232\) 8.09789 0.531652
\(233\) −16.1482 −1.05791 −0.528953 0.848651i \(-0.677415\pi\)
−0.528953 + 0.848651i \(0.677415\pi\)
\(234\) 2.82336 + 4.89021i 0.184569 + 0.319683i
\(235\) 1.33577 2.31362i 0.0871359 0.150924i
\(236\) 14.4782 + 25.0769i 0.942449 + 1.63237i
\(237\) 0.293365 0.508124i 0.0190561 0.0330062i
\(238\) −8.09319 + 14.0178i −0.524604 + 0.908640i
\(239\) 2.51377 4.35398i 0.162602 0.281636i −0.773199 0.634164i \(-0.781345\pi\)
0.935801 + 0.352528i \(0.114678\pi\)
\(240\) 0.749156 0.0483578
\(241\) 14.6060 + 25.2983i 0.940855 + 1.62961i 0.763846 + 0.645399i \(0.223309\pi\)
0.177009 + 0.984209i \(0.443358\pi\)
\(242\) 6.11727 + 10.5954i 0.393233 + 0.681100i
\(243\) −6.85934 + 11.8807i −0.440027 + 0.762149i
\(244\) −23.0593 −1.47622
\(245\) 2.30780 + 3.99723i 0.147440 + 0.255374i
\(246\) 12.9478 0.825522
\(247\) 4.10381 0.261119
\(248\) −6.22037 + 3.13509i −0.394994 + 0.199078i
\(249\) −0.886285 −0.0561661
\(250\) 10.4297 0.659629
\(251\) −1.58991 2.75381i −0.100354 0.173819i 0.811476 0.584385i \(-0.198664\pi\)
−0.911831 + 0.410567i \(0.865331\pi\)
\(252\) 27.4652 1.73015
\(253\) −4.87246 + 8.43934i −0.306329 + 0.530577i
\(254\) −6.70230 11.6087i −0.420540 0.728397i
\(255\) −0.282221 0.488821i −0.0176733 0.0306111i
\(256\) 3.06932 0.191833
\(257\) 2.94786 5.10584i 0.183882 0.318494i −0.759317 0.650721i \(-0.774467\pi\)
0.943199 + 0.332227i \(0.107800\pi\)
\(258\) −6.65784 + 11.5317i −0.414499 + 0.717933i
\(259\) 17.5103 30.3287i 1.08803 1.88453i
\(260\) 0.645543 + 1.11811i 0.0400349 + 0.0693425i
\(261\) 8.53519 14.7834i 0.528315 0.915068i
\(262\) −12.5832 21.7947i −0.777392 1.34648i
\(263\) 14.2010 0.875671 0.437835 0.899055i \(-0.355745\pi\)
0.437835 + 0.899055i \(0.355745\pi\)
\(264\) −1.73229 −0.106615
\(265\) 2.13304 + 3.69453i 0.131031 + 0.226953i
\(266\) 17.7041 30.6643i 1.08551 1.88015i
\(267\) −0.150430 0.260552i −0.00920615 0.0159455i
\(268\) 8.91663 15.4441i 0.544670 0.943396i
\(269\) −3.02456 + 5.23869i −0.184411 + 0.319409i −0.943378 0.331720i \(-0.892371\pi\)
0.758967 + 0.651129i \(0.225704\pi\)
\(270\) −1.81578 + 3.14502i −0.110505 + 0.191400i
\(271\) 2.25483 0.136971 0.0684855 0.997652i \(-0.478183\pi\)
0.0684855 + 0.997652i \(0.478183\pi\)
\(272\) −2.33556 4.04531i −0.141614 0.245283i
\(273\) 1.21346 + 2.10177i 0.0734417 + 0.127205i
\(274\) 21.2530 36.8113i 1.28394 2.22385i
\(275\) 10.9217 0.658602
\(276\) 3.29846 + 5.71311i 0.198544 + 0.343889i
\(277\) 5.33059 0.320284 0.160142 0.987094i \(-0.448805\pi\)
0.160142 + 0.987094i \(0.448805\pi\)
\(278\) −0.565442 −0.0339130
\(279\) −0.832916 + 14.6602i −0.0498654 + 0.877684i
\(280\) 2.51869 0.150521
\(281\) −1.50192 −0.0895970 −0.0447985 0.998996i \(-0.514265\pi\)
−0.0447985 + 0.998996i \(0.514265\pi\)
\(282\) −3.44774 5.97167i −0.205310 0.355608i
\(283\) −0.381449 −0.0226748 −0.0113374 0.999936i \(-0.503609\pi\)
−0.0113374 + 0.999936i \(0.503609\pi\)
\(284\) −14.7178 + 25.4920i −0.873340 + 1.51267i
\(285\) 0.617365 + 1.06931i 0.0365696 + 0.0633403i
\(286\) 2.46131 + 4.26311i 0.145540 + 0.252083i
\(287\) −40.4633 −2.38847
\(288\) −10.3295 + 17.8912i −0.608670 + 1.05425i
\(289\) 6.74030 11.6745i 0.396488 0.686738i
\(290\) 3.46179 5.99600i 0.203283 0.352097i
\(291\) −2.58033 4.46927i −0.151262 0.261993i
\(292\) 14.5940 25.2776i 0.854050 1.47926i
\(293\) −2.48423 4.30281i −0.145130 0.251373i 0.784291 0.620393i \(-0.213027\pi\)
−0.929421 + 0.369020i \(0.879693\pi\)
\(294\) 11.9133 0.694799
\(295\) 5.59766 0.325909
\(296\) −5.43628 9.41592i −0.315978 0.547289i
\(297\) −3.90278 + 6.75982i −0.226463 + 0.392245i
\(298\) 16.2467 + 28.1401i 0.941146 + 1.63011i
\(299\) 2.11929 3.67071i 0.122562 0.212283i
\(300\) 3.69678 6.40301i 0.213434 0.369678i
\(301\) 20.8065 36.0379i 1.19927 2.07719i
\(302\) 9.18470 0.528520
\(303\) −1.71211 2.96546i −0.0983582 0.170361i
\(304\) 5.10911 + 8.84923i 0.293027 + 0.507538i
\(305\) −2.22885 + 3.86047i −0.127623 + 0.221050i
\(306\) 10.5933 0.605578
\(307\) −11.0598 19.1561i −0.631216 1.09330i −0.987304 0.158845i \(-0.949223\pi\)
0.356088 0.934452i \(-0.384110\pi\)
\(308\) 23.9432 1.36429
\(309\) 1.60813 0.0914835
\(310\) −0.337823 + 5.94604i −0.0191870 + 0.337712i
\(311\) −10.7972 −0.612253 −0.306127 0.951991i \(-0.599033\pi\)
−0.306127 + 0.951991i \(0.599033\pi\)
\(312\) 0.753465 0.0426566
\(313\) 15.1342 + 26.2132i 0.855436 + 1.48166i 0.876240 + 0.481875i \(0.160044\pi\)
−0.0208035 + 0.999784i \(0.506622\pi\)
\(314\) 45.0215 2.54071
\(315\) 2.65471 4.59809i 0.149576 0.259073i
\(316\) 1.25887 + 2.18042i 0.0708168 + 0.122658i
\(317\) 4.77770 + 8.27522i 0.268343 + 0.464783i 0.968434 0.249270i \(-0.0801908\pi\)
−0.700091 + 0.714053i \(0.746857\pi\)
\(318\) 11.0111 0.617473
\(319\) 7.44067 12.8876i 0.416598 0.721568i
\(320\) −2.94560 + 5.10193i −0.164664 + 0.285207i
\(321\) −3.90353 + 6.76111i −0.217874 + 0.377368i
\(322\) −18.2854 31.6713i −1.01901 1.76497i
\(323\) 3.84939 6.66733i 0.214186 0.370980i
\(324\) −7.58139 13.1314i −0.421189 0.729520i
\(325\) −4.75042 −0.263506
\(326\) −7.15119 −0.396068
\(327\) −5.49513 9.51785i −0.303882 0.526338i
\(328\) −6.28118 + 10.8793i −0.346820 + 0.600710i
\(329\) 10.7746 + 18.6621i 0.594021 + 1.02888i
\(330\) −0.740543 + 1.28266i −0.0407656 + 0.0706080i
\(331\) −8.03062 + 13.9094i −0.441403 + 0.764532i −0.997794 0.0663885i \(-0.978852\pi\)
0.556391 + 0.830921i \(0.312186\pi\)
\(332\) 1.90158 3.29363i 0.104363 0.180761i
\(333\) −22.9194 −1.25598
\(334\) 0.797334 + 1.38102i 0.0436282 + 0.0755662i
\(335\) −1.72371 2.98555i −0.0941763 0.163118i
\(336\) −3.02142 + 5.23326i −0.164832 + 0.285497i
\(337\) −26.0079 −1.41674 −0.708369 0.705842i \(-0.750569\pi\)
−0.708369 + 0.705842i \(0.750569\pi\)
\(338\) −1.07055 1.85425i −0.0582303 0.100858i
\(339\) −7.95429 −0.432018
\(340\) 2.42209 0.131356
\(341\) −0.726106 + 12.7802i −0.0393209 + 0.692089i
\(342\) −23.1731 −1.25306
\(343\) −9.02217 −0.487151
\(344\) −6.45963 11.1884i −0.348280 0.603239i
\(345\) 1.27528 0.0686586
\(346\) −24.2906 + 42.0725i −1.30587 + 2.26183i
\(347\) 16.6751 + 28.8821i 0.895167 + 1.55047i 0.833598 + 0.552372i \(0.186277\pi\)
0.0615693 + 0.998103i \(0.480389\pi\)
\(348\) −5.03704 8.72442i −0.270014 0.467678i
\(349\) −6.99731 −0.374558 −0.187279 0.982307i \(-0.559967\pi\)
−0.187279 + 0.982307i \(0.559967\pi\)
\(350\) −20.4935 + 35.4959i −1.09543 + 1.89733i
\(351\) 1.69753 2.94020i 0.0906072 0.156936i
\(352\) −9.00486 + 15.5969i −0.479961 + 0.831316i
\(353\) −9.26765 16.0520i −0.493267 0.854364i 0.506703 0.862121i \(-0.330864\pi\)
−0.999970 + 0.00775705i \(0.997531\pi\)
\(354\) 7.22405 12.5124i 0.383954 0.665027i
\(355\) 2.84515 + 4.92795i 0.151005 + 0.261548i
\(356\) 1.29102 0.0684242
\(357\) 4.55290 0.240965
\(358\) 12.4850 + 21.6247i 0.659855 + 1.14290i
\(359\) −9.57736 + 16.5885i −0.505474 + 0.875506i 0.494506 + 0.869174i \(0.335349\pi\)
−0.999980 + 0.00633219i \(0.997984\pi\)
\(360\) −0.824187 1.42753i −0.0434385 0.0752377i
\(361\) 1.07937 1.86952i 0.0568087 0.0983956i
\(362\) 3.74395 6.48471i 0.196778 0.340829i
\(363\) 1.72066 2.98028i 0.0903114 0.156424i
\(364\) −10.4142 −0.545850
\(365\) −2.82123 4.88651i −0.147670 0.255771i
\(366\) 5.75286 + 9.96425i 0.300707 + 0.520839i
\(367\) −4.92909 + 8.53744i −0.257296 + 0.445650i −0.965517 0.260341i \(-0.916165\pi\)
0.708220 + 0.705992i \(0.249498\pi\)
\(368\) 10.5538 0.550153
\(369\) 13.2407 + 22.9336i 0.689285 + 1.19388i
\(370\) −9.29589 −0.483270
\(371\) −34.4110 −1.78653
\(372\) 7.24684 + 4.75155i 0.375731 + 0.246357i
\(373\) 6.33943 0.328243 0.164122 0.986440i \(-0.447521\pi\)
0.164122 + 0.986440i \(0.447521\pi\)
\(374\) 9.23485 0.477522
\(375\) −1.46682 2.54061i −0.0757465 0.131197i
\(376\) 6.69021 0.345021
\(377\) −3.23634 + 5.60550i −0.166680 + 0.288698i
\(378\) −14.6464 25.3684i −0.753332 1.30481i
\(379\) −10.1840 17.6392i −0.523118 0.906067i −0.999638 0.0269031i \(-0.991435\pi\)
0.476520 0.879163i \(-0.341898\pi\)
\(380\) −5.29838 −0.271801
\(381\) −1.88522 + 3.26530i −0.0965828 + 0.167286i
\(382\) −4.44087 + 7.69180i −0.227214 + 0.393547i
\(383\) −1.66590 + 2.88542i −0.0851233 + 0.147438i −0.905444 0.424466i \(-0.860462\pi\)
0.820320 + 0.571904i \(0.193795\pi\)
\(384\) 2.88523 + 4.99737i 0.147236 + 0.255021i
\(385\) 2.31428 4.00845i 0.117947 0.204289i
\(386\) −19.6296 33.9995i −0.999122 1.73053i
\(387\) −27.2339 −1.38438
\(388\) 22.1450 1.12424
\(389\) −15.0700 26.1021i −0.764081 1.32343i −0.940731 0.339153i \(-0.889859\pi\)
0.176650 0.984274i \(-0.443474\pi\)
\(390\) 0.322101 0.557896i 0.0163102 0.0282501i
\(391\) −3.97580 6.88628i −0.201065 0.348254i
\(392\) −5.77933 + 10.0101i −0.291900 + 0.505586i
\(393\) −3.53939 + 6.13041i −0.178539 + 0.309238i
\(394\) 19.2400 33.3247i 0.969298 1.67887i
\(395\) 0.486713 0.0244892
\(396\) −7.83490 13.5704i −0.393718 0.681940i
\(397\) −13.7673 23.8456i −0.690959 1.19678i −0.971524 0.236941i \(-0.923855\pi\)
0.280565 0.959835i \(-0.409478\pi\)
\(398\) −22.4479 + 38.8809i −1.12521 + 1.94892i
\(399\) −9.95958 −0.498603
\(400\) −5.91411 10.2435i −0.295705 0.512177i
\(401\) 30.2799 1.51211 0.756053 0.654511i \(-0.227125\pi\)
0.756053 + 0.654511i \(0.227125\pi\)
\(402\) −8.89811 −0.443797
\(403\) 0.315822 5.55880i 0.0157322 0.276904i
\(404\) 14.6937 0.731041
\(405\) −2.93118 −0.145651
\(406\) 27.9235 + 48.3649i 1.38582 + 2.40031i
\(407\) −19.9803 −0.990388
\(408\) 0.706753 1.22413i 0.0349895 0.0606035i
\(409\) −12.0981 20.9546i −0.598214 1.03614i −0.993085 0.117401i \(-0.962544\pi\)
0.394870 0.918737i \(-0.370790\pi\)
\(410\) 5.37032 + 9.30166i 0.265221 + 0.459376i
\(411\) −11.9561 −0.589749
\(412\) −3.45035 + 5.97618i −0.169986 + 0.294425i
\(413\) −22.5759 + 39.1027i −1.11089 + 1.92412i
\(414\) −11.9670 + 20.7275i −0.588147 + 1.01870i
\(415\) −0.367602 0.636704i −0.0180448 0.0312546i
\(416\) 3.91669 6.78390i 0.192031 0.332608i
\(417\) 0.0795236 + 0.137739i 0.00389429 + 0.00674511i
\(418\) −20.2015 −0.988086
\(419\) 0.857869 0.0419096 0.0209548 0.999780i \(-0.493329\pi\)
0.0209548 + 0.999780i \(0.493329\pi\)
\(420\) −1.56668 2.71356i −0.0764460 0.132408i
\(421\) 11.5427 19.9925i 0.562554 0.974373i −0.434718 0.900567i \(-0.643152\pi\)
0.997273 0.0738063i \(-0.0235147\pi\)
\(422\) −2.44480 4.23452i −0.119011 0.206133i
\(423\) 7.05149 12.2135i 0.342855 0.593843i
\(424\) −5.34166 + 9.25203i −0.259414 + 0.449318i
\(425\) −4.45590 + 7.71785i −0.216143 + 0.374371i
\(426\) 14.6872 0.711598
\(427\) −17.9783 31.1394i −0.870032 1.50694i
\(428\) −16.7505 29.0127i −0.809666 1.40238i
\(429\) 0.692315 1.19912i 0.0334253 0.0578943i
\(430\) −11.0458 −0.532675
\(431\) 2.96685 + 5.13873i 0.142908 + 0.247524i 0.928590 0.371106i \(-0.121021\pi\)
−0.785683 + 0.618630i \(0.787688\pi\)
\(432\) 8.45345 0.406717
\(433\) −26.2879 −1.26331 −0.631657 0.775248i \(-0.717625\pi\)
−0.631657 + 0.775248i \(0.717625\pi\)
\(434\) −40.1738 26.3408i −1.92840 1.26440i
\(435\) −1.94746 −0.0933736
\(436\) 47.1605 2.25858
\(437\) 8.69716 + 15.0639i 0.416041 + 0.720605i
\(438\) −14.5637 −0.695880
\(439\) −4.86495 + 8.42634i −0.232191 + 0.402167i −0.958453 0.285251i \(-0.907923\pi\)
0.726261 + 0.687419i \(0.241256\pi\)
\(440\) −0.718497 1.24447i −0.0342530 0.0593279i
\(441\) 12.1828 + 21.1013i 0.580136 + 1.00482i
\(442\) −4.01672 −0.191056
\(443\) −13.4526 + 23.3006i −0.639154 + 1.10705i 0.346465 + 0.938063i \(0.387382\pi\)
−0.985619 + 0.168984i \(0.945951\pi\)
\(444\) −6.76295 + 11.7138i −0.320955 + 0.555911i
\(445\) 0.124786 0.216137i 0.00591545 0.0102459i
\(446\) −6.69714 11.5998i −0.317119 0.549266i
\(447\) 4.56986 7.91523i 0.216147 0.374378i
\(448\) −23.7598 41.1532i −1.12254 1.94430i
\(449\) 0.801101 0.0378063 0.0189032 0.999821i \(-0.493983\pi\)
0.0189032 + 0.999821i \(0.493983\pi\)
\(450\) 26.8243 1.26451
\(451\) 11.5428 + 19.9927i 0.543529 + 0.941421i
\(452\) 17.0664 29.5599i 0.802736 1.39038i
\(453\) −1.29173 2.23735i −0.0606909 0.105120i
\(454\) −12.1571 + 21.0567i −0.570561 + 0.988240i
\(455\) −1.00660 + 1.74348i −0.0471902 + 0.0817358i
\(456\) −1.54604 + 2.67782i −0.0723999 + 0.125400i
\(457\) 9.22192 0.431383 0.215692 0.976462i \(-0.430799\pi\)
0.215692 + 0.976462i \(0.430799\pi\)
\(458\) 11.9346 + 20.6714i 0.557669 + 0.965911i
\(459\) −3.18457 5.51584i −0.148643 0.257457i
\(460\) −2.73618 + 4.73921i −0.127575 + 0.220967i
\(461\) −13.5273 −0.630030 −0.315015 0.949087i \(-0.602009\pi\)
−0.315015 + 0.949087i \(0.602009\pi\)
\(462\) −5.97337 10.3462i −0.277906 0.481348i
\(463\) −15.2980 −0.710960 −0.355480 0.934684i \(-0.615683\pi\)
−0.355480 + 0.934684i \(0.615683\pi\)
\(464\) −16.1165 −0.748191
\(465\) 1.49594 0.753957i 0.0693725 0.0349639i
\(466\) −34.5750 −1.60166
\(467\) 12.3764 0.572710 0.286355 0.958124i \(-0.407556\pi\)
0.286355 + 0.958124i \(0.407556\pi\)
\(468\) 3.40781 + 5.90250i 0.157526 + 0.272843i
\(469\) 27.8076 1.28403
\(470\) 2.86002 4.95369i 0.131923 0.228497i
\(471\) −6.33182 10.9670i −0.291755 0.505334i
\(472\) 7.00899 + 12.1399i 0.322615 + 0.558785i
\(473\) −23.7415 −1.09164
\(474\) 0.628126 1.08795i 0.0288508 0.0499710i
\(475\) 9.74740 16.8830i 0.447242 0.774645i
\(476\) −9.76851 + 16.9196i −0.447739 + 0.775507i
\(477\) 11.2602 + 19.5033i 0.515571 + 0.892996i
\(478\) 5.38224 9.32232i 0.246178 0.426393i
\(479\) −0.474937 0.822614i −0.0217004 0.0375862i 0.854971 0.518675i \(-0.173575\pi\)
−0.876672 + 0.481089i \(0.840241\pi\)
\(480\) 2.35686 0.107575
\(481\) 8.69049 0.396252
\(482\) 31.2729 + 54.1663i 1.42444 + 2.46721i
\(483\) −5.14332 + 8.90849i −0.234029 + 0.405350i
\(484\) 7.38357 + 12.7887i 0.335617 + 0.581306i
\(485\) 2.14047 3.70741i 0.0971938 0.168345i
\(486\) −14.6866 + 25.4379i −0.666196 + 1.15388i
\(487\) 7.40653 12.8285i 0.335622 0.581314i −0.647982 0.761656i \(-0.724387\pi\)
0.983604 + 0.180341i \(0.0577202\pi\)
\(488\) −11.1632 −0.505334
\(489\) 1.00574 + 1.74200i 0.0454812 + 0.0787758i
\(490\) 4.94125 + 8.55849i 0.223223 + 0.386633i
\(491\) −4.74094 + 8.21155i −0.213956 + 0.370582i −0.952949 0.303131i \(-0.901968\pi\)
0.738993 + 0.673713i \(0.235301\pi\)
\(492\) 15.6281 0.704567
\(493\) 6.07139 + 10.5160i 0.273442 + 0.473615i
\(494\) 8.78668 0.395331
\(495\) −3.02919 −0.136152
\(496\) 12.3799 6.23950i 0.555873 0.280162i
\(497\) −45.8991 −2.05886
\(498\) −1.89763 −0.0850347
\(499\) −18.4128 31.8919i −0.824269 1.42768i −0.902477 0.430739i \(-0.858253\pi\)
0.0782078 0.996937i \(-0.475080\pi\)
\(500\) 12.5886 0.562981
\(501\) 0.224274 0.388454i 0.0100198 0.0173548i
\(502\) −3.40416 5.89618i −0.151935 0.263160i
\(503\) 3.63550 + 6.29686i 0.162099 + 0.280763i 0.935621 0.353006i \(-0.114840\pi\)
−0.773522 + 0.633769i \(0.781507\pi\)
\(504\) 13.2961 0.592256
\(505\) 1.42025 2.45995i 0.0632004 0.109466i
\(506\) −10.4324 + 18.0695i −0.463778 + 0.803287i
\(507\) −0.301124 + 0.521562i −0.0133734 + 0.0231634i
\(508\) −8.08971 14.0118i −0.358923 0.621673i
\(509\) −16.1632 + 27.9956i −0.716423 + 1.24088i 0.245985 + 0.969274i \(0.420889\pi\)
−0.962408 + 0.271608i \(0.912445\pi\)
\(510\) −0.604264 1.04662i −0.0267572 0.0463449i
\(511\) 45.5131 2.01338
\(512\) 25.7348 1.13733
\(513\) 6.96633 + 12.0660i 0.307571 + 0.532728i
\(514\) 6.31167 10.9321i 0.278396 0.482195i
\(515\) 0.667000 + 1.15528i 0.0293915 + 0.0509076i
\(516\) −8.03604 + 13.9188i −0.353767 + 0.612742i
\(517\) 6.14724 10.6473i 0.270355 0.468269i
\(518\) 37.4913 64.9368i 1.64727 2.85316i
\(519\) 13.6649 0.599822
\(520\) 0.312512 + 0.541287i 0.0137046 + 0.0237370i
\(521\) 4.48863 + 7.77454i 0.196650 + 0.340609i 0.947440 0.319933i \(-0.103660\pi\)
−0.750790 + 0.660541i \(0.770327\pi\)
\(522\) 18.2747 31.6527i 0.799862 1.38540i
\(523\) 15.6380 0.683804 0.341902 0.939736i \(-0.388929\pi\)
0.341902 + 0.939736i \(0.388929\pi\)
\(524\) −15.1880 26.3063i −0.663489 1.14920i
\(525\) 11.5288 0.503159
\(526\) 30.4058 1.32576
\(527\) −8.73497 5.72728i −0.380501 0.249484i
\(528\) 3.44763 0.150039
\(529\) −5.03448 −0.218891
\(530\) 4.56705 + 7.91036i 0.198380 + 0.343604i
\(531\) 29.5499 1.28236
\(532\) 21.3689 37.0120i 0.926458 1.60467i
\(533\) −5.02057 8.69589i −0.217465 0.376661i
\(534\) −0.322086 0.557869i −0.0139380 0.0241413i
\(535\) −6.47621 −0.279991
\(536\) 4.31660 7.47658i 0.186449 0.322939i
\(537\) 3.51179 6.08259i 0.151545 0.262483i
\(538\) −6.47590 + 11.2166i −0.279196 + 0.483581i
\(539\) 10.6206 + 18.3954i 0.457460 + 0.792345i
\(540\) −2.19165 + 3.79606i −0.0943138 + 0.163356i
\(541\) 1.68124 + 2.91199i 0.0722820 + 0.125196i 0.899901 0.436094i \(-0.143639\pi\)
−0.827619 + 0.561290i \(0.810305\pi\)
\(542\) 4.82782 0.207372
\(543\) −2.10619 −0.0903854
\(544\) −7.34773 12.7266i −0.315031 0.545650i
\(545\) 4.55839 7.89537i 0.195260 0.338201i
\(546\) 2.59813 + 4.50010i 0.111190 + 0.192586i
\(547\) 2.70281 4.68140i 0.115564 0.200162i −0.802441 0.596731i \(-0.796466\pi\)
0.918005 + 0.396569i \(0.129799\pi\)
\(548\) 25.6525 44.4313i 1.09582 1.89801i
\(549\) −11.7660 + 20.3794i −0.502162 + 0.869770i
\(550\) 23.3844 0.997116
\(551\) −13.2813 23.0039i −0.565804 0.980000i
\(552\) 1.59681 + 2.76576i 0.0679647 + 0.117718i
\(553\) −1.96296 + 3.39995i −0.0834736 + 0.144580i
\(554\) 11.4133 0.484906
\(555\) 1.30737 + 2.26444i 0.0554949 + 0.0961199i
\(556\) −0.682491 −0.0289441
\(557\) −4.53565 −0.192182 −0.0960908 0.995373i \(-0.530634\pi\)
−0.0960908 + 0.995373i \(0.530634\pi\)
\(558\) −1.78336 + 31.3890i −0.0754956 + 1.32880i
\(559\) 10.3264 0.436761
\(560\) −5.01274 −0.211827
\(561\) −1.29879 2.24956i −0.0548348 0.0949767i
\(562\) −3.21576 −0.135649
\(563\) 4.39876 7.61887i 0.185386 0.321097i −0.758321 0.651882i \(-0.773980\pi\)
0.943706 + 0.330784i \(0.107313\pi\)
\(564\) −4.16144 7.20782i −0.175228 0.303504i
\(565\) −3.29917 5.71433i −0.138797 0.240404i
\(566\) −0.816722 −0.0343294
\(567\) 11.8217 20.4758i 0.496466 0.859904i
\(568\) −7.12499 + 12.3408i −0.298958 + 0.517810i
\(569\) −20.7601 + 35.9575i −0.870308 + 1.50742i −0.00862879 + 0.999963i \(0.502747\pi\)
−0.861679 + 0.507454i \(0.830587\pi\)
\(570\) 1.32184 + 2.28950i 0.0553659 + 0.0958965i
\(571\) −22.4133 + 38.8210i −0.937969 + 1.62461i −0.168716 + 0.985665i \(0.553962\pi\)
−0.769253 + 0.638945i \(0.779371\pi\)
\(572\) 2.97081 + 5.14559i 0.124216 + 0.215148i
\(573\) 2.49825 0.104366
\(574\) −86.6361 −3.61612
\(575\) −10.0675 17.4374i −0.419844 0.727190i
\(576\) −15.5498 + 26.9330i −0.647907 + 1.12221i
\(577\) 3.17562 + 5.50034i 0.132203 + 0.228982i 0.924525 0.381120i \(-0.124462\pi\)
−0.792323 + 0.610102i \(0.791128\pi\)
\(578\) 14.4317 24.9964i 0.600279 1.03971i
\(579\) −5.52141 + 9.56337i −0.229462 + 0.397440i
\(580\) 4.17839 7.23719i 0.173498 0.300508i
\(581\) 5.93029 0.246030
\(582\) −5.52476 9.56916i −0.229009 0.396655i
\(583\) 9.81628 + 17.0023i 0.406549 + 0.704163i
\(584\) 7.06507 12.2371i 0.292355 0.506373i
\(585\) 1.31755 0.0544741
\(586\) −5.31898 9.21275i −0.219725 0.380575i
\(587\) 26.7946 1.10593 0.552967 0.833203i \(-0.313496\pi\)
0.552967 + 0.833203i \(0.313496\pi\)
\(588\) 14.3794 0.592998
\(589\) 19.1080 + 12.5286i 0.787330 + 0.516231i
\(590\) 11.9852 0.493422
\(591\) −10.8237 −0.445226
\(592\) 10.8194 + 18.7397i 0.444673 + 0.770197i
\(593\) 25.2464 1.03675 0.518374 0.855154i \(-0.326538\pi\)
0.518374 + 0.855154i \(0.326538\pi\)
\(594\) −8.35626 + 14.4735i −0.342862 + 0.593854i
\(595\) 1.88839 + 3.27079i 0.0774164 + 0.134089i
\(596\) 19.6098 + 33.9652i 0.803250 + 1.39127i
\(597\) 12.6283 0.516841
\(598\) 4.53761 7.85937i 0.185557 0.321394i
\(599\) 21.0874 36.5244i 0.861608 1.49235i −0.00876879 0.999962i \(-0.502791\pi\)
0.870377 0.492387i \(-0.163875\pi\)
\(600\) 1.78964 3.09974i 0.0730616 0.126546i
\(601\) −0.947188 1.64058i −0.0386366 0.0669206i 0.846060 0.533087i \(-0.178968\pi\)
−0.884697 + 0.466166i \(0.845635\pi\)
\(602\) 44.5488 77.1608i 1.81567 3.14484i
\(603\) −9.09942 15.7607i −0.370557 0.641824i
\(604\) 11.0860 0.451082
\(605\) 2.85469 0.116060
\(606\) −3.66581 6.34936i −0.148913 0.257925i
\(607\) −6.13743 + 10.6303i −0.249111 + 0.431472i −0.963279 0.268502i \(-0.913472\pi\)
0.714169 + 0.699974i \(0.246805\pi\)
\(608\) 16.0733 + 27.8399i 0.651860 + 1.12906i
\(609\) 7.85431 13.6041i 0.318273 0.551264i
\(610\) −4.77219 + 8.26567i −0.193220 + 0.334667i
\(611\) −2.67376 + 4.63108i −0.108169 + 0.187354i
\(612\) 12.7861 0.516849
\(613\) −0.883703 1.53062i −0.0356924 0.0618211i 0.847627 0.530592i \(-0.178030\pi\)
−0.883320 + 0.468771i \(0.844697\pi\)
\(614\) −23.6801 41.0152i −0.955653 1.65524i
\(615\) 1.51056 2.61637i 0.0609117 0.105502i
\(616\) 11.5911 0.467018
\(617\) 4.23109 + 7.32846i 0.170337 + 0.295033i 0.938538 0.345177i \(-0.112181\pi\)
−0.768201 + 0.640209i \(0.778848\pi\)
\(618\) 3.44318 0.138505
\(619\) −30.7408 −1.23558 −0.617788 0.786345i \(-0.711971\pi\)
−0.617788 + 0.786345i \(0.711971\pi\)
\(620\) −0.407753 + 7.17689i −0.0163758 + 0.288231i
\(621\) 14.3902 0.577458
\(622\) −23.1179 −0.926944
\(623\) 1.00655 + 1.74340i 0.0403267 + 0.0698479i
\(624\) −1.49956 −0.0600303
\(625\) −10.6593 + 18.4624i −0.426370 + 0.738495i
\(626\) 32.4039 + 56.1252i 1.29512 + 2.24321i
\(627\) 2.84113 + 4.92098i 0.113464 + 0.196525i
\(628\) 54.3412 2.16845
\(629\) 8.15171 14.1192i 0.325030 0.562968i
\(630\) 5.68400 9.84497i 0.226456 0.392233i
\(631\) 22.2951 38.6162i 0.887554 1.53729i 0.0447958 0.998996i \(-0.485736\pi\)
0.842758 0.538292i \(-0.180930\pi\)
\(632\) 0.609426 + 1.05556i 0.0242417 + 0.0419878i
\(633\) −0.687672 + 1.19108i −0.0273325 + 0.0473413i
\(634\) 10.2296 + 17.7181i 0.406267 + 0.703676i
\(635\) −3.12771 −0.124119
\(636\) 13.2905 0.527002
\(637\) −4.61944 8.00111i −0.183029 0.317016i
\(638\) 15.9312 27.5937i 0.630724 1.09245i
\(639\) 15.0195 + 26.0145i 0.594162 + 1.02912i
\(640\) −2.39340 + 4.14548i −0.0946073 + 0.163865i
\(641\) −5.40987 + 9.37017i −0.213677 + 0.370099i −0.952862 0.303403i \(-0.901877\pi\)
0.739186 + 0.673502i \(0.235211\pi\)
\(642\) −8.35785 + 14.4762i −0.329858 + 0.571331i
\(643\) 6.31086 0.248876 0.124438 0.992227i \(-0.460287\pi\)
0.124438 + 0.992227i \(0.460287\pi\)
\(644\) −22.0706 38.2274i −0.869704 1.50637i
\(645\) 1.55348 + 2.69070i 0.0611681 + 0.105946i
\(646\) 8.24193 14.2754i 0.324274 0.561660i
\(647\) 4.44275 0.174663 0.0873313 0.996179i \(-0.472166\pi\)
0.0873313 + 0.996179i \(0.472166\pi\)
\(648\) −3.67021 6.35698i −0.144179 0.249726i
\(649\) 25.7606 1.01119
\(650\) −10.1711 −0.398944
\(651\) −0.766471 + 13.4907i −0.0300404 + 0.528743i
\(652\) −8.63151 −0.338036
\(653\) 24.0053 0.939402 0.469701 0.882826i \(-0.344362\pi\)
0.469701 + 0.882826i \(0.344362\pi\)
\(654\) −11.7656 20.3787i −0.460073 0.796870i
\(655\) −5.87209 −0.229441
\(656\) 12.5009 21.6522i 0.488078 0.845375i
\(657\) −14.8932 25.7958i −0.581039 1.00639i
\(658\) 23.0695 + 39.9575i 0.899341 + 1.55770i
\(659\) −23.7302 −0.924396 −0.462198 0.886777i \(-0.652939\pi\)
−0.462198 + 0.886777i \(0.652939\pi\)
\(660\) −0.893838 + 1.54817i −0.0347926 + 0.0602626i
\(661\) 22.0903 38.2615i 0.859212 1.48820i −0.0134704 0.999909i \(-0.504288\pi\)
0.872682 0.488289i \(-0.162379\pi\)
\(662\) −17.1944 + 29.7815i −0.668279 + 1.15749i
\(663\) 0.564911 + 0.978454i 0.0219393 + 0.0380000i
\(664\) 0.920568 1.59447i 0.0357250 0.0618774i
\(665\) −4.13090 7.15493i −0.160189 0.277456i
\(666\) −49.0728 −1.90153
\(667\) −27.4349 −1.06228
\(668\) 0.962386 + 1.66690i 0.0372358 + 0.0644943i
\(669\) −1.88377 + 3.26278i −0.0728307 + 0.126147i
\(670\) −3.69064 6.39237i −0.142582 0.246959i
\(671\) −10.2572 + 17.7660i −0.395975 + 0.685848i
\(672\) −9.50545 + 16.4639i −0.366681 + 0.635110i
\(673\) 2.60837 4.51783i 0.100545 0.174149i −0.811364 0.584541i \(-0.801275\pi\)
0.911909 + 0.410392i \(0.134608\pi\)
\(674\) −55.6855 −2.14492
\(675\) −8.06395 13.9672i −0.310382 0.537597i
\(676\) −1.29216 2.23809i −0.0496984 0.0860802i
\(677\) 20.5401 35.5765i 0.789420 1.36731i −0.136903 0.990584i \(-0.543715\pi\)
0.926323 0.376731i \(-0.122952\pi\)
\(678\) −17.0309 −0.654069
\(679\) 17.2655 + 29.9047i 0.662588 + 1.14764i
\(680\) 1.17255 0.0449652
\(681\) 6.83908 0.262074
\(682\) −1.55467 + 27.3638i −0.0595313 + 1.04781i
\(683\) 44.0834 1.68680 0.843402 0.537283i \(-0.180549\pi\)
0.843402 + 0.537283i \(0.180549\pi\)
\(684\) −27.9700 −1.06946
\(685\) −4.95898 8.58920i −0.189473 0.328176i
\(686\) −19.3174 −0.737541
\(687\) 3.35697 5.81444i 0.128076 0.221835i
\(688\) 12.8561 + 22.2673i 0.490133 + 0.848935i
\(689\) −4.26962 7.39519i −0.162659 0.281734i
\(690\) 2.73050 0.103948
\(691\) 14.8787 25.7706i 0.566012 0.980361i −0.430943 0.902379i \(-0.641819\pi\)
0.996955 0.0779819i \(-0.0248476\pi\)
\(692\) −29.3188 + 50.7817i −1.11453 + 1.93043i
\(693\) 12.2170 21.1605i 0.464086 0.803821i
\(694\) 35.7031 + 61.8396i 1.35527 + 2.34740i
\(695\) −0.0659675 + 0.114259i −0.00250229 + 0.00433409i
\(696\) −2.43847 4.22355i −0.0924299 0.160093i
\(697\) −18.8372 −0.713512
\(698\) −14.9820 −0.567076
\(699\) 4.86262 + 8.42230i 0.183921 + 0.318561i
\(700\) −24.7358 + 42.8437i −0.934925 + 1.61934i
\(701\) −1.43690 2.48878i −0.0542709 0.0940000i 0.837614 0.546263i \(-0.183950\pi\)
−0.891885 + 0.452263i \(0.850617\pi\)
\(702\) 3.63458 6.29527i 0.137178 0.237600i
\(703\) −17.8321 + 30.8861i −0.672549 + 1.16489i
\(704\) −13.5557 + 23.4792i −0.510900 + 0.884906i
\(705\) −1.60893 −0.0605957
\(706\) −19.8430 34.3691i −0.746801 1.29350i
\(707\) 11.4560 + 19.8424i 0.430849 + 0.746252i
\(708\) 8.71945 15.1025i 0.327697 0.567588i
\(709\) 4.29375 0.161255 0.0806276 0.996744i \(-0.474308\pi\)
0.0806276 + 0.996744i \(0.474308\pi\)
\(710\) 6.09176 + 10.5512i 0.228620 + 0.395981i
\(711\) 2.56935 0.0963580
\(712\) 0.624994 0.0234226
\(713\) 21.0741 10.6214i 0.789230 0.397775i
\(714\) 9.74822 0.364818
\(715\) 1.14860 0.0429551
\(716\) 15.0695 + 26.1011i 0.563173 + 0.975445i
\(717\) −3.02783 −0.113076
\(718\) −20.5061 + 35.5176i −0.765281 + 1.32551i
\(719\) −14.4946 25.1053i −0.540556 0.936271i −0.998872 0.0474817i \(-0.984880\pi\)
0.458316 0.888789i \(-0.348453\pi\)
\(720\) 1.64031 + 2.84110i 0.0611307 + 0.105882i
\(721\) −10.7603 −0.400735
\(722\) 2.31103 4.00283i 0.0860077 0.148970i
\(723\) 8.79643 15.2359i 0.327143 0.566628i
\(724\) 4.51896 7.82707i 0.167946 0.290891i
\(725\) 15.3740 + 26.6285i 0.570974 + 0.988957i
\(726\) 3.68412 6.38108i 0.136730 0.236824i
\(727\) −10.4545 18.1078i −0.387737 0.671580i 0.604408 0.796675i \(-0.293410\pi\)
−0.992145 + 0.125095i \(0.960076\pi\)
\(728\) −5.04157 −0.186853
\(729\) −9.33962 −0.345912
\(730\) −6.04053 10.4625i −0.223570 0.387235i
\(731\) 9.68622 16.7770i 0.358258 0.620521i
\(732\) 6.94373 + 12.0269i 0.256647 + 0.444526i
\(733\) 2.19582 3.80327i 0.0811044 0.140477i −0.822620 0.568591i \(-0.807489\pi\)
0.903725 + 0.428114i \(0.140822\pi\)
\(734\) −10.5537 + 18.2795i −0.389544 + 0.674709i
\(735\) 1.38987 2.40733i 0.0512662 0.0887956i
\(736\) 33.2023 1.22385
\(737\) −7.93255 13.7396i −0.292199 0.506104i
\(738\) 28.3498 + 49.1033i 1.04357 + 1.80752i
\(739\) 2.89447 5.01337i 0.106475 0.184420i −0.807865 0.589368i \(-0.799377\pi\)
0.914340 + 0.404948i \(0.132710\pi\)
\(740\) −11.2202 −0.412462
\(741\) −1.23576 2.14039i −0.0453967 0.0786293i
\(742\) −73.6774 −2.70478
\(743\) 36.3130 1.33220 0.666098 0.745865i \(-0.267963\pi\)
0.666098 + 0.745865i \(0.267963\pi\)
\(744\) 3.50825 + 2.30026i 0.128619 + 0.0843317i
\(745\) 7.58170 0.277772
\(746\) 13.5734 0.496956
\(747\) −1.94056 3.36115i −0.0710014 0.122978i
\(748\) 11.1465 0.407556
\(749\) 26.1192 45.2398i 0.954375 1.65303i
\(750\) −3.14062 5.43971i −0.114679 0.198630i
\(751\) 1.31849 + 2.28369i 0.0481124 + 0.0833331i 0.889079 0.457754i \(-0.151346\pi\)
−0.840966 + 0.541088i \(0.818013\pi\)
\(752\) −13.3149 −0.485546
\(753\) −0.957521 + 1.65848i −0.0348940 + 0.0604382i
\(754\) −6.92933 + 12.0020i −0.252351 + 0.437086i
\(755\) 1.07154 1.85595i 0.0389972 0.0675451i
\(756\) −17.6783 30.6197i −0.642954 1.11363i
\(757\) −5.28490 + 9.15371i −0.192083 + 0.332697i −0.945940 0.324341i \(-0.894858\pi\)
0.753857 + 0.657038i \(0.228191\pi\)
\(758\) −21.8050 37.7674i −0.791994 1.37177i
\(759\) 5.86886 0.213026
\(760\) −2.56498 −0.0930417
\(761\) −6.74433 11.6815i −0.244482 0.423455i 0.717504 0.696554i \(-0.245284\pi\)
−0.961986 + 0.273100i \(0.911951\pi\)
\(762\) −4.03645 + 6.99134i −0.146225 + 0.253270i
\(763\) 36.7689 + 63.6856i 1.33112 + 2.30557i
\(764\) −5.36014 + 9.28404i −0.193923 + 0.335885i
\(765\) 1.23587 2.14059i 0.0446829 0.0773931i
\(766\) −3.56685 + 6.17797i −0.128876 + 0.223219i
\(767\) −11.2046 −0.404576
\(768\) −0.924247 1.60084i −0.0333509 0.0577655i
\(769\) −16.5924 28.7389i −0.598337 1.03635i −0.993067 0.117553i \(-0.962495\pi\)
0.394730 0.918797i \(-0.370838\pi\)
\(770\) 4.95511 8.58249i 0.178570 0.309292i
\(771\) −3.55068 −0.127875