Properties

Label 392.3.k.j.67.4
Level 392
Weight 3
Character 392.67
Analytic conductor 10.681
Analytic rank 0
Dimension 8
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 392.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.6812263629\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.796594176.2
Defining polynomial: \(x^{8} - 4 x^{7} + 18 x^{6} - 40 x^{5} + 83 x^{4} - 104 x^{3} + 22 x^{2} + 24 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 56)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 67.4
Root \(1.20711 - 0.0981308i\) of defining polynomial
Character \(\chi\) \(=\) 392.67
Dual form 392.3.k.j.275.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.97374 - 0.323042i) q^{2} +(0.292893 - 0.507306i) q^{3} +(3.79129 - 1.27520i) q^{4} +(-7.82295 + 4.51658i) q^{5} +(0.414214 - 1.09591i) q^{6} +(7.07107 - 3.74166i) q^{8} +(4.32843 + 7.49706i) q^{9} +O(q^{10})\) \(q+(1.97374 - 0.323042i) q^{2} +(0.292893 - 0.507306i) q^{3} +(3.79129 - 1.27520i) q^{4} +(-7.82295 + 4.51658i) q^{5} +(0.414214 - 1.09591i) q^{6} +(7.07107 - 3.74166i) q^{8} +(4.32843 + 7.49706i) q^{9} +(-13.9814 + 11.4417i) q^{10} +(-6.24264 + 10.8126i) q^{11} +(0.463526 - 2.29684i) q^{12} +9.03316i q^{13} +5.29150i q^{15} +(12.7477 - 9.66930i) q^{16} +(6.17157 - 10.6895i) q^{17} +(10.9650 + 13.3990i) q^{18} +(14.4350 + 25.0022i) q^{19} +(-23.8995 + 27.0995i) q^{20} +(-8.82843 + 23.3578i) q^{22} +(-21.3404 + 12.3209i) q^{23} +(0.172903 - 4.68310i) q^{24} +(28.2990 - 49.0153i) q^{25} +(2.91809 + 17.8291i) q^{26} +10.3431 q^{27} +22.4499i q^{29} +(1.70938 + 10.4440i) q^{30} +(-14.5340 - 8.39119i) q^{31} +(22.0371 - 23.2027i) q^{32} +(3.65685 + 6.33386i) q^{33} +(8.72792 - 23.0919i) q^{34} +(25.9706 + 22.9039i) q^{36} +(14.0734 - 8.12528i) q^{37} +(36.5677 + 44.6847i) q^{38} +(4.58258 + 2.64575i) q^{39} +(-38.4171 + 61.2078i) q^{40} -6.97056 q^{41} -22.8284 q^{43} +(-9.87945 + 48.9542i) q^{44} +(-67.7221 - 39.0994i) q^{45} +(-38.1402 + 31.2120i) q^{46} +(5.36882 - 3.09969i) q^{47} +(-1.17157 - 9.29907i) q^{48} +(40.0208 - 105.885i) q^{50} +(-3.61522 - 6.26175i) q^{51} +(11.5191 + 34.2473i) q^{52} +(-6.94131 - 4.00757i) q^{53} +(20.4147 - 3.34127i) q^{54} -112.782i q^{55} +16.9117 q^{57} +(7.25227 + 44.3103i) q^{58} +(15.2218 - 26.3650i) q^{59} +(6.74773 + 20.0616i) q^{60} +(13.1918 - 7.61627i) q^{61} +(-31.3970 - 11.8669i) q^{62} +(36.0000 - 52.9150i) q^{64} +(-40.7990 - 70.6659i) q^{65} +(9.26378 + 11.3201i) q^{66} +(39.3137 - 68.0933i) q^{67} +(9.76698 - 48.3969i) q^{68} +14.4348i q^{69} -17.5345i q^{71} +(58.6580 + 36.8167i) q^{72} +(23.3431 - 40.4315i) q^{73} +(25.1524 - 20.5835i) q^{74} +(-16.5772 - 28.7125i) q^{75} +(86.6102 + 76.3830i) q^{76} +(9.89949 + 3.74166i) q^{78} +(-70.1762 + 40.5163i) q^{79} +(-56.0526 + 133.219i) q^{80} +(-35.9264 + 62.2264i) q^{81} +(-13.7581 + 2.25178i) q^{82} -40.3848 q^{83} +111.498i q^{85} +(-45.0573 + 7.37454i) q^{86} +(11.3890 + 6.57544i) q^{87} +(-3.68520 + 99.8142i) q^{88} +(55.9706 + 96.9439i) q^{89} +(-146.296 - 55.2949i) q^{90} +(-65.1960 + 73.9253i) q^{92} +(-8.51380 + 4.91545i) q^{93} +(9.59532 - 7.85233i) q^{94} +(-225.849 - 130.394i) q^{95} +(-5.31637 - 17.9755i) q^{96} +164.108 q^{97} -108.083 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{3} + 12q^{4} - 8q^{6} + 12q^{9} + O(q^{10}) \) \( 8q + 8q^{3} + 12q^{4} - 8q^{6} + 12q^{9} - 28q^{10} - 16q^{11} - 24q^{12} - 8q^{16} + 72q^{17} - 16q^{18} + 8q^{19} - 112q^{20} - 48q^{22} - 40q^{24} + 68q^{25} + 28q^{26} + 128q^{27} - 16q^{33} - 32q^{34} + 72q^{36} - 76q^{38} + 56q^{40} + 80q^{41} - 160q^{43} + 48q^{44} - 224q^{46} - 32q^{48} + 224q^{50} - 176q^{51} - 56q^{52} - 16q^{54} - 272q^{57} + 168q^{58} + 184q^{59} - 56q^{60} + 224q^{62} + 288q^{64} - 168q^{65} - 32q^{66} + 224q^{67} - 216q^{68} + 160q^{72} + 232q^{73} + 280q^{74} + 88q^{75} + 48q^{76} - 336q^{80} + 52q^{81} - 48q^{82} - 176q^{83} - 8q^{86} - 240q^{88} + 312q^{89} - 616q^{90} + 112q^{92} - 112q^{94} + 176q^{96} + 272q^{97} - 480q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.97374 0.323042i 0.986869 0.161521i
\(3\) 0.292893 0.507306i 0.0976311 0.169102i −0.813073 0.582162i \(-0.802207\pi\)
0.910704 + 0.413060i \(0.135540\pi\)
\(4\) 3.79129 1.27520i 0.947822 0.318800i
\(5\) −7.82295 + 4.51658i −1.56459 + 0.903316i −0.567807 + 0.823162i \(0.692208\pi\)
−0.996782 + 0.0801541i \(0.974459\pi\)
\(6\) 0.414214 1.09591i 0.0690356 0.182651i
\(7\) 0 0
\(8\) 7.07107 3.74166i 0.883883 0.467707i
\(9\) 4.32843 + 7.49706i 0.480936 + 0.833006i
\(10\) −13.9814 + 11.4417i −1.39814 + 1.14417i
\(11\) −6.24264 + 10.8126i −0.567513 + 0.982961i 0.429298 + 0.903163i \(0.358761\pi\)
−0.996811 + 0.0797982i \(0.974572\pi\)
\(12\) 0.463526 2.29684i 0.0386271 0.191403i
\(13\) 9.03316i 0.694858i 0.937706 + 0.347429i \(0.112945\pi\)
−0.937706 + 0.347429i \(0.887055\pi\)
\(14\) 0 0
\(15\) 5.29150i 0.352767i
\(16\) 12.7477 9.66930i 0.796733 0.604332i
\(17\) 6.17157 10.6895i 0.363034 0.628793i −0.625425 0.780284i \(-0.715074\pi\)
0.988459 + 0.151492i \(0.0484076\pi\)
\(18\) 10.9650 + 13.3990i 0.609169 + 0.744387i
\(19\) 14.4350 + 25.0022i 0.759738 + 1.31591i 0.942984 + 0.332838i \(0.108006\pi\)
−0.183246 + 0.983067i \(0.558660\pi\)
\(20\) −23.8995 + 27.0995i −1.19497 + 1.35497i
\(21\) 0 0
\(22\) −8.82843 + 23.3578i −0.401292 + 1.06172i
\(23\) −21.3404 + 12.3209i −0.927843 + 0.535690i −0.886129 0.463439i \(-0.846615\pi\)
−0.0417142 + 0.999130i \(0.513282\pi\)
\(24\) 0.172903 4.68310i 0.00720428 0.195129i
\(25\) 28.2990 49.0153i 1.13196 1.96061i
\(26\) 2.91809 + 17.8291i 0.112234 + 0.685734i
\(27\) 10.3431 0.383079
\(28\) 0 0
\(29\) 22.4499i 0.774136i 0.922051 + 0.387068i \(0.126512\pi\)
−0.922051 + 0.387068i \(0.873488\pi\)
\(30\) 1.70938 + 10.4440i 0.0569792 + 0.348135i
\(31\) −14.5340 8.39119i −0.468838 0.270684i 0.246915 0.969037i \(-0.420583\pi\)
−0.715753 + 0.698353i \(0.753916\pi\)
\(32\) 22.0371 23.2027i 0.688659 0.725085i
\(33\) 3.65685 + 6.33386i 0.110814 + 0.191935i
\(34\) 8.72792 23.0919i 0.256704 0.679174i
\(35\) 0 0
\(36\) 25.9706 + 22.9039i 0.721405 + 0.636219i
\(37\) 14.0734 8.12528i 0.380362 0.219602i −0.297614 0.954686i \(-0.596191\pi\)
0.677976 + 0.735084i \(0.262857\pi\)
\(38\) 36.5677 + 44.6847i 0.962309 + 1.17591i
\(39\) 4.58258 + 2.64575i 0.117502 + 0.0678398i
\(40\) −38.4171 + 61.2078i −0.960427 + 1.53020i
\(41\) −6.97056 −0.170014 −0.0850069 0.996380i \(-0.527091\pi\)
−0.0850069 + 0.996380i \(0.527091\pi\)
\(42\) 0 0
\(43\) −22.8284 −0.530894 −0.265447 0.964126i \(-0.585519\pi\)
−0.265447 + 0.964126i \(0.585519\pi\)
\(44\) −9.87945 + 48.9542i −0.224533 + 1.11260i
\(45\) −67.7221 39.0994i −1.50494 0.868875i
\(46\) −38.1402 + 31.2120i −0.829134 + 0.678522i
\(47\) 5.36882 3.09969i 0.114230 0.0659509i −0.441796 0.897115i \(-0.645659\pi\)
0.556027 + 0.831165i \(0.312325\pi\)
\(48\) −1.17157 9.29907i −0.0244078 0.193731i
\(49\) 0 0
\(50\) 40.0208 105.885i 0.800416 2.11770i
\(51\) −3.61522 6.26175i −0.0708867 0.122779i
\(52\) 11.5191 + 34.2473i 0.221521 + 0.658602i
\(53\) −6.94131 4.00757i −0.130968 0.0756145i 0.433084 0.901353i \(-0.357425\pi\)
−0.564053 + 0.825739i \(0.690759\pi\)
\(54\) 20.4147 3.34127i 0.378049 0.0618754i
\(55\) 112.782i 2.05057i
\(56\) 0 0
\(57\) 16.9117 0.296696
\(58\) 7.25227 + 44.3103i 0.125039 + 0.763971i
\(59\) 15.2218 26.3650i 0.257997 0.446864i −0.707708 0.706505i \(-0.750271\pi\)
0.965705 + 0.259641i \(0.0836042\pi\)
\(60\) 6.74773 + 20.0616i 0.112462 + 0.334360i
\(61\) 13.1918 7.61627i 0.216258 0.124857i −0.387958 0.921677i \(-0.626819\pi\)
0.604217 + 0.796820i \(0.293486\pi\)
\(62\) −31.3970 11.8669i −0.506403 0.191402i
\(63\) 0 0
\(64\) 36.0000 52.9150i 0.562500 0.826797i
\(65\) −40.7990 70.6659i −0.627677 1.08717i
\(66\) 9.26378 + 11.3201i 0.140360 + 0.171516i
\(67\) 39.3137 68.0933i 0.586772 1.01632i −0.407880 0.913035i \(-0.633732\pi\)
0.994652 0.103283i \(-0.0329348\pi\)
\(68\) 9.76698 48.3969i 0.143632 0.711719i
\(69\) 14.4348i 0.209200i
\(70\) 0 0
\(71\) 17.5345i 0.246965i −0.992347 0.123482i \(-0.960594\pi\)
0.992347 0.123482i \(-0.0394062\pi\)
\(72\) 58.6580 + 36.8167i 0.814695 + 0.511343i
\(73\) 23.3431 40.4315i 0.319769 0.553856i −0.660671 0.750676i \(-0.729728\pi\)
0.980440 + 0.196820i \(0.0630613\pi\)
\(74\) 25.1524 20.5835i 0.339897 0.278155i
\(75\) −16.5772 28.7125i −0.221029 0.382833i
\(76\) 86.6102 + 76.3830i 1.13961 + 1.00504i
\(77\) 0 0
\(78\) 9.89949 + 3.74166i 0.126917 + 0.0479700i
\(79\) −70.1762 + 40.5163i −0.888307 + 0.512864i −0.873388 0.487025i \(-0.838082\pi\)
−0.0149184 + 0.999889i \(0.504749\pi\)
\(80\) −56.0526 + 133.219i −0.700657 + 1.66523i
\(81\) −35.9264 + 62.2264i −0.443536 + 0.768227i
\(82\) −13.7581 + 2.25178i −0.167781 + 0.0274608i
\(83\) −40.3848 −0.486564 −0.243282 0.969956i \(-0.578224\pi\)
−0.243282 + 0.969956i \(0.578224\pi\)
\(84\) 0 0
\(85\) 111.498i 1.31174i
\(86\) −45.0573 + 7.37454i −0.523923 + 0.0857505i
\(87\) 11.3890 + 6.57544i 0.130908 + 0.0755797i
\(88\) −3.68520 + 99.8142i −0.0418773 + 1.13425i
\(89\) 55.9706 + 96.9439i 0.628883 + 1.08926i 0.987776 + 0.155878i \(0.0498208\pi\)
−0.358894 + 0.933379i \(0.616846\pi\)
\(90\) −146.296 55.2949i −1.62552 0.614387i
\(91\) 0 0
\(92\) −65.1960 + 73.9253i −0.708652 + 0.803536i
\(93\) −8.51380 + 4.91545i −0.0915463 + 0.0528543i
\(94\) 9.59532 7.85233i 0.102078 0.0835355i
\(95\) −225.849 130.394i −2.37736 1.37257i
\(96\) −5.31637 17.9755i −0.0553788 0.187244i
\(97\) 164.108 1.69183 0.845916 0.533317i \(-0.179055\pi\)
0.845916 + 0.533317i \(0.179055\pi\)
\(98\) 0 0
\(99\) −108.083 −1.09175
\(100\) 44.7853 221.918i 0.447853 2.21918i
\(101\) 10.5074 + 6.06643i 0.104033 + 0.0600636i 0.551114 0.834430i \(-0.314203\pi\)
−0.447081 + 0.894494i \(0.647536\pi\)
\(102\) −9.15831 11.1912i −0.0897874 0.109718i
\(103\) 92.3029 53.2911i 0.896144 0.517389i 0.0201970 0.999796i \(-0.493571\pi\)
0.875947 + 0.482407i \(0.160237\pi\)
\(104\) 33.7990 + 63.8741i 0.324990 + 0.614174i
\(105\) 0 0
\(106\) −14.9949 5.66756i −0.141462 0.0534675i
\(107\) 31.7990 + 55.0775i 0.297187 + 0.514743i 0.975491 0.220038i \(-0.0706182\pi\)
−0.678304 + 0.734781i \(0.737285\pi\)
\(108\) 39.2138 13.1896i 0.363091 0.122126i
\(109\) 113.318 + 65.4239i 1.03961 + 0.600220i 0.919723 0.392568i \(-0.128413\pi\)
0.119888 + 0.992787i \(0.461747\pi\)
\(110\) −36.4332 222.601i −0.331211 2.02365i
\(111\) 9.51936i 0.0857600i
\(112\) 0 0
\(113\) −138.225 −1.22323 −0.611617 0.791154i \(-0.709481\pi\)
−0.611617 + 0.791154i \(0.709481\pi\)
\(114\) 33.3793 5.46318i 0.292800 0.0479227i
\(115\) 111.296 192.771i 0.967795 1.67627i
\(116\) 28.6282 + 85.1142i 0.246795 + 0.733743i
\(117\) −67.7221 + 39.0994i −0.578821 + 0.334183i
\(118\) 21.5269 56.9549i 0.182431 0.482668i
\(119\) 0 0
\(120\) 19.7990 + 37.4166i 0.164992 + 0.311805i
\(121\) −17.4411 30.2089i −0.144142 0.249660i
\(122\) 23.5767 19.2940i 0.193252 0.158148i
\(123\) −2.04163 + 3.53621i −0.0165986 + 0.0287497i
\(124\) −65.8029 13.2797i −0.530669 0.107094i
\(125\) 285.430i 2.28344i
\(126\) 0 0
\(127\) 114.442i 0.901114i −0.892748 0.450557i \(-0.851225\pi\)
0.892748 0.450557i \(-0.148775\pi\)
\(128\) 53.9608 116.070i 0.421569 0.906796i
\(129\) −6.68629 + 11.5810i −0.0518317 + 0.0897752i
\(130\) −103.355 126.296i −0.795035 0.971510i
\(131\) −84.1751 145.796i −0.642558 1.11294i −0.984860 0.173353i \(-0.944540\pi\)
0.342301 0.939590i \(-0.388794\pi\)
\(132\) 21.9411 + 19.3503i 0.166221 + 0.146593i
\(133\) 0 0
\(134\) 55.5980 147.098i 0.414910 1.09775i
\(135\) −80.9139 + 46.7156i −0.599362 + 0.346042i
\(136\) 3.64325 98.6779i 0.0267886 0.725573i
\(137\) −17.3431 + 30.0392i −0.126592 + 0.219264i −0.922354 0.386345i \(-0.873737\pi\)
0.795762 + 0.605610i \(0.207071\pi\)
\(138\) 4.66305 + 28.4905i 0.0337902 + 0.206453i
\(139\) −107.664 −0.774561 −0.387281 0.921962i \(-0.626586\pi\)
−0.387281 + 0.921962i \(0.626586\pi\)
\(140\) 0 0
\(141\) 3.63151i 0.0257554i
\(142\) −5.66438 34.6085i −0.0398900 0.243722i
\(143\) −97.6717 56.3908i −0.683019 0.394341i
\(144\) 127.669 + 53.7175i 0.886590 + 0.373038i
\(145\) −101.397 175.625i −0.699289 1.21120i
\(146\) 33.0122 87.3421i 0.226111 0.598233i
\(147\) 0 0
\(148\) 42.9949 48.7517i 0.290506 0.329403i
\(149\) 218.391 126.088i 1.46571 0.846229i 0.466447 0.884549i \(-0.345534\pi\)
0.999266 + 0.0383198i \(0.0122006\pi\)
\(150\) −41.9943 51.3158i −0.279962 0.342106i
\(151\) 203.071 + 117.243i 1.34484 + 0.776444i 0.987513 0.157535i \(-0.0503548\pi\)
0.357327 + 0.933979i \(0.383688\pi\)
\(152\) 195.621 + 122.781i 1.28698 + 0.807772i
\(153\) 106.853 0.698384
\(154\) 0 0
\(155\) 151.598 0.978051
\(156\) 20.7477 + 4.18710i 0.132998 + 0.0268404i
\(157\) −8.74409 5.04840i −0.0556948 0.0321554i 0.471894 0.881655i \(-0.343570\pi\)
−0.527589 + 0.849500i \(0.676904\pi\)
\(158\) −125.421 + 102.638i −0.793804 + 0.649610i
\(159\) −4.06613 + 2.34758i −0.0255731 + 0.0147647i
\(160\) −67.5980 + 281.046i −0.422487 + 1.75654i
\(161\) 0 0
\(162\) −50.8076 + 134.424i −0.313627 + 0.829780i
\(163\) −52.2670 90.5291i −0.320657 0.555394i 0.659967 0.751295i \(-0.270570\pi\)
−0.980624 + 0.195901i \(0.937237\pi\)
\(164\) −26.4274 + 8.88887i −0.161143 + 0.0542004i
\(165\) −57.2147 33.0329i −0.346756 0.200200i
\(166\) −79.7090 + 13.0460i −0.480175 + 0.0785902i
\(167\) 296.765i 1.77703i −0.458843 0.888517i \(-0.651736\pi\)
0.458843 0.888517i \(-0.348264\pi\)
\(168\) 0 0
\(169\) 87.4020 0.517172
\(170\) 36.0184 + 220.067i 0.211873 + 1.29451i
\(171\) −124.962 + 216.440i −0.730772 + 1.26573i
\(172\) −86.5491 + 29.1108i −0.503193 + 0.169249i
\(173\) 34.6671 20.0150i 0.200388 0.115694i −0.396449 0.918057i \(-0.629758\pi\)
0.596836 + 0.802363i \(0.296424\pi\)
\(174\) 24.6030 + 9.29907i 0.141397 + 0.0534429i
\(175\) 0 0
\(176\) 24.9706 + 198.198i 0.141878 + 1.12612i
\(177\) −8.91674 15.4442i −0.0503771 0.0872556i
\(178\) 141.788 + 173.261i 0.796563 + 0.973376i
\(179\) −147.397 + 255.299i −0.823447 + 1.42625i 0.0796538 + 0.996823i \(0.474619\pi\)
−0.903101 + 0.429429i \(0.858715\pi\)
\(180\) −306.614 61.8777i −1.70341 0.343765i
\(181\) 40.4706i 0.223595i 0.993731 + 0.111797i \(0.0356608\pi\)
−0.993731 + 0.111797i \(0.964339\pi\)
\(182\) 0 0
\(183\) 8.92302i 0.0487596i
\(184\) −104.799 + 166.970i −0.569559 + 0.907447i
\(185\) −73.3970 + 127.127i −0.396740 + 0.687174i
\(186\) −15.2161 + 12.4521i −0.0818071 + 0.0669469i
\(187\) 77.0538 + 133.461i 0.412053 + 0.713696i
\(188\) 16.4020 18.5981i 0.0872448 0.0989263i
\(189\) 0 0
\(190\) −487.889 184.405i −2.56784 0.970552i
\(191\) 135.905 78.4647i 0.711543 0.410810i −0.100089 0.994979i \(-0.531913\pi\)
0.811632 + 0.584169i \(0.198579\pi\)
\(192\) −16.3000 33.7615i −0.0848956 0.175841i
\(193\) 130.652 226.296i 0.676952 1.17252i −0.298942 0.954271i \(-0.596634\pi\)
0.975894 0.218245i \(-0.0700330\pi\)
\(194\) 323.906 53.0136i 1.66962 0.273266i
\(195\) −47.7990 −0.245123
\(196\) 0 0
\(197\) 145.283i 0.737475i 0.929533 + 0.368738i \(0.120210\pi\)
−0.929533 + 0.368738i \(0.879790\pi\)
\(198\) −213.328 + 34.9154i −1.07741 + 0.176341i
\(199\) 338.189 + 195.254i 1.69944 + 0.981175i 0.946283 + 0.323339i \(0.104805\pi\)
0.753161 + 0.657836i \(0.228528\pi\)
\(200\) 16.7057 452.476i 0.0835283 2.26238i
\(201\) −23.0294 39.8882i −0.114574 0.198449i
\(202\) 22.6985 + 8.57922i 0.112369 + 0.0424714i
\(203\) 0 0
\(204\) −21.6913 19.1300i −0.106330 0.0937743i
\(205\) 54.5303 31.4831i 0.266002 0.153576i
\(206\) 164.966 135.000i 0.800808 0.655342i
\(207\) −184.741 106.660i −0.892467 0.515266i
\(208\) 87.3444 + 115.152i 0.419925 + 0.553617i
\(209\) −360.451 −1.72464
\(210\) 0 0
\(211\) −164.049 −0.777482 −0.388741 0.921347i \(-0.627090\pi\)
−0.388741 + 0.921347i \(0.627090\pi\)
\(212\) −31.4270 6.34228i −0.148240 0.0299164i
\(213\) −8.89535 5.13574i −0.0417622 0.0241114i
\(214\) 80.5552 + 98.4361i 0.376426 + 0.459982i
\(215\) 178.586 103.106i 0.830630 0.479565i
\(216\) 73.1371 38.7005i 0.338598 0.179169i
\(217\) 0 0
\(218\) 244.794 + 92.5234i 1.12291 + 0.424419i
\(219\) −13.6741 23.6842i −0.0624388 0.108147i
\(220\) −143.819 427.587i −0.653723 1.94358i
\(221\) 96.5598 + 55.7488i 0.436922 + 0.252257i
\(222\) −3.07515 18.7887i −0.0138520 0.0846339i
\(223\) 10.5830i 0.0474574i −0.999718 0.0237287i \(-0.992446\pi\)
0.999718 0.0237287i \(-0.00755379\pi\)
\(224\) 0 0
\(225\) 489.960 2.17760
\(226\) −272.821 + 44.6526i −1.20717 + 0.197578i
\(227\) −106.903 + 185.162i −0.470939 + 0.815690i −0.999447 0.0332382i \(-0.989418\pi\)
0.528509 + 0.848928i \(0.322751\pi\)
\(228\) 64.1171 21.5658i 0.281215 0.0945868i
\(229\) −200.942 + 116.014i −0.877478 + 0.506612i −0.869826 0.493359i \(-0.835769\pi\)
−0.00765200 + 0.999971i \(0.502436\pi\)
\(230\) 157.397 416.433i 0.684335 1.81058i
\(231\) 0 0
\(232\) 84.0000 + 158.745i 0.362069 + 0.684246i
\(233\) 96.4315 + 167.024i 0.413869 + 0.716842i 0.995309 0.0967472i \(-0.0308439\pi\)
−0.581440 + 0.813589i \(0.697511\pi\)
\(234\) −121.035 + 99.0490i −0.517244 + 0.423286i
\(235\) −28.0000 + 48.4974i −0.119149 + 0.206372i
\(236\) 24.0897 119.368i 0.102075 0.505797i
\(237\) 47.4678i 0.200286i
\(238\) 0 0
\(239\) 327.917i 1.37204i −0.727583 0.686020i \(-0.759356\pi\)
0.727583 0.686020i \(-0.240644\pi\)
\(240\) 51.1652 + 67.4546i 0.213188 + 0.281061i
\(241\) 35.9361 62.2431i 0.149112 0.258270i −0.781787 0.623545i \(-0.785692\pi\)
0.930900 + 0.365275i \(0.119025\pi\)
\(242\) −44.1830 53.9903i −0.182574 0.223100i
\(243\) 67.5894 + 117.068i 0.278146 + 0.481762i
\(244\) 40.3015 45.6976i 0.165170 0.187285i
\(245\) 0 0
\(246\) −2.88730 + 7.63908i −0.0117370 + 0.0310532i
\(247\) −225.849 + 130.394i −0.914368 + 0.527911i
\(248\) −134.168 4.95355i −0.540999 0.0199740i
\(249\) −11.8284 + 20.4874i −0.0475037 + 0.0822789i
\(250\) 92.2057 + 563.363i 0.368823 + 2.25345i
\(251\) 256.919 1.02358 0.511790 0.859110i \(-0.328982\pi\)
0.511790 + 0.859110i \(0.328982\pi\)
\(252\) 0 0
\(253\) 307.659i 1.21604i
\(254\) −36.9694 225.878i −0.145549 0.889282i
\(255\) 56.5634 + 32.6569i 0.221817 + 0.128066i
\(256\) 69.0091 246.523i 0.269567 0.962982i
\(257\) 159.676 + 276.567i 0.621308 + 1.07614i 0.989242 + 0.146285i \(0.0467318\pi\)
−0.367934 + 0.929852i \(0.619935\pi\)
\(258\) −9.45584 + 25.0178i −0.0366506 + 0.0969683i
\(259\) 0 0
\(260\) −244.794 215.888i −0.941515 0.830338i
\(261\) −168.308 + 97.1729i −0.644860 + 0.372310i
\(262\) −213.238 260.570i −0.813885 0.994543i
\(263\) 326.800 + 188.678i 1.24259 + 0.717408i 0.969620 0.244615i \(-0.0786616\pi\)
0.272967 + 0.962023i \(0.411995\pi\)
\(264\) 49.5570 + 31.1044i 0.187716 + 0.117820i
\(265\) 72.4020 0.273215
\(266\) 0 0
\(267\) 65.5736 0.245594
\(268\) 62.2169 308.294i 0.232153 1.15035i
\(269\) 24.3900 + 14.0816i 0.0906691 + 0.0523478i 0.544649 0.838664i \(-0.316663\pi\)
−0.453980 + 0.891012i \(0.649996\pi\)
\(270\) −144.612 + 118.343i −0.535599 + 0.438308i
\(271\) −346.164 + 199.858i −1.27736 + 0.737482i −0.976362 0.216143i \(-0.930652\pi\)
−0.300995 + 0.953626i \(0.597319\pi\)
\(272\) −24.6863 195.941i −0.0907584 0.720373i
\(273\) 0 0
\(274\) −24.5269 + 64.8921i −0.0895143 + 0.236833i
\(275\) 353.321 + 611.970i 1.28480 + 2.22534i
\(276\) 18.4073 + 54.7265i 0.0666930 + 0.198284i
\(277\) 89.1579 + 51.4753i 0.321870 + 0.185831i 0.652226 0.758025i \(-0.273835\pi\)
−0.330356 + 0.943856i \(0.607169\pi\)
\(278\) −212.501 + 34.7800i −0.764391 + 0.125108i
\(279\) 145.283i 0.520726i
\(280\) 0 0
\(281\) −150.235 −0.534646 −0.267323 0.963607i \(-0.586139\pi\)
−0.267323 + 0.963607i \(0.586139\pi\)
\(282\) −1.17313 7.16766i −0.00416004 0.0254172i
\(283\) −89.2807 + 154.639i −0.315480 + 0.546427i −0.979539 0.201253i \(-0.935499\pi\)
0.664060 + 0.747679i \(0.268832\pi\)
\(284\) −22.3600 66.4783i −0.0787324 0.234079i
\(285\) −132.299 + 76.3830i −0.464208 + 0.268011i
\(286\) −210.995 79.7486i −0.737745 0.278841i
\(287\) 0 0
\(288\) 269.338 + 64.7820i 0.935202 + 0.224937i
\(289\) 68.3234 + 118.340i 0.236413 + 0.409479i
\(290\) −256.865 313.882i −0.885742 1.08235i
\(291\) 48.0660 83.2528i 0.165175 0.286092i
\(292\) 36.9423 183.055i 0.126515 0.626900i
\(293\) 219.189i 0.748085i 0.927411 + 0.374043i \(0.122029\pi\)
−0.927411 + 0.374043i \(0.877971\pi\)
\(294\) 0 0
\(295\) 275.002i 0.932211i
\(296\) 69.1120 110.112i 0.233486 0.372001i
\(297\) −64.5685 + 111.836i −0.217402 + 0.376552i
\(298\) 390.315 319.415i 1.30978 1.07186i
\(299\) −111.296 192.771i −0.372229 0.644720i
\(300\) −99.4630 87.7181i −0.331543 0.292394i
\(301\) 0 0
\(302\) 438.683 + 165.807i 1.45259 + 0.549029i
\(303\) 6.15507 3.55363i 0.0203138 0.0117282i
\(304\) 425.768 + 179.145i 1.40055 + 0.589291i
\(305\) −68.7990 + 119.163i −0.225570 + 0.390699i
\(306\) 210.900 34.5179i 0.689214 0.112804i
\(307\) −316.669 −1.03150 −0.515748 0.856741i \(-0.672486\pi\)
−0.515748 + 0.856741i \(0.672486\pi\)
\(308\) 0 0
\(309\) 62.4344i 0.202053i
\(310\) 299.215 48.9725i 0.965209 0.157976i
\(311\) 62.5836 + 36.1326i 0.201233 + 0.116182i 0.597231 0.802070i \(-0.296268\pi\)
−0.395997 + 0.918252i \(0.629601\pi\)
\(312\) 42.3032 + 1.56186i 0.135587 + 0.00500596i
\(313\) 40.9756 + 70.9718i 0.130913 + 0.226747i 0.924029 0.382323i \(-0.124876\pi\)
−0.793116 + 0.609071i \(0.791543\pi\)
\(314\) −18.8894 7.13952i −0.0601573 0.0227373i
\(315\) 0 0
\(316\) −214.392 + 243.098i −0.678455 + 0.769296i
\(317\) −94.5267 + 54.5750i −0.298191 + 0.172161i −0.641630 0.767014i \(-0.721742\pi\)
0.343439 + 0.939175i \(0.388408\pi\)
\(318\) −7.26710 + 5.94704i −0.0228525 + 0.0187014i
\(319\) −242.742 140.147i −0.760945 0.439332i
\(320\) −42.6311 + 576.548i −0.133222 + 1.80171i
\(321\) 37.2548 0.116059
\(322\) 0 0
\(323\) 356.347 1.10324
\(324\) −56.8563 + 281.731i −0.175482 + 0.869541i
\(325\) 442.763 + 255.629i 1.36235 + 0.786552i
\(326\) −132.406 161.796i −0.406154 0.496308i
\(327\) 66.3799 38.3245i 0.202997 0.117200i
\(328\) −49.2893 + 26.0815i −0.150272 + 0.0795166i
\(329\) 0 0
\(330\) −123.598 46.7156i −0.374539 0.141563i
\(331\) −160.870 278.635i −0.486012 0.841798i 0.513858 0.857875i \(-0.328216\pi\)
−0.999871 + 0.0160770i \(0.994882\pi\)
\(332\) −153.110 + 51.4987i −0.461176 + 0.155117i
\(333\) 121.831 + 70.3394i 0.365860 + 0.211229i
\(334\) −95.8674 585.736i −0.287028 1.75370i
\(335\) 710.254i 2.12016i
\(336\) 0 0
\(337\) −164.049 −0.486792 −0.243396 0.969927i \(-0.578261\pi\)
−0.243396 + 0.969927i \(0.578261\pi\)
\(338\) 172.509 28.2345i 0.510381 0.0835341i
\(339\) −40.4853 + 70.1226i −0.119426 + 0.206851i
\(340\) 142.182 + 422.720i 0.418182 + 1.24329i
\(341\) 181.461 104.766i 0.532143 0.307233i
\(342\) −176.723 + 467.565i −0.516734 + 1.36715i
\(343\) 0 0
\(344\) −161.421 + 85.4162i −0.469248 + 0.248303i
\(345\) −65.1960 112.923i −0.188974 0.327312i
\(346\) 61.9580 50.7034i 0.179069 0.146541i
\(347\) 165.154 286.056i 0.475949 0.824368i −0.523671 0.851920i \(-0.675438\pi\)
0.999620 + 0.0275524i \(0.00877132\pi\)
\(348\) 51.5639 + 10.4061i 0.148172 + 0.0299027i
\(349\) 262.402i 0.751869i −0.926646 0.375934i \(-0.877322\pi\)
0.926646 0.375934i \(-0.122678\pi\)
\(350\) 0 0
\(351\) 93.4313i 0.266186i
\(352\) 113.312 + 383.124i 0.321908 + 1.08842i
\(353\) −289.049 + 500.647i −0.818835 + 1.41826i 0.0877061 + 0.996146i \(0.472046\pi\)
−0.906541 + 0.422118i \(0.861287\pi\)
\(354\) −22.5884 27.6024i −0.0638092 0.0779729i
\(355\) 79.1960 + 137.171i 0.223087 + 0.386398i
\(356\) 335.823 + 296.168i 0.943324 + 0.831934i
\(357\) 0 0
\(358\) −208.451 + 551.509i −0.582265 + 1.54053i
\(359\) 316.198 182.557i 0.880774 0.508515i 0.00986020 0.999951i \(-0.496861\pi\)
0.870913 + 0.491437i \(0.163528\pi\)
\(360\) −625.164 23.0814i −1.73657 0.0641151i
\(361\) −236.240 + 409.180i −0.654405 + 1.13346i
\(362\) 13.0737 + 79.8785i 0.0361152 + 0.220659i
\(363\) −20.4335 −0.0562908
\(364\) 0 0
\(365\) 421.725i 1.15541i
\(366\) −2.88251 17.6117i −0.00787571 0.0481194i
\(367\) −450.395 260.036i −1.22723 0.708544i −0.260784 0.965397i \(-0.583981\pi\)
−0.966451 + 0.256853i \(0.917314\pi\)
\(368\) −152.907 + 363.410i −0.415508 + 0.987527i
\(369\) −30.1716 52.2587i −0.0817658 0.141622i
\(370\) −103.799 + 274.626i −0.280538 + 0.742233i
\(371\) 0 0
\(372\) −26.0101 + 29.4927i −0.0699196 + 0.0792814i
\(373\) 456.145 263.356i 1.22291 0.706048i 0.257373 0.966312i \(-0.417143\pi\)
0.965537 + 0.260265i \(0.0838098\pi\)
\(374\) 195.198 + 238.526i 0.521919 + 0.637769i
\(375\) 144.800 + 83.6004i 0.386134 + 0.222934i
\(376\) 26.3653 42.0064i 0.0701205 0.111719i
\(377\) −202.794 −0.537915
\(378\) 0 0
\(379\) 121.976 0.321835 0.160918 0.986968i \(-0.448555\pi\)
0.160918 + 0.986968i \(0.448555\pi\)
\(380\) −1022.54 206.358i −2.69089 0.543048i
\(381\) −58.0569 33.5191i −0.152380 0.0879768i
\(382\) 242.893 198.772i 0.635846 0.520345i
\(383\) −274.033 + 158.213i −0.715492 + 0.413089i −0.813091 0.582136i \(-0.802217\pi\)
0.0975993 + 0.995226i \(0.468884\pi\)
\(384\) −43.0782 61.3707i −0.112183 0.159820i
\(385\) 0 0
\(386\) 184.770 488.854i 0.478678 1.26646i
\(387\) −98.8112 171.146i −0.255326 0.442238i
\(388\) 622.179 209.270i 1.60355 0.539356i
\(389\) 79.8020 + 46.0737i 0.205146 + 0.118441i 0.599054 0.800709i \(-0.295544\pi\)
−0.393907 + 0.919150i \(0.628877\pi\)
\(390\) −94.3427 + 15.4411i −0.241904 + 0.0395925i
\(391\) 304.157i 0.777895i
\(392\) 0 0
\(393\) −98.6173 −0.250935
\(394\) 46.9324 + 286.750i 0.119118 + 0.727792i
\(395\) 365.990 633.913i 0.926557 1.60484i
\(396\) −409.775 + 137.828i −1.03478 + 0.348050i
\(397\) 486.937 281.133i 1.22654 0.708144i 0.260237 0.965545i \(-0.416199\pi\)
0.966305 + 0.257400i \(0.0828659\pi\)
\(398\) 730.573 + 276.131i 1.83561 + 0.693795i
\(399\) 0 0
\(400\) −113.196 898.465i −0.282990 2.24616i
\(401\) −40.6030 70.3265i −0.101254 0.175378i 0.810947 0.585119i \(-0.198952\pi\)
−0.912202 + 0.409741i \(0.865619\pi\)
\(402\) −58.3396 71.2893i −0.145123 0.177337i
\(403\) 75.7990 131.288i 0.188087 0.325776i
\(404\) 47.5723 + 9.60058i 0.117753 + 0.0237638i
\(405\) 649.058i 1.60261i
\(406\) 0 0
\(407\) 202.893i 0.498508i
\(408\) −48.9928 30.7503i −0.120080 0.0753685i
\(409\) 225.368 390.348i 0.551021 0.954396i −0.447180 0.894444i \(-0.647572\pi\)
0.998201 0.0599523i \(-0.0190949\pi\)
\(410\) 97.4583 79.7550i 0.237703 0.194524i
\(411\) 10.1594 + 17.5966i 0.0247187 + 0.0428140i
\(412\) 281.990 319.746i 0.684442 0.776084i
\(413\) 0 0
\(414\) −399.085 150.840i −0.963974 0.364348i
\(415\) 315.928 182.401i 0.761272 0.439521i
\(416\) 209.594 + 199.065i 0.503832 + 0.478521i
\(417\) −31.5341 + 54.6186i −0.0756212 + 0.130980i
\(418\) −711.436 + 116.441i −1.70200 + 0.278566i
\(419\) −624.988 −1.49162 −0.745809 0.666160i \(-0.767937\pi\)
−0.745809 + 0.666160i \(0.767937\pi\)
\(420\) 0 0
\(421\) 566.476i 1.34555i −0.739848 0.672774i \(-0.765103\pi\)
0.739848 0.672774i \(-0.234897\pi\)
\(422\) −323.789 + 52.9946i −0.767273 + 0.125580i
\(423\) 46.4771 + 26.8336i 0.109875 + 0.0634363i
\(424\) −64.0774 2.36578i −0.151126 0.00557966i
\(425\) −349.299 605.003i −0.821879 1.42354i
\(426\) −19.2162 7.26303i −0.0451084 0.0170494i
\(427\) 0 0
\(428\) 190.794 + 168.264i 0.445780 + 0.393141i
\(429\) −57.2147 + 33.0329i −0.133368 + 0.0769999i
\(430\) 319.174 261.196i 0.742264 0.607432i
\(431\) 250.739 + 144.764i 0.581761 + 0.335880i 0.761833 0.647774i \(-0.224300\pi\)
−0.180072 + 0.983653i \(0.557633\pi\)
\(432\) 131.852 100.011i 0.305212 0.231507i
\(433\) 597.696 1.38036 0.690180 0.723638i \(-0.257532\pi\)
0.690180 + 0.723638i \(0.257532\pi\)
\(434\) 0 0
\(435\) −118.794 −0.273090
\(436\) 513.048 + 103.538i 1.17672 + 0.237473i
\(437\) −616.098 355.704i −1.40984 0.813969i
\(438\) −34.6401 42.3292i −0.0790870 0.0966420i
\(439\) −33.2458 + 19.1945i −0.0757308 + 0.0437232i −0.537387 0.843336i \(-0.680589\pi\)
0.461656 + 0.887059i \(0.347255\pi\)
\(440\) −421.990 797.486i −0.959068 1.81247i
\(441\) 0 0
\(442\) 208.593 + 78.8407i 0.471930 + 0.178373i
\(443\) −299.529 518.799i −0.676138 1.17110i −0.976135 0.217165i \(-0.930319\pi\)
0.299997 0.953940i \(-0.403014\pi\)
\(444\) −12.1391 36.0906i −0.0273403 0.0812852i
\(445\) −875.709 505.591i −1.96789 1.13616i
\(446\) −3.41875 20.8881i −0.00766537 0.0468343i
\(447\) 147.721i 0.330473i
\(448\) 0 0
\(449\) −460.039 −1.02459 −0.512293 0.858811i \(-0.671204\pi\)
−0.512293 + 0.858811i \(0.671204\pi\)
\(450\) 967.054 158.278i 2.14901 0.351728i
\(451\) 43.5147 75.3697i 0.0964850 0.167117i
\(452\) −524.052 + 176.265i −1.15941 + 0.389967i
\(453\) 118.956 68.6794i 0.262596 0.151610i
\(454\) −151.184 + 399.995i −0.333004 + 0.881045i
\(455\) 0 0
\(456\) 119.584 63.2777i 0.262245 0.138767i
\(457\) −133.161 230.642i −0.291382 0.504688i 0.682755 0.730647i \(-0.260782\pi\)
−0.974137 + 0.225959i \(0.927448\pi\)
\(458\) −359.130 + 293.895i −0.784128 + 0.641691i
\(459\) 63.8335 110.563i 0.139071 0.240878i
\(460\) 176.135 872.776i 0.382902 1.89734i
\(461\) 763.123i 1.65537i −0.561196 0.827683i \(-0.689659\pi\)
0.561196 0.827683i \(-0.310341\pi\)
\(462\) 0 0
\(463\) 123.988i 0.267792i −0.990995 0.133896i \(-0.957251\pi\)
0.990995 0.133896i \(-0.0427488\pi\)
\(464\) 217.075 + 286.186i 0.467835 + 0.616780i
\(465\) 44.4020 76.9066i 0.0954882 0.165390i
\(466\) 244.286 + 298.511i 0.524220 + 0.640581i
\(467\) −384.359 665.729i −0.823038 1.42554i −0.903409 0.428779i \(-0.858944\pi\)
0.0803710 0.996765i \(-0.474390\pi\)
\(468\) −206.894 + 234.596i −0.442082 + 0.501274i
\(469\) 0 0
\(470\) −39.5980 + 104.766i −0.0842510 + 0.222907i
\(471\) −5.12217 + 2.95729i −0.0108751 + 0.00627874i
\(472\) 8.98586 243.383i 0.0190378 0.515643i
\(473\) 142.510 246.834i 0.301289 0.521848i
\(474\) 15.3341 + 93.6889i 0.0323504 + 0.197656i
\(475\) 1633.99 3.43997
\(476\) 0 0
\(477\) 69.3859i 0.145463i
\(478\) −105.931 647.223i −0.221613 1.35402i
\(479\) 103.041 + 59.4905i 0.215116 + 0.124197i 0.603687 0.797222i \(-0.293698\pi\)
−0.388571 + 0.921419i \(0.627031\pi\)
\(480\) 122.777 + 116.609i 0.255786 + 0.242936i
\(481\) 73.3970 + 127.127i 0.152592 + 0.264298i
\(482\) 50.8213 134.460i 0.105438 0.278964i
\(483\) 0 0
\(484\) −104.647 92.2898i −0.216212 0.190681i
\(485\) −1283.81 + 741.205i −2.64702 + 1.52826i
\(486\) 171.222 + 209.228i 0.352308 + 0.430510i
\(487\) −244.719 141.288i −0.502503 0.290120i 0.227244 0.973838i \(-0.427029\pi\)
−0.729746 + 0.683718i \(0.760362\pi\)
\(488\) 64.7824 103.214i 0.132751 0.211505i
\(489\) −61.2346 −0.125224
\(490\) 0 0
\(491\) −388.049 −0.790323 −0.395162 0.918612i \(-0.629311\pi\)
−0.395162 + 0.918612i \(0.629311\pi\)
\(492\) −3.23103 + 16.0103i −0.00656714 + 0.0325412i
\(493\) 239.978 + 138.551i 0.486771 + 0.281037i
\(494\) −403.644 + 330.322i −0.817093 + 0.668668i
\(495\) 845.530 488.167i 1.70814 0.986195i
\(496\) −266.412 + 33.5648i −0.537121 + 0.0676709i
\(497\) 0 0
\(498\) −16.7279 + 44.2579i −0.0335902 + 0.0888713i
\(499\) 13.8579 + 24.0025i 0.0277713 + 0.0481013i 0.879577 0.475757i \(-0.157826\pi\)
−0.851806 + 0.523858i \(0.824492\pi\)
\(500\) 363.980 + 1082.15i 0.727960 + 2.16429i
\(501\) −150.551 86.9204i −0.300500 0.173494i
\(502\) 507.091 82.9956i 1.01014 0.165330i
\(503\) 727.477i 1.44628i 0.690703 + 0.723138i \(0.257301\pi\)
−0.690703 + 0.723138i \(0.742699\pi\)
\(504\) 0 0
\(505\) −109.598 −0.217026
\(506\) −99.3868 607.239i −0.196417 1.20008i
\(507\) 25.5995 44.3396i 0.0504920 0.0874548i
\(508\) −145.936 433.881i −0.287275 0.854096i
\(509\) −549.218 + 317.091i −1.07901 + 0.622969i −0.930630 0.365961i \(-0.880740\pi\)
−0.148384 + 0.988930i \(0.547407\pi\)
\(510\) 122.191 + 46.1838i 0.239590 + 0.0905565i
\(511\) 0 0
\(512\) 56.5685 508.865i 0.110485 0.993878i
\(513\) 149.304 + 258.601i 0.291040 + 0.504096i
\(514\) 404.502 + 494.289i 0.786969 + 0.961653i
\(515\) −481.387 + 833.787i −0.934732 + 1.61900i
\(516\) −10.5816 + 52.4333i −0.0205069 + 0.101615i
\(517\) 77.4010i 0.149712i
\(518\) 0 0
\(519\) 23.4491i 0.0451813i
\(520\) −552.900 347.028i −1.06327 0.667361i
\(521\) 416.563 721.509i 0.799546 1.38485i −0.120366 0.992730i \(-0.538407\pi\)
0.919912 0.392125i \(-0.128260\pi\)
\(522\) −300.806 + 246.165i −0.576257 + 0.471580i
\(523\) 438.217 + 759.014i 0.837891 + 1.45127i 0.891655 + 0.452715i \(0.149545\pi\)
−0.0537645 + 0.998554i \(0.517122\pi\)
\(524\) −505.051 445.413i −0.963838 0.850025i
\(525\) 0 0
\(526\) 705.970 + 266.831i 1.34215 + 0.507284i
\(527\) −179.395 + 103.574i −0.340408 + 0.196535i
\(528\) 107.861 + 45.3830i 0.204281 + 0.0859527i
\(529\) 39.1081 67.7372i 0.0739283 0.128048i
\(530\) 142.903 23.3889i 0.269628 0.0441300i
\(531\) 263.546 0.496321
\(532\) 0 0
\(533\) 62.9662i 0.118135i
\(534\) 129.425 21.1830i 0.242369 0.0396686i
\(535\) −497.524 287.245i −0.929951 0.536907i
\(536\) 23.2079 628.591i 0.0432984 1.17274i
\(537\) 86.3431 + 149.551i 0.160788 + 0.278493i
\(538\) 52.6884 + 19.9143i 0.0979338 + 0.0370155i
\(539\) 0 0
\(540\) −247.196 + 280.294i −0.457770 + 0.519063i
\(541\) −351.532 + 202.957i −0.649783 + 0.375152i −0.788373 0.615198i \(-0.789076\pi\)
0.138590 + 0.990350i \(0.455743\pi\)
\(542\) −618.674 + 506.292i −1.14147 + 0.934118i
\(543\) 20.5310 + 11.8536i 0.0378103 + 0.0218298i
\(544\) −112.022 378.762i −0.205922 0.696254i
\(545\) −1181.97 −2.16875
\(546\) 0 0
\(547\) −606.024 −1.10791 −0.553953 0.832548i \(-0.686881\pi\)
−0.553953 + 0.832548i \(0.686881\pi\)
\(548\) −27.4468 + 136.003i −0.0500855 + 0.248181i
\(549\) 114.199 + 65.9329i 0.208013 + 0.120096i
\(550\) 895.055 + 1093.73i 1.62737 + 1.98860i
\(551\) −561.298 + 324.066i −1.01869 + 0.588141i
\(552\) 54.0101 + 102.069i 0.0978444 + 0.184909i
\(553\) 0 0
\(554\) 192.603 + 72.7971i 0.347659 + 0.131403i
\(555\) 42.9949 + 74.4694i 0.0774684 + 0.134179i
\(556\) −408.185 + 137.293i −0.734146 + 0.246930i
\(557\) −31.5616 18.2221i −0.0566635 0.0327147i 0.471401 0.881919i \(-0.343749\pi\)
−0.528064 + 0.849204i \(0.677082\pi\)
\(558\) −46.9324 286.750i −0.0841082 0.513889i
\(559\) 206.213i 0.368896i
\(560\) 0 0
\(561\) 90.2742 0.160917
\(562\) −296.526 + 48.5324i −0.527626 + 0.0863565i
\(563\) −93.1945 + 161.418i −0.165532 + 0.286710i −0.936844 0.349747i \(-0.886267\pi\)
0.771312 + 0.636457i \(0.219601\pi\)
\(564\) −4.63091 13.7681i −0.00821083 0.0244115i
\(565\) 1081.33 624.306i 1.91386 1.10497i
\(566\) −126.262 + 334.058i −0.223078 + 0.590208i
\(567\) 0 0
\(568\) −65.6081 123.988i −0.115507 0.218288i
\(569\) 335.446 + 581.009i 0.589536 + 1.02111i 0.994293 + 0.106682i \(0.0340225\pi\)
−0.404758 + 0.914424i \(0.632644\pi\)
\(570\) −236.449 + 193.498i −0.414823 + 0.339471i
\(571\) 338.541 586.371i 0.592892 1.02692i −0.400949 0.916100i \(-0.631320\pi\)
0.993841 0.110818i \(-0.0353471\pi\)
\(572\) −442.211 89.2427i −0.773096 0.156019i
\(573\) 91.9271i 0.160431i
\(574\) 0 0
\(575\) 1394.67i 2.42552i
\(576\) 552.530 + 40.8552i 0.959254 + 0.0709291i
\(577\) 463.950 803.586i 0.804073 1.39270i −0.112841 0.993613i \(-0.535995\pi\)
0.916915 0.399083i \(-0.130671\pi\)
\(578\) 173.081 + 211.500i 0.299448 + 0.365917i
\(579\) −76.5341 132.561i −0.132183 0.228948i
\(580\) −608.382 536.542i −1.04893 0.925073i
\(581\) 0 0
\(582\) 67.9756 179.847i 0.116797 0.309015i
\(583\) 86.6642 50.0356i 0.148652 0.0858244i
\(584\) 13.7801 373.236i 0.0235960 0.639103i
\(585\) 353.191 611.745i 0.603745 1.04572i
\(586\) 70.8072 + 432.622i 0.120831 + 0.738263i
\(587\) 321.120 0.547053 0.273526 0.961865i \(-0.411810\pi\)
0.273526 + 0.961865i \(0.411810\pi\)
\(588\) 0 0
\(589\) 484.508i 0.822595i
\(590\) 88.8373 + 542.783i 0.150572 + 0.919971i
\(591\) 73.7028 + 42.5523i 0.124709 + 0.0720005i
\(592\) 100.838 239.659i 0.170335 0.404829i
\(593\) −109.627 189.880i −0.184869 0.320203i 0.758663 0.651483i \(-0.225853\pi\)
−0.943532 + 0.331280i \(0.892519\pi\)
\(594\) −91.3137 + 241.593i −0.153727 + 0.406723i
\(595\) 0 0
\(596\) 667.196 756.529i 1.11946 1.26934i
\(597\) 198.107 114.377i 0.331837 0.191586i
\(598\) −281.943 344.526i −0.471477 0.576131i
\(599\) −134.062 77.4010i −0.223811 0.129217i 0.383903 0.923373i \(-0.374580\pi\)
−0.607713 + 0.794156i \(0.707913\pi\)
\(600\) −224.651 141.002i −0.374418 0.235003i
\(601\) −205.862 −0.342533 −0.171266 0.985225i \(-0.554786\pi\)
−0.171266 + 0.985225i \(0.554786\pi\)
\(602\) 0 0
\(603\) 680.666 1.12880
\(604\) 919.409 + 185.546i 1.52220 + 0.307195i
\(605\) 272.882 + 157.548i 0.451045 + 0.260411i
\(606\) 11.0005 9.00228i 0.0181527 0.0148552i
\(607\) −684.735 + 395.332i −1.12806 + 0.651288i −0.943447 0.331523i \(-0.892438\pi\)
−0.184616 + 0.982811i \(0.559104\pi\)
\(608\) 898.225 + 216.044i 1.47734 + 0.355335i
\(609\) 0 0
\(610\) −97.2965 + 257.422i −0.159502 + 0.422004i
\(611\) 28.0000 + 48.4974i 0.0458265 + 0.0793739i
\(612\) 405.110 136.259i 0.661944 0.222645i
\(613\) −642.133 370.736i −1.04753 0.604789i −0.125570 0.992085i \(-0.540076\pi\)
−0.921955 + 0.387296i \(0.873409\pi\)
\(614\) −625.022 + 102.297i −1.01795 + 0.166608i
\(615\) 36.8848i 0.0599752i
\(616\) 0 0
\(617\) 171.578 0.278084 0.139042 0.990286i \(-0.455598\pi\)
0.139042 + 0.990286i \(0.455598\pi\)
\(618\) −20.1689 123.229i −0.0326358 0.199400i
\(619\) −270.099 + 467.825i −0.436347 + 0.755776i −0.997405 0.0720012i \(-0.977061\pi\)
0.561057 + 0.827777i \(0.310395\pi\)
\(620\) 574.752 193.318i 0.927019 0.311803i
\(621\) −220.727 + 127.437i −0.355438 + 0.205212i
\(622\) 135.196 + 51.0993i 0.217357 + 0.0821532i
\(623\) 0 0
\(624\) 84.0000 10.5830i 0.134615 0.0169599i
\(625\) −581.691 1007.52i −0.930705 1.61203i
\(626\) 103.802 + 126.843i 0.165818 + 0.202625i
\(627\) −105.574 + 182.859i −0.168379 + 0.291641i
\(628\) −39.5891 7.98948i −0.0630400 0.0127221i
\(629\) 200.583i 0.318892i
\(630\) 0 0
\(631\) 269.399i 0.426940i 0.976950 + 0.213470i \(0.0684766\pi\)
−0.976950 + 0.213470i \(0.931523\pi\)
\(632\) −344.623 + 549.069i −0.545289 + 0.868780i
\(633\) −48.0488 + 83.2229i −0.0759064 + 0.131474i
\(634\) −168.941 + 138.253i −0.266468 + 0.218065i
\(635\) 516.884 + 895.270i 0.813991 + 1.40987i
\(636\) −12.4222 + 14.0855i −0.0195318 + 0.0221470i
\(637\) 0 0
\(638\) −524.382 198.198i −0.821915 0.310655i
\(639\) 131.457 75.8968i 0.205723 0.118774i
\(640\) 102.107 + 1151.73i 0.159542 + 1.79957i
\(641\) −18.0934 + 31.3386i −0.0282268 + 0.0488902i −0.879794 0.475356i \(-0.842319\pi\)
0.851567 + 0.524246i \(0.175653\pi\)
\(642\) 73.5313 12.0349i 0.114535 0.0187459i
\(643\) −266.297 −0.414148 −0.207074 0.978325i \(-0.566394\pi\)
−0.207074 + 0.978325i \(0.566394\pi\)
\(644\) 0 0
\(645\) 120.797i 0.187282i
\(646\) 703.336 115.115i 1.08876 0.178197i
\(647\) −940.708 543.118i −1.45395 0.839440i −0.455250 0.890363i \(-0.650450\pi\)
−0.998703 + 0.0509233i \(0.983784\pi\)
\(648\) −21.2083 + 574.431i −0.0327289 + 0.886468i
\(649\) 190.049 + 329.174i 0.292833 + 0.507202i
\(650\) 956.477 + 361.514i 1.47150 + 0.556176i
\(651\) 0 0
\(652\) −313.602 276.571i −0.480985 0.424189i
\(653\) 1035.20 597.674i 1.58530 0.915274i 0.591234 0.806500i \(-0.298641\pi\)
0.994066 0.108774i \(-0.0346926\pi\)
\(654\) 118.636 97.0859i 0.181401 0.148449i
\(655\) 1317.00 + 760.368i 2.01068 + 1.16087i
\(656\) −88.8588 + 67.4005i −0.135456 + 0.102745i
\(657\) 404.156 0.615154
\(658\) 0 0
\(659\) −685.220 −1.03979 −0.519894 0.854231i \(-0.674029\pi\)
−0.519894 + 0.854231i \(0.674029\pi\)
\(660\) −259.041 52.2771i −0.392487 0.0792078i
\(661\) −860.294 496.691i −1.30150 0.751423i −0.320842 0.947133i \(-0.603966\pi\)
−0.980662 + 0.195710i \(0.937299\pi\)
\(662\) −407.526 497.985i −0.615599 0.752243i
\(663\) 56.5634 32.6569i 0.0853143 0.0492563i
\(664\) −285.563 + 151.106i −0.430065 + 0.227569i
\(665\) 0 0
\(666\) 263.186 + 99.4749i 0.395174 + 0.149362i
\(667\) −276.603 479.091i −0.414697 0.718277i
\(668\) −378.435 1125.12i −0.566519 1.68431i
\(669\) −5.36882 3.09969i −0.00802514 0.00463332i
\(670\) 229.442 + 1401.86i 0.342450 + 2.09232i
\(671\) 190.183i 0.283432i
\(672\) 0 0
\(673\) 106.569 0.158349 0.0791743 0.996861i \(-0.474772\pi\)
0.0791743 + 0.996861i \(0.474772\pi\)
\(674\) −323.789 + 52.9946i −0.480400 + 0.0786270i
\(675\) 292.701 506.972i 0.433630 0.751070i
\(676\) 331.366 111.455i 0.490187 0.164874i
\(677\) −869.650 + 502.092i −1.28456 + 0.741643i −0.977679 0.210103i \(-0.932620\pi\)
−0.306885 + 0.951747i \(0.599287\pi\)
\(678\) −57.2548 + 151.482i −0.0844467 + 0.223425i
\(679\) 0 0
\(680\) 417.186 + 788.407i 0.613509 + 1.15942i
\(681\) 62.6224 + 108.465i 0.0919565 + 0.159273i
\(682\) 324.312 265.401i 0.475531 0.389151i
\(683\) 339.113 587.360i 0.496505 0.859971i −0.503487 0.864003i \(-0.667950\pi\)
0.999992 + 0.00403135i \(0.00128322\pi\)
\(684\) −197.762 + 979.940i −0.289125 + 1.43266i
\(685\) 313.327i 0.457411i
\(686\) 0 0
\(687\) 135.919i 0.197844i
\(688\) −291.011 + 220.735i −0.422980 + 0.320836i
\(689\) 36.2010 62.7020i 0.0525414 0.0910043i
\(690\) −165.159 201.819i −0.239360 0.292491i
\(691\) −182.587 316.250i −0.264236 0.457671i 0.703127 0.711064i \(-0.251787\pi\)
−0.967363 + 0.253394i \(0.918453\pi\)
\(692\) 105.910 120.090i 0.153049 0.173541i
\(693\) 0 0
\(694\) 233.563 617.951i 0.336547 0.890419i
\(695\) 842.250 486.273i 1.21187 0.699673i
\(696\) 105.135 + 3.88166i 0.151057 + 0.00557710i
\(697\) −43.0193 + 74.5117i −0.0617207 + 0.106903i
\(698\) −84.7669 517.913i −0.121443 0.741996i
\(699\) 112.976 0.161626
\(700\) 0 0
\(701\) 940.292i 1.34136i 0.741748 + 0.670679i \(0.233997\pi\)
−0.741748 + 0.670679i \(0.766003\pi\)
\(702\) 30.1822 + 184.409i 0.0429946 + 0.262691i
\(703\) 406.300 + 234.577i 0.577951 + 0.333680i
\(704\) 347.412 + 719.582i 0.493484 + 1.02213i
\(705\) 16.4020 + 28.4091i 0.0232653 + 0.0402966i
\(706\) −408.777 + 1081.52i −0.579004 + 1.53190i
\(707\) 0 0
\(708\) −53.5004 47.1829i −0.0755656 0.0666426i
\(709\) −915.785 + 528.729i −1.29166 + 0.745738i −0.978948 0.204110i \(-0.934570\pi\)
−0.312709 + 0.949849i \(0.601236\pi\)
\(710\) 200.624 + 245.157i 0.282569 + 0.345291i
\(711\) −607.505 350.743i −0.854438 0.493310i
\(712\) 758.502 + 476.074i 1.06531 + 0.668643i
\(713\) 413.547 0.580010
\(714\) 0 0
\(715\) 1018.77 1.42486
\(716\) −233.267 + 1155.87i −0.325792 + 1.61435i
\(717\) −166.354 96.0448i −0.232015 0.133954i
\(718\) 565.118 462.465i 0.787073 0.644101i
\(719\) 896.185 517.412i 1.24643 0.719628i 0.276036 0.961147i \(-0.410979\pi\)
0.970396 + 0.241520i \(0.0776458\pi\)
\(720\) −1241.37 + 156.397i −1.72412 + 0.217219i
\(721\) 0 0
\(722\) −334.094 + 883.930i −0.462734 + 1.22428i
\(723\) −21.0509 36.4612i −0.0291160 0.0504304i
\(724\) 51.6082 + 153.436i 0.0712820 + 0.211928i
\(725\) 1100.39 + 635.311i 1.51778 + 0.876291i
\(726\) −40.3305 + 6.60089i −0.0555516 + 0.00909214i
\(727\) 495.145i 0.681080i 0.940230 + 0.340540i \(0.110610\pi\)
−0.940230 + 0.340540i \(0.889390\pi\)
\(728\) 0 0
\(729\) −567.489 −0.778449
\(730\) 136.235 + 832.374i 0.186623 + 1.14024i
\(731\) −140.887 + 244.024i −0.192732 + 0.333822i
\(732\) −11.3786 33.8297i −0.0155446 0.0462155i
\(733\) 491.464 283.747i 0.670483 0.387103i −0.125777 0.992059i \(-0.540142\pi\)
0.796260 + 0.604955i \(0.206809\pi\)
\(734\) −972.965 367.746i −1.32556 0.501016i
\(735\) 0 0
\(736\) −184.402 + 766.672i −0.250546 + 1.04167i
\(737\) 490.843 + 850.165i 0.666001 + 1.15355i
\(738\) −76.4325 93.3983i −0.103567 0.126556i
\(739\) 272.350 471.725i 0.368539 0.638328i −0.620798 0.783970i \(-0.713191\pi\)
0.989337 + 0.145642i \(0.0465248\pi\)
\(740\) −116.156 + 575.572i −0.156968 + 0.777800i
\(741\) 152.766i 0.206162i
\(742\) 0 0
\(743\) 731.264i 0.984205i −0.870537 0.492102i \(-0.836229\pi\)
0.870537 0.492102i \(-0.163771\pi\)
\(744\) −41.8098 + 66.6132i −0.0561959 + 0.0895339i
\(745\) −1138.97 + 1972.76i −1.52883 + 2.64800i
\(746\) 815.237 667.149i 1.09281 0.894302i
\(747\) −174.803 302.767i −0.234006 0.405310i
\(748\) 462.323 + 407.731i 0.618079 + 0.545094i
\(749\) 0 0
\(750\) 312.804 + 118.229i 0.417072 + 0.157638i
\(751\) −577.000 + 333.131i −0.768309 + 0.443583i −0.832271 0.554369i \(-0.812960\pi\)
0.0639622 + 0.997952i \(0.479626\pi\)
\(752\) 38.4684 91.4268i 0.0511548 0.121578i
\(753\) 75.2498 130.336i 0.0999333 0.173090i
\(754\) −400.262 + 65.5109i −0.530852 + 0.0868845i
\(755\) −2118.15 −2.80550
\(756\) 0 0
\(757\) 238.623i 0.315222i 0.987501 + 0.157611i \(0.0503791\pi\)
−0.987501 + 0.157611i \(0.949621\pi\)
\(758\) 240.748 39.4032i 0.317609 0.0519832i
\(759\) −156.077 90.1113i −0.205636 0.118724i
\(760\) −2084.88 76.9751i −2.74327 0.101283i
\(761\) 307.465 + 532.545i 0.404028 + 0.699797i 0.994208 0.107475i \(-0.0342766\pi\)
−0.590180 + 0.807272i \(0.700943\pi\)
\(762\) −125.417 47.4032i −0.164589 0.0622090i
\(763\) 0 0
\(764\) 415.196 470.788i 0.543450 0.616215i
\(765\) −835.904 + 482.609i −1.09268 + 0.630862i
\(766\) −489.761 + 400.796i −0.639374 + 0.523232i
\(767\) 238.159 + 137.501i 0.310507 + 0.179271i
\(768\) −104.850 107.214i −0.136524 0.139601i
\(769\) −178.950 −0.232705 −0.116353 0.993208i \(-0.537120\pi\)
−0.116353 + 0.993208i \(0.537120\pi\)
\(770\) 0 0
\(771\) 187.072 0.242636
\(772\) 206.766 1024.56i 0.267832 1.32715i
\(773\) 546.994 + 315.807i 0.707625 + 0.408548i 0.810181 0.586180i \(-0.199369\pi\)
−0.102556 + 0.994727i \(0.532702\pi\)
\(774\) −250.315 305.877i −0.323404 0.395190i
\(775\) −822.593 + 474.925i −1.06141 + 0.612806i
\(776\) 1160.42 614.035i 1.49538 0.791282i
\(777\) 0 0
\(778\) 172.392 + 65.1580i 0.221583 + 0.0837507i
\(779\) −100.620 174.279i −0.129166 0.223722i
\(780\) −181.220 + 60.9533i −0.232333 + 0.0781453i