Properties

Label 294.3.g.c.19.1
Level $294$
Weight $3$
Character 294.19
Analytic conductor $8.011$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 294.g (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.01091977219\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 294.19
Dual form 294.3.g.c.31.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.878680 - 0.507306i) q^{5} +2.44949i q^{6} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.878680 - 0.507306i) q^{5} +2.44949i q^{6} +2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(1.24264 - 0.717439i) q^{10} +(5.12132 + 8.87039i) q^{11} +(-3.00000 - 1.73205i) q^{12} -8.95743i q^{13} -1.75736 q^{15} +(-2.00000 + 3.46410i) q^{16} +(26.3345 - 15.2042i) q^{17} +(2.12132 + 3.67423i) q^{18} +(13.9706 + 8.06591i) q^{19} +2.02922i q^{20} -14.4853 q^{22} +(3.36396 - 5.82655i) q^{23} +(4.24264 - 2.44949i) q^{24} +(-11.9853 - 20.7591i) q^{25} +(10.9706 + 6.33386i) q^{26} -5.19615i q^{27} +30.0000 q^{29} +(1.24264 - 2.15232i) q^{30} +(43.4558 - 25.0892i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(15.3640 + 8.87039i) q^{33} +43.0041i q^{34} -6.00000 q^{36} +(-15.4558 + 26.7703i) q^{37} +(-19.7574 + 11.4069i) q^{38} +(-7.75736 - 13.4361i) q^{39} +(-2.48528 - 1.43488i) q^{40} -7.10228i q^{41} -74.4264 q^{43} +(10.2426 - 17.7408i) q^{44} +(-2.63604 + 1.52192i) q^{45} +(4.75736 + 8.23999i) q^{46} +(50.4853 + 29.1477i) q^{47} +6.92820i q^{48} +33.8995 q^{50} +(26.3345 - 45.6127i) q^{51} +(-15.5147 + 8.95743i) q^{52} +(35.4853 + 61.4623i) q^{53} +(6.36396 + 3.67423i) q^{54} -10.3923i q^{55} +27.9411 q^{57} +(-21.2132 + 36.7423i) q^{58} +(-0.426407 + 0.246186i) q^{59} +(1.75736 + 3.04384i) q^{60} +(-2.48528 - 1.43488i) q^{61} +70.9631i q^{62} +8.00000 q^{64} +(-4.54416 + 7.87071i) q^{65} +(-21.7279 + 12.5446i) q^{66} +(-13.5147 - 23.4082i) q^{67} +(-52.6690 - 30.4085i) q^{68} -11.6531i q^{69} +50.6102 q^{71} +(4.24264 - 7.34847i) q^{72} +(-61.1543 + 35.3075i) q^{73} +(-21.8579 - 37.8589i) q^{74} +(-35.9558 - 20.7591i) q^{75} -32.2636i q^{76} +21.9411 q^{78} +(-66.9117 + 115.894i) q^{79} +(3.51472 - 2.02922i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(8.69848 + 5.02207i) q^{82} -104.415i q^{83} -30.8528 q^{85} +(52.6274 - 91.1534i) q^{86} +(45.0000 - 25.9808i) q^{87} +(14.4853 + 25.0892i) q^{88} +(-125.548 - 72.4850i) q^{89} -4.30463i q^{90} -13.4558 q^{92} +(43.4558 - 75.2677i) q^{93} +(-71.3970 + 41.2211i) q^{94} +(-8.18377 - 14.1747i) q^{95} +(-8.48528 - 4.89898i) q^{96} -100.705i q^{97} +30.7279 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 6q^{3} - 4q^{4} - 12q^{5} + 6q^{9} + O(q^{10}) \) \( 4q + 6q^{3} - 4q^{4} - 12q^{5} + 6q^{9} - 12q^{10} + 12q^{11} - 12q^{12} - 24q^{15} - 8q^{16} + 12q^{17} - 12q^{19} - 24q^{22} - 12q^{23} - 14q^{25} - 24q^{26} + 120q^{29} - 12q^{30} + 72q^{31} + 36q^{33} - 24q^{36} + 40q^{37} - 96q^{38} - 48q^{39} + 24q^{40} - 128q^{43} + 24q^{44} - 36q^{45} + 36q^{46} + 168q^{47} + 96q^{50} + 12q^{51} - 96q^{52} + 108q^{53} - 24q^{57} + 168q^{59} + 24q^{60} + 24q^{61} + 32q^{64} - 120q^{65} - 36q^{66} - 88q^{67} - 24q^{68} - 120q^{71} - 24q^{73} - 144q^{74} - 42q^{75} - 48q^{78} - 64q^{79} + 48q^{80} - 18q^{81} - 84q^{82} + 216q^{85} + 120q^{86} + 180q^{87} + 24q^{88} - 324q^{89} + 48q^{92} + 72q^{93} - 48q^{94} + 120q^{95} + 72q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 1.22474i −0.353553 + 0.612372i
\(3\) 1.50000 0.866025i 0.500000 0.288675i
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) −0.878680 0.507306i −0.175736 0.101461i 0.409552 0.912287i \(-0.365685\pi\)
−0.585288 + 0.810826i \(0.699018\pi\)
\(6\) 2.44949i 0.408248i
\(7\) 0 0
\(8\) 2.82843 0.353553
\(9\) 1.50000 2.59808i 0.166667 0.288675i
\(10\) 1.24264 0.717439i 0.124264 0.0717439i
\(11\) 5.12132 + 8.87039i 0.465575 + 0.806399i 0.999227 0.0393049i \(-0.0125144\pi\)
−0.533653 + 0.845704i \(0.679181\pi\)
\(12\) −3.00000 1.73205i −0.250000 0.144338i
\(13\) 8.95743i 0.689033i −0.938780 0.344516i \(-0.888043\pi\)
0.938780 0.344516i \(-0.111957\pi\)
\(14\) 0 0
\(15\) −1.75736 −0.117157
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 26.3345 15.2042i 1.54909 0.894367i 0.550878 0.834586i \(-0.314293\pi\)
0.998211 0.0597816i \(-0.0190404\pi\)
\(18\) 2.12132 + 3.67423i 0.117851 + 0.204124i
\(19\) 13.9706 + 8.06591i 0.735293 + 0.424521i 0.820355 0.571854i \(-0.193776\pi\)
−0.0850625 + 0.996376i \(0.527109\pi\)
\(20\) 2.02922i 0.101461i
\(21\) 0 0
\(22\) −14.4853 −0.658422
\(23\) 3.36396 5.82655i 0.146259 0.253328i −0.783583 0.621287i \(-0.786610\pi\)
0.929842 + 0.367959i \(0.119943\pi\)
\(24\) 4.24264 2.44949i 0.176777 0.102062i
\(25\) −11.9853 20.7591i −0.479411 0.830365i
\(26\) 10.9706 + 6.33386i 0.421945 + 0.243610i
\(27\) 5.19615i 0.192450i
\(28\) 0 0
\(29\) 30.0000 1.03448 0.517241 0.855840i \(-0.326959\pi\)
0.517241 + 0.855840i \(0.326959\pi\)
\(30\) 1.24264 2.15232i 0.0414214 0.0717439i
\(31\) 43.4558 25.0892i 1.40180 0.809330i 0.407224 0.913328i \(-0.366497\pi\)
0.994578 + 0.103998i \(0.0331635\pi\)
\(32\) −2.82843 4.89898i −0.0883883 0.153093i
\(33\) 15.3640 + 8.87039i 0.465575 + 0.268800i
\(34\) 43.0041i 1.26483i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) −15.4558 + 26.7703i −0.417726 + 0.723522i −0.995710 0.0925257i \(-0.970506\pi\)
0.577985 + 0.816048i \(0.303839\pi\)
\(38\) −19.7574 + 11.4069i −0.519931 + 0.300182i
\(39\) −7.75736 13.4361i −0.198907 0.344516i
\(40\) −2.48528 1.43488i −0.0621320 0.0358719i
\(41\) 7.10228i 0.173226i −0.996242 0.0866132i \(-0.972396\pi\)
0.996242 0.0866132i \(-0.0276044\pi\)
\(42\) 0 0
\(43\) −74.4264 −1.73085 −0.865423 0.501041i \(-0.832950\pi\)
−0.865423 + 0.501041i \(0.832950\pi\)
\(44\) 10.2426 17.7408i 0.232787 0.403199i
\(45\) −2.63604 + 1.52192i −0.0585786 + 0.0338204i
\(46\) 4.75736 + 8.23999i 0.103421 + 0.179130i
\(47\) 50.4853 + 29.1477i 1.07415 + 0.620164i 0.929314 0.369291i \(-0.120400\pi\)
0.144841 + 0.989455i \(0.453733\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 0 0
\(50\) 33.8995 0.677990
\(51\) 26.3345 45.6127i 0.516363 0.894367i
\(52\) −15.5147 + 8.95743i −0.298360 + 0.172258i
\(53\) 35.4853 + 61.4623i 0.669534 + 1.15967i 0.978035 + 0.208442i \(0.0668393\pi\)
−0.308501 + 0.951224i \(0.599827\pi\)
\(54\) 6.36396 + 3.67423i 0.117851 + 0.0680414i
\(55\) 10.3923i 0.188951i
\(56\) 0 0
\(57\) 27.9411 0.490195
\(58\) −21.2132 + 36.7423i −0.365745 + 0.633489i
\(59\) −0.426407 + 0.246186i −0.00722724 + 0.00417265i −0.503609 0.863932i \(-0.667995\pi\)
0.496382 + 0.868104i \(0.334662\pi\)
\(60\) 1.75736 + 3.04384i 0.0292893 + 0.0507306i
\(61\) −2.48528 1.43488i −0.0407423 0.0235226i 0.479490 0.877547i \(-0.340821\pi\)
−0.520233 + 0.854024i \(0.674155\pi\)
\(62\) 70.9631i 1.14457i
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) −4.54416 + 7.87071i −0.0699101 + 0.121088i
\(66\) −21.7279 + 12.5446i −0.329211 + 0.190070i
\(67\) −13.5147 23.4082i −0.201712 0.349376i 0.747368 0.664410i \(-0.231317\pi\)
−0.949080 + 0.315035i \(0.897984\pi\)
\(68\) −52.6690 30.4085i −0.774545 0.447184i
\(69\) 11.6531i 0.168886i
\(70\) 0 0
\(71\) 50.6102 0.712819 0.356410 0.934330i \(-0.384001\pi\)
0.356410 + 0.934330i \(0.384001\pi\)
\(72\) 4.24264 7.34847i 0.0589256 0.102062i
\(73\) −61.1543 + 35.3075i −0.837731 + 0.483664i −0.856492 0.516160i \(-0.827361\pi\)
0.0187616 + 0.999824i \(0.494028\pi\)
\(74\) −21.8579 37.8589i −0.295377 0.511607i
\(75\) −35.9558 20.7591i −0.479411 0.276788i
\(76\) 32.2636i 0.424521i
\(77\) 0 0
\(78\) 21.9411 0.281296
\(79\) −66.9117 + 115.894i −0.846983 + 1.46702i 0.0369042 + 0.999319i \(0.488250\pi\)
−0.883888 + 0.467699i \(0.845083\pi\)
\(80\) 3.51472 2.02922i 0.0439340 0.0253653i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 8.69848 + 5.02207i 0.106079 + 0.0612448i
\(83\) 104.415i 1.25802i −0.777398 0.629009i \(-0.783461\pi\)
0.777398 0.629009i \(-0.216539\pi\)
\(84\) 0 0
\(85\) −30.8528 −0.362974
\(86\) 52.6274 91.1534i 0.611947 1.05992i
\(87\) 45.0000 25.9808i 0.517241 0.298629i
\(88\) 14.4853 + 25.0892i 0.164605 + 0.285105i
\(89\) −125.548 72.4850i −1.41065 0.814438i −0.415199 0.909730i \(-0.636288\pi\)
−0.995449 + 0.0952921i \(0.969621\pi\)
\(90\) 4.30463i 0.0478293i
\(91\) 0 0
\(92\) −13.4558 −0.146259
\(93\) 43.4558 75.2677i 0.467267 0.809330i
\(94\) −71.3970 + 41.2211i −0.759542 + 0.438522i
\(95\) −8.18377 14.1747i −0.0861449 0.149207i
\(96\) −8.48528 4.89898i −0.0883883 0.0510310i
\(97\) 100.705i 1.03820i −0.854714 0.519099i \(-0.826268\pi\)
0.854714 0.519099i \(-0.173732\pi\)
\(98\) 0 0
\(99\) 30.7279 0.310383
\(100\) −23.9706 + 41.5182i −0.239706 + 0.415182i
\(101\) −120.276 + 69.4412i −1.19085 + 0.687536i −0.958499 0.285096i \(-0.907975\pi\)
−0.232349 + 0.972632i \(0.574641\pi\)
\(102\) 37.2426 + 64.5061i 0.365124 + 0.632413i
\(103\) −68.3087 39.4380i −0.663191 0.382893i 0.130301 0.991475i \(-0.458406\pi\)
−0.793492 + 0.608581i \(0.791739\pi\)
\(104\) 25.3354i 0.243610i
\(105\) 0 0
\(106\) −100.368 −0.946864
\(107\) 18.8787 32.6988i 0.176436 0.305597i −0.764221 0.644954i \(-0.776876\pi\)
0.940657 + 0.339358i \(0.110210\pi\)
\(108\) −9.00000 + 5.19615i −0.0833333 + 0.0481125i
\(109\) −15.9706 27.6618i −0.146519 0.253778i 0.783420 0.621493i \(-0.213474\pi\)
−0.929939 + 0.367715i \(0.880140\pi\)
\(110\) 12.7279 + 7.34847i 0.115708 + 0.0668043i
\(111\) 53.5406i 0.482348i
\(112\) 0 0
\(113\) −106.971 −0.946642 −0.473321 0.880890i \(-0.656945\pi\)
−0.473321 + 0.880890i \(0.656945\pi\)
\(114\) −19.7574 + 34.2208i −0.173310 + 0.300182i
\(115\) −5.91169 + 3.41311i −0.0514060 + 0.0296793i
\(116\) −30.0000 51.9615i −0.258621 0.447944i
\(117\) −23.2721 13.4361i −0.198907 0.114839i
\(118\) 0.696320i 0.00590101i
\(119\) 0 0
\(120\) −4.97056 −0.0414214
\(121\) 8.04416 13.9329i 0.0664806 0.115148i
\(122\) 3.51472 2.02922i 0.0288092 0.0166330i
\(123\) −6.15076 10.6534i −0.0500062 0.0866132i
\(124\) −86.9117 50.1785i −0.700901 0.404665i
\(125\) 49.6861i 0.397489i
\(126\) 0 0
\(127\) 22.0589 0.173692 0.0868460 0.996222i \(-0.472321\pi\)
0.0868460 + 0.996222i \(0.472321\pi\)
\(128\) −5.65685 + 9.79796i −0.0441942 + 0.0765466i
\(129\) −111.640 + 64.4552i −0.865423 + 0.499652i
\(130\) −6.42641 11.1309i −0.0494339 0.0856220i
\(131\) 61.4558 + 35.4815i 0.469129 + 0.270852i 0.715875 0.698229i \(-0.246028\pi\)
−0.246746 + 0.969080i \(0.579361\pi\)
\(132\) 35.4815i 0.268800i
\(133\) 0 0
\(134\) 38.2254 0.285264
\(135\) −2.63604 + 4.56575i −0.0195262 + 0.0338204i
\(136\) 74.4853 43.0041i 0.547686 0.316207i
\(137\) 52.8823 + 91.5947i 0.386002 + 0.668575i 0.991908 0.126962i \(-0.0405225\pi\)
−0.605906 + 0.795536i \(0.707189\pi\)
\(138\) 14.2721 + 8.23999i 0.103421 + 0.0597101i
\(139\) 181.322i 1.30447i 0.758015 + 0.652237i \(0.226169\pi\)
−0.758015 + 0.652237i \(0.773831\pi\)
\(140\) 0 0
\(141\) 100.971 0.716103
\(142\) −35.7868 + 61.9845i −0.252020 + 0.436511i
\(143\) 79.4558 45.8739i 0.555635 0.320796i
\(144\) 6.00000 + 10.3923i 0.0416667 + 0.0721688i
\(145\) −26.3604 15.2192i −0.181796 0.104960i
\(146\) 99.8646i 0.684004i
\(147\) 0 0
\(148\) 61.8234 0.417726
\(149\) −20.5736 + 35.6345i −0.138078 + 0.239158i −0.926769 0.375632i \(-0.877426\pi\)
0.788691 + 0.614790i \(0.210759\pi\)
\(150\) 50.8492 29.3578i 0.338995 0.195719i
\(151\) −40.1838 69.6003i −0.266118 0.460929i 0.701738 0.712435i \(-0.252408\pi\)
−0.967856 + 0.251506i \(0.919074\pi\)
\(152\) 39.5147 + 22.8138i 0.259965 + 0.150091i
\(153\) 91.2255i 0.596245i
\(154\) 0 0
\(155\) −50.9117 −0.328463
\(156\) −15.5147 + 26.8723i −0.0994533 + 0.172258i
\(157\) −49.6325 + 28.6553i −0.316130 + 0.182518i −0.649666 0.760219i \(-0.725091\pi\)
0.333536 + 0.942737i \(0.391758\pi\)
\(158\) −94.6274 163.899i −0.598908 1.03734i
\(159\) 106.456 + 61.4623i 0.669534 + 0.386555i
\(160\) 5.73951i 0.0358719i
\(161\) 0 0
\(162\) 12.7279 0.0785674
\(163\) 87.4558 151.478i 0.536539 0.929313i −0.462548 0.886594i \(-0.653065\pi\)
0.999087 0.0427185i \(-0.0136019\pi\)
\(164\) −12.3015 + 7.10228i −0.0750092 + 0.0433066i
\(165\) −9.00000 15.5885i −0.0545455 0.0944755i
\(166\) 127.882 + 73.8329i 0.770375 + 0.444776i
\(167\) 196.163i 1.17463i 0.809359 + 0.587315i \(0.199815\pi\)
−0.809359 + 0.587315i \(0.800185\pi\)
\(168\) 0 0
\(169\) 88.7645 0.525234
\(170\) 21.8162 37.7868i 0.128331 0.222275i
\(171\) 41.9117 24.1977i 0.245098 0.141507i
\(172\) 74.4264 + 128.910i 0.432712 + 0.749479i
\(173\) 33.3640 + 19.2627i 0.192855 + 0.111345i 0.593319 0.804968i \(-0.297817\pi\)
−0.400463 + 0.916313i \(0.631151\pi\)
\(174\) 73.4847i 0.422326i
\(175\) 0 0
\(176\) −40.9706 −0.232787
\(177\) −0.426407 + 0.738558i −0.00240908 + 0.00417265i
\(178\) 177.551 102.509i 0.997479 0.575895i
\(179\) 95.5477 + 165.494i 0.533786 + 0.924545i 0.999221 + 0.0394627i \(0.0125646\pi\)
−0.465435 + 0.885082i \(0.654102\pi\)
\(180\) 5.27208 + 3.04384i 0.0292893 + 0.0169102i
\(181\) 120.793i 0.667367i 0.942685 + 0.333683i \(0.108292\pi\)
−0.942685 + 0.333683i \(0.891708\pi\)
\(182\) 0 0
\(183\) −4.97056 −0.0271615
\(184\) 9.51472 16.4800i 0.0517104 0.0895651i
\(185\) 27.1615 15.6817i 0.146819 0.0847659i
\(186\) 61.4558 + 106.445i 0.330408 + 0.572283i
\(187\) 269.735 + 155.732i 1.44243 + 0.832789i
\(188\) 116.591i 0.620164i
\(189\) 0 0
\(190\) 23.1472 0.121827
\(191\) −56.0330 + 97.0520i −0.293367 + 0.508126i −0.974604 0.223937i \(-0.928109\pi\)
0.681237 + 0.732063i \(0.261442\pi\)
\(192\) 12.0000 6.92820i 0.0625000 0.0360844i
\(193\) 11.4558 + 19.8421i 0.0593567 + 0.102809i 0.894177 0.447714i \(-0.147762\pi\)
−0.834820 + 0.550523i \(0.814428\pi\)
\(194\) 123.338 + 71.2093i 0.635763 + 0.367058i
\(195\) 15.7414i 0.0807252i
\(196\) 0 0
\(197\) −116.059 −0.589131 −0.294566 0.955631i \(-0.595175\pi\)
−0.294566 + 0.955631i \(0.595175\pi\)
\(198\) −21.7279 + 37.6339i −0.109737 + 0.190070i
\(199\) 141.250 81.5506i 0.709798 0.409802i −0.101188 0.994867i \(-0.532264\pi\)
0.810986 + 0.585065i \(0.198931\pi\)
\(200\) −33.8995 58.7156i −0.169497 0.293578i
\(201\) −40.5442 23.4082i −0.201712 0.116459i
\(202\) 196.409i 0.972323i
\(203\) 0 0
\(204\) −105.338 −0.516363
\(205\) −3.60303 + 6.24063i −0.0175758 + 0.0304421i
\(206\) 96.6030 55.7738i 0.468947 0.270747i
\(207\) −10.0919 17.4797i −0.0487531 0.0844428i
\(208\) 31.0294 + 17.9149i 0.149180 + 0.0861291i
\(209\) 165.232i 0.790586i
\(210\) 0 0
\(211\) 106.426 0.504391 0.252195 0.967676i \(-0.418847\pi\)
0.252195 + 0.967676i \(0.418847\pi\)
\(212\) 70.9706 122.925i 0.334767 0.579833i
\(213\) 75.9153 43.8297i 0.356410 0.205773i
\(214\) 26.6985 + 46.2431i 0.124759 + 0.216089i
\(215\) 65.3970 + 37.7570i 0.304172 + 0.175614i
\(216\) 14.6969i 0.0680414i
\(217\) 0 0
\(218\) 45.1716 0.207209
\(219\) −61.1543 + 105.922i −0.279244 + 0.483664i
\(220\) −18.0000 + 10.3923i −0.0818182 + 0.0472377i
\(221\) −136.191 235.890i −0.616248 1.06737i
\(222\) −65.5736 37.8589i −0.295377 0.170536i
\(223\) 57.0047i 0.255627i −0.991798 0.127813i \(-0.959204\pi\)
0.991798 0.127813i \(-0.0407958\pi\)
\(224\) 0 0
\(225\) −71.9117 −0.319608
\(226\) 75.6396 131.012i 0.334689 0.579698i
\(227\) 248.912 143.709i 1.09653 0.633080i 0.161221 0.986918i \(-0.448457\pi\)
0.935307 + 0.353838i \(0.115124\pi\)
\(228\) −27.9411 48.3954i −0.122549 0.212261i
\(229\) −120.728 69.7023i −0.527196 0.304377i 0.212678 0.977122i \(-0.431782\pi\)
−0.739874 + 0.672746i \(0.765115\pi\)
\(230\) 9.65375i 0.0419728i
\(231\) 0 0
\(232\) 84.8528 0.365745
\(233\) −181.368 + 314.138i −0.778401 + 1.34823i 0.154461 + 0.987999i \(0.450636\pi\)
−0.932863 + 0.360232i \(0.882698\pi\)
\(234\) 32.9117 19.0016i 0.140648 0.0812033i
\(235\) −29.5736 51.2230i −0.125845 0.217970i
\(236\) 0.852814 + 0.492372i 0.00361362 + 0.00208632i
\(237\) 231.789i 0.978012i
\(238\) 0 0
\(239\) 18.4781 0.0773144 0.0386572 0.999253i \(-0.487692\pi\)
0.0386572 + 0.999253i \(0.487692\pi\)
\(240\) 3.51472 6.08767i 0.0146447 0.0253653i
\(241\) −154.243 + 89.0520i −0.640011 + 0.369510i −0.784619 0.619979i \(-0.787141\pi\)
0.144608 + 0.989489i \(0.453808\pi\)
\(242\) 11.3762 + 19.7041i 0.0470089 + 0.0814218i
\(243\) −13.5000 7.79423i −0.0555556 0.0320750i
\(244\) 5.73951i 0.0235226i
\(245\) 0 0
\(246\) 17.3970 0.0707194
\(247\) 72.2498 125.140i 0.292509 0.506641i
\(248\) 122.912 70.9631i 0.495612 0.286142i
\(249\) −90.4264 156.623i −0.363158 0.629009i
\(250\) −60.8528 35.1334i −0.243411 0.140534i
\(251\) 50.6709i 0.201876i 0.994893 + 0.100938i \(0.0321844\pi\)
−0.994893 + 0.100938i \(0.967816\pi\)
\(252\) 0 0
\(253\) 68.9117 0.272378
\(254\) −15.5980 + 27.0165i −0.0614094 + 0.106364i
\(255\) −46.2792 + 26.7193i −0.181487 + 0.104782i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −162.452 93.7919i −0.632110 0.364949i 0.149459 0.988768i \(-0.452247\pi\)
−0.781569 + 0.623819i \(0.785580\pi\)
\(258\) 182.307i 0.706615i
\(259\) 0 0
\(260\) 18.1766 0.0699101
\(261\) 45.0000 77.9423i 0.172414 0.298629i
\(262\) −86.9117 + 50.1785i −0.331724 + 0.191521i
\(263\) 201.489 + 348.989i 0.766117 + 1.32695i 0.939654 + 0.342127i \(0.111147\pi\)
−0.173537 + 0.984827i \(0.555519\pi\)
\(264\) 43.4558 + 25.0892i 0.164605 + 0.0950350i
\(265\) 72.0076i 0.271727i
\(266\) 0 0
\(267\) −251.095 −0.940432
\(268\) −27.0294 + 46.8164i −0.100856 + 0.174688i
\(269\) −416.158 + 240.269i −1.54706 + 0.893193i −0.548691 + 0.836025i \(0.684874\pi\)
−0.998365 + 0.0571675i \(0.981793\pi\)
\(270\) −3.72792 6.45695i −0.0138071 0.0239146i
\(271\) 32.3087 + 18.6534i 0.119220 + 0.0688318i 0.558424 0.829556i \(-0.311406\pi\)
−0.439204 + 0.898387i \(0.644739\pi\)
\(272\) 121.634i 0.447184i
\(273\) 0 0
\(274\) −149.574 −0.545889
\(275\) 122.761 212.628i 0.446403 0.773193i
\(276\) −20.1838 + 11.6531i −0.0731296 + 0.0422214i
\(277\) 41.3381 + 71.5997i 0.149235 + 0.258483i 0.930945 0.365160i \(-0.118986\pi\)
−0.781710 + 0.623642i \(0.785652\pi\)
\(278\) −222.073 128.214i −0.798824 0.461201i
\(279\) 150.535i 0.539554i
\(280\) 0 0
\(281\) −150.853 −0.536843 −0.268421 0.963302i \(-0.586502\pi\)
−0.268421 + 0.963302i \(0.586502\pi\)
\(282\) −71.3970 + 123.663i −0.253181 + 0.438522i
\(283\) 246.088 142.079i 0.869570 0.502046i 0.00236468 0.999997i \(-0.499247\pi\)
0.867205 + 0.497951i \(0.165914\pi\)
\(284\) −50.6102 87.6594i −0.178205 0.308660i
\(285\) −24.5513 14.1747i −0.0861449 0.0497358i
\(286\) 129.751i 0.453674i
\(287\) 0 0
\(288\) −16.9706 −0.0589256
\(289\) 317.838 550.512i 1.09979 1.90488i
\(290\) 37.2792 21.5232i 0.128549 0.0742178i
\(291\) −87.2132 151.058i −0.299702 0.519099i
\(292\) 122.309 + 70.6149i 0.418865 + 0.241832i
\(293\) 537.237i 1.83357i −0.399379 0.916786i \(-0.630774\pi\)
0.399379 0.916786i \(-0.369226\pi\)
\(294\) 0 0
\(295\) 0.499567 0.00169345
\(296\) −43.7157 + 75.7179i −0.147688 + 0.255804i
\(297\) 46.0919 26.6112i 0.155192 0.0895999i
\(298\) −29.0955 50.3948i −0.0976358 0.169110i
\(299\) −52.1909 30.1324i −0.174552 0.100777i
\(300\) 83.0365i 0.276788i
\(301\) 0 0
\(302\) 113.657 0.376347
\(303\) −120.276 + 208.324i −0.396949 + 0.687536i
\(304\) −55.8823 + 32.2636i −0.183823 + 0.106130i
\(305\) 1.45584 + 2.52160i 0.00477326 + 0.00826753i
\(306\) 111.728 + 64.5061i 0.365124 + 0.210804i
\(307\) 34.7430i 0.113169i −0.998398 0.0565847i \(-0.981979\pi\)
0.998398 0.0565847i \(-0.0180211\pi\)
\(308\) 0 0
\(309\) −136.617 −0.442127
\(310\) 36.0000 62.3538i 0.116129 0.201141i
\(311\) −77.2203 + 44.5832i −0.248297 + 0.143354i −0.618984 0.785403i \(-0.712456\pi\)
0.370687 + 0.928758i \(0.379122\pi\)
\(312\) −21.9411 38.0031i −0.0703241 0.121805i
\(313\) −450.073 259.850i −1.43793 0.830191i −0.440227 0.897886i \(-0.645102\pi\)
−0.997706 + 0.0676951i \(0.978435\pi\)
\(314\) 81.0495i 0.258119i
\(315\) 0 0
\(316\) 267.647 0.846983
\(317\) −271.014 + 469.411i −0.854935 + 1.48079i 0.0217710 + 0.999763i \(0.493070\pi\)
−0.876706 + 0.481027i \(0.840264\pi\)
\(318\) −150.551 + 86.9208i −0.473432 + 0.273336i
\(319\) 153.640 + 266.112i 0.481629 + 0.834206i
\(320\) −7.02944 4.05845i −0.0219670 0.0126826i
\(321\) 65.3977i 0.203731i
\(322\) 0 0
\(323\) 490.544 1.51871
\(324\) −9.00000 + 15.5885i −0.0277778 + 0.0481125i
\(325\) −185.948 + 107.357i −0.572149 + 0.330330i
\(326\) 123.681 + 214.222i 0.379390 + 0.657123i
\(327\) −47.9117 27.6618i −0.146519 0.0845927i
\(328\) 20.0883i 0.0612448i
\(329\) 0 0
\(330\) 25.4558 0.0771389
\(331\) −89.8162 + 155.566i −0.271348 + 0.469989i −0.969207 0.246246i \(-0.920803\pi\)
0.697859 + 0.716235i \(0.254136\pi\)
\(332\) −180.853 + 104.415i −0.544737 + 0.314504i
\(333\) 46.3675 + 80.3109i 0.139242 + 0.241174i
\(334\) −240.250 138.708i −0.719311 0.415294i
\(335\) 27.4244i 0.0818638i
\(336\) 0 0
\(337\) 291.823 0.865945 0.432972 0.901407i \(-0.357465\pi\)
0.432972 + 0.901407i \(0.357465\pi\)
\(338\) −62.7660 + 108.714i −0.185698 + 0.321639i
\(339\) −160.456 + 92.6392i −0.473321 + 0.273272i
\(340\) 30.8528 + 53.4386i 0.0907436 + 0.157172i
\(341\) 445.103 + 256.980i 1.30529 + 0.753607i
\(342\) 68.4415i 0.200121i
\(343\) 0 0
\(344\) −210.510 −0.611947
\(345\) −5.91169 + 10.2393i −0.0171353 + 0.0296793i
\(346\) −47.1838 + 27.2416i −0.136369 + 0.0787328i
\(347\) −226.040 391.513i −0.651413 1.12828i −0.982780 0.184778i \(-0.940843\pi\)
0.331368 0.943502i \(-0.392490\pi\)
\(348\) −90.0000 51.9615i −0.258621 0.149315i
\(349\) 235.067i 0.673543i 0.941586 + 0.336772i \(0.109335\pi\)
−0.941586 + 0.336772i \(0.890665\pi\)
\(350\) 0 0
\(351\) −46.5442 −0.132604
\(352\) 28.9706 50.1785i 0.0823027 0.142553i
\(353\) −21.8635 + 12.6229i −0.0619363 + 0.0357590i −0.530648 0.847592i \(-0.678052\pi\)
0.468712 + 0.883351i \(0.344718\pi\)
\(354\) −0.603030 1.04448i −0.00170348 0.00295051i
\(355\) −44.4701 25.6748i −0.125268 0.0723235i
\(356\) 289.940i 0.814438i
\(357\) 0 0
\(358\) −270.250 −0.754888
\(359\) 53.1213 92.0088i 0.147970 0.256292i −0.782507 0.622642i \(-0.786059\pi\)
0.930477 + 0.366350i \(0.119393\pi\)
\(360\) −7.45584 + 4.30463i −0.0207107 + 0.0119573i
\(361\) −50.3823 87.2646i −0.139563 0.241730i
\(362\) −147.941 85.4138i −0.408677 0.235950i
\(363\) 27.8658i 0.0767652i
\(364\) 0 0
\(365\) 71.6468 0.196292
\(366\) 3.51472 6.08767i 0.00960306 0.0166330i
\(367\) −248.044 + 143.208i −0.675868 + 0.390213i −0.798297 0.602265i \(-0.794265\pi\)
0.122428 + 0.992477i \(0.460932\pi\)
\(368\) 13.4558 + 23.3062i 0.0365648 + 0.0633321i
\(369\) −18.4523 10.6534i −0.0500062 0.0288711i
\(370\) 44.3545i 0.119877i
\(371\) 0 0
\(372\) −173.823 −0.467267
\(373\) 211.735 366.736i 0.567654 0.983206i −0.429143 0.903237i \(-0.641184\pi\)
0.996797 0.0799696i \(-0.0254823\pi\)
\(374\) −381.463 + 220.238i −1.01995 + 0.588871i
\(375\) 43.0294 + 74.5292i 0.114745 + 0.198744i
\(376\) 142.794 + 82.4421i 0.379771 + 0.219261i
\(377\) 268.723i 0.712793i
\(378\) 0 0
\(379\) 101.103 0.266761 0.133381 0.991065i \(-0.457417\pi\)
0.133381 + 0.991065i \(0.457417\pi\)
\(380\) −16.3675 + 28.3494i −0.0430725 + 0.0746037i
\(381\) 33.0883 19.1035i 0.0868460 0.0501405i
\(382\) −79.2426 137.252i −0.207441 0.359299i
\(383\) −190.867 110.197i −0.498348 0.287721i 0.229683 0.973265i \(-0.426231\pi\)
−0.728031 + 0.685544i \(0.759564\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −32.4020 −0.0839431
\(387\) −111.640 + 193.365i −0.288474 + 0.499652i
\(388\) −174.426 + 100.705i −0.449553 + 0.259549i
\(389\) 191.735 + 332.095i 0.492892 + 0.853714i 0.999966 0.00818803i \(-0.00260636\pi\)
−0.507074 + 0.861902i \(0.669273\pi\)
\(390\) −19.2792 11.1309i −0.0494339 0.0285407i
\(391\) 204.586i 0.523238i
\(392\) 0 0
\(393\) 122.912 0.312752
\(394\) 82.0660 142.143i 0.208289 0.360768i
\(395\) 117.588 67.8894i 0.297691 0.171872i
\(396\) −30.7279 53.2223i −0.0775958 0.134400i
\(397\) 420.177 + 242.589i 1.05838 + 0.611056i 0.924984 0.380007i \(-0.124078\pi\)
0.133396 + 0.991063i \(0.457412\pi\)
\(398\) 230.660i 0.579548i
\(399\) 0 0
\(400\) 95.8823 0.239706
\(401\) 126.588 219.257i 0.315680 0.546775i −0.663901 0.747820i \(-0.731101\pi\)
0.979582 + 0.201045i \(0.0644339\pi\)
\(402\) 57.3381 33.1042i 0.142632 0.0823487i
\(403\) −224.735 389.253i −0.557655 0.965887i
\(404\) 240.551 + 138.882i 0.595424 + 0.343768i
\(405\) 9.13151i 0.0225469i
\(406\) 0 0
\(407\) −316.617 −0.777930
\(408\) 74.4853 129.012i 0.182562 0.316207i
\(409\) 4.66905 2.69568i 0.0114158 0.00659089i −0.494281 0.869302i \(-0.664569\pi\)
0.505697 + 0.862711i \(0.331235\pi\)
\(410\) −5.09545 8.82559i −0.0124279 0.0215258i
\(411\) 158.647 + 91.5947i 0.386002 + 0.222858i
\(412\) 157.752i 0.382893i
\(413\) 0 0
\(414\) 28.5442 0.0689472
\(415\) −52.9706 + 91.7477i −0.127640 + 0.221079i
\(416\) −43.8823 + 25.3354i −0.105486 + 0.0609025i
\(417\) 157.029 + 271.983i 0.376569 + 0.652237i
\(418\) −202.368 116.837i −0.484133 0.279514i
\(419\) 294.431i 0.702700i 0.936244 + 0.351350i \(0.114277\pi\)
−0.936244 + 0.351350i \(0.885723\pi\)
\(420\) 0 0
\(421\) −290.441 −0.689883 −0.344941 0.938624i \(-0.612101\pi\)
−0.344941 + 0.938624i \(0.612101\pi\)
\(422\) −75.2548 + 130.345i −0.178329 + 0.308875i
\(423\) 151.456 87.4431i 0.358052 0.206721i
\(424\) 100.368 + 173.842i 0.236716 + 0.410004i
\(425\) −631.253 364.454i −1.48530 0.857540i
\(426\) 123.969i 0.291007i
\(427\) 0 0
\(428\) −75.5147 −0.176436
\(429\) 79.4558 137.622i 0.185212 0.320796i
\(430\) −92.4853 + 53.3964i −0.215082 + 0.124178i
\(431\) −25.3568 43.9193i −0.0588325 0.101901i 0.835109 0.550084i \(-0.185404\pi\)
−0.893942 + 0.448183i \(0.852071\pi\)
\(432\) 18.0000 + 10.3923i 0.0416667 + 0.0240563i
\(433\) 724.761i 1.67381i −0.547347 0.836906i \(-0.684362\pi\)
0.547347 0.836906i \(-0.315638\pi\)
\(434\) 0 0
\(435\) −52.7208 −0.121197
\(436\) −31.9411 + 55.3237i −0.0732595 + 0.126889i
\(437\) 93.9929 54.2668i 0.215087 0.124180i
\(438\) −86.4853 149.797i −0.197455 0.342002i
\(439\) 321.926 + 185.864i 0.733317 + 0.423381i 0.819634 0.572887i \(-0.194177\pi\)
−0.0863177 + 0.996268i \(0.527510\pi\)
\(440\) 29.3939i 0.0668043i
\(441\) 0 0
\(442\) 385.206 0.871507
\(443\) 114.629 198.543i 0.258756 0.448178i −0.707153 0.707061i \(-0.750021\pi\)
0.965909 + 0.258882i \(0.0833541\pi\)
\(444\) 92.7351 53.5406i 0.208863 0.120587i
\(445\) 73.5442 + 127.382i 0.165268 + 0.286252i
\(446\) 69.8162 + 40.3084i 0.156539 + 0.0903776i
\(447\) 71.2690i 0.159439i
\(448\) 0 0
\(449\) −600.323 −1.33702 −0.668511 0.743702i \(-0.733068\pi\)
−0.668511 + 0.743702i \(0.733068\pi\)
\(450\) 50.8492 88.0735i 0.112998 0.195719i
\(451\) 63.0000 36.3731i 0.139690 0.0806498i
\(452\) 106.971 + 185.278i 0.236661 + 0.409908i
\(453\) −120.551 69.6003i −0.266118 0.153643i
\(454\) 406.471i 0.895311i
\(455\) 0 0
\(456\) 79.0294 0.173310
\(457\) −241.912 + 419.003i −0.529347 + 0.916856i 0.470067 + 0.882631i \(0.344230\pi\)
−0.999414 + 0.0342255i \(0.989104\pi\)
\(458\) 170.735 98.5739i 0.372784 0.215227i
\(459\) −79.0036 136.838i −0.172121 0.298122i
\(460\) 11.8234 + 6.82623i 0.0257030 + 0.0148396i
\(461\) 274.661i 0.595794i 0.954598 + 0.297897i \(0.0962852\pi\)
−0.954598 + 0.297897i \(0.903715\pi\)
\(462\) 0 0
\(463\) −153.470 −0.331469 −0.165734 0.986170i \(-0.552999\pi\)
−0.165734 + 0.986170i \(0.552999\pi\)
\(464\) −60.0000 + 103.923i −0.129310 + 0.223972i
\(465\) −76.3675 + 44.0908i −0.164231 + 0.0948190i
\(466\) −256.492 444.258i −0.550413 0.953343i
\(467\) 53.4701 + 30.8710i 0.114497 + 0.0661049i 0.556155 0.831079i \(-0.312276\pi\)
−0.441658 + 0.897184i \(0.645609\pi\)
\(468\) 53.7446i 0.114839i
\(469\) 0 0
\(470\) 83.6468 0.177972
\(471\) −49.6325 + 85.9660i −0.105377 + 0.182518i
\(472\) −1.20606 + 0.696320i −0.00255521 + 0.00147525i
\(473\) −381.161 660.191i −0.805838 1.39575i
\(474\) −283.882 163.899i −0.598908 0.345780i
\(475\) 386.689i 0.814082i
\(476\) 0 0
\(477\) 212.912 0.446356
\(478\) −13.0660 + 22.6310i −0.0273348 + 0.0473452i
\(479\) 481.955 278.257i 1.00617 0.580912i 0.0961020 0.995371i \(-0.469363\pi\)
0.910068 + 0.414459i \(0.136029\pi\)
\(480\) 4.97056 + 8.60927i 0.0103553 + 0.0179360i
\(481\) 239.793 + 138.445i 0.498530 + 0.287827i
\(482\) 251.877i 0.522567i
\(483\) 0 0
\(484\) −32.1766 −0.0664806
\(485\) −51.0883 + 88.4876i −0.105337 + 0.182449i
\(486\) 19.0919 11.0227i 0.0392837 0.0226805i
\(487\) 162.610 + 281.649i 0.333902 + 0.578335i 0.983273 0.182136i \(-0.0583013\pi\)
−0.649371 + 0.760471i \(0.724968\pi\)
\(488\) −7.02944 4.05845i −0.0144046 0.00831649i
\(489\) 302.956i 0.619542i
\(490\) 0 0
\(491\) 643.477 1.31054 0.655272 0.755393i \(-0.272554\pi\)
0.655272 + 0.755393i \(0.272554\pi\)
\(492\) −12.3015 + 21.3068i −0.0250031 + 0.0433066i
\(493\) 790.036 456.127i 1.60251 0.925208i
\(494\) 102.177 + 176.975i 0.206835 + 0.358249i
\(495\) −27.0000 15.5885i −0.0545455 0.0314918i
\(496\) 200.714i 0.404665i
\(497\) 0 0
\(498\) 255.765 0.513583
\(499\) −377.713 + 654.218i −0.756939 + 1.31106i 0.187465 + 0.982271i \(0.439973\pi\)
−0.944404 + 0.328786i \(0.893360\pi\)
\(500\) 86.0589 49.6861i 0.172118 0.0993722i
\(501\) 169.882 + 294.245i 0.339086 + 0.587315i
\(502\) −62.0589 35.8297i −0.123623 0.0713739i
\(503\) 509.409i 1.01274i −0.862316 0.506371i \(-0.830987\pi\)
0.862316 0.506371i \(-0.169013\pi\)
\(504\) 0 0
\(505\) 140.912 0.279033
\(506\) −48.7279 + 84.3992i −0.0963002 + 0.166797i
\(507\) 133.147 76.8723i 0.262617 0.151622i
\(508\) −22.0589 38.2071i −0.0434230 0.0752108i
\(509\) 666.349 + 384.717i 1.30913 + 0.755828i 0.981951 0.189133i \(-0.0605677\pi\)
0.327182 + 0.944961i \(0.393901\pi\)
\(510\) 75.5737i 0.148184i
\(511\) 0 0
\(512\) 22.6274 0.0441942
\(513\) 41.9117 72.5932i 0.0816992 0.141507i
\(514\) 229.742 132.642i 0.446969 0.258058i
\(515\) 40.0143 + 69.3068i 0.0776976 + 0.134576i
\(516\) 223.279 + 128.910i 0.432712 + 0.249826i
\(517\) 597.099i 1.15493i
\(518\) 0 0
\(519\) 66.7279 0.128570
\(520\) −12.8528 + 22.2617i −0.0247169 + 0.0428110i
\(521\) 463.503 267.604i 0.889641 0.513635i 0.0158162 0.999875i \(-0.494965\pi\)
0.873825 + 0.486240i \(0.161632\pi\)
\(522\) 63.6396 + 110.227i 0.121915 + 0.211163i
\(523\) −726.999 419.733i −1.39006 0.802549i −0.396735 0.917933i \(-0.629857\pi\)
−0.993321 + 0.115384i \(0.963190\pi\)
\(524\) 141.926i 0.270852i
\(525\) 0 0
\(526\) −569.897 −1.08345
\(527\) 762.926 1321.43i 1.44768 2.50745i
\(528\) −61.4558 + 35.4815i −0.116394 + 0.0671999i
\(529\) 241.868 + 418.927i 0.457217 + 0.791922i
\(530\) 88.1909 + 50.9170i 0.166398 + 0.0960699i
\(531\) 1.47712i 0.00278176i
\(532\) 0 0
\(533\) −63.6182 −0.119359
\(534\) 177.551 307.528i 0.332493 0.575895i
\(535\) −33.1766 + 19.1545i −0.0620124 + 0.0358029i
\(536\) −38.2254 66.2083i −0.0713160 0.123523i
\(537\) 286.643 + 165.494i 0.533786 + 0.308182i
\(538\) 679.583i 1.26317i
\(539\) 0 0
\(540\) 10.5442 0.0195262
\(541\) −142.926 + 247.555i −0.264188 + 0.457588i −0.967351 0.253442i \(-0.918437\pi\)
0.703162 + 0.711029i \(0.251771\pi\)
\(542\) −45.6913 + 26.3799i −0.0843014 + 0.0486714i
\(543\) 104.610 + 181.190i 0.192652 + 0.333683i
\(544\) −148.971 86.0082i −0.273843 0.158103i
\(545\) 32.4078i 0.0594639i
\(546\) 0 0
\(547\) −741.470 −1.35552 −0.677761 0.735283i \(-0.737049\pi\)
−0.677761 + 0.735283i \(0.737049\pi\)
\(548\) 105.765 183.189i 0.193001 0.334287i
\(549\) −7.45584 + 4.30463i −0.0135808 + 0.00784086i
\(550\) 173.610 + 300.702i 0.315655 + 0.546730i
\(551\) 419.117 + 241.977i 0.760648 + 0.439160i
\(552\) 32.9600i 0.0597101i
\(553\) 0 0
\(554\) −116.922 −0.211050
\(555\) 27.1615 47.0450i 0.0489396 0.0847659i
\(556\) 314.059 181.322i 0.564854 0.326119i
\(557\) −417.426 723.004i −0.749419 1.29803i −0.948101 0.317968i \(-0.897000\pi\)
0.198682 0.980064i \(-0.436334\pi\)
\(558\) 184.368 + 106.445i 0.330408 + 0.190761i
\(559\) 666.669i 1.19261i
\(560\) 0 0
\(561\) 539.470 0.961622
\(562\) 106.669 184.756i 0.189803 0.328748i
\(563\) −361.809 + 208.891i −0.642645 + 0.371031i −0.785633 0.618693i \(-0.787662\pi\)
0.142988 + 0.989724i \(0.454329\pi\)
\(564\) −100.971 174.886i −0.179026 0.310082i
\(565\) 93.9929 + 54.2668i 0.166359 + 0.0960474i
\(566\) 401.861i 0.710001i
\(567\) 0 0
\(568\) 143.147 0.252020
\(569\) −336.515 + 582.861i −0.591414 + 1.02436i 0.402628 + 0.915364i \(0.368097\pi\)
−0.994042 + 0.108996i \(0.965236\pi\)
\(570\) 34.7208 20.0461i 0.0609136 0.0351685i
\(571\) 132.544 + 229.573i 0.232126 + 0.402055i 0.958434 0.285315i \(-0.0920984\pi\)
−0.726307 + 0.687370i \(0.758765\pi\)
\(572\) −158.912 91.7477i −0.277818 0.160398i
\(573\) 194.104i 0.338750i
\(574\) 0 0
\(575\) −161.272 −0.280473
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) 405.941 234.370i 0.703537 0.406188i −0.105126 0.994459i \(-0.533525\pi\)
0.808664 + 0.588271i \(0.200191\pi\)
\(578\) 449.491 + 778.541i 0.777666 + 1.34696i
\(579\) 34.3675 + 19.8421i 0.0593567 + 0.0342696i
\(580\) 60.8767i 0.104960i
\(581\) 0 0
\(582\) 246.676 0.423842
\(583\) −363.463 + 629.536i −0.623436 + 1.07982i
\(584\) −172.971 + 99.8646i −0.296182 + 0.171001i
\(585\) 13.6325 + 23.6121i 0.0233034 + 0.0403626i
\(586\) 657.978 + 379.884i 1.12283 + 0.648266i
\(587\) 120.530i 0.205332i −0.994716 0.102666i \(-0.967263\pi\)
0.994716 0.102666i \(-0.0327372\pi\)
\(588\) 0 0
\(589\) 809.470 1.37431
\(590\) −0.353247 + 0.611842i −0.000598724 + 0.00103702i
\(591\) −174.088 + 100.510i −0.294566 + 0.170068i
\(592\) −61.8234 107.081i −0.104431 0.180880i
\(593\) −486.245 280.734i −0.819975 0.473413i 0.0304327 0.999537i \(-0.490311\pi\)
−0.850408 + 0.526124i \(0.823645\pi\)
\(594\) 75.2677i 0.126713i
\(595\) 0 0
\(596\) 82.2944 0.138078
\(597\) 141.250 244.652i 0.236599 0.409802i
\(598\) 73.8091 42.6137i 0.123427 0.0712604i
\(599\) −470.054 814.158i −0.784732 1.35920i −0.929159 0.369680i \(-0.879467\pi\)
0.144427 0.989515i \(-0.453866\pi\)
\(600\) −101.698 58.7156i −0.169497 0.0978594i
\(601\) 563.527i 0.937649i 0.883291 + 0.468824i \(0.155322\pi\)
−0.883291 + 0.468824i \(0.844678\pi\)
\(602\) 0 0
\(603\) −81.0883 −0.134475
\(604\) −80.3675 + 139.201i −0.133059 + 0.230465i
\(605\) −14.1365 + 8.16170i −0.0233661 + 0.0134904i
\(606\) −170.095 294.614i −0.280686 0.486162i
\(607\) 265.514 + 153.294i 0.437420 + 0.252544i 0.702503 0.711681i \(-0.252066\pi\)
−0.265083 + 0.964226i \(0.585399\pi\)
\(608\) 91.2553i 0.150091i
\(609\) 0 0
\(610\) −4.11775 −0.00675041
\(611\) 261.088 452.218i 0.427313 0.740128i
\(612\) −158.007 + 91.2255i −0.258182 + 0.149061i
\(613\) −137.794 238.666i −0.224786 0.389341i 0.731469 0.681875i \(-0.238835\pi\)
−0.956255 + 0.292533i \(0.905502\pi\)
\(614\) 42.5513 + 24.5670i 0.0693018 + 0.0400114i
\(615\) 12.4813i 0.0202947i
\(616\) 0 0
\(617\) 461.294 0.747639 0.373820 0.927501i \(-0.378048\pi\)
0.373820 + 0.927501i \(0.378048\pi\)
\(618\) 96.6030 167.321i 0.156316 0.270747i
\(619\) −324.676 + 187.452i −0.524517 + 0.302830i −0.738781 0.673946i \(-0.764598\pi\)
0.214264 + 0.976776i \(0.431265\pi\)
\(620\) 50.9117 + 88.1816i 0.0821156 + 0.142228i
\(621\) −30.2756 17.4797i −0.0487531 0.0281476i
\(622\) 126.100i 0.202734i
\(623\) 0 0
\(624\) 62.0589 0.0994533
\(625\) −274.426 + 475.320i −0.439082 + 0.760512i
\(626\) 636.500 367.483i 1.01677 0.587034i
\(627\) 143.095 + 247.849i 0.228222 + 0.395293i
\(628\) 99.2649 + 57.3106i 0.158065 + 0.0912590i
\(629\) 939.978i 1.49440i
\(630\) 0 0
\(631\) −1127.32 −1.78656 −0.893282 0.449496i \(-0.851603\pi\)
−0.893282 + 0.449496i \(0.851603\pi\)
\(632\) −189.255 + 327.799i −0.299454 + 0.518669i
\(633\) 159.640 92.1680i 0.252195 0.145605i
\(634\) −383.272 663.847i −0.604530 1.04708i
\(635\) −19.3827 11.1906i −0.0305239 0.0176230i
\(636\) 245.849i 0.386555i
\(637\) 0 0
\(638\) −434.558 −0.681126
\(639\) 75.9153 131.489i 0.118803 0.205773i
\(640\) 9.94113 5.73951i 0.0155330 0.00896799i
\(641\) 442.176 + 765.871i 0.689822 + 1.19481i 0.971895 + 0.235414i \(0.0756445\pi\)
−0.282074 + 0.959393i \(0.591022\pi\)
\(642\) 80.0955 + 46.2431i 0.124759 + 0.0720298i
\(643\) 300.765i 0.467753i −0.972266 0.233876i \(-0.924859\pi\)
0.972266 0.233876i \(-0.0751411\pi\)
\(644\) 0 0
\(645\) 130.794 0.202781
\(646\) −346.867 + 600.791i −0.536946 + 0.930018i
\(647\) −814.587 + 470.302i −1.25902 + 0.726896i −0.972884 0.231292i \(-0.925705\pi\)
−0.286137 + 0.958189i \(0.592371\pi\)
\(648\) −12.7279 22.0454i −0.0196419 0.0340207i
\(649\) −4.36753 2.52160i −0.00672963 0.00388536i
\(650\) 303.652i 0.467157i
\(651\) 0 0
\(652\) −349.823 −0.536539
\(653\) 227.985 394.881i 0.349135 0.604719i −0.636961 0.770896i \(-0.719809\pi\)
0.986096 + 0.166177i \(0.0531423\pi\)
\(654\) 67.7574 39.1197i 0.103605 0.0598161i
\(655\) −36.0000 62.3538i −0.0549618 0.0951967i
\(656\) 24.6030 + 14.2046i 0.0375046 + 0.0216533i
\(657\) 211.845i 0.322443i
\(658\) 0 0
\(659\) 403.684 0.612571 0.306285 0.951940i \(-0.400914\pi\)
0.306285 + 0.951940i \(0.400914\pi\)
\(660\) −18.0000 + 31.1769i −0.0272727 + 0.0472377i
\(661\) −998.881 + 576.704i −1.51117 + 0.872473i −0.511252 + 0.859431i \(0.670818\pi\)
−0.999915 + 0.0130418i \(0.995849\pi\)
\(662\) −127.019 220.004i −0.191872 0.332332i
\(663\) −408.573 235.890i −0.616248 0.355791i
\(664\) 295.331i 0.444776i
\(665\) 0 0
\(666\) −131.147 −0.196918
\(667\) 100.919 174.797i 0.151303 0.262064i
\(668\) 339.765 196.163i 0.508629 0.293657i
\(669\) −49.3675 85.5071i −0.0737930 0.127813i
\(670\) −33.5879 19.3920i −0.0501312 0.0289432i
\(671\) 29.3939i 0.0438061i
\(672\) 0 0
\(673\) −607.440 −0.902585 −0.451293 0.892376i \(-0.649037\pi\)
−0.451293 + 0.892376i \(0.649037\pi\)
\(674\) −206.350 + 357.409i −0.306158 + 0.530281i
\(675\) −107.868 + 62.2773i −0.159804 + 0.0922627i
\(676\) −88.7645 153.745i −0.131308 0.227433i
\(677\) 985.180 + 568.794i 1.45521 + 0.840168i 0.998770 0.0495834i \(-0.0157894\pi\)
0.456444 + 0.889752i \(0.349123\pi\)
\(678\) 262.023i 0.386465i
\(679\) 0 0
\(680\) −87.2649 −0.128331
\(681\) 248.912 431.128i 0.365509 0.633080i
\(682\) −629.470 + 363.425i −0.922977 + 0.532881i
\(683\) 409.055 + 708.505i 0.598910 + 1.03734i 0.992982 + 0.118263i \(0.0377325\pi\)
−0.394073 + 0.919079i \(0.628934\pi\)
\(684\) −83.8234 48.3954i −0.122549 0.0707536i
\(685\) 107.310i 0.156657i
\(686\) 0 0
\(687\) −241.456 −0.351464
\(688\) 148.853 257.821i 0.216356 0.374739i
\(689\) 550.544 317.857i 0.799048 0.461331i
\(690\) −8.36039 14.4806i −0.0121165 0.0209864i
\(691\) −176.912 102.140i −0.256023 0.147815i 0.366496 0.930420i \(-0.380557\pi\)
−0.622519 + 0.782605i \(0.713891\pi\)
\(692\) 77.0508i 0.111345i
\(693\) 0 0
\(694\) 639.338 0.921236
\(695\) 91.9857 159.324i 0.132354 0.229243i
\(696\) 127.279 73.4847i 0.182872 0.105581i
\(697\) −107.985 187.035i −0.154928 0.268343i
\(698\) −287.897 166.217i −0.412459 0.238133i
\(699\) 628.276i 0.898821i
\(700\) 0 0
\(701\) −318.853 −0.454854 −0.227427 0.973795i \(-0.573031\pi\)
−0.227427 + 0.973795i \(0.573031\pi\)
\(702\) 32.9117 57.0047i 0.0468827 0.0812033i
\(703\) −431.854 + 249.331i −0.614301 + 0.354667i
\(704\) 40.9706 + 70.9631i 0.0581968 + 0.100800i
\(705\) −88.7208 51.2230i −0.125845 0.0726567i
\(706\) 35.7030i 0.0505708i
\(707\) 0 0
\(708\) 1.70563 0.00240908
\(709\) 108.823 188.488i 0.153489 0.265850i −0.779019 0.627000i \(-0.784283\pi\)
0.932508 + 0.361150i \(0.117616\pi\)
\(710\) 62.8903 36.3097i 0.0885778 0.0511404i
\(711\) 200.735 + 347.683i 0.282328 + 0.489006i
\(712\) −355.103 205.019i −0.498740 0.287947i
\(713\) 337.597i 0.473488i
\(714\) 0 0
\(715\) −93.0883 −0.130193
\(716\) 191.095 330.987i 0.266893 0.462272i
\(717\) 27.7172 16.0025i 0.0386572 0.0223187i
\(718\) 75.1249 + 130.120i 0.104631 + 0.181226i
\(719\) −1045.60 603.679i −1.45425 0.839609i −0.455527 0.890222i \(-0.650549\pi\)
−0.998718 + 0.0506134i \(0.983882\pi\)
\(720\) 12.1753i 0.0169102i
\(721\) 0 0
\(722\) 142.503 0.197372
\(723\) −154.243 + 267.156i −0.213337 + 0.369510i
\(724\) 209.220 120.793i 0.288978 0.166842i
\(725\) −359.558 622.773i −0.495943 0.858998i
\(726\) 34.1285 + 19.7041i 0.0470089 + 0.0271406i
\(727\) 123.231i 0.169506i 0.996402 + 0.0847528i \(0.0270100\pi\)
−0.996402 + 0.0847528i \(0.972990\pi\)
\(728\) 0 0
\(729\) −27.0000 −0.0370370
\(730\) −50.6619 + 87.7490i −0.0693999 + 0.120204i
\(731\) −1959.98 + 1131.60i −2.68124 + 1.54801i
\(732\) 4.97056 + 8.60927i 0.00679039 + 0.0117613i
\(733\) 325.434 + 187.890i 0.443976 + 0.256330i 0.705283 0.708926i \(-0.250820\pi\)
−0.261307 + 0.965256i \(0.584153\pi\)
\(734\) 405.054i 0.551844i
\(735\) 0 0
\(736\) −38.0589 −0.0517104
\(737\) 138.426 239.762i 0.187824 0.325321i
\(738\) 26.0955 15.0662i 0.0353597 0.0204149i
\(739\) −361.265 625.729i −0.488856 0.846724i 0.511061 0.859544i \(-0.329252\pi\)
−0.999918 + 0.0128200i \(0.995919\pi\)
\(740\) −54.3229 31.3634i −0.0734094 0.0423829i
\(741\) 250.281i 0.337761i
\(742\) 0 0
\(743\) 1268.48 1.70724 0.853618 0.520899i \(-0.174403\pi\)
0.853618 + 0.520899i \(0.174403\pi\)
\(744\) 122.912 212.889i 0.165204 0.286142i
\(745\) 36.1552 20.8742i 0.0485305 0.0280191i
\(746\) 299.439 + 518.643i 0.401392 + 0.695232i
\(747\) −271.279 156.623i −0.363158 0.209670i
\(748\) 622.926i 0.832789i
\(749\) 0 0
\(750\) −121.706 −0.162274
\(751\) −219.581 + 380.325i −0.292384 + 0.506425i −0.974373 0.224938i \(-0.927782\pi\)
0.681989 + 0.731363i \(0.261115\pi\)
\(752\) −201.941 + 116.591i −0.268539 + 0.155041i
\(753\) 43.8823 + 76.0063i 0.0582766 + 0.100938i
\(754\) 329.117 + 190.016i 0.436495 + 0.252010i
\(755\) 81.5419i 0.108002i
\(756\) 0 0
\(757\) −668.530 −0.883131 −0.441565 0.897229i \(-0.645577\pi\)
−0.441565 + 0.897229i \(0.645577\pi\)
\(758\) −71.4903 + 123.825i −0.0943144 + 0.163357i
\(759\) 103.368 59.6793i 0.136189 0.0786288i
\(760\) −23.1472 40.0921i −0.0304568 0.0527528i
\(761\) −762.202 440.058i −1.00158 0.578263i −0.0928647 0.995679i \(-0.529602\pi\)
−0.908715 + 0.417416i \(0.862936\pi\)
\(762\) 54.0330i 0.0709094i
\(763\) 0 0
\(764\) 224.132 0.293367
\(765\) −46.2792 + 80.1580i −0.0604957 + 0.104782i
\(766\) 269.927 155.842i 0.352385 0.203450i
\(767\) 2.20519 + 3.81951i 0.00287509 + 0.00497980i
\(768\) −24.0000 13.8564i −0.0312500 0.0180422i
\(769\) 1163.41i 1.51289i −0.654059 0.756444i \(-0.726935\pi\)
0.654059 0.756444i \(-0.273065\pi\)
\(770\) 0 0
\(771\) −324.905 −0.421407
\(772\) 22.9117 39.6842i 0.0296784 0.0514044i
\(773\) 464.511 268.186i 0.600920 0.346941i −0.168483 0.985704i \(-0.553887\pi\)
0.769403 + 0.638763i \(0.220554\pi\)
\(774\) −157.882 273.460i −0.203982 0.353308i
\(775\) −1041.66 601.403i −1.34408 0.776004i
\(776\) 284.837i 0.367058i
\(777\) 0 0
\(778\) −542.309 −0.697055
\(779\) 57.2864 99.2229i 0.0735383 0.127372i
\(780\) 27.2649 15.7414i