Properties

Label 294.3.g.c.31.2
Level $294$
Weight $3$
Character 294.31
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 31.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 294.31
Dual form 294.3.g.c.19.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-5.12132 + 2.95680i) q^{5} +2.44949i q^{6} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.707107 + 1.22474i) q^{2} +(1.50000 + 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(-5.12132 + 2.95680i) q^{5} +2.44949i q^{6} -2.82843 q^{8} +(1.50000 + 2.59808i) q^{9} +(-7.24264 - 4.18154i) q^{10} +(0.878680 - 1.52192i) q^{11} +(-3.00000 + 1.73205i) q^{12} +18.7554i q^{13} -10.2426 q^{15} +(-2.00000 - 3.46410i) q^{16} +(-20.3345 - 11.7401i) q^{17} +(-2.12132 + 3.67423i) q^{18} +(-19.9706 + 11.5300i) q^{19} -11.8272i q^{20} +2.48528 q^{22} +(-9.36396 - 16.2189i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(4.98528 - 8.63476i) q^{25} +(-22.9706 + 13.2621i) q^{26} +5.19615i q^{27} +30.0000 q^{29} +(-7.24264 - 12.5446i) q^{30} +(-7.45584 - 4.30463i) q^{31} +(2.82843 - 4.89898i) q^{32} +(2.63604 - 1.52192i) q^{33} -33.2061i q^{34} -6.00000 q^{36} +(35.4558 + 61.4113i) q^{37} +(-28.2426 - 16.3059i) q^{38} +(-16.2426 + 28.1331i) q^{39} +(14.4853 - 8.36308i) q^{40} +41.3951i q^{41} +10.4264 q^{43} +(1.75736 + 3.04384i) q^{44} +(-15.3640 - 8.87039i) q^{45} +(13.2426 - 22.9369i) q^{46} +(33.5147 - 19.3497i) q^{47} -6.92820i q^{48} +14.1005 q^{50} +(-20.3345 - 35.2204i) q^{51} +(-32.4853 - 18.7554i) q^{52} +(18.5147 - 32.0684i) q^{53} +(-6.36396 + 3.67423i) q^{54} +10.3923i q^{55} -39.9411 q^{57} +(21.2132 + 36.7423i) q^{58} +(84.4264 + 48.7436i) q^{59} +(10.2426 - 17.7408i) q^{60} +(14.4853 - 8.36308i) q^{61} -12.1753i q^{62} +8.00000 q^{64} +(-55.4558 - 96.0523i) q^{65} +(3.72792 + 2.15232i) q^{66} +(-30.4853 + 52.8021i) q^{67} +(40.6690 - 23.4803i) q^{68} -32.4377i q^{69} -110.610 q^{71} +(-4.24264 - 7.34847i) q^{72} +(49.1543 + 28.3793i) q^{73} +(-50.1421 + 86.8487i) q^{74} +(14.9558 - 8.63476i) q^{75} -46.1200i q^{76} -45.9411 q^{78} +(34.9117 + 60.4688i) q^{79} +(20.4853 + 11.8272i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-50.6985 + 29.2708i) q^{82} +6.43583i q^{83} +138.853 q^{85} +(7.37258 + 12.7697i) q^{86} +(45.0000 + 25.9808i) q^{87} +(-2.48528 + 4.30463i) q^{88} +(-36.4523 + 21.0457i) q^{89} -25.0892i q^{90} +37.4558 q^{92} +(-7.45584 - 12.9139i) q^{93} +(47.3970 + 27.3647i) q^{94} +(68.1838 - 118.098i) q^{95} +(8.48528 - 4.89898i) q^{96} +51.7153i q^{97} +5.27208 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 \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

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

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
\(5\) −5.12132 + 2.95680i −1.02426 + 0.591359i −0.915336 0.402691i \(-0.868075\pi\)
−0.108928 + 0.994050i \(0.534742\pi\)
\(6\) 2.44949i 0.408248i
\(7\) 0 0
\(8\) −2.82843 −0.353553
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) −7.24264 4.18154i −0.724264 0.418154i
\(11\) 0.878680 1.52192i 0.0798800 0.138356i −0.823318 0.567580i \(-0.807880\pi\)
0.903198 + 0.429224i \(0.141213\pi\)
\(12\) −3.00000 + 1.73205i −0.250000 + 0.144338i
\(13\) 18.7554i 1.44272i 0.692559 + 0.721361i \(0.256483\pi\)
−0.692559 + 0.721361i \(0.743517\pi\)
\(14\) 0 0
\(15\) −10.2426 −0.682843
\(16\) −2.00000 3.46410i −0.125000 0.216506i
\(17\) −20.3345 11.7401i −1.19615 0.690597i −0.236454 0.971643i \(-0.575985\pi\)
−0.959694 + 0.281046i \(0.909319\pi\)
\(18\) −2.12132 + 3.67423i −0.117851 + 0.204124i
\(19\) −19.9706 + 11.5300i −1.05108 + 0.606843i −0.922952 0.384915i \(-0.874231\pi\)
−0.128130 + 0.991757i \(0.540898\pi\)
\(20\) 11.8272i 0.591359i
\(21\) 0 0
\(22\) 2.48528 0.112967
\(23\) −9.36396 16.2189i −0.407129 0.705168i 0.587438 0.809269i \(-0.300137\pi\)
−0.994567 + 0.104102i \(0.966803\pi\)
\(24\) −4.24264 2.44949i −0.176777 0.102062i
\(25\) 4.98528 8.63476i 0.199411 0.345390i
\(26\) −22.9706 + 13.2621i −0.883483 + 0.510079i
\(27\) 5.19615i 0.192450i
\(28\) 0 0
\(29\) 30.0000 1.03448 0.517241 0.855840i \(-0.326959\pi\)
0.517241 + 0.855840i \(0.326959\pi\)
\(30\) −7.24264 12.5446i −0.241421 0.418154i
\(31\) −7.45584 4.30463i −0.240511 0.138859i 0.374901 0.927065i \(-0.377677\pi\)
−0.615412 + 0.788206i \(0.711010\pi\)
\(32\) 2.82843 4.89898i 0.0883883 0.153093i
\(33\) 2.63604 1.52192i 0.0798800 0.0461187i
\(34\) 33.2061i 0.976651i
\(35\) 0 0
\(36\) −6.00000 −0.166667
\(37\) 35.4558 + 61.4113i 0.958266 + 1.65977i 0.726711 + 0.686944i \(0.241048\pi\)
0.231556 + 0.972822i \(0.425619\pi\)
\(38\) −28.2426 16.3059i −0.743227 0.429103i
\(39\) −16.2426 + 28.1331i −0.416478 + 0.721361i
\(40\) 14.4853 8.36308i 0.362132 0.209077i
\(41\) 41.3951i 1.00964i 0.863225 + 0.504819i \(0.168441\pi\)
−0.863225 + 0.504819i \(0.831559\pi\)
\(42\) 0 0
\(43\) 10.4264 0.242475 0.121237 0.992624i \(-0.461314\pi\)
0.121237 + 0.992624i \(0.461314\pi\)
\(44\) 1.75736 + 3.04384i 0.0399400 + 0.0691781i
\(45\) −15.3640 8.87039i −0.341421 0.197120i
\(46\) 13.2426 22.9369i 0.287883 0.498629i
\(47\) 33.5147 19.3497i 0.713079 0.411696i −0.0991210 0.995075i \(-0.531603\pi\)
0.812200 + 0.583379i \(0.198270\pi\)
\(48\) 6.92820i 0.144338i
\(49\) 0 0
\(50\) 14.1005 0.282010
\(51\) −20.3345 35.2204i −0.398716 0.690597i
\(52\) −32.4853 18.7554i −0.624717 0.360680i
\(53\) 18.5147 32.0684i 0.349334 0.605065i −0.636797 0.771031i \(-0.719741\pi\)
0.986131 + 0.165967i \(0.0530744\pi\)
\(54\) −6.36396 + 3.67423i −0.117851 + 0.0680414i
\(55\) 10.3923i 0.188951i
\(56\) 0 0
\(57\) −39.9411 −0.700721
\(58\) 21.2132 + 36.7423i 0.365745 + 0.633489i
\(59\) 84.4264 + 48.7436i 1.43096 + 0.826163i 0.997194 0.0748645i \(-0.0238524\pi\)
0.433762 + 0.901027i \(0.357186\pi\)
\(60\) 10.2426 17.7408i 0.170711 0.295680i
\(61\) 14.4853 8.36308i 0.237464 0.137100i −0.376547 0.926398i \(-0.622889\pi\)
0.614010 + 0.789298i \(0.289555\pi\)
\(62\) 12.1753i 0.196376i
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) −55.4558 96.0523i −0.853167 1.47773i
\(66\) 3.72792 + 2.15232i 0.0564837 + 0.0326109i
\(67\) −30.4853 + 52.8021i −0.455004 + 0.788090i −0.998688 0.0511995i \(-0.983696\pi\)
0.543684 + 0.839290i \(0.317029\pi\)
\(68\) 40.6690 23.4803i 0.598074 0.345298i
\(69\) 32.4377i 0.470112i
\(70\) 0 0
\(71\) −110.610 −1.55789 −0.778945 0.627092i \(-0.784245\pi\)
−0.778945 + 0.627092i \(0.784245\pi\)
\(72\) −4.24264 7.34847i −0.0589256 0.102062i
\(73\) 49.1543 + 28.3793i 0.673347 + 0.388757i 0.797344 0.603526i \(-0.206238\pi\)
−0.123997 + 0.992283i \(0.539571\pi\)
\(74\) −50.1421 + 86.8487i −0.677596 + 1.17363i
\(75\) 14.9558 8.63476i 0.199411 0.115130i
\(76\) 46.1200i 0.606843i
\(77\) 0 0
\(78\) −45.9411 −0.588989
\(79\) 34.9117 + 60.4688i 0.441920 + 0.765428i 0.997832 0.0658132i \(-0.0209641\pi\)
−0.555912 + 0.831241i \(0.687631\pi\)
\(80\) 20.4853 + 11.8272i 0.256066 + 0.147840i
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) −50.6985 + 29.2708i −0.618274 + 0.356961i
\(83\) 6.43583i 0.0775401i 0.999248 + 0.0387701i \(0.0123440\pi\)
−0.999248 + 0.0387701i \(0.987656\pi\)
\(84\) 0 0
\(85\) 138.853 1.63356
\(86\) 7.37258 + 12.7697i 0.0857277 + 0.148485i
\(87\) 45.0000 + 25.9808i 0.517241 + 0.298629i
\(88\) −2.48528 + 4.30463i −0.0282418 + 0.0489163i
\(89\) −36.4523 + 21.0457i −0.409576 + 0.236469i −0.690608 0.723230i \(-0.742657\pi\)
0.281031 + 0.959699i \(0.409323\pi\)
\(90\) 25.0892i 0.278769i
\(91\) 0 0
\(92\) 37.4558 0.407129
\(93\) −7.45584 12.9139i −0.0801704 0.138859i
\(94\) 47.3970 + 27.3647i 0.504223 + 0.291113i
\(95\) 68.1838 118.098i 0.717724 1.24313i
\(96\) 8.48528 4.89898i 0.0883883 0.0510310i
\(97\) 51.7153i 0.533148i 0.963814 + 0.266574i \(0.0858916\pi\)
−0.963814 + 0.266574i \(0.914108\pi\)
\(98\) 0 0
\(99\) 5.27208 0.0532533
\(100\) 9.97056 + 17.2695i 0.0997056 + 0.172695i
\(101\) −5.72435 3.30496i −0.0566767 0.0327223i 0.471394 0.881923i \(-0.343751\pi\)
−0.528071 + 0.849200i \(0.677084\pi\)
\(102\) 28.7574 49.8092i 0.281935 0.488326i
\(103\) 152.309 87.9354i 1.47872 0.853742i 0.479014 0.877807i \(-0.340994\pi\)
0.999710 + 0.0240648i \(0.00766082\pi\)
\(104\) 53.0482i 0.510079i
\(105\) 0 0
\(106\) 52.3675 0.494033
\(107\) 23.1213 + 40.0473i 0.216087 + 0.374274i 0.953608 0.301050i \(-0.0973371\pi\)
−0.737521 + 0.675324i \(0.764004\pi\)
\(108\) −9.00000 5.19615i −0.0833333 0.0481125i
\(109\) 17.9706 31.1259i 0.164868 0.285559i −0.771741 0.635937i \(-0.780614\pi\)
0.936608 + 0.350378i \(0.113947\pi\)
\(110\) −12.7279 + 7.34847i −0.115708 + 0.0668043i
\(111\) 122.823i 1.10651i
\(112\) 0 0
\(113\) −73.0294 −0.646278 −0.323139 0.946351i \(-0.604738\pi\)
−0.323139 + 0.946351i \(0.604738\pi\)
\(114\) −28.2426 48.9177i −0.247742 0.429103i
\(115\) 95.9117 + 55.3746i 0.834015 + 0.481519i
\(116\) −30.0000 + 51.9615i −0.258621 + 0.447944i
\(117\) −48.7279 + 28.1331i −0.416478 + 0.240454i
\(118\) 137.868i 1.16837i
\(119\) 0 0
\(120\) 28.9706 0.241421
\(121\) 58.9558 + 102.115i 0.487238 + 0.843922i
\(122\) 20.4853 + 11.8272i 0.167912 + 0.0969441i
\(123\) −35.8492 + 62.0927i −0.291457 + 0.504819i
\(124\) 14.9117 8.60927i 0.120256 0.0694296i
\(125\) 88.8780i 0.711024i
\(126\) 0 0
\(127\) 89.9411 0.708198 0.354099 0.935208i \(-0.384788\pi\)
0.354099 + 0.935208i \(0.384788\pi\)
\(128\) 5.65685 + 9.79796i 0.0441942 + 0.0765466i
\(129\) 15.6396 + 9.02953i 0.121237 + 0.0699964i
\(130\) 78.4264 135.839i 0.603280 1.04491i
\(131\) 10.5442 6.08767i 0.0804897 0.0464708i −0.459215 0.888325i \(-0.651869\pi\)
0.539705 + 0.841854i \(0.318536\pi\)
\(132\) 6.08767i 0.0461187i
\(133\) 0 0
\(134\) −86.2254 −0.643473
\(135\) −15.3640 26.6112i −0.113807 0.197120i
\(136\) 57.5147 + 33.2061i 0.422902 + 0.244163i
\(137\) −82.8823 + 143.556i −0.604980 + 1.04786i 0.387075 + 0.922048i \(0.373486\pi\)
−0.992055 + 0.125808i \(0.959848\pi\)
\(138\) 39.7279 22.9369i 0.287883 0.166210i
\(139\) 220.514i 1.58643i −0.608941 0.793215i \(-0.708406\pi\)
0.608941 0.793215i \(-0.291594\pi\)
\(140\) 0 0
\(141\) 67.0294 0.475386
\(142\) −78.2132 135.469i −0.550797 0.954009i
\(143\) 28.5442 + 16.4800i 0.199609 + 0.115245i
\(144\) 6.00000 10.3923i 0.0416667 0.0721688i
\(145\) −153.640 + 88.7039i −1.05958 + 0.611751i
\(146\) 80.2687i 0.549786i
\(147\) 0 0
\(148\) −141.823 −0.958266
\(149\) −105.426 182.604i −0.707560 1.22553i −0.965760 0.259438i \(-0.916463\pi\)
0.258200 0.966091i \(-0.416871\pi\)
\(150\) 21.1508 + 12.2114i 0.141005 + 0.0814093i
\(151\) 36.1838 62.6721i 0.239628 0.415047i −0.720980 0.692956i \(-0.756308\pi\)
0.960607 + 0.277909i \(0.0896413\pi\)
\(152\) 56.4853 32.6118i 0.371614 0.214551i
\(153\) 70.4409i 0.460398i
\(154\) 0 0
\(155\) 50.9117 0.328463
\(156\) −32.4853 56.2662i −0.208239 0.360680i
\(157\) −202.368 116.837i −1.28897 0.744184i −0.310495 0.950575i \(-0.600495\pi\)
−0.978470 + 0.206390i \(0.933828\pi\)
\(158\) −49.3726 + 85.5158i −0.312485 + 0.541239i
\(159\) 55.5442 32.0684i 0.349334 0.201688i
\(160\) 33.4523i 0.209077i
\(161\) 0 0
\(162\) −12.7279 −0.0785674
\(163\) 36.5442 + 63.2963i 0.224197 + 0.388321i 0.956078 0.293111i \(-0.0946907\pi\)
−0.731881 + 0.681432i \(0.761357\pi\)
\(164\) −71.6985 41.3951i −0.437186 0.252409i
\(165\) −9.00000 + 15.5885i −0.0545455 + 0.0944755i
\(166\) −7.88225 + 4.55082i −0.0474834 + 0.0274146i
\(167\) 39.3958i 0.235903i −0.993019 0.117951i \(-0.962367\pi\)
0.993019 0.117951i \(-0.0376327\pi\)
\(168\) 0 0
\(169\) −182.765 −1.08145
\(170\) 98.1838 + 170.059i 0.577552 + 1.00035i
\(171\) −59.9117 34.5900i −0.350361 0.202281i
\(172\) −10.4264 + 18.0591i −0.0606186 + 0.104995i
\(173\) 20.6360 11.9142i 0.119283 0.0688683i −0.439171 0.898403i \(-0.644728\pi\)
0.558455 + 0.829535i \(0.311394\pi\)
\(174\) 73.4847i 0.422326i
\(175\) 0 0
\(176\) −7.02944 −0.0399400
\(177\) 84.4264 + 146.231i 0.476985 + 0.826163i
\(178\) −51.5513 29.7632i −0.289614 0.167209i
\(179\) 6.45227 11.1757i 0.0360462 0.0624339i −0.847439 0.530892i \(-0.821857\pi\)
0.883486 + 0.468458i \(0.155190\pi\)
\(180\) 30.7279 17.7408i 0.170711 0.0985599i
\(181\) 65.3678i 0.361148i 0.983561 + 0.180574i \(0.0577955\pi\)
−0.983561 + 0.180574i \(0.942204\pi\)
\(182\) 0 0
\(183\) 28.9706 0.158309
\(184\) 26.4853 + 45.8739i 0.143942 + 0.249314i
\(185\) −363.161 209.671i −1.96303 1.13336i
\(186\) 10.5442 18.2630i 0.0566890 0.0981882i
\(187\) −35.7351 + 20.6316i −0.191097 + 0.110330i
\(188\) 77.3989i 0.411696i
\(189\) 0 0
\(190\) 192.853 1.01501
\(191\) 50.0330 + 86.6597i 0.261953 + 0.453716i 0.966761 0.255682i \(-0.0823001\pi\)
−0.704808 + 0.709398i \(0.748967\pi\)
\(192\) 12.0000 + 6.92820i 0.0625000 + 0.0360844i
\(193\) −39.4558 + 68.3395i −0.204434 + 0.354091i −0.949952 0.312395i \(-0.898869\pi\)
0.745518 + 0.666486i \(0.232202\pi\)
\(194\) −63.3381 + 36.5683i −0.326485 + 0.188496i
\(195\) 192.105i 0.985152i
\(196\) 0 0
\(197\) −183.941 −0.933711 −0.466856 0.884334i \(-0.654613\pi\)
−0.466856 + 0.884334i \(0.654613\pi\)
\(198\) 3.72792 + 6.45695i 0.0188279 + 0.0326109i
\(199\) −147.250 85.0147i −0.739949 0.427210i 0.0821020 0.996624i \(-0.473837\pi\)
−0.822051 + 0.569414i \(0.807170\pi\)
\(200\) −14.1005 + 24.4228i −0.0705025 + 0.122114i
\(201\) −91.4558 + 52.8021i −0.455004 + 0.262697i
\(202\) 9.34783i 0.0462764i
\(203\) 0 0
\(204\) 81.3381 0.398716
\(205\) −122.397 211.998i −0.597058 1.03414i
\(206\) 215.397 + 124.359i 1.04562 + 0.603687i
\(207\) 28.0919 48.6566i 0.135710 0.235056i
\(208\) 64.9706 37.5108i 0.312358 0.180340i
\(209\) 40.5247i 0.193898i
\(210\) 0 0
\(211\) 21.5736 0.102245 0.0511223 0.998692i \(-0.483720\pi\)
0.0511223 + 0.998692i \(0.483720\pi\)
\(212\) 37.0294 + 64.1369i 0.174667 + 0.302532i
\(213\) −165.915 95.7912i −0.778945 0.449724i
\(214\) −32.6985 + 56.6354i −0.152797 + 0.264652i
\(215\) −53.3970 + 30.8288i −0.248358 + 0.143390i
\(216\) 14.6969i 0.0680414i
\(217\) 0 0
\(218\) 50.8284 0.233158
\(219\) 49.1543 + 85.1378i 0.224449 + 0.388757i
\(220\) −18.0000 10.3923i −0.0818182 0.0472377i
\(221\) 220.191 381.382i 0.996339 1.72571i
\(222\) −150.426 + 86.8487i −0.677596 + 0.391210i
\(223\) 119.359i 0.535240i −0.963525 0.267620i \(-0.913763\pi\)
0.963525 0.267620i \(-0.0862372\pi\)
\(224\) 0 0
\(225\) 29.9117 0.132941
\(226\) −51.6396 89.4424i −0.228494 0.395763i
\(227\) 147.088 + 84.9215i 0.647966 + 0.374103i 0.787677 0.616089i \(-0.211284\pi\)
−0.139710 + 0.990192i \(0.544617\pi\)
\(228\) 39.9411 69.1801i 0.175180 0.303421i
\(229\) −95.2721 + 55.0054i −0.416035 + 0.240198i −0.693380 0.720573i \(-0.743879\pi\)
0.277344 + 0.960771i \(0.410546\pi\)
\(230\) 156.623i 0.680970i
\(231\) 0 0
\(232\) −84.8528 −0.365745
\(233\) −28.6325 49.5929i −0.122886 0.212845i 0.798019 0.602633i \(-0.205882\pi\)
−0.920905 + 0.389788i \(0.872548\pi\)
\(234\) −68.9117 39.7862i −0.294494 0.170026i
\(235\) −114.426 + 198.192i −0.486921 + 0.843372i
\(236\) −168.853 + 97.4872i −0.715478 + 0.413081i
\(237\) 120.938i 0.510285i
\(238\) 0 0
\(239\) 281.522 1.17792 0.588958 0.808164i \(-0.299538\pi\)
0.588958 + 0.808164i \(0.299538\pi\)
\(240\) 20.4853 + 35.4815i 0.0853553 + 0.147840i
\(241\) −145.757 84.1531i −0.604802 0.349183i 0.166126 0.986105i \(-0.446874\pi\)
−0.770928 + 0.636922i \(0.780207\pi\)
\(242\) −83.3762 + 144.412i −0.344530 + 0.596743i
\(243\) −13.5000 + 7.79423i −0.0555556 + 0.0320750i
\(244\) 33.4523i 0.137100i
\(245\) 0 0
\(246\) −101.397 −0.412183
\(247\) −216.250 374.556i −0.875505 1.51642i
\(248\) 21.0883 + 12.1753i 0.0850335 + 0.0490941i
\(249\) −5.57359 + 9.65375i −0.0223839 + 0.0387701i
\(250\) 108.853 62.8462i 0.435411 0.251385i
\(251\) 106.096i 0.422695i 0.977411 + 0.211348i \(0.0677852\pi\)
−0.977411 + 0.211348i \(0.932215\pi\)
\(252\) 0 0
\(253\) −32.9117 −0.130086
\(254\) 63.5980 + 110.155i 0.250386 + 0.433681i
\(255\) 208.279 + 120.250i 0.816781 + 0.471569i
\(256\) −8.00000 + 13.8564i −0.0312500 + 0.0541266i
\(257\) −251.548 + 145.231i −0.978785 + 0.565102i −0.901903 0.431938i \(-0.857830\pi\)
−0.0768819 + 0.997040i \(0.524496\pi\)
\(258\) 25.5394i 0.0989898i
\(259\) 0 0
\(260\) 221.823 0.853167
\(261\) 45.0000 + 77.9423i 0.172414 + 0.298629i
\(262\) 14.9117 + 8.60927i 0.0569148 + 0.0328598i
\(263\) 44.5111 77.0956i 0.169244 0.293139i −0.768910 0.639357i \(-0.779201\pi\)
0.938154 + 0.346218i \(0.112534\pi\)
\(264\) −7.45584 + 4.30463i −0.0282418 + 0.0163054i
\(265\) 218.977i 0.826328i
\(266\) 0 0
\(267\) −72.9045 −0.273051
\(268\) −60.9706 105.604i −0.227502 0.394045i
\(269\) −165.842 95.7490i −0.616513 0.355944i 0.158997 0.987279i \(-0.449174\pi\)
−0.775510 + 0.631335i \(0.782507\pi\)
\(270\) 21.7279 37.6339i 0.0804738 0.139385i
\(271\) −188.309 + 108.720i −0.694866 + 0.401181i −0.805432 0.592688i \(-0.798067\pi\)
0.110566 + 0.993869i \(0.464734\pi\)
\(272\) 93.9211i 0.345298i
\(273\) 0 0
\(274\) −234.426 −0.855571
\(275\) −8.76093 15.1744i −0.0318579 0.0551796i
\(276\) 56.1838 + 32.4377i 0.203564 + 0.117528i
\(277\) −145.338 + 251.733i −0.524686 + 0.908783i 0.474901 + 0.880039i \(0.342484\pi\)
−0.999587 + 0.0287438i \(0.990849\pi\)
\(278\) 270.073 155.927i 0.971486 0.560888i
\(279\) 25.8278i 0.0925728i
\(280\) 0 0
\(281\) 18.8528 0.0670919 0.0335459 0.999437i \(-0.489320\pi\)
0.0335459 + 0.999437i \(0.489320\pi\)
\(282\) 47.3970 + 82.0940i 0.168074 + 0.291113i
\(283\) 347.912 + 200.867i 1.22937 + 0.709777i 0.966898 0.255163i \(-0.0821290\pi\)
0.262472 + 0.964940i \(0.415462\pi\)
\(284\) 110.610 191.582i 0.389472 0.674586i
\(285\) 204.551 118.098i 0.717724 0.414378i
\(286\) 46.6124i 0.162980i
\(287\) 0 0
\(288\) 16.9706 0.0589256
\(289\) 131.162 + 227.179i 0.453847 + 0.786087i
\(290\) −217.279 125.446i −0.749239 0.432573i
\(291\) −44.7868 + 77.5730i −0.153907 + 0.266574i
\(292\) −98.3087 + 56.7585i −0.336673 + 0.194379i
\(293\) 280.893i 0.958679i −0.877629 0.479340i \(-0.840876\pi\)
0.877629 0.479340i \(-0.159124\pi\)
\(294\) 0 0
\(295\) −576.500 −1.95424
\(296\) −100.284 173.697i −0.338798 0.586816i
\(297\) 7.90812 + 4.56575i 0.0266267 + 0.0153729i
\(298\) 149.095 258.241i 0.500320 0.866580i
\(299\) 304.191 175.625i 1.01736 0.587374i
\(300\) 34.5390i 0.115130i
\(301\) 0 0
\(302\) 102.343 0.338885
\(303\) −5.72435 9.91487i −0.0188922 0.0327223i
\(304\) 79.8823 + 46.1200i 0.262771 + 0.151711i
\(305\) −49.4558 + 85.6600i −0.162150 + 0.280853i
\(306\) 86.2721 49.8092i 0.281935 0.162775i
\(307\) 152.318i 0.496151i 0.968741 + 0.248076i \(0.0797982\pi\)
−0.968741 + 0.248076i \(0.920202\pi\)
\(308\) 0 0
\(309\) 304.617 0.985817
\(310\) 36.0000 + 62.3538i 0.116129 + 0.201141i
\(311\) 245.220 + 141.578i 0.788490 + 0.455235i 0.839431 0.543467i \(-0.182889\pi\)
−0.0509408 + 0.998702i \(0.516222\pi\)
\(312\) 45.9411 79.5724i 0.147247 0.255040i
\(313\) 42.0732 24.2910i 0.134419 0.0776069i −0.431282 0.902217i \(-0.641939\pi\)
0.565702 + 0.824610i \(0.308605\pi\)
\(314\) 330.465i 1.05244i
\(315\) 0 0
\(316\) −139.647 −0.441920
\(317\) 289.014 + 500.587i 0.911717 + 1.57914i 0.811638 + 0.584161i \(0.198576\pi\)
0.100079 + 0.994980i \(0.468090\pi\)
\(318\) 78.5513 + 45.3516i 0.247017 + 0.142615i
\(319\) 26.3604 45.6575i 0.0826345 0.143127i
\(320\) −40.9706 + 23.6544i −0.128033 + 0.0739199i
\(321\) 80.0946i 0.249516i
\(322\) 0 0
\(323\) 541.456 1.67633
\(324\) −9.00000 15.5885i −0.0277778 0.0481125i
\(325\) 161.948 + 93.5009i 0.498302 + 0.287695i
\(326\) −51.6812 + 89.5145i −0.158531 + 0.274584i
\(327\) 53.9117 31.1259i 0.164868 0.0951863i
\(328\) 117.083i 0.356961i
\(329\) 0 0
\(330\) −25.4558 −0.0771389
\(331\) −166.184 287.839i −0.502066 0.869603i −0.999997 0.00238698i \(-0.999240\pi\)
0.497931 0.867216i \(-0.334093\pi\)
\(332\) −11.1472 6.43583i −0.0335759 0.0193850i
\(333\) −106.368 + 184.234i −0.319422 + 0.553255i
\(334\) 48.2498 27.8570i 0.144460 0.0834043i
\(335\) 360.555i 1.07628i
\(336\) 0 0
\(337\) 88.1766 0.261652 0.130826 0.991405i \(-0.458237\pi\)
0.130826 + 0.991405i \(0.458237\pi\)
\(338\) −129.234 223.840i −0.382349 0.662248i
\(339\) −109.544 63.2453i −0.323139 0.186564i
\(340\) −138.853 + 240.500i −0.408391 + 0.707353i
\(341\) −13.1026 + 7.56479i −0.0384240 + 0.0221841i
\(342\) 97.8354i 0.286068i
\(343\) 0 0
\(344\) −29.4903 −0.0857277
\(345\) 95.9117 + 166.124i 0.278005 + 0.481519i
\(346\) 29.1838 + 16.8493i 0.0843461 + 0.0486973i
\(347\) 160.040 277.198i 0.461211 0.798841i −0.537811 0.843066i \(-0.680749\pi\)
0.999022 + 0.0442250i \(0.0140819\pi\)
\(348\) −90.0000 + 51.9615i −0.258621 + 0.149315i
\(349\) 333.046i 0.954287i −0.878825 0.477143i \(-0.841672\pi\)
0.878825 0.477143i \(-0.158328\pi\)
\(350\) 0 0
\(351\) −97.4558 −0.277652
\(352\) −4.97056 8.60927i −0.0141209 0.0244581i
\(353\) 567.864 + 327.856i 1.60868 + 0.928771i 0.989666 + 0.143390i \(0.0458002\pi\)
0.619012 + 0.785381i \(0.287533\pi\)
\(354\) −119.397 + 206.802i −0.337280 + 0.584185i
\(355\) 566.470 327.052i 1.59569 0.921272i
\(356\) 84.1829i 0.236469i
\(357\) 0 0
\(358\) 18.2498 0.0509770
\(359\) 48.8787 + 84.6604i 0.136152 + 0.235823i 0.926037 0.377433i \(-0.123193\pi\)
−0.789885 + 0.613255i \(0.789860\pi\)
\(360\) 43.4558 + 25.0892i 0.120711 + 0.0696923i
\(361\) 85.3823 147.886i 0.236516 0.409658i
\(362\) −80.0589 + 46.2220i −0.221157 + 0.127685i
\(363\) 204.229i 0.562614i
\(364\) 0 0
\(365\) −335.647 −0.919580
\(366\) 20.4853 + 35.4815i 0.0559707 + 0.0969441i
\(367\) 278.044 + 160.529i 0.757612 + 0.437408i 0.828438 0.560081i \(-0.189230\pi\)
−0.0708255 + 0.997489i \(0.522563\pi\)
\(368\) −37.4558 + 64.8754i −0.101782 + 0.176292i
\(369\) −107.548 + 62.0927i −0.291457 + 0.168273i
\(370\) 593.040i 1.60281i
\(371\) 0 0
\(372\) 29.8234 0.0801704
\(373\) −93.7351 162.354i −0.251300 0.435265i 0.712584 0.701587i \(-0.247525\pi\)
−0.963884 + 0.266322i \(0.914192\pi\)
\(374\) −50.5370 29.1776i −0.135126 0.0780149i
\(375\) 76.9706 133.317i 0.205255 0.355512i
\(376\) −94.7939 + 54.7293i −0.252112 + 0.145557i
\(377\) 562.662i 1.49247i
\(378\) 0 0
\(379\) −357.103 −0.942223 −0.471112 0.882074i \(-0.656147\pi\)
−0.471112 + 0.882074i \(0.656147\pi\)
\(380\) 136.368 + 236.195i 0.358862 + 0.621567i
\(381\) 134.912 + 77.8913i 0.354099 + 0.204439i
\(382\) −70.7574 + 122.555i −0.185229 + 0.320826i
\(383\) 538.867 311.115i 1.40696 0.812311i 0.411870 0.911243i \(-0.364876\pi\)
0.995094 + 0.0989320i \(0.0315426\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) 0 0
\(386\) −111.598 −0.289114
\(387\) 15.6396 + 27.0886i 0.0404124 + 0.0699964i
\(388\) −89.5736 51.7153i −0.230860 0.133287i
\(389\) −113.735 + 196.995i −0.292378 + 0.506414i −0.974372 0.224945i \(-0.927780\pi\)
0.681994 + 0.731358i \(0.261113\pi\)
\(390\) 235.279 135.839i 0.603280 0.348304i
\(391\) 439.737i 1.12465i
\(392\) 0 0
\(393\) 21.0883 0.0536598
\(394\) −130.066 225.281i −0.330117 0.571779i
\(395\) −357.588 206.453i −0.905286 0.522667i
\(396\) −5.27208 + 9.13151i −0.0133133 + 0.0230594i
\(397\) 623.823 360.165i 1.57134 0.907216i 0.575339 0.817915i \(-0.304870\pi\)
0.996005 0.0893004i \(-0.0284631\pi\)
\(398\) 240.458i 0.604166i
\(399\) 0 0
\(400\) −39.8823 −0.0997056
\(401\) −348.588 603.772i −0.869296 1.50567i −0.862717 0.505687i \(-0.831239\pi\)
−0.00657959 0.999978i \(-0.502094\pi\)
\(402\) −129.338 74.6734i −0.321737 0.185755i
\(403\) 80.7351 139.837i 0.200335 0.346991i
\(404\) 11.4487 6.60991i 0.0283384 0.0163612i
\(405\) 53.2223i 0.131413i
\(406\) 0 0
\(407\) 124.617 0.306185
\(408\) 57.5147 + 99.6184i 0.140967 + 0.244163i
\(409\) −88.6690 51.1931i −0.216795 0.125166i 0.387671 0.921798i \(-0.373280\pi\)
−0.604465 + 0.796632i \(0.706613\pi\)
\(410\) 173.095 299.810i 0.422184 0.731244i
\(411\) −248.647 + 143.556i −0.604980 + 0.349285i
\(412\) 351.742i 0.853742i
\(413\) 0 0
\(414\) 79.4558 0.191922
\(415\) −19.0294 32.9600i −0.0458541 0.0794216i
\(416\) 91.8823 + 53.0482i 0.220871 + 0.127520i
\(417\) 190.971 330.771i 0.457963 0.793215i
\(418\) −49.6325 + 28.6553i −0.118738 + 0.0685534i
\(419\) 391.426i 0.934191i 0.884207 + 0.467095i \(0.154700\pi\)
−0.884207 + 0.467095i \(0.845300\pi\)
\(420\) 0 0
\(421\) 354.441 0.841902 0.420951 0.907083i \(-0.361696\pi\)
0.420951 + 0.907083i \(0.361696\pi\)
\(422\) 15.2548 + 26.4221i 0.0361489 + 0.0626117i
\(423\) 100.544 + 58.0492i 0.237693 + 0.137232i
\(424\) −52.3675 + 90.7032i −0.123508 + 0.213923i
\(425\) −202.747 + 117.056i −0.477051 + 0.275425i
\(426\) 270.938i 0.636006i
\(427\) 0 0
\(428\) −92.4853 −0.216087
\(429\) 28.5442 + 49.4399i 0.0665365 + 0.115245i
\(430\) −75.5147 43.5984i −0.175616 0.101392i
\(431\) −292.643 + 506.873i −0.678987 + 1.17604i 0.296300 + 0.955095i \(0.404247\pi\)
−0.975286 + 0.220944i \(0.929086\pi\)
\(432\) 18.0000 10.3923i 0.0416667 0.0240563i
\(433\) 392.207i 0.905789i −0.891564 0.452895i \(-0.850391\pi\)
0.891564 0.452895i \(-0.149609\pi\)
\(434\) 0 0
\(435\) −307.279 −0.706389
\(436\) 35.9411 + 62.2519i 0.0824338 + 0.142779i
\(437\) 374.007 + 215.933i 0.855852 + 0.494126i
\(438\) −69.5147 + 120.403i −0.158709 + 0.274893i
\(439\) −339.926 + 196.256i −0.774319 + 0.447053i −0.834413 0.551140i \(-0.814193\pi\)
0.0600943 + 0.998193i \(0.480860\pi\)
\(440\) 29.3939i 0.0668043i
\(441\) 0 0
\(442\) 622.794 1.40904
\(443\) 407.371 + 705.587i 0.919574 + 1.59275i 0.800064 + 0.599915i \(0.204799\pi\)
0.119510 + 0.992833i \(0.461868\pi\)
\(444\) −212.735 122.823i −0.479133 0.276628i
\(445\) 124.456 215.564i 0.279676 0.484413i
\(446\) 146.184 84.3992i 0.327766 0.189236i
\(447\) 365.208i 0.817020i
\(448\) 0 0
\(449\) 180.323 0.401610 0.200805 0.979631i \(-0.435644\pi\)
0.200805 + 0.979631i \(0.435644\pi\)
\(450\) 21.1508 + 36.6342i 0.0470017 + 0.0814093i
\(451\) 63.0000 + 36.3731i 0.139690 + 0.0806498i
\(452\) 73.0294 126.491i 0.161570 0.279847i
\(453\) 108.551 62.6721i 0.239628 0.138349i
\(454\) 240.194i 0.529062i
\(455\) 0 0
\(456\) 112.971 0.247742
\(457\) −140.088 242.640i −0.306539 0.530941i 0.671064 0.741400i \(-0.265838\pi\)
−0.977603 + 0.210459i \(0.932504\pi\)
\(458\) −134.735 77.7893i −0.294181 0.169846i
\(459\) 61.0036 105.661i 0.132905 0.230199i
\(460\) −191.823 + 110.749i −0.417007 + 0.240759i
\(461\) 406.297i 0.881338i 0.897670 + 0.440669i \(0.145259\pi\)
−0.897670 + 0.440669i \(0.854741\pi\)
\(462\) 0 0
\(463\) 457.470 0.988056 0.494028 0.869446i \(-0.335524\pi\)
0.494028 + 0.869446i \(0.335524\pi\)
\(464\) −60.0000 103.923i −0.129310 0.223972i
\(465\) 76.3675 + 44.0908i 0.164231 + 0.0948190i
\(466\) 40.4924 70.1349i 0.0868936 0.150504i
\(467\) −557.470 + 321.856i −1.19373 + 0.689198i −0.959150 0.282899i \(-0.908704\pi\)
−0.234577 + 0.972098i \(0.575370\pi\)
\(468\) 112.532i 0.240454i
\(469\) 0 0
\(470\) −323.647 −0.688610
\(471\) −202.368 350.511i −0.429655 0.744184i
\(472\) −238.794 137.868i −0.505919 0.292093i
\(473\) 9.16147 15.8681i 0.0193689 0.0335479i
\(474\) −148.118 + 85.5158i −0.312485 + 0.180413i
\(475\) 229.921i 0.484045i
\(476\) 0 0
\(477\) 111.088 0.232890
\(478\) 199.066 + 344.792i 0.416456 + 0.721323i
\(479\) −145.955 84.2674i −0.304709 0.175924i 0.339848 0.940481i \(-0.389624\pi\)
−0.644556 + 0.764557i \(0.722958\pi\)
\(480\) −28.9706 + 50.1785i −0.0603553 + 0.104539i
\(481\) −1151.79 + 664.988i −2.39458 + 1.38251i
\(482\) 238.021i 0.493819i
\(483\) 0 0
\(484\) −235.823 −0.487238
\(485\) −152.912 264.851i −0.315282 0.546084i
\(486\) −19.0919 11.0227i −0.0392837 0.0226805i
\(487\) 1.38983 2.40725i 0.00285385 0.00494302i −0.864595 0.502469i \(-0.832425\pi\)
0.867449 + 0.497526i \(0.165758\pi\)
\(488\) −40.9706 + 23.6544i −0.0839561 + 0.0484721i
\(489\) 126.593i 0.258881i
\(490\) 0 0
\(491\) −247.477 −0.504027 −0.252014 0.967724i \(-0.581093\pi\)
−0.252014 + 0.967724i \(0.581093\pi\)
\(492\) −71.6985 124.185i −0.145729 0.252409i
\(493\) −610.036 352.204i −1.23739 0.714410i
\(494\) 305.823 529.702i 0.619076 1.07227i
\(495\) −27.0000 + 15.5885i −0.0545455 + 0.0314918i
\(496\) 34.4371i 0.0694296i
\(497\) 0 0
\(498\) −15.7645 −0.0316556
\(499\) 241.713 + 418.659i 0.484394 + 0.838996i 0.999839 0.0179271i \(-0.00570668\pi\)
−0.515445 + 0.856923i \(0.672373\pi\)
\(500\) 153.941 + 88.8780i 0.307882 + 0.177756i
\(501\) 34.1177 59.0937i 0.0680993 0.117951i
\(502\) −129.941 + 75.0215i −0.258847 + 0.149445i
\(503\) 58.7033i 0.116706i 0.998296 + 0.0583532i \(0.0185849\pi\)
−0.998296 + 0.0583532i \(0.981415\pi\)
\(504\) 0 0
\(505\) 39.0883 0.0774026
\(506\) −23.2721 40.3084i −0.0459922 0.0796609i
\(507\) −274.147 158.279i −0.540723 0.312187i
\(508\) −89.9411 + 155.783i −0.177049 + 0.306659i
\(509\) 59.6512 34.4396i 0.117193 0.0676614i −0.440258 0.897871i \(-0.645113\pi\)
0.557451 + 0.830210i \(0.311780\pi\)
\(510\) 340.119i 0.666899i
\(511\) 0 0
\(512\) −22.6274 −0.0441942
\(513\) −59.9117 103.770i −0.116787 0.202281i
\(514\) −355.742 205.388i −0.692105 0.399587i
\(515\) −520.014 + 900.691i −1.00974 + 1.74891i
\(516\) −31.2792 + 18.0591i −0.0606186 + 0.0349982i
\(517\) 68.0089i 0.131545i
\(518\) 0 0
\(519\) 41.2721 0.0795223
\(520\) 156.853 + 271.677i 0.301640 + 0.522456i
\(521\) −253.503 146.360i −0.486570 0.280922i 0.236580 0.971612i \(-0.423973\pi\)
−0.723151 + 0.690690i \(0.757307\pi\)
\(522\) −63.6396 + 110.227i −0.121915 + 0.211163i
\(523\) 426.999 246.528i 0.816442 0.471373i −0.0327460 0.999464i \(-0.510425\pi\)
0.849188 + 0.528091i \(0.177092\pi\)
\(524\) 24.3507i 0.0464708i
\(525\) 0 0
\(526\) 125.897 0.239347
\(527\) 101.074 + 175.065i 0.191791 + 0.332192i
\(528\) −10.5442 6.08767i −0.0199700 0.0115297i
\(529\) 89.1325 154.382i 0.168492 0.291837i
\(530\) −268.191 + 154.840i −0.506021 + 0.292151i
\(531\) 292.462i 0.550775i
\(532\) 0 0
\(533\) −776.382 −1.45663
\(534\) −51.5513 89.2895i −0.0965380 0.167209i
\(535\) −236.823 136.730i −0.442661 0.255570i
\(536\) 86.2254 149.347i 0.160868 0.278632i
\(537\) 19.3568 11.1757i 0.0360462 0.0208113i
\(538\) 270.819i 0.503381i
\(539\) 0 0
\(540\) 61.4558 0.113807
\(541\) 518.926 + 898.806i 0.959198 + 1.66138i 0.724456 + 0.689322i \(0.242091\pi\)
0.234742 + 0.972058i \(0.424575\pi\)
\(542\) −266.309 153.753i −0.491344 0.283678i
\(543\) −56.6102 + 98.0517i −0.104254 + 0.180574i
\(544\) −115.029 + 66.4123i −0.211451 + 0.122081i
\(545\) 212.541i 0.389984i
\(546\) 0 0
\(547\) −130.530 −0.238629 −0.119314 0.992857i \(-0.538070\pi\)
−0.119314 + 0.992857i \(0.538070\pi\)
\(548\) −165.765 287.113i −0.302490 0.523928i
\(549\) 43.4558 + 25.0892i 0.0791545 + 0.0456999i
\(550\) 12.3898 21.4598i 0.0225270 0.0390178i
\(551\) −599.117 + 345.900i −1.08733 + 0.627768i
\(552\) 91.7477i 0.166210i
\(553\) 0 0
\(554\) −411.078 −0.742018
\(555\) −363.161 629.014i −0.654345 1.13336i
\(556\) 381.941 + 220.514i 0.686944 + 0.396608i
\(557\) −332.574 + 576.034i −0.597080 + 1.03417i 0.396170 + 0.918177i \(0.370339\pi\)
−0.993250 + 0.115996i \(0.962994\pi\)
\(558\) 31.6325 18.2630i 0.0566890 0.0327294i
\(559\) 195.551i 0.349823i
\(560\) 0 0
\(561\) −71.4701 −0.127398
\(562\) 13.3310 + 23.0899i 0.0237206 + 0.0410852i
\(563\) −718.191 414.648i −1.27565 0.736497i −0.299604 0.954064i \(-0.596855\pi\)
−0.976045 + 0.217567i \(0.930188\pi\)
\(564\) −67.0294 + 116.098i −0.118847 + 0.205848i
\(565\) 374.007 215.933i 0.661960 0.382183i
\(566\) 568.137i 1.00378i
\(567\) 0 0
\(568\) 312.853 0.550797
\(569\) −353.485 612.254i −0.621240 1.07602i −0.989255 0.146199i \(-0.953296\pi\)
0.368016 0.929820i \(-0.380037\pi\)
\(570\) 289.279 + 167.015i 0.507507 + 0.293010i
\(571\) 183.456 317.755i 0.321289 0.556488i −0.659466 0.751735i \(-0.729217\pi\)
0.980754 + 0.195246i \(0.0625507\pi\)
\(572\) −57.0883 + 32.9600i −0.0998047 + 0.0576223i
\(573\) 173.319i 0.302477i
\(574\) 0 0
\(575\) −186.728 −0.324744
\(576\) 12.0000 + 20.7846i 0.0208333 + 0.0360844i
\(577\) 338.059 + 195.178i 0.585891 + 0.338264i 0.763471 0.645842i \(-0.223494\pi\)
−0.177580 + 0.984106i \(0.556827\pi\)
\(578\) −185.491 + 321.280i −0.320919 + 0.555847i
\(579\) −118.368 + 68.3395i −0.204434 + 0.118030i
\(580\) 354.815i 0.611751i
\(581\) 0 0
\(582\) −126.676 −0.217657
\(583\) −32.5370 56.3558i −0.0558096 0.0966651i
\(584\) −139.029 80.2687i −0.238064 0.137446i
\(585\) 166.368 288.157i 0.284389 0.492576i
\(586\) 344.022 198.621i 0.587069 0.338944i
\(587\) 702.499i 1.19676i −0.801212 0.598381i \(-0.795811\pi\)
0.801212 0.598381i \(-0.204189\pi\)
\(588\) 0 0
\(589\) 198.530 0.337063
\(590\) −407.647 706.065i −0.690927 1.19672i
\(591\) −275.912 159.298i −0.466856 0.269539i
\(592\) 141.823 245.645i 0.239567 0.414941i
\(593\) 816.245 471.259i 1.37647 0.794704i 0.384735 0.923027i \(-0.374293\pi\)
0.991732 + 0.128323i \(0.0409594\pi\)
\(594\) 12.9139i 0.0217406i
\(595\) 0 0
\(596\) 421.706 0.707560
\(597\) −147.250 255.044i −0.246650 0.427210i
\(598\) 430.191 + 248.371i 0.719383 + 0.415336i
\(599\) 476.054 824.550i 0.794749 1.37655i −0.128250 0.991742i \(-0.540936\pi\)
0.922999 0.384803i \(-0.125731\pi\)
\(600\) −42.3015 + 24.4228i −0.0705025 + 0.0407047i
\(601\) 729.804i 1.21432i 0.794581 + 0.607158i \(0.207690\pi\)
−0.794581 + 0.607158i \(0.792310\pi\)
\(602\) 0 0
\(603\) −182.912 −0.303336
\(604\) 72.3675 + 125.344i 0.119814 + 0.207524i
\(605\) −603.864 348.641i −0.998122 0.576266i
\(606\) 8.09545 14.0217i 0.0133588 0.0231382i
\(607\) −871.514 + 503.169i −1.43577 + 0.828944i −0.997552 0.0699241i \(-0.977724\pi\)
−0.438220 + 0.898868i \(0.644391\pi\)
\(608\) 130.447i 0.214551i
\(609\) 0 0
\(610\) −139.882 −0.229315
\(611\) 362.912 + 628.581i 0.593963 + 1.02877i
\(612\) 122.007 + 70.4409i 0.199358 + 0.115099i
\(613\) 99.7939 172.848i 0.162796 0.281971i −0.773074 0.634315i \(-0.781282\pi\)
0.935870 + 0.352344i \(0.114615\pi\)
\(614\) −186.551 + 107.705i −0.303829 + 0.175416i
\(615\) 423.996i 0.689424i
\(616\) 0 0
\(617\) −353.294 −0.572599 −0.286299 0.958140i \(-0.592425\pi\)
−0.286299 + 0.958140i \(0.592425\pi\)
\(618\) 215.397 + 373.078i 0.348539 + 0.603687i
\(619\) 48.6762 + 28.1032i 0.0786368 + 0.0454010i 0.538803 0.842432i \(-0.318877\pi\)
−0.460166 + 0.887833i \(0.652210\pi\)
\(620\) −50.9117 + 88.1816i −0.0821156 + 0.142228i
\(621\) 84.2756 48.6566i 0.135710 0.0783520i
\(622\) 400.443i 0.643799i
\(623\) 0 0
\(624\) 129.941 0.208239
\(625\) 387.426 + 671.041i 0.619882 + 1.07367i
\(626\) 59.5004 + 34.3526i 0.0950486 + 0.0548763i
\(627\) −35.0955 + 60.7871i −0.0559736 + 0.0969491i
\(628\) 404.735 233.674i 0.644483 0.372092i
\(629\) 1665.03i 2.64710i
\(630\) 0 0
\(631\) 807.322 1.27943 0.639716 0.768611i \(-0.279052\pi\)
0.639716 + 0.768611i \(0.279052\pi\)
\(632\) −98.7452 171.032i −0.156242 0.270620i
\(633\) 32.3604 + 18.6833i 0.0511223 + 0.0295154i
\(634\) −408.728 + 707.938i −0.644681 + 1.11662i
\(635\) −460.617 + 265.938i −0.725382 + 0.418799i
\(636\) 128.274i 0.201688i
\(637\) 0 0
\(638\) 74.5584 0.116863
\(639\) −165.915 287.374i −0.259648 0.449724i
\(640\) −57.9411 33.4523i −0.0905330 0.0522693i
\(641\) −508.176 + 880.186i −0.792786 + 1.37315i 0.131450 + 0.991323i \(0.458037\pi\)
−0.924236 + 0.381823i \(0.875297\pi\)
\(642\) −98.0955 + 56.6354i −0.152797 + 0.0882172i
\(643\) 404.688i 0.629375i −0.949195 0.314687i \(-0.898100\pi\)
0.949195 0.314687i \(-0.101900\pi\)
\(644\) 0 0
\(645\) −106.794 −0.165572
\(646\) 382.867 + 663.145i 0.592674 + 1.02654i
\(647\) 814.587 + 470.302i 1.25902 + 0.726896i 0.972884 0.231292i \(-0.0742953\pi\)
0.286137 + 0.958189i \(0.407629\pi\)
\(648\) 12.7279 22.0454i 0.0196419 0.0340207i
\(649\) 148.368 85.6600i 0.228609 0.131988i
\(650\) 264.460i 0.406862i
\(651\) 0 0
\(652\) −146.177 −0.224197
\(653\) −365.985 633.904i −0.560467 0.970757i −0.997456 0.0712901i \(-0.977288\pi\)
0.436989 0.899467i \(-0.356045\pi\)
\(654\) 76.2426 + 44.0187i 0.116579 + 0.0673069i
\(655\) −36.0000 + 62.3538i −0.0549618 + 0.0951967i
\(656\) 143.397 82.7903i 0.218593 0.126205i
\(657\) 170.276i 0.259171i
\(658\) 0 0
\(659\) 904.316 1.37225 0.686127 0.727481i \(-0.259309\pi\)
0.686127 + 0.727481i \(0.259309\pi\)
\(660\) −18.0000 31.1769i −0.0272727 0.0472377i
\(661\) 290.881 + 167.940i 0.440063 + 0.254070i 0.703624 0.710572i \(-0.251564\pi\)
−0.263562 + 0.964643i \(0.584897\pi\)
\(662\) 235.019 407.065i 0.355014 0.614902i
\(663\) 660.573 381.382i 0.996339 0.575237i
\(664\) 18.2033i 0.0274146i
\(665\) 0 0
\(666\) −300.853 −0.451731
\(667\) −280.919 486.566i −0.421168 0.729484i
\(668\) 68.2355 + 39.3958i 0.102149 + 0.0589757i
\(669\) 103.368 179.038i 0.154511 0.267620i
\(670\) 441.588 254.951i 0.659086 0.380524i
\(671\) 29.3939i 0.0438061i
\(672\) 0 0
\(673\) 1191.44 1.77034 0.885171 0.465266i \(-0.154041\pi\)
0.885171 + 0.465266i \(0.154041\pi\)
\(674\) 62.3503 + 107.994i 0.0925078 + 0.160228i
\(675\) 44.8675 + 25.9043i 0.0664704 + 0.0383767i
\(676\) 182.765 316.557i 0.270362 0.468280i
\(677\) 1048.82 605.536i 1.54922 0.894441i 0.551015 0.834495i \(-0.314241\pi\)
0.998202 0.0599456i \(-0.0190927\pi\)
\(678\) 178.885i 0.263842i
\(679\) 0 0
\(680\) −392.735 −0.577552
\(681\) 147.088 + 254.764i 0.215989 + 0.374103i
\(682\) −18.5299 10.6982i −0.0271699 0.0156865i
\(683\) 616.945 1068.58i 0.903287 1.56454i 0.0800856 0.996788i \(-0.474481\pi\)
0.823201 0.567750i \(-0.192186\pi\)
\(684\) 119.823 69.1801i 0.175180 0.101140i
\(685\) 980.264i 1.43104i
\(686\) 0 0
\(687\) −190.544 −0.277357
\(688\) −20.8528 36.1181i −0.0303093 0.0524973i
\(689\) 601.456 + 347.251i 0.872940 + 0.503992i
\(690\) −135.640 + 234.935i −0.196579 + 0.340485i
\(691\) −75.0883 + 43.3523i −0.108666 + 0.0627384i −0.553348 0.832950i \(-0.686650\pi\)
0.444682 + 0.895689i \(0.353317\pi\)
\(692\) 47.6569i 0.0688683i
\(693\) 0 0
\(694\) 452.662 0.652251
\(695\) 652.014 + 1129.32i 0.938150 + 1.62492i
\(696\) −127.279 73.4847i −0.182872 0.105581i
\(697\) 485.985 841.750i 0.697252 1.20768i
\(698\) 407.897 235.499i 0.584379 0.337391i
\(699\) 99.1858i 0.141897i
\(700\) 0 0
\(701\) −149.147 −0.212763 −0.106382 0.994325i \(-0.533927\pi\)
−0.106382 + 0.994325i \(0.533927\pi\)
\(702\) −68.9117 119.359i −0.0981648 0.170026i
\(703\) −1416.15 817.612i −2.01443 1.16303i
\(704\) 7.02944 12.1753i 0.00998500 0.0172945i
\(705\) −343.279 + 198.192i −0.486921 + 0.281124i
\(706\) 927.317i 1.31348i
\(707\) 0 0
\(708\) −337.706 −0.476985
\(709\) −94.8234 164.239i −0.133742 0.231649i 0.791374 0.611332i \(-0.209366\pi\)
−0.925116 + 0.379684i \(0.876033\pi\)
\(710\) 801.110 + 462.521i 1.12832 + 0.651438i
\(711\) −104.735 + 181.406i −0.147307 + 0.255143i
\(712\) 103.103 59.5263i 0.144807 0.0836044i
\(713\) 161.234i 0.226134i
\(714\) 0 0
\(715\) −194.912 −0.272604
\(716\) 12.9045 + 22.3513i 0.0180231 + 0.0312169i
\(717\) 422.283 + 243.805i 0.588958 + 0.340035i
\(718\) −69.1249 + 119.728i −0.0962742 + 0.166752i
\(719\) −10.3978 + 6.00319i −0.0144615 + 0.00834937i −0.507213 0.861821i \(-0.669324\pi\)
0.492752 + 0.870170i \(0.335991\pi\)
\(720\) 70.9631i 0.0985599i
\(721\) 0 0
\(722\) 241.497 0.334484
\(723\) −145.757 252.459i −0.201601 0.349183i
\(724\) −113.220 65.3678i −0.156382 0.0902870i
\(725\) 149.558 259.043i 0.206288 0.357300i
\(726\) −250.128 + 144.412i −0.344530 + 0.198914i
\(727\) 417.169i 0.573823i −0.957957 0.286911i \(-0.907371\pi\)
0.957957 0.286911i \(-0.0926286\pi\)
\(728\) 0 0
\(729\) −27.0000 −0.0370370
\(730\) −237.338 411.082i −0.325121 0.563126i
\(731\) −212.016 122.408i −0.290036 0.167452i
\(732\) −28.9706 + 50.1785i −0.0395773 + 0.0685498i
\(733\) 1114.57 643.495i 1.52055 0.877892i 0.520847 0.853650i \(-0.325616\pi\)
0.999706 0.0242419i \(-0.00771721\pi\)
\(734\) 454.043i 0.618588i
\(735\) 0 0
\(736\) −105.941 −0.143942
\(737\) 53.5736 + 92.7922i 0.0726914 + 0.125905i
\(738\) −152.095 87.8124i −0.206091 0.118987i
\(739\) −666.735 + 1154.82i −0.902213 + 1.56268i −0.0775967 + 0.996985i \(0.524725\pi\)
−0.824616 + 0.565693i \(0.808609\pi\)
\(740\) 726.323 419.343i 0.981517 0.566679i
\(741\) 749.111i 1.01095i
\(742\) 0 0
\(743\) −776.476 −1.04506 −0.522528 0.852622i \(-0.675011\pi\)
−0.522528 + 0.852622i \(0.675011\pi\)
\(744\) 21.0883 + 36.5260i 0.0283445 + 0.0490941i
\(745\) 1079.84 + 623.449i 1.44946 + 0.836844i
\(746\) 132.561 229.603i 0.177696 0.307779i
\(747\) −16.7208 + 9.65375i −0.0223839 + 0.0129234i
\(748\) 82.5266i 0.110330i
\(749\) 0 0
\(750\) 217.706 0.290274
\(751\) −24.4193 42.2954i −0.0325157 0.0563188i 0.849310 0.527895i \(-0.177019\pi\)
−0.881825 + 0.471576i \(0.843685\pi\)
\(752\) −134.059 77.3989i −0.178270 0.102924i
\(753\) −91.8823 + 159.145i −0.122022 + 0.211348i
\(754\) −689.117 + 397.862i −0.913948 + 0.527668i
\(755\) 427.952i 0.566824i
\(756\) 0 0
\(757\) −1279.47 −1.69019 −0.845093 0.534620i \(-0.820455\pi\)
−0.845093 + 0.534620i \(0.820455\pi\)
\(758\) −252.510 437.360i −0.333126 0.576992i
\(759\) −49.3675 28.5024i −0.0650429 0.0375525i
\(760\) −192.853 + 334.031i −0.253754 + 0.439514i
\(761\) −1139.80 + 658.062i −1.49776 + 0.864734i −0.999997 0.00257751i \(-0.999180\pi\)
−0.497766 + 0.867311i \(0.665846\pi\)
\(762\) 220.310i 0.289121i
\(763\) 0 0
\(764\) −200.132 −0.261953
\(765\) 208.279 + 360.750i 0.272260 + 0.471569i
\(766\) 762.073 + 439.983i 0.994874 + 0.574391i
\(767\) −914.205 + 1583.45i −1.19192 + 2.06447i
\(768\) −24.0000 + 13.8564i −0.0312500 + 0.0180422i
\(769\) 110.324i 0.143464i −0.997424 0.0717320i \(-0.977147\pi\)
0.997424 0.0717320i \(-0.0228526\pi\)
\(770\) 0 0
\(771\) −503.095 −0.652523
\(772\) −78.9117 136.679i −0.102217 0.177045i
\(773\) 621.489 + 358.817i 0.803996 + 0.464187i 0.844867 0.534977i \(-0.179680\pi\)
−0.0408706 + 0.999164i \(0.513013\pi\)
\(774\) −22.1177 + 38.3091i −0.0285759 + 0.0494949i
\(775\) −74.3390 + 42.9196i −0.0959212 + 0.0553802i
\(776\) 146.273i 0.188496i
\(777\) 0 0
\(778\) −321.691 −0.413485
\(779\) −477.286 826.684i −0.612691 1.06121i
\(780\) 332.735 + 192.105i 0.426583 + 0.246288i