Properties

Label 1950.2.y.j.199.1
Level $1950$
Weight $2$
Character 1950.199
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.17284886784.1
Defining polynomial: \(x^{8} - 2 x^{7} + 2 x^{6} + 30 x^{5} + 185 x^{4} + 36 x^{3} + 8 x^{2} + 208 x + 2704\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.1
Root \(-1.80668 + 1.80668i\) of defining polynomial
Character \(\chi\) \(=\) 1950.199
Dual form 1950.2.y.j.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-0.661290 - 1.14539i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{6} +(-0.661290 - 1.14539i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-3.99528 - 2.30668i) q^{11} +1.00000i q^{12} +(1.66129 + 3.20002i) q^{13} +1.32258 q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.46410 - 2.00000i) q^{17} -1.00000 q^{18} +(-1.98387 + 1.14539i) q^{19} +1.32258i q^{21} +(3.99528 - 2.30668i) q^{22} +(7.50670 + 4.33399i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-3.60194 - 0.161290i) q^{26} -1.00000i q^{27} +(-0.661290 + 1.14539i) q^{28} +(-1.01141 + 1.75182i) q^{29} -10.1321i q^{31} +(-0.500000 - 0.866025i) q^{32} +(2.30668 + 3.99528i) q^{33} +4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(3.40475 - 5.89721i) q^{37} -2.29078i q^{38} +(0.161290 - 3.60194i) q^{39} +(-4.02283 - 2.32258i) q^{41} +(-1.14539 - 0.661290i) q^{42} +(-7.45269 + 4.30281i) q^{43} +4.61335i q^{44} +(-7.50670 + 4.33399i) q^{46} -9.10926 q^{47} +(0.866025 - 0.500000i) q^{48} +(2.62539 - 4.54731i) q^{49} -4.00000 q^{51} +(1.94065 - 3.03873i) q^{52} +0.826674i q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.661290 - 1.14539i) q^{56} +2.29078 q^{57} +(-1.01141 - 1.75182i) q^{58} +(-2.72064 + 1.57076i) q^{59} +(-0.267949 - 0.464102i) q^{61} +(8.77464 + 5.06604i) q^{62} +(0.661290 - 1.14539i) q^{63} +1.00000 q^{64} -4.61335 q^{66} +(-1.59053 + 2.75488i) q^{67} +(-3.46410 - 2.00000i) q^{68} +(-4.33399 - 7.50670i) q^{69} +(-9.81724 + 5.66799i) q^{71} +(0.500000 + 0.866025i) q^{72} +6.28304 q^{73} +(3.40475 + 5.89721i) q^{74} +(1.98387 + 1.14539i) q^{76} +6.10153i q^{77} +(3.03873 + 1.94065i) q^{78} -2.96774 q^{79} +(-0.500000 + 0.866025i) q^{81} +(4.02283 - 2.32258i) q^{82} -15.8719 q^{83} +(1.14539 - 0.661290i) q^{84} -8.60562i q^{86} +(1.75182 - 1.01141i) q^{87} +(-3.99528 - 2.30668i) q^{88} +(-10.2746 - 5.93207i) q^{89} +(2.56667 - 4.01896i) q^{91} -8.66799i q^{92} +(-5.06604 + 8.77464i) q^{93} +(4.55463 - 7.88885i) q^{94} +1.00000i q^{96} +(4.40947 + 7.63743i) q^{97} +(2.62539 + 4.54731i) q^{98} -4.61335i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} - 4q^{4} + 2q^{7} + 8q^{8} + 4q^{9} + O(q^{10}) \) \( 8q - 4q^{2} - 4q^{4} + 2q^{7} + 8q^{8} + 4q^{9} + 6q^{11} + 6q^{13} - 4q^{14} - 4q^{16} - 8q^{18} + 6q^{19} - 6q^{22} + 6q^{23} - 12q^{26} + 2q^{28} + 8q^{29} - 4q^{32} + 2q^{33} + 4q^{36} - 10q^{37} - 6q^{39} - 48q^{43} - 6q^{46} - 16q^{47} - 14q^{49} - 32q^{51} + 6q^{52} + 2q^{56} + 8q^{58} - 24q^{59} - 16q^{61} + 30q^{62} - 2q^{63} + 8q^{64} - 4q^{66} - 12q^{67} - 4q^{69} - 12q^{71} + 4q^{72} + 24q^{73} - 10q^{74} - 6q^{76} - 6q^{78} + 20q^{79} - 4q^{81} - 32q^{83} + 6q^{87} + 6q^{88} - 42q^{89} - 10q^{91} + 4q^{93} + 8q^{94} + 36q^{97} - 14q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0.866025 0.500000i 0.353553 0.204124i
\(7\) −0.661290 1.14539i −0.249944 0.432916i 0.713566 0.700588i \(-0.247079\pi\)
−0.963510 + 0.267672i \(0.913746\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −3.99528 2.30668i −1.20462 0.695489i −0.243043 0.970015i \(-0.578146\pi\)
−0.961580 + 0.274526i \(0.911479\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.66129 + 3.20002i 0.460759 + 0.887525i
\(14\) 1.32258 0.353474
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.46410 2.00000i 0.840168 0.485071i −0.0171533 0.999853i \(-0.505460\pi\)
0.857321 + 0.514782i \(0.172127\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.98387 + 1.14539i −0.455131 + 0.262770i −0.709995 0.704207i \(-0.751303\pi\)
0.254864 + 0.966977i \(0.417969\pi\)
\(20\) 0 0
\(21\) 1.32258i 0.288611i
\(22\) 3.99528 2.30668i 0.851797 0.491785i
\(23\) 7.50670 + 4.33399i 1.56525 + 0.903700i 0.996710 + 0.0810471i \(0.0258264\pi\)
0.568544 + 0.822653i \(0.307507\pi\)
\(24\) −0.866025 0.500000i −0.176777 0.102062i
\(25\) 0 0
\(26\) −3.60194 0.161290i −0.706399 0.0316315i
\(27\) 1.00000i 0.192450i
\(28\) −0.661290 + 1.14539i −0.124972 + 0.216458i
\(29\) −1.01141 + 1.75182i −0.187815 + 0.325305i −0.944521 0.328450i \(-0.893474\pi\)
0.756707 + 0.653755i \(0.226807\pi\)
\(30\) 0 0
\(31\) 10.1321i 1.81978i −0.414853 0.909888i \(-0.636167\pi\)
0.414853 0.909888i \(-0.363833\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 2.30668 + 3.99528i 0.401541 + 0.695489i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 3.40475 5.89721i 0.559738 0.969495i −0.437780 0.899082i \(-0.644235\pi\)
0.997518 0.0704126i \(-0.0224316\pi\)
\(38\) 2.29078i 0.371613i
\(39\) 0.161290 3.60194i 0.0258270 0.576772i
\(40\) 0 0
\(41\) −4.02283 2.32258i −0.628260 0.362726i 0.151818 0.988408i \(-0.451487\pi\)
−0.780078 + 0.625682i \(0.784821\pi\)
\(42\) −1.14539 0.661290i −0.176737 0.102039i
\(43\) −7.45269 + 4.30281i −1.13652 + 0.656173i −0.945568 0.325426i \(-0.894492\pi\)
−0.190957 + 0.981598i \(0.561159\pi\)
\(44\) 4.61335i 0.695489i
\(45\) 0 0
\(46\) −7.50670 + 4.33399i −1.10680 + 0.639012i
\(47\) −9.10926 −1.32872 −0.664361 0.747412i \(-0.731296\pi\)
−0.664361 + 0.747412i \(0.731296\pi\)
\(48\) 0.866025 0.500000i 0.125000 0.0721688i
\(49\) 2.62539 4.54731i 0.375056 0.649616i
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) 1.94065 3.03873i 0.269120 0.421396i
\(53\) 0.826674i 0.113552i 0.998387 + 0.0567762i \(0.0180821\pi\)
−0.998387 + 0.0567762i \(0.981918\pi\)
\(54\) 0.866025 + 0.500000i 0.117851 + 0.0680414i
\(55\) 0 0
\(56\) −0.661290 1.14539i −0.0883686 0.153059i
\(57\) 2.29078 0.303421
\(58\) −1.01141 1.75182i −0.132805 0.230025i
\(59\) −2.72064 + 1.57076i −0.354197 + 0.204496i −0.666532 0.745476i \(-0.732222\pi\)
0.312335 + 0.949972i \(0.398889\pi\)
\(60\) 0 0
\(61\) −0.267949 0.464102i −0.0343074 0.0594221i 0.848362 0.529417i \(-0.177589\pi\)
−0.882669 + 0.469995i \(0.844256\pi\)
\(62\) 8.77464 + 5.06604i 1.11438 + 0.643388i
\(63\) 0.661290 1.14539i 0.0833147 0.144305i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −4.61335 −0.567865
\(67\) −1.59053 + 2.75488i −0.194314 + 0.336562i −0.946675 0.322189i \(-0.895581\pi\)
0.752361 + 0.658751i \(0.228915\pi\)
\(68\) −3.46410 2.00000i −0.420084 0.242536i
\(69\) −4.33399 7.50670i −0.521751 0.903700i
\(70\) 0 0
\(71\) −9.81724 + 5.66799i −1.16509 + 0.672666i −0.952519 0.304479i \(-0.901518\pi\)
−0.212573 + 0.977145i \(0.568184\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 6.28304 0.735375 0.367687 0.929949i \(-0.380150\pi\)
0.367687 + 0.929949i \(0.380150\pi\)
\(74\) 3.40475 + 5.89721i 0.395795 + 0.685536i
\(75\) 0 0
\(76\) 1.98387 + 1.14539i 0.227565 + 0.131385i
\(77\) 6.10153i 0.695334i
\(78\) 3.03873 + 1.94065i 0.344068 + 0.219736i
\(79\) −2.96774 −0.333897 −0.166948 0.985966i \(-0.553391\pi\)
−0.166948 + 0.985966i \(0.553391\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 4.02283 2.32258i 0.444247 0.256486i
\(83\) −15.8719 −1.74216 −0.871082 0.491138i \(-0.836581\pi\)
−0.871082 + 0.491138i \(0.836581\pi\)
\(84\) 1.14539 0.661290i 0.124972 0.0721526i
\(85\) 0 0
\(86\) 8.60562i 0.927968i
\(87\) 1.75182 1.01141i 0.187815 0.108435i
\(88\) −3.99528 2.30668i −0.425899 0.245893i
\(89\) −10.2746 5.93207i −1.08911 0.628798i −0.155771 0.987793i \(-0.549786\pi\)
−0.933339 + 0.358995i \(0.883119\pi\)
\(90\) 0 0
\(91\) 2.56667 4.01896i 0.269060 0.421302i
\(92\) 8.66799i 0.903700i
\(93\) −5.06604 + 8.77464i −0.525324 + 0.909888i
\(94\) 4.55463 7.88885i 0.469774 0.813673i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 4.40947 + 7.63743i 0.447714 + 0.775463i 0.998237 0.0593568i \(-0.0189050\pi\)
−0.550523 + 0.834820i \(0.685572\pi\)
\(98\) 2.62539 + 4.54731i 0.265205 + 0.459348i
\(99\) 4.61335i 0.463660i
\(100\) 0 0
\(101\) −3.61335 + 6.25851i −0.359542 + 0.622745i −0.987884 0.155192i \(-0.950400\pi\)
0.628342 + 0.777937i \(0.283734\pi\)
\(102\) 2.00000 3.46410i 0.198030 0.342997i
\(103\) 18.4000i 1.81301i −0.422196 0.906505i \(-0.638740\pi\)
0.422196 0.906505i \(-0.361260\pi\)
\(104\) 1.66129 + 3.20002i 0.162903 + 0.313788i
\(105\) 0 0
\(106\) −0.715920 0.413337i −0.0695363 0.0401468i
\(107\) 2.66025 + 1.53590i 0.257176 + 0.148481i 0.623046 0.782185i \(-0.285895\pi\)
−0.365869 + 0.930666i \(0.619228\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) 13.2267i 1.26689i −0.773788 0.633445i \(-0.781640\pi\)
0.773788 0.633445i \(-0.218360\pi\)
\(110\) 0 0
\(111\) −5.89721 + 3.40475i −0.559738 + 0.323165i
\(112\) 1.32258 0.124972
\(113\) −7.00306 + 4.04322i −0.658792 + 0.380354i −0.791817 0.610759i \(-0.790864\pi\)
0.133024 + 0.991113i \(0.457531\pi\)
\(114\) −1.14539 + 1.98387i −0.107275 + 0.185806i
\(115\) 0 0
\(116\) 2.02283 0.187815
\(117\) −1.94065 + 3.03873i −0.179413 + 0.280931i
\(118\) 3.14152i 0.289201i
\(119\) −4.58155 2.64516i −0.419990 0.242481i
\(120\) 0 0
\(121\) 5.14152 + 8.90538i 0.467411 + 0.809580i
\(122\) 0.535898 0.0485180
\(123\) 2.32258 + 4.02283i 0.209420 + 0.362726i
\(124\) −8.77464 + 5.06604i −0.787986 + 0.454944i
\(125\) 0 0
\(126\) 0.661290 + 1.14539i 0.0589124 + 0.102039i
\(127\) −9.93490 5.73592i −0.881580 0.508980i −0.0104008 0.999946i \(-0.503311\pi\)
−0.871179 + 0.490966i \(0.836644\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 8.60562 0.757683
\(130\) 0 0
\(131\) −15.9906 −1.39710 −0.698551 0.715560i \(-0.746172\pi\)
−0.698551 + 0.715560i \(0.746172\pi\)
\(132\) 2.30668 3.99528i 0.200771 0.347745i
\(133\) 2.62383 + 1.51487i 0.227515 + 0.131356i
\(134\) −1.59053 2.75488i −0.137401 0.237985i
\(135\) 0 0
\(136\) 3.46410 2.00000i 0.297044 0.171499i
\(137\) −8.03486 13.9168i −0.686465 1.18899i −0.972974 0.230914i \(-0.925828\pi\)
0.286509 0.958077i \(-0.407505\pi\)
\(138\) 8.66799 0.737868
\(139\) 4.66129 + 8.07359i 0.395365 + 0.684793i 0.993148 0.116865i \(-0.0372846\pi\)
−0.597782 + 0.801658i \(0.703951\pi\)
\(140\) 0 0
\(141\) 7.88885 + 4.55463i 0.664361 + 0.383569i
\(142\) 11.3360i 0.951294i
\(143\) 0.744087 16.6170i 0.0622237 1.38959i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) −3.14152 + 5.44128i −0.259994 + 0.450323i
\(147\) −4.54731 + 2.62539i −0.375056 + 0.216539i
\(148\) −6.80951 −0.559738
\(149\) −3.53788 + 2.04259i −0.289834 + 0.167336i −0.637867 0.770146i \(-0.720183\pi\)
0.348033 + 0.937482i \(0.386850\pi\)
\(150\) 0 0
\(151\) 19.9811i 1.62604i −0.582235 0.813021i \(-0.697822\pi\)
0.582235 0.813021i \(-0.302178\pi\)
\(152\) −1.98387 + 1.14539i −0.160913 + 0.0929032i
\(153\) 3.46410 + 2.00000i 0.280056 + 0.161690i
\(154\) −5.28408 3.05076i −0.425803 0.245838i
\(155\) 0 0
\(156\) −3.20002 + 1.66129i −0.256206 + 0.133010i
\(157\) 7.13379i 0.569338i −0.958626 0.284669i \(-0.908116\pi\)
0.958626 0.284669i \(-0.0918838\pi\)
\(158\) 1.48387 2.57014i 0.118050 0.204469i
\(159\) 0.413337 0.715920i 0.0327797 0.0567762i
\(160\) 0 0
\(161\) 11.4641i 0.903498i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) −4.94735 8.56906i −0.387506 0.671180i 0.604607 0.796524i \(-0.293330\pi\)
−0.992113 + 0.125343i \(0.959997\pi\)
\(164\) 4.64516i 0.362726i
\(165\) 0 0
\(166\) 7.93593 13.7454i 0.615948 1.06685i
\(167\) 12.0187 20.8171i 0.930037 1.61087i 0.146785 0.989168i \(-0.453108\pi\)
0.783253 0.621704i \(-0.213559\pi\)
\(168\) 1.32258i 0.102039i
\(169\) −7.48023 + 10.6323i −0.575402 + 0.817870i
\(170\) 0 0
\(171\) −1.98387 1.14539i −0.151710 0.0875900i
\(172\) 7.45269 + 4.30281i 0.568262 + 0.328086i
\(173\) −2.18946 + 1.26408i −0.166461 + 0.0961065i −0.580916 0.813963i \(-0.697306\pi\)
0.414455 + 0.910070i \(0.363972\pi\)
\(174\) 2.02283i 0.153350i
\(175\) 0 0
\(176\) 3.99528 2.30668i 0.301156 0.173872i
\(177\) 3.14152 0.236131
\(178\) 10.2746 5.93207i 0.770117 0.444627i
\(179\) 3.13784 5.43490i 0.234533 0.406223i −0.724604 0.689166i \(-0.757977\pi\)
0.959137 + 0.282942i \(0.0913105\pi\)
\(180\) 0 0
\(181\) −12.2830 −0.912991 −0.456496 0.889726i \(-0.650896\pi\)
−0.456496 + 0.889726i \(0.650896\pi\)
\(182\) 2.19719 + 4.23228i 0.162866 + 0.313717i
\(183\) 0.535898i 0.0396147i
\(184\) 7.50670 + 4.33399i 0.553401 + 0.319506i
\(185\) 0 0
\(186\) −5.06604 8.77464i −0.371460 0.643388i
\(187\) −18.4534 −1.34945
\(188\) 4.55463 + 7.88885i 0.332181 + 0.575354i
\(189\) −1.14539 + 0.661290i −0.0833147 + 0.0481018i
\(190\) 0 0
\(191\) 4.87357 + 8.44128i 0.352639 + 0.610789i 0.986711 0.162485i \(-0.0519509\pi\)
−0.634072 + 0.773274i \(0.718618\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) 6.88130 11.9188i 0.495327 0.857932i −0.504658 0.863319i \(-0.668382\pi\)
0.999985 + 0.00538741i \(0.00171487\pi\)
\(194\) −8.81894 −0.633163
\(195\) 0 0
\(196\) −5.25078 −0.375056
\(197\) −5.07076 + 8.78282i −0.361277 + 0.625750i −0.988171 0.153354i \(-0.950992\pi\)
0.626894 + 0.779104i \(0.284326\pi\)
\(198\) 3.99528 + 2.30668i 0.283932 + 0.163928i
\(199\) −4.78668 8.29078i −0.339319 0.587717i 0.644986 0.764194i \(-0.276863\pi\)
−0.984305 + 0.176477i \(0.943530\pi\)
\(200\) 0 0
\(201\) 2.75488 1.59053i 0.194314 0.112187i
\(202\) −3.61335 6.25851i −0.254235 0.440348i
\(203\) 2.67535 0.187773
\(204\) 2.00000 + 3.46410i 0.140028 + 0.242536i
\(205\) 0 0
\(206\) 15.9349 + 9.20002i 1.11024 + 0.640996i
\(207\) 8.66799i 0.602467i
\(208\) −3.60194 0.161290i −0.249750 0.0111834i
\(209\) 10.5682 0.731015
\(210\) 0 0
\(211\) 0.542594 0.939800i 0.0373537 0.0646985i −0.846744 0.532000i \(-0.821441\pi\)
0.884098 + 0.467302i \(0.154774\pi\)
\(212\) 0.715920 0.413337i 0.0491696 0.0283881i
\(213\) 11.3360 0.776728
\(214\) −2.66025 + 1.53590i −0.181851 + 0.104992i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −11.6052 + 6.70025i −0.787810 + 0.454842i
\(218\) 11.4547 + 6.61335i 0.775808 + 0.447913i
\(219\) −5.44128 3.14152i −0.367687 0.212284i
\(220\) 0 0
\(221\) 12.1549 + 7.76261i 0.817628 + 0.522170i
\(222\) 6.80951i 0.457024i
\(223\) −12.4708 + 21.6001i −0.835106 + 1.44645i 0.0588375 + 0.998268i \(0.481261\pi\)
−0.893944 + 0.448179i \(0.852073\pi\)
\(224\) −0.661290 + 1.14539i −0.0441843 + 0.0765294i
\(225\) 0 0
\(226\) 8.08643i 0.537902i
\(227\) 9.66025 + 16.7321i 0.641174 + 1.11055i 0.985171 + 0.171575i \(0.0548855\pi\)
−0.343998 + 0.938971i \(0.611781\pi\)
\(228\) −1.14539 1.98387i −0.0758551 0.131385i
\(229\) 4.15491i 0.274564i −0.990532 0.137282i \(-0.956163\pi\)
0.990532 0.137282i \(-0.0438367\pi\)
\(230\) 0 0
\(231\) 3.05076 5.28408i 0.200726 0.347667i
\(232\) −1.01141 + 1.75182i −0.0664025 + 0.115013i
\(233\) 16.9665i 1.11151i 0.831346 + 0.555756i \(0.187571\pi\)
−0.831346 + 0.555756i \(0.812429\pi\)
\(234\) −1.66129 3.20002i −0.108602 0.209192i
\(235\) 0 0
\(236\) 2.72064 + 1.57076i 0.177098 + 0.102248i
\(237\) 2.57014 + 1.48387i 0.166948 + 0.0963877i
\(238\) 4.58155 2.64516i 0.296978 0.171460i
\(239\) 6.34416i 0.410370i 0.978723 + 0.205185i \(0.0657795\pi\)
−0.978723 + 0.205185i \(0.934220\pi\)
\(240\) 0 0
\(241\) 20.9452 12.0927i 1.34920 0.778962i 0.361065 0.932541i \(-0.382413\pi\)
0.988136 + 0.153579i \(0.0490800\pi\)
\(242\) −10.2830 −0.661019
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) −0.267949 + 0.464102i −0.0171537 + 0.0297111i
\(245\) 0 0
\(246\) −4.64516 −0.296165
\(247\) −6.96104 4.44560i −0.442921 0.282867i
\(248\) 10.1321i 0.643388i
\(249\) 13.7454 + 7.93593i 0.871082 + 0.502919i
\(250\) 0 0
\(251\) 4.41249 + 7.64265i 0.278514 + 0.482400i 0.971016 0.239016i \(-0.0768249\pi\)
−0.692502 + 0.721416i \(0.743492\pi\)
\(252\) −1.32258 −0.0833147
\(253\) −19.9942 34.6311i −1.25703 2.17724i
\(254\) 9.93490 5.73592i 0.623371 0.359903i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −7.26157 4.19247i −0.452964 0.261519i 0.256117 0.966646i \(-0.417557\pi\)
−0.709081 + 0.705127i \(0.750890\pi\)
\(258\) −4.30281 + 7.45269i −0.267881 + 0.463984i
\(259\) −9.00612 −0.559613
\(260\) 0 0
\(261\) −2.02283 −0.125210
\(262\) 7.99528 13.8482i 0.493950 0.855547i
\(263\) −1.66389 0.960648i −0.102600 0.0592361i 0.447822 0.894123i \(-0.352200\pi\)
−0.550422 + 0.834887i \(0.685533\pi\)
\(264\) 2.30668 + 3.99528i 0.141966 + 0.245893i
\(265\) 0 0
\(266\) −2.62383 + 1.51487i −0.160877 + 0.0928824i
\(267\) 5.93207 + 10.2746i 0.363037 + 0.628798i
\(268\) 3.18106 0.194314
\(269\) −16.1549 27.9811i −0.984982 1.70604i −0.642014 0.766693i \(-0.721901\pi\)
−0.342968 0.939347i \(-0.611432\pi\)
\(270\) 0 0
\(271\) 20.3105 + 11.7263i 1.23378 + 0.712322i 0.967815 0.251662i \(-0.0809770\pi\)
0.265962 + 0.963983i \(0.414310\pi\)
\(272\) 4.00000i 0.242536i
\(273\) −4.23228 + 2.19719i −0.256149 + 0.132980i
\(274\) 16.0697 0.970808
\(275\) 0 0
\(276\) −4.33399 + 7.50670i −0.260876 + 0.451850i
\(277\) −7.79913 + 4.50283i −0.468604 + 0.270549i −0.715655 0.698454i \(-0.753872\pi\)
0.247051 + 0.969002i \(0.420538\pi\)
\(278\) −9.32258 −0.559131
\(279\) 8.77464 5.06604i 0.525324 0.303296i
\(280\) 0 0
\(281\) 1.71696i 0.102425i 0.998688 + 0.0512125i \(0.0163086\pi\)
−0.998688 + 0.0512125i \(0.983691\pi\)
\(282\) −7.88885 + 4.55463i −0.469774 + 0.271224i
\(283\) −1.34172 0.774645i −0.0797572 0.0460479i 0.459591 0.888131i \(-0.347996\pi\)
−0.539348 + 0.842083i \(0.681329\pi\)
\(284\) 9.81724 + 5.66799i 0.582546 + 0.336333i
\(285\) 0 0
\(286\) 14.0187 + 8.95292i 0.828945 + 0.529397i
\(287\) 6.14359i 0.362645i
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 8.81894i 0.516976i
\(292\) −3.14152 5.44128i −0.183844 0.318427i
\(293\) 15.2028 + 26.3321i 0.888160 + 1.53834i 0.842049 + 0.539402i \(0.181350\pi\)
0.0461113 + 0.998936i \(0.485317\pi\)
\(294\) 5.25078i 0.306232i
\(295\) 0 0
\(296\) 3.40475 5.89721i 0.197897 0.342768i
\(297\) −2.30668 + 3.99528i −0.133847 + 0.231830i
\(298\) 4.08519i 0.236649i
\(299\) −1.39806 + 31.2216i −0.0808518 + 1.80559i
\(300\) 0 0
\(301\) 9.85677 + 5.69081i 0.568135 + 0.328013i
\(302\) 17.3042 + 9.99057i 0.995743 + 0.574892i
\(303\) 6.25851 3.61335i 0.359542 0.207582i
\(304\) 2.29078i 0.131385i
\(305\) 0 0
\(306\) −3.46410 + 2.00000i −0.198030 + 0.114332i
\(307\) 9.82622 0.560812 0.280406 0.959882i \(-0.409531\pi\)
0.280406 + 0.959882i \(0.409531\pi\)
\(308\) 5.28408 3.05076i 0.301088 0.173833i
\(309\) −9.20002 + 15.9349i −0.523371 + 0.906505i
\(310\) 0 0
\(311\) −3.40049 −0.192824 −0.0964121 0.995342i \(-0.530737\pi\)
−0.0964121 + 0.995342i \(0.530737\pi\)
\(312\) 0.161290 3.60194i 0.00913124 0.203920i
\(313\) 16.2340i 0.917599i −0.888540 0.458800i \(-0.848280\pi\)
0.888540 0.458800i \(-0.151720\pi\)
\(314\) 6.17804 + 3.56690i 0.348647 + 0.201292i
\(315\) 0 0
\(316\) 1.48387 + 2.57014i 0.0834742 + 0.144582i
\(317\) 23.5231 1.32119 0.660596 0.750742i \(-0.270304\pi\)
0.660596 + 0.750742i \(0.270304\pi\)
\(318\) 0.413337 + 0.715920i 0.0231788 + 0.0401468i
\(319\) 8.08176 4.66601i 0.452492 0.261246i
\(320\) 0 0
\(321\) −1.53590 2.66025i −0.0857255 0.148481i
\(322\) 9.92820 + 5.73205i 0.553277 + 0.319435i
\(323\) −4.58155 + 7.93548i −0.254924 + 0.441542i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 9.89470 0.548016
\(327\) −6.61335 + 11.4547i −0.365719 + 0.633445i
\(328\) −4.02283 2.32258i −0.222123 0.128243i
\(329\) 6.02386 + 10.4336i 0.332106 + 0.575225i
\(330\) 0 0
\(331\) 15.6667 9.04520i 0.861122 0.497169i −0.00326597 0.999995i \(-0.501040\pi\)
0.864388 + 0.502826i \(0.167706\pi\)
\(332\) 7.93593 + 13.7454i 0.435541 + 0.754379i
\(333\) 6.80951 0.373159
\(334\) 12.0187 + 20.8171i 0.657636 + 1.13906i
\(335\) 0 0
\(336\) −1.14539 0.661290i −0.0624860 0.0360763i
\(337\) 5.69900i 0.310444i 0.987880 + 0.155222i \(0.0496093\pi\)
−0.987880 + 0.155222i \(0.950391\pi\)
\(338\) −5.46774 11.7942i −0.297406 0.641521i
\(339\) 8.08643 0.439195
\(340\) 0 0
\(341\) −23.3715 + 40.4806i −1.26564 + 2.19214i
\(342\) 1.98387 1.14539i 0.107275 0.0619355i
\(343\) −16.2026 −0.874860
\(344\) −7.45269 + 4.30281i −0.401822 + 0.231992i
\(345\) 0 0
\(346\) 2.52817i 0.135915i
\(347\) 13.6374 7.87357i 0.732095 0.422676i −0.0870928 0.996200i \(-0.527758\pi\)
0.819188 + 0.573525i \(0.194424\pi\)
\(348\) −1.75182 1.01141i −0.0939073 0.0542174i
\(349\) −13.2679 7.66025i −0.710217 0.410044i 0.100924 0.994894i \(-0.467820\pi\)
−0.811141 + 0.584850i \(0.801153\pi\)
\(350\) 0 0
\(351\) 3.20002 1.66129i 0.170804 0.0886731i
\(352\) 4.61335i 0.245893i
\(353\) −0.599964 + 1.03917i −0.0319328 + 0.0553093i −0.881550 0.472090i \(-0.843500\pi\)
0.849617 + 0.527400i \(0.176833\pi\)
\(354\) −1.57076 + 2.72064i −0.0834850 + 0.144600i
\(355\) 0 0
\(356\) 11.8641i 0.628798i
\(357\) 2.64516 + 4.58155i 0.139997 + 0.242481i
\(358\) 3.13784 + 5.43490i 0.165840 + 0.287243i
\(359\) 16.2830i 0.859386i −0.902975 0.429693i \(-0.858622\pi\)
0.902975 0.429693i \(-0.141378\pi\)
\(360\) 0 0
\(361\) −6.87617 + 11.9099i −0.361904 + 0.626836i
\(362\) 6.14152 10.6374i 0.322791 0.559091i
\(363\) 10.2830i 0.539720i
\(364\) −4.76386 0.213319i −0.249694 0.0111809i
\(365\) 0 0
\(366\) −0.464102 0.267949i −0.0242590 0.0140059i
\(367\) −17.0040 9.81724i −0.887599 0.512456i −0.0144428 0.999896i \(-0.504597\pi\)
−0.873156 + 0.487440i \(0.837931\pi\)
\(368\) −7.50670 + 4.33399i −0.391314 + 0.225925i
\(369\) 4.64516i 0.241817i
\(370\) 0 0
\(371\) 0.946862 0.546671i 0.0491586 0.0283817i
\(372\) 10.1321 0.525324
\(373\) −2.21484 + 1.27874i −0.114680 + 0.0662106i −0.556243 0.831020i \(-0.687758\pi\)
0.441563 + 0.897230i \(0.354424\pi\)
\(374\) 9.22671 15.9811i 0.477102 0.826365i
\(375\) 0 0
\(376\) −9.10926 −0.469774
\(377\) −7.28610 0.326261i −0.375253 0.0168033i
\(378\) 1.32258i 0.0680262i
\(379\) 13.0846 + 7.55440i 0.672111 + 0.388044i 0.796876 0.604143i \(-0.206484\pi\)
−0.124765 + 0.992186i \(0.539818\pi\)
\(380\) 0 0
\(381\) 5.73592 + 9.93490i 0.293860 + 0.508980i
\(382\) −9.74715 −0.498707
\(383\) −9.36517 16.2210i −0.478538 0.828852i 0.521159 0.853459i \(-0.325500\pi\)
−0.999697 + 0.0246073i \(0.992166\pi\)
\(384\) 0.866025 0.500000i 0.0441942 0.0255155i
\(385\) 0 0
\(386\) 6.88130 + 11.9188i 0.350249 + 0.606649i
\(387\) −7.45269 4.30281i −0.378841 0.218724i
\(388\) 4.40947 7.63743i 0.223857 0.387732i
\(389\) −6.96899 −0.353342 −0.176671 0.984270i \(-0.556533\pi\)
−0.176671 + 0.984270i \(0.556533\pi\)
\(390\) 0 0
\(391\) 34.6719 1.75344
\(392\) 2.62539 4.54731i 0.132602 0.229674i
\(393\) 13.8482 + 7.99528i 0.698551 + 0.403309i
\(394\) −5.07076 8.78282i −0.255461 0.442472i
\(395\) 0 0
\(396\) −3.99528 + 2.30668i −0.200771 + 0.115915i
\(397\) 9.28606 + 16.0839i 0.466054 + 0.807229i 0.999248 0.0387637i \(-0.0123420\pi\)
−0.533195 + 0.845993i \(0.679009\pi\)
\(398\) 9.57336 0.479869
\(399\) −1.51487 2.62383i −0.0758382 0.131356i
\(400\) 0 0
\(401\) −25.7126 14.8452i −1.28403 0.741333i −0.306444 0.951889i \(-0.599139\pi\)
−0.977582 + 0.210556i \(0.932473\pi\)
\(402\) 3.18106i 0.158657i
\(403\) 32.4229 16.8323i 1.61510 0.838478i
\(404\) 7.22671 0.359542
\(405\) 0 0
\(406\) −1.33767 + 2.31692i −0.0663877 + 0.114987i
\(407\) −27.2059 + 15.7073i −1.34855 + 0.778584i
\(408\) −4.00000 −0.198030
\(409\) 21.0752 12.1678i 1.04210 0.601657i 0.121673 0.992570i \(-0.461174\pi\)
0.920427 + 0.390913i \(0.127841\pi\)
\(410\) 0 0
\(411\) 16.0697i 0.792661i
\(412\) −15.9349 + 9.20002i −0.785056 + 0.453252i
\(413\) 3.59826 + 2.07746i 0.177059 + 0.102225i
\(414\) −7.50670 4.33399i −0.368934 0.213004i
\(415\) 0 0
\(416\) 1.94065 3.03873i 0.0951483 0.148986i
\(417\) 9.32258i 0.456529i
\(418\) −5.28408 + 9.15229i −0.258453 + 0.447653i
\(419\) −1.44128 + 2.49636i −0.0704109 + 0.121955i −0.899081 0.437781i \(-0.855764\pi\)
0.828671 + 0.559737i \(0.189098\pi\)
\(420\) 0 0
\(421\) 4.94707i 0.241106i −0.992707 0.120553i \(-0.961533\pi\)
0.992707 0.120553i \(-0.0384667\pi\)
\(422\) 0.542594 + 0.939800i 0.0264131 + 0.0457488i
\(423\) −4.55463 7.88885i −0.221454 0.383569i
\(424\) 0.826674i 0.0401468i
\(425\) 0 0
\(426\) −5.66799 + 9.81724i −0.274615 + 0.475647i
\(427\) −0.354384 + 0.613811i −0.0171499 + 0.0297044i
\(428\) 3.07180i 0.148481i
\(429\) −8.95292 + 14.0187i −0.432251 + 0.676831i
\(430\) 0 0
\(431\) −15.3829 8.88130i −0.740967 0.427797i 0.0814539 0.996677i \(-0.474044\pi\)
−0.822421 + 0.568880i \(0.807377\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) −31.0362 + 17.9188i −1.49151 + 0.861121i −0.999953 0.00972676i \(-0.996904\pi\)
−0.491553 + 0.870848i \(0.663570\pi\)
\(434\) 13.4005i 0.643244i
\(435\) 0 0
\(436\) −11.4547 + 6.61335i −0.548579 + 0.316722i
\(437\) −19.8564 −0.949861
\(438\) 5.44128 3.14152i 0.259994 0.150108i
\(439\) −5.04520 + 8.73854i −0.240794 + 0.417068i −0.960941 0.276754i \(-0.910741\pi\)
0.720147 + 0.693822i \(0.244075\pi\)
\(440\) 0 0
\(441\) 5.25078 0.250037
\(442\) −12.8001 + 6.64516i −0.608837 + 0.316078i
\(443\) 13.6981i 0.650816i 0.945574 + 0.325408i \(0.105502\pi\)
−0.945574 + 0.325408i \(0.894498\pi\)
\(444\) 5.89721 + 3.40475i 0.279869 + 0.161582i
\(445\) 0 0
\(446\) −12.4708 21.6001i −0.590509 1.02279i
\(447\) 4.08519 0.193223
\(448\) −0.661290 1.14539i −0.0312430 0.0541145i
\(449\) −13.2613 + 7.65639i −0.625837 + 0.361327i −0.779138 0.626852i \(-0.784343\pi\)
0.153301 + 0.988180i \(0.451010\pi\)
\(450\) 0 0
\(451\) 10.7149 + 18.5587i 0.504544 + 0.873896i
\(452\) 7.00306 + 4.04322i 0.329396 + 0.190177i
\(453\) −9.99057 + 17.3042i −0.469398 + 0.813021i
\(454\) −19.3205 −0.906756
\(455\) 0 0
\(456\) 2.29078 0.107275
\(457\) −7.77770 + 13.4714i −0.363826 + 0.630164i −0.988587 0.150651i \(-0.951863\pi\)
0.624761 + 0.780816i \(0.285196\pi\)
\(458\) 3.59826 + 2.07746i 0.168136 + 0.0970732i
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 0 0
\(461\) 13.5473 7.82154i 0.630961 0.364286i −0.150163 0.988661i \(-0.547980\pi\)
0.781124 + 0.624376i \(0.214647\pi\)
\(462\) 3.05076 + 5.28408i 0.141934 + 0.245838i
\(463\) −13.7170 −0.637481 −0.318741 0.947842i \(-0.603260\pi\)
−0.318741 + 0.947842i \(0.603260\pi\)
\(464\) −1.01141 1.75182i −0.0469537 0.0813261i
\(465\) 0 0
\(466\) −14.6934 8.48325i −0.680659 0.392979i
\(467\) 0.943666i 0.0436677i 0.999762 + 0.0218338i \(0.00695048\pi\)
−0.999762 + 0.0218338i \(0.993050\pi\)
\(468\) 3.60194 + 0.161290i 0.166500 + 0.00745563i
\(469\) 4.20720 0.194271
\(470\) 0 0
\(471\) −3.56690 + 6.17804i −0.164354 + 0.284669i
\(472\) −2.72064 + 1.57076i −0.125228 + 0.0723001i
\(473\) 39.7008 1.82544
\(474\) −2.57014 + 1.48387i −0.118050 + 0.0681564i
\(475\) 0 0
\(476\) 5.29032i 0.242481i
\(477\) −0.715920 + 0.413337i −0.0327797 + 0.0189254i
\(478\) −5.49420 3.17208i −0.251299 0.145088i
\(479\) 9.61460 + 5.55099i 0.439302 + 0.253631i 0.703302 0.710892i \(-0.251708\pi\)
−0.263999 + 0.964523i \(0.585042\pi\)
\(480\) 0 0
\(481\) 24.5275 + 1.09830i 1.11836 + 0.0500784i
\(482\) 24.1855i 1.10162i
\(483\) −5.73205 + 9.92820i −0.260817 + 0.451749i
\(484\) 5.14152 8.90538i 0.233706 0.404790i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 16.4708 + 28.5283i 0.746363 + 1.29274i 0.949555 + 0.313600i \(0.101535\pi\)
−0.203192 + 0.979139i \(0.565132\pi\)
\(488\) −0.267949 0.464102i −0.0121295 0.0210089i
\(489\) 9.89470i 0.447454i
\(490\) 0 0
\(491\) 14.2257 24.6396i 0.641996 1.11197i −0.342991 0.939339i \(-0.611440\pi\)
0.984987 0.172630i \(-0.0552266\pi\)
\(492\) 2.32258 4.02283i 0.104710 0.181363i
\(493\) 8.09130i 0.364414i
\(494\) 7.33052 3.80564i 0.329816 0.171224i
\(495\) 0 0
\(496\) 8.77464 + 5.06604i 0.393993 + 0.227472i
\(497\) 12.9841 + 7.49636i 0.582416 + 0.336258i
\(498\) −13.7454 + 7.93593i −0.615948 + 0.355618i
\(499\) 4.10926i 0.183956i 0.995761 + 0.0919779i \(0.0293189\pi\)
−0.995761 + 0.0919779i \(0.970681\pi\)
\(500\) 0 0
\(501\) −20.8171 + 12.0187i −0.930037 + 0.536957i
\(502\) −8.82497 −0.393878
\(503\) 4.96753 2.86800i 0.221491 0.127878i −0.385149 0.922854i \(-0.625850\pi\)
0.606641 + 0.794976i \(0.292517\pi\)
\(504\) 0.661290 1.14539i 0.0294562 0.0510196i
\(505\) 0 0
\(506\) 39.9885 1.77771
\(507\) 11.7942 5.46774i 0.523800 0.242831i
\(508\) 11.4718i 0.508980i
\(509\) 13.1129 + 7.57076i 0.581221 + 0.335568i 0.761618 0.648026i \(-0.224405\pi\)
−0.180397 + 0.983594i \(0.557738\pi\)
\(510\) 0 0
\(511\) −4.15491 7.19652i −0.183803 0.318355i
\(512\) 1.00000 0.0441942
\(513\) 1.14539 + 1.98387i 0.0505701 + 0.0875900i
\(514\) 7.26157 4.19247i 0.320294 0.184922i
\(515\) 0 0
\(516\) −4.30281 7.45269i −0.189421 0.328086i
\(517\) 36.3941 + 21.0121i 1.60061 + 0.924112i
\(518\) 4.50306 7.79953i 0.197853 0.342691i
\(519\) 2.52817 0.110974
\(520\) 0 0
\(521\) 8.93027 0.391242 0.195621 0.980680i \(-0.437328\pi\)
0.195621 + 0.980680i \(0.437328\pi\)
\(522\) 1.01141 1.75182i 0.0442683 0.0766750i
\(523\) 8.50166 + 4.90844i 0.371752 + 0.214631i 0.674223 0.738527i \(-0.264478\pi\)
−0.302472 + 0.953158i \(0.597812\pi\)
\(524\) 7.99528 + 13.8482i 0.349276 + 0.604963i
\(525\) 0 0
\(526\) 1.66389 0.960648i 0.0725491 0.0418863i
\(527\) −20.2642 35.0986i −0.882721 1.52892i
\(528\) −4.61335 −0.200771
\(529\) 26.0670 + 45.1493i 1.13335 + 1.96301i
\(530\) 0 0
\(531\) −2.72064 1.57076i −0.118066 0.0681652i
\(532\) 3.02973i 0.131356i
\(533\) 0.749217 16.7316i 0.0324522 0.724726i
\(534\) −11.8641 −0.513411
\(535\) 0 0
\(536\) −1.59053 + 2.75488i −0.0687004 + 0.118993i
\(537\) −5.43490 + 3.13784i −0.234533 + 0.135408i
\(538\) 32.3098 1.39298
\(539\) −20.9784 + 12.1119i −0.903602 + 0.521695i
\(540\) 0 0
\(541\) 3.80826i 0.163730i 0.996643 + 0.0818650i \(0.0260876\pi\)
−0.996643 + 0.0818650i \(0.973912\pi\)
\(542\) −20.3105 + 11.7263i −0.872413 + 0.503688i
\(543\) 10.6374 + 6.14152i 0.456496 + 0.263558i
\(544\) −3.46410 2.00000i −0.148522 0.0857493i
\(545\) 0 0
\(546\) 0.213319 4.76386i 0.00912920 0.203874i
\(547\) 45.5847i 1.94906i −0.224257 0.974530i \(-0.571995\pi\)
0.224257 0.974530i \(-0.428005\pi\)
\(548\) −8.03486 + 13.9168i −0.343232 + 0.594496i
\(549\) 0.267949 0.464102i 0.0114358 0.0198074i
\(550\) 0 0
\(551\) 4.63384i 0.197408i
\(552\) −4.33399 7.50670i −0.184467 0.319506i
\(553\) 1.96254 + 3.39921i 0.0834555 + 0.144549i
\(554\) 9.00566i 0.382614i
\(555\) 0 0
\(556\) 4.66129 8.07359i 0.197683 0.342397i
\(557\) −18.4296 + 31.9209i −0.780885 + 1.35253i 0.150541 + 0.988604i \(0.451898\pi\)
−0.931427 + 0.363929i \(0.881435\pi\)
\(558\) 10.1321i 0.428925i
\(559\) −26.1502 16.7005i −1.10603 0.706357i
\(560\) 0 0
\(561\) 15.9811 + 9.22671i 0.674724 + 0.389552i
\(562\) −1.48693 0.858478i −0.0627223 0.0362127i
\(563\) −29.2491 + 16.8870i −1.23270 + 0.711701i −0.967592 0.252518i \(-0.918741\pi\)
−0.265109 + 0.964218i \(0.585408\pi\)
\(564\) 9.10926i 0.383569i
\(565\) 0 0
\(566\) 1.34172 0.774645i 0.0563969 0.0325607i
\(567\) 1.32258 0.0555431
\(568\) −9.81724 + 5.66799i −0.411922 + 0.237823i
\(569\) 12.7159 22.0246i 0.533079 0.923320i −0.466175 0.884693i \(-0.654368\pi\)
0.999254 0.0386274i \(-0.0122985\pi\)
\(570\) 0 0
\(571\) 13.3682 0.559443 0.279722 0.960081i \(-0.409758\pi\)
0.279722 + 0.960081i \(0.409758\pi\)
\(572\) −14.7628 + 7.66412i −0.617264 + 0.320453i
\(573\) 9.74715i 0.407193i
\(574\) −5.32051 3.07180i −0.222074 0.128214i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) −9.57428 −0.398582 −0.199291 0.979940i \(-0.563864\pi\)
−0.199291 + 0.979940i \(0.563864\pi\)
\(578\) −0.500000 0.866025i −0.0207973 0.0360219i
\(579\) −11.9188 + 6.88130i −0.495327 + 0.285977i
\(580\) 0 0
\(581\) 10.4959 + 18.1794i 0.435444 + 0.754210i
\(582\) 7.63743 + 4.40947i 0.316582 + 0.182778i
\(583\) 1.90687 3.30279i 0.0789745 0.136788i
\(584\) 6.28304 0.259994
\(585\) 0 0
\(586\) −30.4057 −1.25605
\(587\) 0.700246 1.21286i 0.0289023 0.0500602i −0.851212 0.524821i \(-0.824132\pi\)
0.880115 + 0.474761i \(0.157466\pi\)
\(588\) 4.54731 + 2.62539i 0.187528 + 0.108269i
\(589\) 11.6052 + 20.1007i 0.478183 + 0.828237i
\(590\) 0 0
\(591\) 8.78282 5.07076i 0.361277 0.208583i
\(592\) 3.40475 + 5.89721i 0.139935 + 0.242374i
\(593\) 10.7303 0.440643 0.220321 0.975427i \(-0.429289\pi\)
0.220321 + 0.975427i \(0.429289\pi\)
\(594\) −2.30668 3.99528i −0.0946441 0.163928i
\(595\) 0 0
\(596\) 3.53788 + 2.04259i 0.144917 + 0.0836679i
\(597\) 9.57336i 0.391812i
\(598\) −26.3397 16.8215i −1.07711 0.687884i
\(599\) 40.7967 1.66691 0.833453 0.552590i \(-0.186360\pi\)
0.833453 + 0.552590i \(0.186360\pi\)
\(600\) 0 0
\(601\) −21.4416 + 37.1379i −0.874621 + 1.51489i −0.0174548 + 0.999848i \(0.505556\pi\)
−0.857166 + 0.515040i \(0.827777\pi\)
\(602\) −9.85677 + 5.69081i −0.401732 + 0.231940i
\(603\) −3.18106 −0.129543
\(604\) −17.3042 + 9.99057i −0.704097 + 0.406510i
\(605\) 0 0
\(606\) 7.22671i 0.293565i
\(607\) 5.95161 3.43616i 0.241568 0.139470i −0.374329 0.927296i \(-0.622127\pi\)
0.615897 + 0.787826i \(0.288794\pi\)
\(608\) 1.98387 + 1.14539i 0.0804565 + 0.0464516i
\(609\) −2.31692 1.33767i −0.0938863 0.0542053i
\(610\) 0 0
\(611\) −15.1331 29.1498i −0.612221 1.17927i
\(612\) 4.00000i 0.161690i
\(613\) 0.380681 0.659358i 0.0153755 0.0266312i −0.858235 0.513257i \(-0.828439\pi\)
0.873611 + 0.486625i \(0.161772\pi\)
\(614\) −4.91311 + 8.50975i −0.198277 + 0.343426i
\(615\) 0 0
\(616\) 6.10153i 0.245838i
\(617\) −12.3011 21.3061i −0.495224 0.857753i 0.504761 0.863259i \(-0.331581\pi\)
−0.999985 + 0.00550613i \(0.998247\pi\)
\(618\) −9.20002 15.9349i −0.370079 0.640996i
\(619\) 17.2035i 0.691468i −0.938333 0.345734i \(-0.887630\pi\)
0.938333 0.345734i \(-0.112370\pi\)
\(620\) 0 0
\(621\) 4.33399 7.50670i 0.173917 0.301233i
\(622\) 1.70025 2.94491i 0.0681737 0.118080i
\(623\) 15.6913i 0.628657i
\(624\) 3.03873 + 1.94065i 0.121646 + 0.0776883i
\(625\) 0 0
\(626\) 14.0590 + 8.11699i 0.561912 + 0.324420i
\(627\) −9.15229 5.28408i −0.365507 0.211026i
\(628\) −6.17804 + 3.56690i −0.246531 + 0.142335i
\(629\) 27.2380i 1.08605i
\(630\) 0 0
\(631\) 2.08519 1.20388i 0.0830100 0.0479259i −0.457920 0.888993i \(-0.651406\pi\)
0.540930 + 0.841067i \(0.318072\pi\)
\(632\) −2.96774 −0.118050
\(633\) −0.939800 + 0.542594i −0.0373537 + 0.0215662i
\(634\) −11.7616 + 20.3716i −0.467112 + 0.809061i
\(635\) 0 0
\(636\) −0.826674 −0.0327797
\(637\) 18.9130 + 0.846898i 0.749361 + 0.0335553i
\(638\) 9.33201i 0.369458i
\(639\) −9.81724 5.66799i −0.388364 0.224222i
\(640\) 0 0
\(641\) −9.73875 16.8680i −0.384657 0.666246i 0.607064 0.794653i \(-0.292347\pi\)
−0.991722 + 0.128407i \(0.959014\pi\)
\(642\) 3.07180 0.121234
\(643\) −11.9772 20.7451i −0.472334 0.818106i 0.527165 0.849763i \(-0.323255\pi\)
−0.999499 + 0.0316570i \(0.989922\pi\)
\(644\) −9.92820 + 5.73205i −0.391226 + 0.225874i
\(645\) 0 0
\(646\) −4.58155 7.93548i −0.180259 0.312217i
\(647\) −15.7710 9.10540i −0.620022 0.357970i 0.156855 0.987622i \(-0.449864\pi\)
−0.776878 + 0.629652i \(0.783198\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) 14.4930 0.568898
\(650\) 0 0
\(651\) 13.4005 0.525207
\(652\) −4.94735 + 8.56906i −0.193753 + 0.335590i
\(653\) 41.7065 + 24.0793i 1.63210 + 0.942294i 0.983444 + 0.181213i \(0.0580024\pi\)
0.648657 + 0.761081i \(0.275331\pi\)
\(654\) −6.61335 11.4547i −0.258603 0.447913i
\(655\) 0 0
\(656\) 4.02283 2.32258i 0.157065 0.0906815i
\(657\) 3.14152 + 5.44128i 0.122562 + 0.212284i
\(658\) −12.0477 −0.469669
\(659\) −18.4127 31.8917i −0.717257 1.24233i −0.962083 0.272758i \(-0.912064\pi\)
0.244826 0.969567i \(-0.421269\pi\)
\(660\) 0 0
\(661\) −19.5131 11.2659i −0.758971 0.438192i 0.0699555 0.997550i \(-0.477714\pi\)
−0.828926 + 0.559358i \(0.811048\pi\)
\(662\) 18.0904i 0.703103i
\(663\) −6.64516 12.8001i −0.258077 0.497114i
\(664\) −15.8719 −0.615948
\(665\) 0 0
\(666\) −3.40475 + 5.89721i −0.131932 + 0.228512i
\(667\) −15.1847 + 8.76691i −0.587955 + 0.339456i
\(668\) −24.0375 −0.930037
\(669\) 21.6001 12.4708i 0.835106 0.482149i
\(670\) 0 0
\(671\) 2.47229i 0.0954417i
\(672\) 1.14539 0.661290i 0.0441843 0.0255098i
\(673\) 20.5627 + 11.8719i 0.792633 + 0.457627i 0.840889 0.541208i \(-0.182033\pi\)
−0.0482556 + 0.998835i \(0.515366\pi\)
\(674\) −4.93548 2.84950i −0.190108 0.109759i
\(675\) 0 0
\(676\) 12.9480 + 1.16191i 0.497999 + 0.0446890i
\(677\) 1.16559i 0.0447975i −0.999749 0.0223987i \(-0.992870\pi\)
0.999749 0.0223987i \(-0.00713033\pi\)
\(678\) −4.04322 + 7.00306i −0.155279 + 0.268951i
\(679\) 5.83188 10.1011i 0.223807 0.387645i
\(680\) 0 0
\(681\) 19.3205i 0.740363i
\(682\) −23.3715 40.4806i −0.894939 1.55008i
\(683\) 6.93593 + 12.0134i 0.265396 + 0.459680i 0.967667 0.252230i \(-0.0811639\pi\)
−0.702271 + 0.711910i \(0.747831\pi\)
\(684\) 2.29078i 0.0875900i
\(685\) 0 0
\(686\) 8.10132 14.0319i 0.309310 0.535740i
\(687\) −2.07746 + 3.59826i −0.0792599 + 0.137282i
\(688\) 8.60562i 0.328086i
\(689\) −2.64537 + 1.37334i −0.100781 + 0.0523203i
\(690\) 0 0
\(691\) −35.6967 20.6095i −1.35797 0.784022i −0.368616 0.929582i \(-0.620168\pi\)
−0.989349 + 0.145560i \(0.953502\pi\)
\(692\) 2.18946 + 1.26408i 0.0832307 + 0.0480532i
\(693\) −5.28408 + 3.05076i −0.200726 + 0.115889i
\(694\) 15.7471i 0.597753i
\(695\) 0 0
\(696\) 1.75182 1.01141i 0.0664025 0.0383375i
\(697\) −18.5806 −0.703792
\(698\) 13.2679 7.66025i 0.502199 0.289945i
\(699\) 8.48325 14.6934i 0.320866 0.555756i
\(700\) 0 0
\(701\) −23.0112 −0.869122 −0.434561 0.900642i \(-0.643096\pi\)
−0.434561 + 0.900642i \(0.643096\pi\)
\(702\) −0.161290 + 3.60194i −0.00608749 + 0.135947i
\(703\) 15.5991i 0.588329i
\(704\) −3.99528 2.30668i −0.150578 0.0869362i
\(705\) 0 0
\(706\) −0.599964 1.03917i −0.0225799 0.0391096i
\(707\) 9.55790 0.359462
\(708\) −1.57076 2.72064i −0.0590328 0.102248i
\(709\) 14.7944 8.54156i 0.555616 0.320785i −0.195768 0.980650i \(-0.562720\pi\)
0.751384 + 0.659865i \(0.229387\pi\)
\(710\) 0 0
\(711\) −1.48387 2.57014i −0.0556495 0.0963877i
\(712\) −10.2746 5.93207i −0.385059 0.222314i
\(713\) 43.9124 76.0585i 1.64453 2.84841i
\(714\) −5.29032 −0.197985
\(715\) 0 0
\(716\) −6.27568 −0.234533
\(717\) 3.17208 5.49420i 0.118463 0.205185i
\(718\) 14.1015 + 8.14152i 0.526264 + 0.303839i
\(719\) 21.8564 + 37.8564i 0.815106 + 1.41181i 0.909251 + 0.416247i \(0.136655\pi\)
−0.0941451 + 0.995558i \(0.530012\pi\)
\(720\) 0 0
\(721\) −21.0752 + 12.1678i −0.784880 + 0.453151i
\(722\) −6.87617 11.9099i −0.255905 0.443240i
\(723\) −24.1855 −0.899467
\(724\) 6.14152 + 10.6374i 0.228248 + 0.395337i
\(725\) 0 0
\(726\) 8.90538 + 5.14152i 0.330510 + 0.190820i
\(727\) 31.8453i 1.18108i −0.807010 0.590538i \(-0.798916\pi\)
0.807010 0.590538i \(-0.201084\pi\)
\(728\) 2.56667 4.01896i 0.0951270 0.148953i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −17.2112 + 29.8108i −0.636581 + 1.10259i
\(732\) 0.464102 0.267949i 0.0171537 0.00990369i
\(733\) 5.96774 0.220423 0.110212 0.993908i \(-0.464847\pi\)
0.110212 + 0.993908i \(0.464847\pi\)
\(734\) 17.0040 9.81724i 0.627627 0.362361i
\(735\) 0 0
\(736\) 8.66799i 0.319506i
\(737\) 12.7092 7.33767i 0.468150 0.270287i
\(738\) 4.02283 + 2.32258i 0.148082 + 0.0854953i
\(739\) −9.37833 5.41458i −0.344988 0.199179i 0.317488 0.948262i \(-0.397161\pi\)
−0.662475 + 0.749084i \(0.730494\pi\)
\(740\) 0 0
\(741\) 3.80564 + 7.33052i 0.139804 + 0.269293i
\(742\) 1.09334i 0.0401378i
\(743\) −9.92515 + 17.1909i −0.364118 + 0.630671i −0.988634 0.150341i \(-0.951963\pi\)
0.624516 + 0.781012i \(0.285296\pi\)
\(744\) −5.06604 + 8.77464i −0.185730 + 0.321694i
\(745\) 0 0
\(746\) 2.55748i 0.0936359i
\(747\) −7.93593 13.7454i −0.290361 0.502919i
\(748\) 9.22671 + 15.9811i 0.337362 + 0.584328i
\(749\) 4.06270i 0.148448i
\(750\) 0 0
\(751\) −7.66538 + 13.2768i −0.279714 + 0.484479i −0.971314 0.237802i \(-0.923573\pi\)
0.691600 + 0.722281i \(0.256906\pi\)
\(752\) 4.55463 7.88885i 0.166090 0.287677i
\(753\) 8.82497i 0.321600i
\(754\) 3.92560 6.14682i 0.142962 0.223854i
\(755\) 0 0
\(756\) 1.14539 + 0.661290i 0.0416573 + 0.0240509i
\(757\) 39.1125 + 22.5816i 1.42157 + 0.820744i 0.996433 0.0843855i \(-0.0268927\pi\)
0.425137 + 0.905129i \(0.360226\pi\)
\(758\) −13.0846 + 7.55440i −0.475254 + 0.274388i
\(759\) 39.9885i 1.45149i
\(760\) 0 0
\(761\) −18.7978 + 10.8529i −0.681419 + 0.393418i −0.800390 0.599480i \(-0.795374\pi\)
0.118970 + 0.992898i \(0.462041\pi\)
\(762\) −11.4718 −0.415581
\(763\) −15.1497 + 8.74669i −0.548456 + 0.316651i
\(764\) 4.87357 8.44128i 0.176320 0.305395i
\(765\) 0 0
\(766\) 18.7303 0.676755
\(767\) −9.54623 6.09660i −0.344694 0.220136i
\(768\) 1.00000i 0.0360844i
\(769\) −36.4711 21.0566i −1.31518 0.759321i −0.332233 0.943197i \(-0.607802\pi\)
−0.982949 + 0.183877i \(0.941135\pi\)
\(770\) 0 0
\(771\) 4.19247 + 7.26157i 0.150988 + 0.261519i
\(772\) −13.7626 −0.495327
\(773\) 14.8803 + 25.7734i 0.535206 + 0.927004i 0.999153 + 0.0411413i \(0.0130994\pi\)
−0.463947 + 0.885863i \(0.653567\pi\)
\(774\) 7.45269 4.30281i 0.267881 0.154661i
\(775\) 0 0
\(776\) 4.40947 + 7.63743i 0.158291 + 0.274168i
\(777\) 7.79953 + 4.50306i 0.279806 + 0.161546i
\(778\) 3.48449 6.03532i 0.124925 0.216377i
\(779\) 10.6410 0.381254
\(780\) 0 0
\(781\) 52.2969 1.87133
\(782\) −17.3360 + 30.0268i −0.619933 + 1.07376i
\(783\) 1.75182 + 1.01141i 0.0626049 + 0.0361450i
\(784\) 2.62539 + 4.54731i 0.0937640 + 0.162404i
\(785\)