Properties

Label 261.3.s.a.10.3
Level $261$
Weight $3$
Character 261.10
Analytic conductor $7.112$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 261.s (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.11173489980\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{28})\)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 10.3
Character \(\chi\) \(=\) 261.10
Dual form 261.3.s.a.235.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.29187 - 0.811733i) q^{2} +(-0.725528 + 1.50658i) q^{4} +(-3.36294 - 0.767569i) q^{5} +(-0.255710 + 0.123143i) q^{7} +(0.968958 + 8.59974i) q^{8} +O(q^{10})\) \(q+(1.29187 - 0.811733i) q^{2} +(-0.725528 + 1.50658i) q^{4} +(-3.36294 - 0.767569i) q^{5} +(-0.255710 + 0.123143i) q^{7} +(0.968958 + 8.59974i) q^{8} +(-4.96753 + 1.73821i) q^{10} +(-1.62739 + 14.4435i) q^{11} +(-4.30976 + 3.43692i) q^{13} +(-0.230383 + 0.366653i) q^{14} +(4.06213 + 5.09375i) q^{16} +(-5.25353 - 5.25353i) q^{17} +(9.56906 + 27.3468i) q^{19} +(3.59631 - 4.50963i) q^{20} +(9.62189 + 19.9801i) q^{22} +(6.05686 + 26.5368i) q^{23} +(-11.8040 - 5.68451i) q^{25} +(-2.77777 + 7.93841i) q^{26} -0.474590i q^{28} +(-2.32625 - 28.9065i) q^{29} +(-12.9513 + 8.13783i) q^{31} +(-23.2916 - 8.15007i) q^{32} +(-11.0513 - 2.52239i) q^{34} +(0.954457 - 0.217849i) q^{35} +(3.05571 + 27.1202i) q^{37} +(34.5602 + 27.5609i) q^{38} +(3.34235 - 29.6642i) q^{40} +(45.8791 - 45.8791i) q^{41} +(35.9543 - 57.2209i) q^{43} +(-20.5795 - 12.9310i) q^{44} +(29.3655 + 29.3655i) q^{46} +(-17.2732 - 1.94622i) q^{47} +(-30.5008 + 38.2468i) q^{49} +(-19.8635 + 2.23808i) q^{50} +(-2.05112 - 8.98655i) q^{52} +(-1.31097 + 5.74372i) q^{53} +(16.5592 - 47.3235i) q^{55} +(-1.30677 - 2.07972i) q^{56} +(-26.4696 - 35.4551i) q^{58} +43.1476 q^{59} +(104.863 + 36.6931i) q^{61} +(-10.1256 + 21.0260i) q^{62} +(-62.1125 + 14.1768i) q^{64} +(17.1315 - 8.25011i) q^{65} +(-67.4283 - 53.7723i) q^{67} +(11.7264 - 4.10325i) q^{68} +(1.05620 - 1.05620i) q^{70} +(-45.1943 + 36.0413i) q^{71} +(-42.0399 - 26.4154i) q^{73} +(25.9619 + 32.5552i) q^{74} +(-48.1426 - 5.42437i) q^{76} +(-1.36248 - 3.89374i) q^{77} +(96.9173 - 10.9200i) q^{79} +(-9.75090 - 20.2479i) q^{80} +(22.0280 - 96.5112i) q^{82} +(0.956785 + 0.460763i) q^{83} +(13.6349 + 21.6998i) q^{85} -103.107i q^{86} -125.787 q^{88} +(-73.6381 + 46.2699i) q^{89} +(0.678813 - 1.40957i) q^{91} +(-44.3742 - 10.1281i) q^{92} +(-23.8944 + 11.5070i) q^{94} +(-11.1896 - 99.3106i) q^{95} +(54.6355 - 19.1178i) q^{97} +(-8.35675 + 74.1682i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/261\mathbb{Z}\right)^\times\).

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{23}{28}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.29187 0.811733i 0.645933 0.405867i −0.168843 0.985643i \(-0.554003\pi\)
0.814776 + 0.579776i \(0.196860\pi\)
\(3\) 0 0
\(4\) −0.725528 + 1.50658i −0.181382 + 0.376644i
\(5\) −3.36294 0.767569i −0.672588 0.153514i −0.127431 0.991847i \(-0.540673\pi\)
−0.545158 + 0.838334i \(0.683530\pi\)
\(6\) 0 0
\(7\) −0.255710 + 0.123143i −0.0365299 + 0.0175919i −0.452060 0.891988i \(-0.649311\pi\)
0.415530 + 0.909580i \(0.363596\pi\)
\(8\) 0.968958 + 8.59974i 0.121120 + 1.07497i
\(9\) 0 0
\(10\) −4.96753 + 1.73821i −0.496753 + 0.173821i
\(11\) −1.62739 + 14.4435i −0.147945 + 1.31305i 0.671978 + 0.740571i \(0.265445\pi\)
−0.819923 + 0.572474i \(0.805984\pi\)
\(12\) 0 0
\(13\) −4.30976 + 3.43692i −0.331520 + 0.264378i −0.775076 0.631869i \(-0.782288\pi\)
0.443556 + 0.896247i \(0.353717\pi\)
\(14\) −0.230383 + 0.366653i −0.0164559 + 0.0261895i
\(15\) 0 0
\(16\) 4.06213 + 5.09375i 0.253883 + 0.318359i
\(17\) −5.25353 5.25353i −0.309031 0.309031i 0.535503 0.844534i \(-0.320122\pi\)
−0.844534 + 0.535503i \(0.820122\pi\)
\(18\) 0 0
\(19\) 9.56906 + 27.3468i 0.503635 + 1.43930i 0.862568 + 0.505942i \(0.168855\pi\)
−0.358933 + 0.933363i \(0.616859\pi\)
\(20\) 3.59631 4.50963i 0.179816 0.225482i
\(21\) 0 0
\(22\) 9.62189 + 19.9801i 0.437359 + 0.908185i
\(23\) 6.05686 + 26.5368i 0.263342 + 1.15378i 0.917600 + 0.397505i \(0.130124\pi\)
−0.654258 + 0.756271i \(0.727019\pi\)
\(24\) 0 0
\(25\) −11.8040 5.68451i −0.472160 0.227380i
\(26\) −2.77777 + 7.93841i −0.106837 + 0.305323i
\(27\) 0 0
\(28\) 0.474590i 0.0169496i
\(29\) −2.32625 28.9065i −0.0802155 0.996778i
\(30\) 0 0
\(31\) −12.9513 + 8.13783i −0.417783 + 0.262511i −0.724479 0.689297i \(-0.757920\pi\)
0.306695 + 0.951808i \(0.400777\pi\)
\(32\) −23.2916 8.15007i −0.727862 0.254690i
\(33\) 0 0
\(34\) −11.0513 2.52239i −0.325039 0.0741880i
\(35\) 0.954457 0.217849i 0.0272702 0.00622425i
\(36\) 0 0
\(37\) 3.05571 + 27.1202i 0.0825867 + 0.732977i 0.964955 + 0.262417i \(0.0845196\pi\)
−0.882368 + 0.470560i \(0.844052\pi\)
\(38\) 34.5602 + 27.5609i 0.909480 + 0.725286i
\(39\) 0 0
\(40\) 3.34235 29.6642i 0.0835587 0.741604i
\(41\) 45.8791 45.8791i 1.11900 1.11900i 0.127114 0.991888i \(-0.459429\pi\)
0.991888 0.127114i \(-0.0405713\pi\)
\(42\) 0 0
\(43\) 35.9543 57.2209i 0.836146 1.33072i −0.105605 0.994408i \(-0.533678\pi\)
0.941751 0.336311i \(-0.109179\pi\)
\(44\) −20.5795 12.9310i −0.467716 0.293885i
\(45\) 0 0
\(46\) 29.3655 + 29.3655i 0.638380 + 0.638380i
\(47\) −17.2732 1.94622i −0.367514 0.0414089i −0.0737238 0.997279i \(-0.523488\pi\)
−0.293791 + 0.955870i \(0.594917\pi\)
\(48\) 0 0
\(49\) −30.5008 + 38.2468i −0.622465 + 0.780546i
\(50\) −19.8635 + 2.23808i −0.397270 + 0.0447616i
\(51\) 0 0
\(52\) −2.05112 8.98655i −0.0394447 0.172818i
\(53\) −1.31097 + 5.74372i −0.0247352 + 0.108372i −0.985789 0.167991i \(-0.946272\pi\)
0.961053 + 0.276363i \(0.0891292\pi\)
\(54\) 0 0
\(55\) 16.5592 47.3235i 0.301077 0.860427i
\(56\) −1.30677 2.07972i −0.0233352 0.0371378i
\(57\) 0 0
\(58\) −26.4696 35.4551i −0.456372 0.611295i
\(59\) 43.1476 0.731315 0.365658 0.930749i \(-0.380844\pi\)
0.365658 + 0.930749i \(0.380844\pi\)
\(60\) 0 0
\(61\) 104.863 + 36.6931i 1.71906 + 0.601526i 0.996008 0.0892649i \(-0.0284518\pi\)
0.723055 + 0.690791i \(0.242737\pi\)
\(62\) −10.1256 + 21.0260i −0.163316 + 0.339129i
\(63\) 0 0
\(64\) −62.1125 + 14.1768i −0.970507 + 0.221512i
\(65\) 17.1315 8.25011i 0.263562 0.126925i
\(66\) 0 0
\(67\) −67.4283 53.7723i −1.00639 0.802571i −0.0260070 0.999662i \(-0.508279\pi\)
−0.980385 + 0.197091i \(0.936851\pi\)
\(68\) 11.7264 4.10325i 0.172447 0.0603419i
\(69\) 0 0
\(70\) 1.05620 1.05620i 0.0150885 0.0150885i
\(71\) −45.1943 + 36.0413i −0.636540 + 0.507623i −0.887760 0.460306i \(-0.847740\pi\)
0.251220 + 0.967930i \(0.419168\pi\)
\(72\) 0 0
\(73\) −42.0399 26.4154i −0.575889 0.361855i 0.212379 0.977187i \(-0.431879\pi\)
−0.788268 + 0.615332i \(0.789022\pi\)
\(74\) 25.9619 + 32.5552i 0.350836 + 0.439935i
\(75\) 0 0
\(76\) −48.1426 5.42437i −0.633456 0.0713733i
\(77\) −1.36248 3.89374i −0.0176945 0.0505681i
\(78\) 0 0
\(79\) 96.9173 10.9200i 1.22680 0.138227i 0.525314 0.850909i \(-0.323948\pi\)
0.701488 + 0.712681i \(0.252519\pi\)
\(80\) −9.75090 20.2479i −0.121886 0.253099i
\(81\) 0 0
\(82\) 22.0280 96.5112i 0.268635 1.17697i
\(83\) 0.956785 + 0.460763i 0.0115275 + 0.00555137i 0.439639 0.898175i \(-0.355107\pi\)
−0.428111 + 0.903726i \(0.640821\pi\)
\(84\) 0 0
\(85\) 13.6349 + 21.6998i 0.160410 + 0.255291i
\(86\) 103.107i 1.19892i
\(87\) 0 0
\(88\) −125.787 −1.42940
\(89\) −73.6381 + 46.2699i −0.827394 + 0.519886i −0.877904 0.478837i \(-0.841058\pi\)
0.0505095 + 0.998724i \(0.483915\pi\)
\(90\) 0 0
\(91\) 0.678813 1.40957i 0.00745949 0.0154898i
\(92\) −44.3742 10.1281i −0.482328 0.110088i
\(93\) 0 0
\(94\) −23.8944 + 11.5070i −0.254196 + 0.122414i
\(95\) −11.1896 99.3106i −0.117785 1.04537i
\(96\) 0 0
\(97\) 54.6355 19.1178i 0.563252 0.197091i −0.0336088 0.999435i \(-0.510700\pi\)
0.596861 + 0.802345i \(0.296414\pi\)
\(98\) −8.35675 + 74.1682i −0.0852729 + 0.756818i
\(99\) 0 0
\(100\) 17.1283 13.6594i 0.171283 0.136594i
\(101\) 43.1797 68.7201i 0.427522 0.680397i −0.561614 0.827399i \(-0.689819\pi\)
0.989136 + 0.147002i \(0.0469623\pi\)
\(102\) 0 0
\(103\) 117.601 + 147.466i 1.14175 + 1.43171i 0.885217 + 0.465179i \(0.154010\pi\)
0.256537 + 0.966534i \(0.417419\pi\)
\(104\) −33.7326 33.7326i −0.324352 0.324352i
\(105\) 0 0
\(106\) 2.96878 + 8.48427i 0.0280073 + 0.0800403i
\(107\) −17.2592 + 21.6423i −0.161300 + 0.202264i −0.855913 0.517119i \(-0.827004\pi\)
0.694613 + 0.719384i \(0.255576\pi\)
\(108\) 0 0
\(109\) −40.5822 84.2699i −0.372314 0.773118i 0.627672 0.778478i \(-0.284008\pi\)
−0.999986 + 0.00536026i \(0.998294\pi\)
\(110\) −17.0218 74.5773i −0.154743 0.677975i
\(111\) 0 0
\(112\) −1.66599 0.802297i −0.0148749 0.00716336i
\(113\) −49.3986 + 141.173i −0.437156 + 1.24932i 0.489035 + 0.872264i \(0.337349\pi\)
−0.926191 + 0.377055i \(0.876937\pi\)
\(114\) 0 0
\(115\) 93.8909i 0.816443i
\(116\) 45.2377 + 17.4679i 0.389980 + 0.150585i
\(117\) 0 0
\(118\) 55.7409 35.0243i 0.472381 0.296816i
\(119\) 1.99031 + 0.696441i 0.0167253 + 0.00585245i
\(120\) 0 0
\(121\) −88.0000 20.0854i −0.727272 0.165995i
\(122\) 165.254 37.7181i 1.35454 0.309165i
\(123\) 0 0
\(124\) −2.86373 25.4163i −0.0230946 0.204970i
\(125\) 102.755 + 81.9441i 0.822037 + 0.655553i
\(126\) 0 0
\(127\) −10.7711 + 95.5964i −0.0848120 + 0.752727i 0.877276 + 0.479987i \(0.159359\pi\)
−0.962088 + 0.272740i \(0.912070\pi\)
\(128\) 1.06196 1.06196i 0.00829659 0.00829659i
\(129\) 0 0
\(130\) 15.4348 24.5643i 0.118729 0.188956i
\(131\) 86.3851 + 54.2793i 0.659428 + 0.414346i 0.819752 0.572718i \(-0.194111\pi\)
−0.160324 + 0.987064i \(0.551254\pi\)
\(132\) 0 0
\(133\) −5.81447 5.81447i −0.0437178 0.0437178i
\(134\) −130.757 14.7328i −0.975798 0.109946i
\(135\) 0 0
\(136\) 40.0885 50.2694i 0.294769 0.369628i
\(137\) 43.6939 4.92312i 0.318933 0.0359351i 0.0489532 0.998801i \(-0.484411\pi\)
0.269980 + 0.962866i \(0.412983\pi\)
\(138\) 0 0
\(139\) 13.4998 + 59.1466i 0.0971211 + 0.425515i 0.999990 0.00439991i \(-0.00140054\pi\)
−0.902869 + 0.429915i \(0.858543\pi\)
\(140\) −0.364281 + 1.59602i −0.00260200 + 0.0114001i
\(141\) 0 0
\(142\) −29.1291 + 83.2462i −0.205135 + 0.586241i
\(143\) −42.6274 67.8412i −0.298094 0.474414i
\(144\) 0 0
\(145\) −14.3647 + 98.9966i −0.0990672 + 0.682735i
\(146\) −75.7522 −0.518851
\(147\) 0 0
\(148\) −43.0756 15.0728i −0.291051 0.101843i
\(149\) 42.6095 88.4796i 0.285970 0.593823i −0.707655 0.706558i \(-0.750247\pi\)
0.993625 + 0.112735i \(0.0359612\pi\)
\(150\) 0 0
\(151\) 2.28538 0.521624i 0.0151350 0.00345446i −0.214947 0.976626i \(-0.568958\pi\)
0.230082 + 0.973171i \(0.426101\pi\)
\(152\) −225.903 + 108.789i −1.48621 + 0.715719i
\(153\) 0 0
\(154\) −4.92082 3.92422i −0.0319534 0.0254820i
\(155\) 49.8008 17.4260i 0.321295 0.112426i
\(156\) 0 0
\(157\) 55.3939 55.3939i 0.352828 0.352828i −0.508333 0.861161i \(-0.669738\pi\)
0.861161 + 0.508333i \(0.169738\pi\)
\(158\) 116.340 92.7781i 0.736330 0.587203i
\(159\) 0 0
\(160\) 72.0724 + 45.2861i 0.450453 + 0.283038i
\(161\) −4.81663 6.03986i −0.0299170 0.0375147i
\(162\) 0 0
\(163\) −59.0143 6.64931i −0.362051 0.0407933i −0.0709343 0.997481i \(-0.522598\pi\)
−0.291116 + 0.956688i \(0.594027\pi\)
\(164\) 35.8337 + 102.407i 0.218498 + 0.624432i
\(165\) 0 0
\(166\) 1.61005 0.181410i 0.00969913 0.00109283i
\(167\) −35.2685 73.2358i −0.211189 0.438538i 0.768285 0.640107i \(-0.221110\pi\)
−0.979474 + 0.201569i \(0.935396\pi\)
\(168\) 0 0
\(169\) −30.8444 + 135.138i −0.182511 + 0.799635i
\(170\) 35.2288 + 16.9653i 0.207228 + 0.0997959i
\(171\) 0 0
\(172\) 60.1218 + 95.6833i 0.349545 + 0.556298i
\(173\) 34.1362i 0.197319i 0.995121 + 0.0986597i \(0.0314555\pi\)
−0.995121 + 0.0986597i \(0.968544\pi\)
\(174\) 0 0
\(175\) 3.71841 0.0212481
\(176\) −80.1822 + 50.3818i −0.455581 + 0.286260i
\(177\) 0 0
\(178\) −57.5717 + 119.549i −0.323437 + 0.671623i
\(179\) 71.0369 + 16.2137i 0.396854 + 0.0905793i 0.416290 0.909232i \(-0.363330\pi\)
−0.0194363 + 0.999811i \(0.506187\pi\)
\(180\) 0 0
\(181\) 113.506 54.6618i 0.627107 0.301999i −0.0932070 0.995647i \(-0.529712\pi\)
0.720314 + 0.693648i \(0.243998\pi\)
\(182\) −0.267259 2.37199i −0.00146846 0.0130329i
\(183\) 0 0
\(184\) −222.341 + 77.8005i −1.20838 + 0.422829i
\(185\) 10.5404 93.5489i 0.0569753 0.505670i
\(186\) 0 0
\(187\) 84.4289 67.3298i 0.451491 0.360052i
\(188\) 15.4643 24.6113i 0.0822570 0.130911i
\(189\) 0 0
\(190\) −95.0691 119.213i −0.500364 0.627437i
\(191\) 107.857 + 107.857i 0.564698 + 0.564698i 0.930638 0.365940i \(-0.119253\pi\)
−0.365940 + 0.930638i \(0.619253\pi\)
\(192\) 0 0
\(193\) 66.7211 + 190.678i 0.345705 + 0.987969i 0.977151 + 0.212548i \(0.0681763\pi\)
−0.631445 + 0.775420i \(0.717538\pi\)
\(194\) 55.0632 69.0470i 0.283831 0.355913i
\(195\) 0 0
\(196\) −35.4925 73.7008i −0.181084 0.376025i
\(197\) 76.3058 + 334.317i 0.387339 + 1.69704i 0.673769 + 0.738942i \(0.264674\pi\)
−0.286431 + 0.958101i \(0.592469\pi\)
\(198\) 0 0
\(199\) 267.208 + 128.681i 1.34275 + 0.646636i 0.960722 0.277513i \(-0.0895101\pi\)
0.382032 + 0.924149i \(0.375224\pi\)
\(200\) 37.4477 107.020i 0.187239 0.535098i
\(201\) 0 0
\(202\) 123.828i 0.613008i
\(203\) 4.15449 + 7.10522i 0.0204655 + 0.0350011i
\(204\) 0 0
\(205\) −189.504 + 119.073i −0.924410 + 0.580845i
\(206\) 271.628 + 95.0466i 1.31858 + 0.461391i
\(207\) 0 0
\(208\) −35.0136 7.99162i −0.168335 0.0384213i
\(209\) −410.556 + 93.7067i −1.96438 + 0.448357i
\(210\) 0 0
\(211\) −23.1896 205.814i −0.109903 0.975420i −0.920748 0.390158i \(-0.872420\pi\)
0.810845 0.585262i \(-0.199008\pi\)
\(212\) −7.70221 6.14231i −0.0363312 0.0289731i
\(213\) 0 0
\(214\) −4.72874 + 41.9688i −0.0220969 + 0.196116i
\(215\) −164.833 + 164.833i −0.766666 + 0.766666i
\(216\) 0 0
\(217\) 2.30965 3.67579i 0.0106435 0.0169391i
\(218\) −120.831 75.9234i −0.554273 0.348272i
\(219\) 0 0
\(220\) 59.2822 + 59.2822i 0.269465 + 0.269465i
\(221\) 40.6974 + 4.58549i 0.184151 + 0.0207488i
\(222\) 0 0
\(223\) −17.9820 + 22.5487i −0.0806367 + 0.101115i −0.820513 0.571627i \(-0.806312\pi\)
0.739877 + 0.672742i \(0.234884\pi\)
\(224\) 6.95951 0.784148i 0.0310692 0.00350066i
\(225\) 0 0
\(226\) 50.7785 + 222.475i 0.224684 + 0.984403i
\(227\) 34.9328 153.050i 0.153889 0.674231i −0.837844 0.545910i \(-0.816184\pi\)
0.991733 0.128321i \(-0.0409588\pi\)
\(228\) 0 0
\(229\) −104.546 + 298.776i −0.456534 + 1.30470i 0.453902 + 0.891051i \(0.350031\pi\)
−0.910437 + 0.413648i \(0.864254\pi\)
\(230\) −76.2143 121.294i −0.331367 0.527367i
\(231\) 0 0
\(232\) 246.335 48.0144i 1.06179 0.206959i
\(233\) −421.117 −1.80737 −0.903684 0.428200i \(-0.859148\pi\)
−0.903684 + 0.428200i \(0.859148\pi\)
\(234\) 0 0
\(235\) 56.5948 + 19.8034i 0.240829 + 0.0842697i
\(236\) −31.3048 + 65.0051i −0.132648 + 0.275445i
\(237\) 0 0
\(238\) 3.13654 0.715895i 0.0131788 0.00300796i
\(239\) 187.354 90.2247i 0.783906 0.377509i 0.00127824 0.999999i \(-0.499593\pi\)
0.782628 + 0.622490i \(0.213879\pi\)
\(240\) 0 0
\(241\) 10.8085 + 8.61948i 0.0448485 + 0.0357655i 0.645658 0.763627i \(-0.276583\pi\)
−0.600809 + 0.799393i \(0.705155\pi\)
\(242\) −129.988 + 45.4848i −0.537141 + 0.187954i
\(243\) 0 0
\(244\) −131.362 + 131.362i −0.538368 + 0.538368i
\(245\) 131.929 105.210i 0.538487 0.429429i
\(246\) 0 0
\(247\) −135.229 84.9700i −0.547486 0.344008i
\(248\) −82.5325 103.493i −0.332792 0.417309i
\(249\) 0 0
\(250\) 199.262 + 22.4514i 0.797048 + 0.0898057i
\(251\) 20.8320 + 59.5343i 0.0829959 + 0.237189i 0.977901 0.209067i \(-0.0670428\pi\)
−0.894905 + 0.446256i \(0.852757\pi\)
\(252\) 0 0
\(253\) −393.142 + 44.2964i −1.55392 + 0.175085i
\(254\) 63.6839 + 132.241i 0.250724 + 0.520634i
\(255\) 0 0
\(256\) 57.2170 250.684i 0.223504 0.979234i
\(257\) 387.505 + 186.613i 1.50780 + 0.726120i 0.991478 0.130273i \(-0.0415854\pi\)
0.516325 + 0.856393i \(0.327300\pi\)
\(258\) 0 0
\(259\) −4.12104 6.55859i −0.0159113 0.0253228i
\(260\) 31.7956i 0.122291i
\(261\) 0 0
\(262\) 155.658 0.594116
\(263\) −10.7365 + 6.74620i −0.0408232 + 0.0256509i −0.552289 0.833653i \(-0.686246\pi\)
0.511466 + 0.859304i \(0.329103\pi\)
\(264\) 0 0
\(265\) 8.81741 18.3095i 0.0332733 0.0690926i
\(266\) −12.2313 2.79172i −0.0459824 0.0104952i
\(267\) 0 0
\(268\) 129.933 62.5725i 0.484825 0.233479i
\(269\) 28.0878 + 249.286i 0.104416 + 0.926714i 0.931278 + 0.364310i \(0.118695\pi\)
−0.826862 + 0.562404i \(0.809876\pi\)
\(270\) 0 0
\(271\) 214.664 75.1142i 0.792119 0.277174i 0.0962629 0.995356i \(-0.469311\pi\)
0.695856 + 0.718182i \(0.255025\pi\)
\(272\) 5.41964 48.1007i 0.0199252 0.176841i
\(273\) 0 0
\(274\) 52.4503 41.8278i 0.191425 0.152656i
\(275\) 101.314 161.240i 0.368415 0.586328i
\(276\) 0 0
\(277\) −266.485 334.162i −0.962040 1.20636i −0.978448 0.206495i \(-0.933794\pi\)
0.0164075 0.999865i \(-0.494777\pi\)
\(278\) 65.4513 + 65.4513i 0.235436 + 0.235436i
\(279\) 0 0
\(280\) 2.79827 + 7.99700i 0.00999383 + 0.0285607i
\(281\) 259.886 325.887i 0.924862 1.15974i −0.0619844 0.998077i \(-0.519743\pi\)
0.986846 0.161663i \(-0.0516857\pi\)
\(282\) 0 0
\(283\) −202.446 420.383i −0.715356 1.48545i −0.867681 0.497121i \(-0.834390\pi\)
0.152325 0.988330i \(-0.451324\pi\)
\(284\) −21.5091 94.2376i −0.0757363 0.331823i
\(285\) 0 0
\(286\) −110.138 53.0396i −0.385097 0.185453i
\(287\) −6.08202 + 17.3814i −0.0211917 + 0.0605624i
\(288\) 0 0
\(289\) 233.801i 0.809000i
\(290\) 61.8015 + 139.551i 0.213109 + 0.481209i
\(291\) 0 0
\(292\) 70.2980 44.1712i 0.240747 0.151271i
\(293\) −285.468 99.8897i −0.974295 0.340921i −0.204256 0.978917i \(-0.565478\pi\)
−0.770039 + 0.637997i \(0.779763\pi\)
\(294\) 0 0
\(295\) −145.103 33.1188i −0.491874 0.112267i
\(296\) −230.265 + 52.5566i −0.777924 + 0.177556i
\(297\) 0 0
\(298\) −16.7760 148.891i −0.0562954 0.499635i
\(299\) −117.309 93.5504i −0.392336 0.312878i
\(300\) 0 0
\(301\) −2.14749 + 19.0595i −0.00713451 + 0.0633205i
\(302\) 2.52899 2.52899i 0.00837414 0.00837414i
\(303\) 0 0
\(304\) −100.427 + 159.829i −0.330352 + 0.525752i
\(305\) −324.483 203.886i −1.06388 0.668479i
\(306\) 0 0
\(307\) −271.866 271.866i −0.885558 0.885558i 0.108534 0.994093i \(-0.465384\pi\)
−0.994093 + 0.108534i \(0.965384\pi\)
\(308\) 6.85474 + 0.772343i 0.0222556 + 0.00250761i
\(309\) 0 0
\(310\) 50.1906 62.9370i 0.161905 0.203023i
\(311\) 124.784 14.0597i 0.401233 0.0452081i 0.0909576 0.995855i \(-0.471007\pi\)
0.310276 + 0.950647i \(0.399579\pi\)
\(312\) 0 0
\(313\) 13.5770 + 59.4846i 0.0433769 + 0.190047i 0.991975 0.126438i \(-0.0403545\pi\)
−0.948598 + 0.316485i \(0.897497\pi\)
\(314\) 26.5964 116.527i 0.0847020 0.371104i
\(315\) 0 0
\(316\) −53.8645 + 153.936i −0.170457 + 0.487139i
\(317\) −239.824 381.678i −0.756543 1.20403i −0.973686 0.227892i \(-0.926817\pi\)
0.217143 0.976140i \(-0.430326\pi\)
\(318\) 0 0
\(319\) 421.297 + 13.4431i 1.32068 + 0.0421413i
\(320\) 219.762 0.686757
\(321\) 0 0
\(322\) −11.1252 3.89288i −0.0345503 0.0120897i
\(323\) 93.3958 193.938i 0.289151 0.600429i
\(324\) 0 0
\(325\) 70.4096 16.0705i 0.216645 0.0494478i
\(326\) −81.6360 + 39.3138i −0.250417 + 0.120594i
\(327\) 0 0
\(328\) 439.003 + 350.093i 1.33842 + 1.06736i
\(329\) 4.65658 1.62941i 0.0141537 0.00495261i
\(330\) 0 0
\(331\) 295.773 295.773i 0.893575 0.893575i −0.101283 0.994858i \(-0.532295\pi\)
0.994858 + 0.101283i \(0.0322946\pi\)
\(332\) −1.38835 + 1.10717i −0.00418178 + 0.00333486i
\(333\) 0 0
\(334\) −105.010 65.9822i −0.314402 0.197552i
\(335\) 185.483 + 232.589i 0.553682 + 0.694295i
\(336\) 0 0
\(337\) −90.2891 10.1731i −0.267920 0.0301873i −0.0230176 0.999735i \(-0.507327\pi\)
−0.244902 + 0.969548i \(0.578756\pi\)
\(338\) 69.8493 + 199.618i 0.206655 + 0.590586i
\(339\) 0 0
\(340\) −42.5848 + 4.79815i −0.125249 + 0.0141122i
\(341\) −96.4620 200.305i −0.282880 0.587406i
\(342\) 0 0
\(343\) 6.18411 27.0944i 0.0180295 0.0789923i
\(344\) 526.923 + 253.753i 1.53175 + 0.737654i
\(345\) 0 0
\(346\) 27.7095 + 44.0994i 0.0800853 + 0.127455i
\(347\) 392.579i 1.13135i −0.824628 0.565676i \(-0.808615\pi\)
0.824628 0.565676i \(-0.191385\pi\)
\(348\) 0 0
\(349\) −487.106 −1.39572 −0.697860 0.716234i \(-0.745864\pi\)
−0.697860 + 0.716234i \(0.745864\pi\)
\(350\) 4.80368 3.01836i 0.0137248 0.00862387i
\(351\) 0 0
\(352\) 155.620 323.148i 0.442103 0.918035i
\(353\) −98.6003 22.5049i −0.279321 0.0637532i 0.0805655 0.996749i \(-0.474327\pi\)
−0.359886 + 0.932996i \(0.617185\pi\)
\(354\) 0 0
\(355\) 179.650 86.5149i 0.506056 0.243704i
\(356\) −16.2825 144.511i −0.0457374 0.405931i
\(357\) 0 0
\(358\) 104.931 36.7170i 0.293104 0.102562i
\(359\) −3.96158 + 35.1600i −0.0110350 + 0.0979386i −0.998022 0.0628592i \(-0.979978\pi\)
0.986987 + 0.160798i \(0.0514067\pi\)
\(360\) 0 0
\(361\) −374.039 + 298.286i −1.03612 + 0.826277i
\(362\) 102.264 162.753i 0.282498 0.449593i
\(363\) 0 0
\(364\) 1.63113 + 2.04537i 0.00448111 + 0.00561914i
\(365\) 121.102 + 121.102i 0.331787 + 0.331787i
\(366\) 0 0
\(367\) −76.1146 217.523i −0.207397 0.592706i 0.792455 0.609930i \(-0.208803\pi\)
−0.999852 + 0.0172247i \(0.994517\pi\)
\(368\) −110.568 + 138.648i −0.300457 + 0.376761i
\(369\) 0 0
\(370\) −62.3199 129.409i −0.168432 0.349753i
\(371\) −0.372074 1.63016i −0.00100289 0.00439397i
\(372\) 0 0
\(373\) 402.935 + 194.043i 1.08026 + 0.520224i 0.887398 0.461003i \(-0.152510\pi\)
0.192857 + 0.981227i \(0.438225\pi\)
\(374\) 54.4170 155.515i 0.145500 0.415815i
\(375\) 0 0
\(376\) 150.431i 0.400082i
\(377\) 109.375 + 116.585i 0.290119 + 0.309244i
\(378\) 0 0
\(379\) −215.124 + 135.171i −0.567609 + 0.356653i −0.785061 0.619419i \(-0.787368\pi\)
0.217452 + 0.976071i \(0.430226\pi\)
\(380\) 157.737 + 55.1946i 0.415098 + 0.145249i
\(381\) 0 0
\(382\) 226.888 + 51.7858i 0.593949 + 0.135565i
\(383\) 215.485 49.1830i 0.562624 0.128415i 0.0682557 0.997668i \(-0.478257\pi\)
0.494368 + 0.869253i \(0.335399\pi\)
\(384\) 0 0
\(385\) 1.59322 + 14.1402i 0.00413824 + 0.0367279i
\(386\) 240.974 + 192.171i 0.624286 + 0.497851i
\(387\) 0 0
\(388\) −10.8372 + 96.1830i −0.0279310 + 0.247894i
\(389\) −408.712 + 408.712i −1.05067 + 1.05067i −0.0520279 + 0.998646i \(0.516568\pi\)
−0.998646 + 0.0520279i \(0.983432\pi\)
\(390\) 0 0
\(391\) 107.592 171.232i 0.275172 0.437933i
\(392\) −358.466 225.239i −0.914455 0.574590i
\(393\) 0 0
\(394\) 369.953 + 369.953i 0.938968 + 0.938968i
\(395\) −334.309 37.6676i −0.846352 0.0953610i
\(396\) 0 0
\(397\) −173.996 + 218.184i −0.438277 + 0.549582i −0.951088 0.308919i \(-0.900033\pi\)
0.512811 + 0.858501i \(0.328604\pi\)
\(398\) 449.651 50.6635i 1.12978 0.127295i
\(399\) 0 0
\(400\) −18.9939 83.2179i −0.0474849 0.208045i
\(401\) 71.9206 315.105i 0.179353 0.785797i −0.802576 0.596549i \(-0.796538\pi\)
0.981929 0.189248i \(-0.0606049\pi\)
\(402\) 0 0
\(403\) 27.8478 79.5846i 0.0691014 0.197480i
\(404\) 72.2040 + 114.912i 0.178723 + 0.284435i
\(405\) 0 0
\(406\) 11.1346 + 5.80665i 0.0274251 + 0.0143021i
\(407\) −396.683 −0.974650
\(408\) 0 0
\(409\) 138.542 + 48.4780i 0.338734 + 0.118528i 0.494285 0.869300i \(-0.335430\pi\)
−0.155552 + 0.987828i \(0.549715\pi\)
\(410\) −148.158 + 307.653i −0.361361 + 0.750374i
\(411\) 0 0
\(412\) −307.492 + 70.1830i −0.746340 + 0.170347i
\(413\) −11.0333 + 5.31334i −0.0267149 + 0.0128652i
\(414\) 0 0
\(415\) −2.86394 2.28392i −0.00690107 0.00550342i
\(416\) 128.392 44.9264i 0.308635 0.107996i
\(417\) 0 0
\(418\) −454.318 + 454.318i −1.08689 + 1.08689i
\(419\) −554.089 + 441.871i −1.32241 + 1.05459i −0.328485 + 0.944509i \(0.606538\pi\)
−0.993923 + 0.110076i \(0.964891\pi\)
\(420\) 0 0
\(421\) −408.042 256.390i −0.969220 0.609001i −0.0483331 0.998831i \(-0.515391\pi\)
−0.920887 + 0.389830i \(0.872534\pi\)
\(422\) −197.024 247.060i −0.466880 0.585449i
\(423\) 0 0
\(424\) −50.6648 5.70855i −0.119492 0.0134636i
\(425\) 32.1490 + 91.8764i 0.0756446 + 0.216180i
\(426\) 0 0
\(427\) −31.3329 + 3.53037i −0.0733792 + 0.00826786i
\(428\) −20.0837 41.7043i −0.0469246 0.0974400i
\(429\) 0 0
\(430\) −79.1418 + 346.743i −0.184051 + 0.806379i
\(431\) −158.220 76.1946i −0.367099 0.176786i 0.241235 0.970467i \(-0.422448\pi\)
−0.608334 + 0.793681i \(0.708162\pi\)
\(432\) 0 0
\(433\) 2.79964 + 4.45560i 0.00646568 + 0.0102901i 0.849941 0.526877i \(-0.176637\pi\)
−0.843476 + 0.537167i \(0.819494\pi\)
\(434\) 6.62344i 0.0152614i
\(435\) 0 0
\(436\) 156.402 0.358721
\(437\) −667.739 + 419.568i −1.52801 + 0.960110i
\(438\) 0 0
\(439\) −232.675 + 483.154i −0.530010 + 1.10058i 0.448386 + 0.893840i \(0.351999\pi\)
−0.978396 + 0.206738i \(0.933715\pi\)
\(440\) 423.015 + 96.5504i 0.961398 + 0.219433i
\(441\) 0 0
\(442\) 56.2977 27.1116i 0.127370 0.0613384i
\(443\) −49.1601 436.308i −0.110971 0.984894i −0.918596 0.395198i \(-0.870676\pi\)
0.807625 0.589696i \(-0.200753\pi\)
\(444\) 0 0
\(445\) 283.156 99.0805i 0.636305 0.222653i
\(446\) −4.92679 + 43.7265i −0.0110466 + 0.0980414i
\(447\) 0 0
\(448\) 14.1370 11.2739i 0.0315558 0.0251649i
\(449\) −27.2504 + 43.3687i −0.0606912 + 0.0965896i −0.875691 0.482871i \(-0.839594\pi\)
0.815000 + 0.579461i \(0.196737\pi\)
\(450\) 0 0
\(451\) 587.991 + 737.318i 1.30375 + 1.63485i
\(452\) −176.848 176.848i −0.391256 0.391256i
\(453\) 0 0
\(454\) −79.1076 226.077i −0.174246 0.497966i
\(455\) −3.36475 + 4.21927i −0.00739506 + 0.00927311i
\(456\) 0 0
\(457\) 141.198 + 293.202i 0.308968 + 0.641579i 0.996410 0.0846606i \(-0.0269806\pi\)
−0.687442 + 0.726240i \(0.741266\pi\)
\(458\) 107.467 + 470.843i 0.234644 + 1.02804i
\(459\) 0 0
\(460\) 141.454 + 68.1205i 0.307508 + 0.148088i
\(461\) 3.04533 8.70305i 0.00660592 0.0188786i −0.940533 0.339702i \(-0.889674\pi\)
0.947139 + 0.320823i \(0.103960\pi\)
\(462\) 0 0
\(463\) 107.108i 0.231334i 0.993288 + 0.115667i \(0.0369005\pi\)
−0.993288 + 0.115667i \(0.963099\pi\)
\(464\) 137.793 129.271i 0.296968 0.278602i
\(465\) 0 0
\(466\) −544.026 + 341.834i −1.16744 + 0.733550i
\(467\) 666.211 + 233.117i 1.42658 + 0.499180i 0.929595 0.368582i \(-0.120157\pi\)
0.496980 + 0.867762i \(0.334442\pi\)
\(468\) 0 0
\(469\) 23.8638 + 5.44675i 0.0508822 + 0.0116135i
\(470\) 89.1880 20.3566i 0.189762 0.0433119i
\(471\) 0 0
\(472\) 41.8082 + 371.058i 0.0885768 + 0.786140i
\(473\) 767.959 + 612.427i 1.62359 + 1.29477i
\(474\) 0 0
\(475\) 42.4999 377.197i 0.0894735 0.794099i
\(476\) −2.49327 + 2.49327i −0.00523796 + 0.00523796i
\(477\) 0 0
\(478\) 168.797 268.639i 0.353132 0.562007i
\(479\) 268.422 + 168.661i 0.560380 + 0.352110i 0.782249 0.622966i \(-0.214073\pi\)
−0.221868 + 0.975077i \(0.571216\pi\)
\(480\) 0 0
\(481\) −106.379 106.379i −0.221162 0.221162i
\(482\) 20.9598 + 2.36160i 0.0434851 + 0.00489959i
\(483\) 0 0
\(484\) 94.1067 118.006i 0.194435 0.243814i
\(485\) −198.410 + 22.3555i −0.409093 + 0.0460937i
\(486\) 0 0
\(487\) −60.5532 265.301i −0.124339 0.544765i −0.998274 0.0587228i \(-0.981297\pi\)
0.873935 0.486042i \(-0.161560\pi\)
\(488\) −213.943 + 937.347i −0.438409 + 1.92079i
\(489\) 0 0
\(490\) 85.0325 243.009i 0.173536 0.495936i
\(491\) 21.2173 + 33.7671i 0.0432123 + 0.0687720i 0.867632 0.497207i \(-0.165641\pi\)
−0.824420 + 0.565979i \(0.808498\pi\)
\(492\) 0 0
\(493\) −139.640 + 164.082i −0.283246 + 0.332824i
\(494\) −243.671 −0.493260
\(495\) 0 0
\(496\) −94.0619 32.9137i −0.189641 0.0663582i
\(497\) 7.11838 14.7815i 0.0143227 0.0297414i
\(498\) 0 0
\(499\) −733.757 + 167.475i −1.47046 + 0.335622i −0.881362 0.472442i \(-0.843372\pi\)
−0.589094 + 0.808064i \(0.700515\pi\)
\(500\) −198.006 + 95.3549i −0.396013 + 0.190710i
\(501\) 0 0
\(502\) 75.2381 + 60.0004i 0.149877 + 0.119523i
\(503\) 475.580 166.413i 0.945487 0.330840i 0.186875 0.982384i \(-0.440164\pi\)
0.758611 + 0.651544i \(0.225878\pi\)
\(504\) 0 0
\(505\) −197.958 + 197.958i −0.391997 + 0.391997i
\(506\) −471.929 + 376.351i −0.932667 + 0.743777i
\(507\) 0 0
\(508\) −136.208 85.5854i −0.268127 0.168475i
\(509\) 156.669 + 196.457i 0.307798 + 0.385967i 0.911539 0.411214i \(-0.134895\pi\)
−0.603741 + 0.797181i \(0.706324\pi\)
\(510\) 0 0
\(511\) 14.0029 + 1.57775i 0.0274029 + 0.00308757i
\(512\) −127.588 364.624i −0.249195 0.712157i
\(513\) 0 0
\(514\) 652.085 73.4723i 1.26865 0.142942i
\(515\) −282.293 586.188i −0.548142 1.13823i
\(516\) 0 0
\(517\) 56.2205 246.318i 0.108744 0.476437i
\(518\) −10.6477 5.12764i −0.0205553 0.00989892i
\(519\) 0 0
\(520\) 87.5486 + 139.333i 0.168363 + 0.267948i
\(521\) 240.735i 0.462063i −0.972946 0.231031i \(-0.925790\pi\)
0.972946 0.231031i \(-0.0742100\pi\)
\(522\) 0 0
\(523\) −250.645 −0.479245 −0.239623 0.970866i \(-0.577024\pi\)
−0.239623 + 0.970866i \(0.577024\pi\)
\(524\) −144.451 + 90.7644i −0.275669 + 0.173215i
\(525\) 0 0
\(526\) −8.39402 + 17.4304i −0.0159582 + 0.0331376i
\(527\) 110.792 + 25.2876i 0.210232 + 0.0479841i
\(528\) 0 0
\(529\) −190.906 + 91.9355i −0.360881 + 0.173791i
\(530\) −3.47155 30.8109i −0.00655009 0.0581337i
\(531\) 0 0
\(532\) 12.9785 4.54138i 0.0243957 0.00853642i
\(533\) −40.0451 + 355.410i −0.0751315 + 0.666811i
\(534\) 0 0
\(535\) 74.6535 59.5342i 0.139539 0.111279i
\(536\) 397.092 631.969i 0.740844 1.17905i
\(537\) 0 0
\(538\) 238.639 + 299.244i 0.443568 + 0.556216i
\(539\) −502.780 502.780i −0.932802 0.932802i
\(540\) 0 0
\(541\) 288.943 + 825.753i 0.534091 + 1.52635i 0.822458 + 0.568826i \(0.192602\pi\)
−0.288367 + 0.957520i \(0.593112\pi\)
\(542\) 216.345 271.287i 0.399160 0.500530i
\(543\) 0 0
\(544\) 79.5463 + 165.180i 0.146225 + 0.303639i
\(545\) 71.7927 + 314.544i 0.131730 + 0.577145i
\(546\) 0 0
\(547\) 885.756 + 426.558i 1.61930 + 0.779813i 0.999986 0.00533110i \(-0.00169695\pi\)
0.619313 + 0.785144i \(0.287411\pi\)
\(548\) −24.2841 + 69.3999i −0.0443140 + 0.126642i
\(549\) 0 0
\(550\) 290.541i 0.528256i
\(551\) 768.241 340.224i 1.39427 0.617466i
\(552\) 0 0
\(553\) −23.4380 + 14.7271i −0.0423833 + 0.0266312i
\(554\) −615.513 215.377i −1.11103 0.388768i
\(555\) 0 0
\(556\) −98.9034 22.5741i −0.177884 0.0406008i
\(557\) 697.102 159.109i 1.25153 0.285653i 0.455130 0.890425i \(-0.349593\pi\)
0.796399 + 0.604771i \(0.206736\pi\)
\(558\) 0 0
\(559\) 41.7093 + 370.180i 0.0746141 + 0.662219i
\(560\) 4.98680 + 3.97684i 0.00890499 + 0.00710150i
\(561\) 0 0
\(562\) 71.2048 631.960i 0.126699 1.12448i
\(563\) −509.988 + 509.988i −0.905840 + 0.905840i −0.995933 0.0900931i \(-0.971284\pi\)
0.0900931 + 0.995933i \(0.471284\pi\)
\(564\) 0 0
\(565\) 274.485 436.840i 0.485814 0.773168i
\(566\) −602.771 378.746i −1.06497 0.669163i
\(567\) 0 0
\(568\) −353.737 353.737i −0.622776 0.622776i
\(569\) −19.5814 2.20630i −0.0344137 0.00387750i 0.0947408 0.995502i \(-0.469798\pi\)
−0.129155 + 0.991624i \(0.541226\pi\)
\(570\) 0 0
\(571\) 153.514 192.500i 0.268851 0.337128i −0.629019 0.777390i \(-0.716543\pi\)
0.897869 + 0.440262i \(0.145115\pi\)
\(572\) 133.135 15.0007i 0.232754 0.0262251i
\(573\) 0 0
\(574\) 6.25192 + 27.3914i 0.0108918 + 0.0477203i
\(575\) 79.3537 347.671i 0.138007 0.604646i
\(576\) 0 0
\(577\) 305.351 872.644i 0.529205 1.51238i −0.300279 0.953852i \(-0.597080\pi\)
0.829484 0.558530i \(-0.188635\pi\)
\(578\) −189.784 302.039i −0.328346 0.522559i
\(579\) 0 0
\(580\) −138.724 93.4664i −0.239179 0.161149i
\(581\) −0.301399 −0.000518759
\(582\) 0 0
\(583\) −80.8260 28.2822i −0.138638 0.0485116i
\(584\) 186.431 387.128i 0.319231 0.662890i
\(585\) 0 0
\(586\) −449.871 + 102.680i −0.767697 + 0.175222i
\(587\) 507.435 244.368i 0.864456 0.416300i 0.0515328 0.998671i \(-0.483589\pi\)
0.812923 + 0.582371i \(0.197875\pi\)
\(588\) 0 0
\(589\) −346.475 276.305i −0.588243 0.469108i
\(590\) −214.337 + 74.9998i −0.363283 + 0.127118i
\(591\) 0 0
\(592\) −125.731 + 125.731i −0.212383 + 0.212383i
\(593\) −40.7023 + 32.4590i −0.0686380 + 0.0547370i −0.657208 0.753709i \(-0.728263\pi\)
0.588570 + 0.808446i \(0.299691\pi\)
\(594\) 0 0
\(595\) −6.15874 3.86979i −0.0103508 0.00650386i
\(596\) 102.387 + 128.389i 0.171790 + 0.215418i
\(597\) 0 0
\(598\) −227.485 25.6314i −0.380409 0.0428618i
\(599\) 211.707 + 605.024i 0.353434 + 1.01006i 0.974127 + 0.226002i \(0.0725657\pi\)
−0.620693 + 0.784054i \(0.713149\pi\)
\(600\) 0 0
\(601\) 333.408 37.5661i 0.554756 0.0625060i 0.169864 0.985468i \(-0.445667\pi\)
0.384892 + 0.922962i \(0.374239\pi\)
\(602\) 12.6969 + 26.3655i 0.0210913 + 0.0437964i
\(603\) 0 0
\(604\) −0.872245 + 3.82156i −0.00144411 + 0.00632708i
\(605\) 280.522 + 135.092i 0.463672 + 0.223293i
\(606\) 0 0
\(607\) −54.8088 87.2277i −0.0902945 0.143703i 0.798523 0.601965i \(-0.205615\pi\)
−0.888817 + 0.458262i \(0.848472\pi\)
\(608\) 714.938i 1.17589i
\(609\) 0 0
\(610\) −584.690 −0.958508
\(611\) 81.1322 50.9787i 0.132786 0.0834349i
\(612\) 0 0
\(613\) 356.350 739.969i 0.581322 1.20713i −0.378261 0.925699i \(-0.623478\pi\)
0.959582 0.281428i \(-0.0908080\pi\)
\(614\) −571.898 130.532i −0.931430 0.212593i
\(615\) 0 0
\(616\) 32.1650 15.4899i 0.0522159 0.0251459i
\(617\) −12.5149 111.073i −0.0202835 0.180021i 0.979486 0.201515i \(-0.0645863\pi\)
−0.999769 + 0.0214938i \(0.993158\pi\)
\(618\) 0 0
\(619\) −86.4870 + 30.2631i −0.139721 + 0.0488903i −0.399233 0.916849i \(-0.630724\pi\)
0.259513 + 0.965740i \(0.416438\pi\)
\(620\) −9.87823 + 87.6717i −0.0159326 + 0.141406i
\(621\) 0 0
\(622\) 149.791 119.454i 0.240821 0.192049i
\(623\) 13.1321 20.8997i 0.0210789 0.0335468i
\(624\) 0 0
\(625\) −78.4444 98.3662i −0.125511 0.157386i
\(626\) 65.8253 + 65.8253i 0.105152 + 0.105152i
\(627\) 0 0
\(628\) 43.2653 + 123.645i 0.0688937 + 0.196887i
\(629\) 126.423 158.530i 0.200991 0.252035i
\(630\) 0 0
\(631\) 106.650 + 221.460i 0.169017 + 0.350967i 0.968222 0.250091i \(-0.0804605\pi\)
−0.799206 + 0.601058i \(0.794746\pi\)
\(632\) 187.818 + 822.883i 0.297180 + 1.30203i
\(633\) 0 0
\(634\) −619.641 298.404i −0.977352 0.470668i
\(635\) 109.600 313.217i 0.172598 0.493256i
\(636\) 0 0
\(637\) 269.663i 0.423333i
\(638\) 555.172 324.614i 0.870175 0.508800i
\(639\) 0 0
\(640\) −4.38645 + 2.75619i −0.00685383 + 0.00430655i
\(641\) −916.494 320.695i −1.42979 0.500305i −0.499237 0.866466i \(-0.666386\pi\)
−0.930551 + 0.366161i \(0.880672\pi\)
\(642\) 0 0
\(643\) 48.0847 + 10.9750i 0.0747817 + 0.0170684i 0.259748 0.965676i \(-0.416360\pi\)
−0.184966 + 0.982745i \(0.559218\pi\)
\(644\) 12.5941 2.87452i 0.0195561 0.00446355i
\(645\) 0 0
\(646\) −36.7714 326.355i −0.0569216 0.505193i
\(647\) 71.4194 + 56.9551i 0.110386 + 0.0880295i 0.677127 0.735866i \(-0.263225\pi\)
−0.566742 + 0.823896i \(0.691796\pi\)
\(648\) 0 0
\(649\) −70.2180 + 623.202i −0.108194 + 0.960250i
\(650\) 77.9148 77.9148i 0.119869 0.119869i
\(651\) 0 0
\(652\) 52.8342 84.0852i 0.0810341 0.128965i
\(653\) −207.926 130.649i −0.318416 0.200074i 0.363334 0.931659i \(-0.381638\pi\)
−0.681751 + 0.731585i \(0.738781\pi\)
\(654\) 0 0
\(655\) −248.845 248.845i −0.379916 0.379916i
\(656\) 420.063 + 47.3298i 0.640340 + 0.0721490i
\(657\) 0 0
\(658\) 4.69303 5.88488i 0.00713227 0.00894359i
\(659\) 259.653 29.2559i 0.394011 0.0443943i 0.0872632 0.996185i \(-0.472188\pi\)
0.306747 + 0.951791i \(0.400759\pi\)
\(660\) 0 0
\(661\) 217.845 + 954.443i 0.329569 + 1.44394i 0.819953 + 0.572431i \(0.194000\pi\)
−0.490383 + 0.871507i \(0.663143\pi\)
\(662\) 142.010 622.188i 0.214517 0.939862i
\(663\) 0 0
\(664\) −3.03536 + 8.67457i −0.00457133 + 0.0130641i
\(665\) 15.0907 + 24.0167i 0.0226928 + 0.0361154i
\(666\) 0 0
\(667\) 752.999 236.814i 1.12893 0.355044i
\(668\) 135.924 0.203478
\(669\) 0 0
\(670\) 428.420 + 149.911i 0.639432 + 0.223747i
\(671\) −700.629 + 1454.87i −1.04416 + 2.16821i
\(672\) 0 0
\(673\) 593.737 135.517i 0.882225 0.201362i 0.242671 0.970109i \(-0.421976\pi\)
0.639554 + 0.768747i \(0.279119\pi\)
\(674\) −124.899 + 60.1483i −0.185310 + 0.0892408i
\(675\) 0 0
\(676\) −181.217 144.516i −0.268073 0.213781i
\(677\) −559.076 + 195.629i −0.825814 + 0.288965i −0.709907 0.704295i \(-0.751263\pi\)
−0.115907 + 0.993260i \(0.536977\pi\)
\(678\) 0 0
\(679\) −11.6166 + 11.6166i −0.0171084 + 0.0171084i
\(680\) −173.401 + 138.282i −0.255001 + 0.203357i
\(681\) 0 0
\(682\) −287.210 180.466i −0.421130 0.264613i
\(683\) −217.747 273.046i −0.318809 0.399774i 0.596443 0.802656i \(-0.296580\pi\)
−0.915252 + 0.402881i \(0.868009\pi\)
\(684\) 0 0
\(685\) −150.719 16.9819i −0.220027 0.0247911i
\(686\) −14.0043 40.0221i −0.0204145 0.0583413i
\(687\) 0 0
\(688\) 437.520 49.2967i 0.635930 0.0716521i
\(689\) −14.0907 29.2597i −0.0204510 0.0424670i
\(690\) 0 0
\(691\) 181.564 795.482i 0.262755 1.15120i −0.655494 0.755200i \(-0.727540\pi\)
0.918249 0.396004i \(-0.129603\pi\)
\(692\) −51.4288 24.7668i −0.0743191 0.0357902i
\(693\) 0 0
\(694\) −318.669 507.159i −0.459178 0.730777i
\(695\) 209.269i 0.301106i
\(696\) 0 0
\(697\) −482.054 −0.691613
\(698\) −629.276 + 395.400i −0.901541 + 0.566476i
\(699\) 0 0
\(700\) −2.69781 + 5.60206i −0.00385402 + 0.00800295i
\(701\) 924.382 + 210.984i 1.31866 + 0.300976i 0.823249 0.567681i \(-0.192159\pi\)
0.495414 + 0.868657i \(0.335016\pi\)
\(702\) 0 0
\(703\) −712.409 + 343.078i −1.01338 + 0.488020i
\(704\) −103.681 920.193i −0.147274 1.30709i
\(705\) 0 0
\(706\) −145.646 + 50.9638i −0.206298 + 0.0721867i
\(707\) −2.57905 + 22.8897i −0.00364788 + 0.0323758i
\(708\) 0 0
\(709\) −268.833 + 214.387i −0.379172 + 0.302380i −0.794467 0.607307i \(-0.792250\pi\)
0.415295 + 0.909687i \(0.363678\pi\)
\(710\) 161.857 257.593i 0.227967 0.362808i
\(711\) 0 0
\(712\) −469.261 588.435i −0.659075 0.826454i
\(713\) −294.397 294.397i −0.412898 0.412898i
\(714\) 0 0
\(715\) 91.2808 + 260.865i 0.127665 + 0.364847i
\(716\) −75.9664 + 95.2589i −0.106098 + 0.133043i
\(717\) 0 0
\(718\) 23.4227 + 48.6377i 0.0326221 + 0.0677405i
\(719\) 258.798 + 1133.87i 0.359942 + 1.57701i 0.753334 + 0.657639i \(0.228445\pi\)
−0.393391 + 0.919371i \(0.628698\pi\)
\(720\) 0 0
\(721\) −48.2311 23.2269i −0.0668947 0.0322148i
\(722\) −241.079 + 688.965i −0.333905 + 0.954246i
\(723\) 0 0
\(724\) 210.665i 0.290973i
\(725\) −136.861 + 354.437i −0.188773 + 0.488878i
\(726\) 0 0
\(727\) 606.627 381.169i 0.834425 0.524304i −0.0457500 0.998953i \(-0.514568\pi\)
0.880175 + 0.474649i \(0.157425\pi\)
\(728\) 12.7797 + 4.47180i 0.0175545 + 0.00614259i
\(729\) 0 0
\(730\) 254.750 + 58.1451i 0.348973 + 0.0796508i
\(731\) −489.499 + 111.725i −0.669629 + 0.152838i
\(732\) 0 0
\(733\) −5.44223 48.3011i −0.00742460 0.0658951i 0.989454 0.144850i \(-0.0462701\pi\)
−0.996878 + 0.0789554i \(0.974842\pi\)
\(734\) −274.900 219.226i −0.374524 0.298673i
\(735\) 0 0
\(736\) 75.2034 667.449i 0.102179 0.906860i
\(737\) 886.392 886.392i 1.20270 1.20270i
\(738\) 0 0
\(739\) 266.443 424.041i 0.360545 0.573804i −0.616364 0.787462i \(-0.711395\pi\)
0.976909 + 0.213658i \(0.0685378\pi\)
\(740\) 133.291 + 83.7524i 0.180123 + 0.113179i
\(741\) 0 0
\(742\) −1.80393 1.80393i −0.00243117 0.00243117i
\(743\) 353.124 + 39.7875i 0.475267 + 0.0535498i 0.346350 0.938106i \(-0.387421\pi\)
0.128918 + 0.991655i \(0.458850\pi\)
\(744\) 0 0
\(745\) −211.208 + 264.846i −0.283500 + 0.355498i
\(746\) 678.050 76.3979i 0.908914 0.102410i
\(747\) 0 0
\(748\) 40.1818 + 176.048i 0.0537190 + 0.235358i
\(749\) 1.74823 7.65949i 0.00233408 0.0102263i
\(750\) 0 0
\(751\) −225.087 + 643.260i −0.299716 + 0.856539i 0.691273 + 0.722594i \(0.257050\pi\)
−0.990989 + 0.133945i \(0.957235\pi\)
\(752\) −60.2523 95.8910i −0.0801228 0.127515i
\(753\) 0 0
\(754\) 235.934 + 61.8290i 0.312909 + 0.0820013i
\(755\) −8.08599 −0.0107099
\(756\) 0 0
\(757\) −546.623 191.272i −0.722091 0.252671i −0.0558840 0.998437i \(-0.517798\pi\)
−0.666207 + 0.745767i \(0.732083\pi\)
\(758\) −168.188 + 349.246i −0.221884 + 0.460747i
\(759\) 0 0
\(760\) 843.203 192.456i 1.10948 0.253231i
\(761\) −918.062 + 442.116i −1.20639 + 0.580966i −0.925490 0.378771i \(-0.876347\pi\)
−0.280899 + 0.959737i \(0.590633\pi\)
\(762\) 0 0
\(763\) 20.7545 + 16.5512i 0.0272012 + 0.0216922i
\(764\) −240.749 + 84.2416i −0.315116 + 0.110264i
\(765\) 0 0
\(766\) 238.454 238.454i 0.311298 0.311298i
\(767\) −185.956 + 148.295i −0.242446 + 0.193344i
\(768\) 0 0
\(769\) 165.357 + 103.901i 0.215028 + 0.135111i 0.635240 0.772315i \(-0.280901\pi\)
−0.420211 + 0.907426i \(0.638044\pi\)
\(770\) 13.5363 + 16.9740i 0.0175796 + 0.0220442i
\(771\) 0 0
\(772\) −335.679 37.8219i −0.434817 0.0489921i
\(773\) −269.245 769.458i −0.348312 0.995418i −0.976154 0.217078i \(-0.930347\pi\)
0.627842 0.778341i \(-0.283938\pi\)
\(774\) 0 0
\(775\) 199.137 22.4373i 0.256951 0.0289514i
\(776\) 217.348 + 451.327i 0.280087 + 0.581607i
\(777\) 0 0
\(778\) −196.236 + 859.766i −0.252231 + 1.10510i
\(779\) 1693.66 + 815.626i 2.17415 + 1.04702i
\(780\) 0 0
\(781\) −447.013 711.417i −0.572360 0.910906i
\(782\) 308.545i 0.394559i
\(783\) 0 0
\(784\) −318.718 −0.406527
\(785\) −228.805 + 143.768i −0.291472 + 0.183144i
\(786\) 0 0
\(787\) 354.355 735.826i 0.450261