Properties

Label 1386.2.ba.a.989.5
Level $1386$
Weight $2$
Character 1386.989
Analytic conductor $11.067$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.ba (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 989.5
Character \(\chi\) \(=\) 1386.989
Dual form 1386.2.ba.a.1187.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.78334 - 1.02961i) q^{5} +(0.289722 - 2.62984i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.78334 - 1.02961i) q^{5} +(0.289722 - 2.62984i) q^{7} +1.00000 q^{8} +(1.78334 - 1.02961i) q^{10} +(1.29385 - 3.05384i) q^{11} +6.97891i q^{13} +(2.13265 + 1.56583i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.66515 - 4.61618i) q^{17} +(7.36851 + 4.25421i) q^{19} +2.05923i q^{20} +(1.99778 + 2.64743i) q^{22} +(-1.35506 - 0.782344i) q^{23} +(-0.379791 - 0.657818i) q^{25} +(-6.04391 - 3.48945i) q^{26} +(-2.42237 + 1.06401i) q^{28} +2.87708 q^{29} +(-4.39314 - 7.60915i) q^{31} +(-0.500000 - 0.866025i) q^{32} +5.33030 q^{34} +(-3.22439 + 4.39161i) q^{35} +(-1.82231 + 3.15633i) q^{37} +(-7.36851 + 4.25421i) q^{38} +(-1.78334 - 1.02961i) q^{40} -2.42621 q^{41} -7.55213i q^{43} +(-3.29163 + 0.406418i) q^{44} +(1.35506 - 0.782344i) q^{46} +(-10.2450 - 5.91497i) q^{47} +(-6.83212 - 1.52384i) q^{49} +0.759582 q^{50} +(6.04391 - 3.48945i) q^{52} +(-9.93207 + 5.73428i) q^{53} +(-5.45165 + 4.11389i) q^{55} +(0.289722 - 2.62984i) q^{56} +(-1.43854 + 2.49162i) q^{58} +(3.49197 - 2.01609i) q^{59} +(-4.39206 - 2.53576i) q^{61} +8.78629 q^{62} +1.00000 q^{64} +(7.18558 - 12.4458i) q^{65} +(-4.75461 - 8.23523i) q^{67} +(-2.66515 + 4.61618i) q^{68} +(-2.19105 - 4.98821i) q^{70} -3.30443i q^{71} +(-0.828178 + 0.478149i) q^{73} +(-1.82231 - 3.15633i) q^{74} -8.50842i q^{76} +(-7.65627 - 4.28737i) q^{77} +(7.75287 + 4.47612i) q^{79} +(1.78334 - 1.02961i) q^{80} +(1.21310 - 2.10116i) q^{82} -7.50706 q^{83} +10.9763i q^{85} +(6.54033 + 3.77606i) q^{86} +(1.29385 - 3.05384i) q^{88} +(2.99174 + 1.72728i) q^{89} +(18.3534 + 2.02194i) q^{91} +1.56469i q^{92} +(10.2450 - 5.91497i) q^{94} +(-8.76039 - 15.1734i) q^{95} -5.95332 q^{97} +(4.73575 - 5.15487i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} + O(q^{10}) \) \( 32q - 16q^{2} - 16q^{4} + 32q^{8} - 2q^{11} - 16q^{16} - 4q^{17} + 4q^{22} + 4q^{25} - 16q^{29} + 4q^{31} - 16q^{32} + 8q^{34} - 16q^{35} + 4q^{37} + 32q^{41} - 2q^{44} + 20q^{49} - 8q^{50} - 12q^{55} + 8q^{58} - 8q^{62} + 32q^{64} - 8q^{67} - 4q^{68} - 4q^{70} + 4q^{74} - 14q^{77} - 16q^{82} - 88q^{83} - 2q^{88} + 24q^{95} - 32q^{97} + 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −1.78334 1.02961i −0.797535 0.460457i 0.0450733 0.998984i \(-0.485648\pi\)
−0.842609 + 0.538526i \(0.818981\pi\)
\(6\) 0 0
\(7\) 0.289722 2.62984i 0.109504 0.993986i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.78334 1.02961i 0.563943 0.325592i
\(11\) 1.29385 3.05384i 0.390109 0.920768i
\(12\) 0 0
\(13\) 6.97891i 1.93560i 0.251719 + 0.967800i \(0.419004\pi\)
−0.251719 + 0.967800i \(0.580996\pi\)
\(14\) 2.13265 + 1.56583i 0.569974 + 0.418485i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.66515 4.61618i −0.646394 1.11959i −0.983978 0.178292i \(-0.942943\pi\)
0.337584 0.941295i \(-0.390390\pi\)
\(18\) 0 0
\(19\) 7.36851 + 4.25421i 1.69045 + 0.975983i 0.954149 + 0.299331i \(0.0967636\pi\)
0.736303 + 0.676652i \(0.236570\pi\)
\(20\) 2.05923i 0.460457i
\(21\) 0 0
\(22\) 1.99778 + 2.64743i 0.425929 + 0.564433i
\(23\) −1.35506 0.782344i −0.282549 0.163130i 0.352028 0.935990i \(-0.385492\pi\)
−0.634577 + 0.772860i \(0.718826\pi\)
\(24\) 0 0
\(25\) −0.379791 0.657818i −0.0759582 0.131564i
\(26\) −6.04391 3.48945i −1.18531 0.684338i
\(27\) 0 0
\(28\) −2.42237 + 1.06401i −0.457785 + 0.201080i
\(29\) 2.87708 0.534260 0.267130 0.963660i \(-0.413925\pi\)
0.267130 + 0.963660i \(0.413925\pi\)
\(30\) 0 0
\(31\) −4.39314 7.60915i −0.789032 1.36664i −0.926561 0.376145i \(-0.877249\pi\)
0.137529 0.990498i \(-0.456084\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 5.33030 0.914139
\(35\) −3.22439 + 4.39161i −0.545022 + 0.742317i
\(36\) 0 0
\(37\) −1.82231 + 3.15633i −0.299585 + 0.518897i −0.976041 0.217586i \(-0.930182\pi\)
0.676456 + 0.736483i \(0.263515\pi\)
\(38\) −7.36851 + 4.25421i −1.19533 + 0.690124i
\(39\) 0 0
\(40\) −1.78334 1.02961i −0.281971 0.162796i
\(41\) −2.42621 −0.378910 −0.189455 0.981889i \(-0.560672\pi\)
−0.189455 + 0.981889i \(0.560672\pi\)
\(42\) 0 0
\(43\) 7.55213i 1.15169i −0.817559 0.575844i \(-0.804673\pi\)
0.817559 0.575844i \(-0.195327\pi\)
\(44\) −3.29163 + 0.406418i −0.496232 + 0.0612698i
\(45\) 0 0
\(46\) 1.35506 0.782344i 0.199793 0.115350i
\(47\) −10.2450 5.91497i −1.49439 0.862787i −0.494412 0.869228i \(-0.664616\pi\)
−0.999979 + 0.00644106i \(0.997950\pi\)
\(48\) 0 0
\(49\) −6.83212 1.52384i −0.976018 0.217692i
\(50\) 0.759582 0.107421
\(51\) 0 0
\(52\) 6.04391 3.48945i 0.838140 0.483900i
\(53\) −9.93207 + 5.73428i −1.36427 + 0.787664i −0.990190 0.139730i \(-0.955376\pi\)
−0.374085 + 0.927395i \(0.622043\pi\)
\(54\) 0 0
\(55\) −5.45165 + 4.11389i −0.735101 + 0.554717i
\(56\) 0.289722 2.62984i 0.0387157 0.351427i
\(57\) 0 0
\(58\) −1.43854 + 2.49162i −0.188890 + 0.327166i
\(59\) 3.49197 2.01609i 0.454616 0.262473i −0.255162 0.966898i \(-0.582129\pi\)
0.709778 + 0.704426i \(0.248795\pi\)
\(60\) 0 0
\(61\) −4.39206 2.53576i −0.562346 0.324670i 0.191741 0.981446i \(-0.438587\pi\)
−0.754086 + 0.656775i \(0.771920\pi\)
\(62\) 8.78629 1.11586
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 7.18558 12.4458i 0.891261 1.54371i
\(66\) 0 0
\(67\) −4.75461 8.23523i −0.580868 1.00609i −0.995377 0.0960479i \(-0.969380\pi\)
0.414508 0.910045i \(-0.363954\pi\)
\(68\) −2.66515 + 4.61618i −0.323197 + 0.559794i
\(69\) 0 0
\(70\) −2.19105 4.98821i −0.261880 0.596205i
\(71\) 3.30443i 0.392163i −0.980588 0.196082i \(-0.937178\pi\)
0.980588 0.196082i \(-0.0628217\pi\)
\(72\) 0 0
\(73\) −0.828178 + 0.478149i −0.0969309 + 0.0559631i −0.547682 0.836687i \(-0.684490\pi\)
0.450751 + 0.892650i \(0.351156\pi\)
\(74\) −1.82231 3.15633i −0.211839 0.366915i
\(75\) 0 0
\(76\) 8.50842i 0.975983i
\(77\) −7.65627 4.28737i −0.872513 0.488592i
\(78\) 0 0
\(79\) 7.75287 + 4.47612i 0.872266 + 0.503603i 0.868101 0.496388i \(-0.165341\pi\)
0.00416551 + 0.999991i \(0.498674\pi\)
\(80\) 1.78334 1.02961i 0.199384 0.115114i
\(81\) 0 0
\(82\) 1.21310 2.10116i 0.133965 0.232034i
\(83\) −7.50706 −0.824007 −0.412003 0.911182i \(-0.635171\pi\)
−0.412003 + 0.911182i \(0.635171\pi\)
\(84\) 0 0
\(85\) 10.9763i 1.19055i
\(86\) 6.54033 + 3.77606i 0.705262 + 0.407183i
\(87\) 0 0
\(88\) 1.29385 3.05384i 0.137925 0.325541i
\(89\) 2.99174 + 1.72728i 0.317124 + 0.183092i 0.650110 0.759840i \(-0.274723\pi\)
−0.332986 + 0.942932i \(0.608056\pi\)
\(90\) 0 0
\(91\) 18.3534 + 2.02194i 1.92396 + 0.211957i
\(92\) 1.56469i 0.163130i
\(93\) 0 0
\(94\) 10.2450 5.91497i 1.05669 0.610082i
\(95\) −8.76039 15.1734i −0.898797 1.55676i
\(96\) 0 0
\(97\) −5.95332 −0.604468 −0.302234 0.953234i \(-0.597732\pi\)
−0.302234 + 0.953234i \(0.597732\pi\)
\(98\) 4.73575 5.15487i 0.478383 0.520721i
\(99\) 0 0
\(100\) −0.379791 + 0.657818i −0.0379791 + 0.0657818i
\(101\) −1.95460 3.38547i −0.194490 0.336867i 0.752243 0.658886i \(-0.228972\pi\)
−0.946733 + 0.322019i \(0.895639\pi\)
\(102\) 0 0
\(103\) 1.72042 2.97985i 0.169518 0.293614i −0.768733 0.639570i \(-0.779112\pi\)
0.938250 + 0.345957i \(0.112446\pi\)
\(104\) 6.97891i 0.684338i
\(105\) 0 0
\(106\) 11.4686i 1.11393i
\(107\) −1.00997 + 1.74932i −0.0976377 + 0.169114i −0.910706 0.413054i \(-0.864462\pi\)
0.813069 + 0.582168i \(0.197795\pi\)
\(108\) 0 0
\(109\) −3.05488 + 1.76373i −0.292604 + 0.168935i −0.639116 0.769111i \(-0.720699\pi\)
0.346512 + 0.938046i \(0.387366\pi\)
\(110\) −0.836906 6.77821i −0.0797959 0.646277i
\(111\) 0 0
\(112\) 2.13265 + 1.56583i 0.201516 + 0.147957i
\(113\) 7.60125i 0.715065i −0.933901 0.357533i \(-0.883618\pi\)
0.933901 0.357533i \(-0.116382\pi\)
\(114\) 0 0
\(115\) 1.61102 + 2.79038i 0.150229 + 0.260204i
\(116\) −1.43854 2.49162i −0.133565 0.231342i
\(117\) 0 0
\(118\) 4.03218i 0.371193i
\(119\) −12.9120 + 5.67151i −1.18364 + 0.519907i
\(120\) 0 0
\(121\) −7.65192 7.90241i −0.695629 0.718401i
\(122\) 4.39206 2.53576i 0.397638 0.229577i
\(123\) 0 0
\(124\) −4.39314 + 7.60915i −0.394516 + 0.683322i
\(125\) 11.8603i 1.06082i
\(126\) 0 0
\(127\) 6.33932i 0.562523i −0.959631 0.281262i \(-0.909247\pi\)
0.959631 0.281262i \(-0.0907529\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 7.18558 + 12.4458i 0.630217 + 1.09157i
\(131\) −6.50013 + 11.2586i −0.567919 + 0.983664i 0.428853 + 0.903374i \(0.358918\pi\)
−0.996772 + 0.0802898i \(0.974415\pi\)
\(132\) 0 0
\(133\) 13.3227 18.1455i 1.15523 1.57341i
\(134\) 9.50922 0.821472
\(135\) 0 0
\(136\) −2.66515 4.61618i −0.228535 0.395834i
\(137\) 7.97258 4.60297i 0.681144 0.393258i −0.119142 0.992877i \(-0.538014\pi\)
0.800286 + 0.599619i \(0.204681\pi\)
\(138\) 0 0
\(139\) 18.5202i 1.57087i 0.618946 + 0.785433i \(0.287560\pi\)
−0.618946 + 0.785433i \(0.712440\pi\)
\(140\) 5.41544 + 0.596603i 0.457688 + 0.0504221i
\(141\) 0 0
\(142\) 2.86172 + 1.65221i 0.240150 + 0.138651i
\(143\) 21.3125 + 9.02964i 1.78224 + 0.755096i
\(144\) 0 0
\(145\) −5.13082 2.96228i −0.426092 0.246004i
\(146\) 0.956297i 0.0791437i
\(147\) 0 0
\(148\) 3.64461 0.299585
\(149\) 6.04969 10.4784i 0.495610 0.858422i −0.504377 0.863483i \(-0.668278\pi\)
0.999987 + 0.00506166i \(0.00161118\pi\)
\(150\) 0 0
\(151\) −4.47659 + 2.58456i −0.364300 + 0.210329i −0.670965 0.741489i \(-0.734120\pi\)
0.306665 + 0.951817i \(0.400787\pi\)
\(152\) 7.36851 + 4.25421i 0.597665 + 0.345062i
\(153\) 0 0
\(154\) 7.54111 4.48683i 0.607680 0.361559i
\(155\) 18.0930i 1.45326i
\(156\) 0 0
\(157\) 0.478738 + 0.829198i 0.0382074 + 0.0661772i 0.884497 0.466546i \(-0.154502\pi\)
−0.846289 + 0.532724i \(0.821169\pi\)
\(158\) −7.75287 + 4.47612i −0.616785 + 0.356101i
\(159\) 0 0
\(160\) 2.05923i 0.162796i
\(161\) −2.45003 + 3.33693i −0.193089 + 0.262987i
\(162\) 0 0
\(163\) 8.54401 14.7987i 0.669219 1.15912i −0.308904 0.951093i \(-0.599962\pi\)
0.978123 0.208027i \(-0.0667043\pi\)
\(164\) 1.21310 + 2.10116i 0.0947274 + 0.164073i
\(165\) 0 0
\(166\) 3.75353 6.50130i 0.291330 0.504599i
\(167\) 17.6200 1.36348 0.681738 0.731596i \(-0.261224\pi\)
0.681738 + 0.731596i \(0.261224\pi\)
\(168\) 0 0
\(169\) −35.7051 −2.74655
\(170\) −9.50576 5.48815i −0.729058 0.420922i
\(171\) 0 0
\(172\) −6.54033 + 3.77606i −0.498696 + 0.287922i
\(173\) −8.05455 + 13.9509i −0.612376 + 1.06067i 0.378462 + 0.925617i \(0.376453\pi\)
−0.990839 + 0.135050i \(0.956880\pi\)
\(174\) 0 0
\(175\) −1.83999 + 0.808206i −0.139090 + 0.0610947i
\(176\) 1.99778 + 2.64743i 0.150589 + 0.199557i
\(177\) 0 0
\(178\) −2.99174 + 1.72728i −0.224241 + 0.129465i
\(179\) 7.99155 4.61392i 0.597316 0.344861i −0.170669 0.985328i \(-0.554593\pi\)
0.767985 + 0.640468i \(0.221259\pi\)
\(180\) 0 0
\(181\) 5.46346 0.406096 0.203048 0.979169i \(-0.434915\pi\)
0.203048 + 0.979169i \(0.434915\pi\)
\(182\) −10.9278 + 14.8836i −0.810019 + 1.10324i
\(183\) 0 0
\(184\) −1.35506 0.782344i −0.0998963 0.0576752i
\(185\) 6.49959 3.75254i 0.477859 0.275892i
\(186\) 0 0
\(187\) −17.5454 + 2.16633i −1.28304 + 0.158418i
\(188\) 11.8299i 0.862787i
\(189\) 0 0
\(190\) 17.5208 1.27109
\(191\) −17.8512 10.3064i −1.29167 0.745746i −0.312720 0.949845i \(-0.601240\pi\)
−0.978950 + 0.204099i \(0.934573\pi\)
\(192\) 0 0
\(193\) 11.2631 6.50274i 0.810734 0.468077i −0.0364770 0.999334i \(-0.511614\pi\)
0.847211 + 0.531257i \(0.178280\pi\)
\(194\) 2.97666 5.15573i 0.213712 0.370160i
\(195\) 0 0
\(196\) 2.09637 + 6.67871i 0.149741 + 0.477051i
\(197\) −18.4806 −1.31669 −0.658345 0.752716i \(-0.728743\pi\)
−0.658345 + 0.752716i \(0.728743\pi\)
\(198\) 0 0
\(199\) 5.65478 + 9.79436i 0.400856 + 0.694304i 0.993829 0.110919i \(-0.0353793\pi\)
−0.592973 + 0.805222i \(0.702046\pi\)
\(200\) −0.379791 0.657818i −0.0268553 0.0465147i
\(201\) 0 0
\(202\) 3.90921 0.275051
\(203\) 0.833552 7.56626i 0.0585039 0.531048i
\(204\) 0 0
\(205\) 4.32676 + 2.49806i 0.302194 + 0.174472i
\(206\) 1.72042 + 2.97985i 0.119867 + 0.207616i
\(207\) 0 0
\(208\) −6.04391 3.48945i −0.419070 0.241950i
\(209\) 22.5254 16.9980i 1.55812 1.17578i
\(210\) 0 0
\(211\) 21.8547i 1.50454i −0.658854 0.752271i \(-0.728959\pi\)
0.658854 0.752271i \(-0.271041\pi\)
\(212\) 9.93207 + 5.73428i 0.682137 + 0.393832i
\(213\) 0 0
\(214\) −1.00997 1.74932i −0.0690403 0.119581i
\(215\) −7.77577 + 13.4680i −0.530303 + 0.918512i
\(216\) 0 0
\(217\) −21.2836 + 9.34873i −1.44483 + 0.634633i
\(218\) 3.52747i 0.238910i
\(219\) 0 0
\(220\) 6.28856 + 2.66432i 0.423975 + 0.179629i
\(221\) 32.2159 18.5998i 2.16707 1.25116i
\(222\) 0 0
\(223\) −18.3441 −1.22841 −0.614207 0.789145i \(-0.710524\pi\)
−0.614207 + 0.789145i \(0.710524\pi\)
\(224\) −2.42237 + 1.06401i −0.161851 + 0.0710924i
\(225\) 0 0
\(226\) 6.58287 + 3.80062i 0.437886 + 0.252814i
\(227\) −0.871542 1.50956i −0.0578463 0.100193i 0.835652 0.549259i \(-0.185090\pi\)
−0.893498 + 0.449066i \(0.851757\pi\)
\(228\) 0 0
\(229\) 14.1778 24.5567i 0.936895 1.62275i 0.165676 0.986180i \(-0.447019\pi\)
0.771219 0.636570i \(-0.219647\pi\)
\(230\) −3.22205 −0.212456
\(231\) 0 0
\(232\) 2.87708 0.188890
\(233\) 10.4076 18.0264i 0.681823 1.18095i −0.292601 0.956235i \(-0.594521\pi\)
0.974424 0.224717i \(-0.0721458\pi\)
\(234\) 0 0
\(235\) 12.1803 + 21.0968i 0.794553 + 1.37621i
\(236\) −3.49197 2.01609i −0.227308 0.131236i
\(237\) 0 0
\(238\) 1.54430 14.0178i 0.100102 0.908642i
\(239\) 7.45803 0.482420 0.241210 0.970473i \(-0.422456\pi\)
0.241210 + 0.970473i \(0.422456\pi\)
\(240\) 0 0
\(241\) 5.76722 3.32971i 0.371500 0.214485i −0.302614 0.953113i \(-0.597859\pi\)
0.674113 + 0.738628i \(0.264526\pi\)
\(242\) 10.6696 2.67555i 0.685871 0.171991i
\(243\) 0 0
\(244\) 5.07151i 0.324670i
\(245\) 10.6151 + 9.75198i 0.678171 + 0.623031i
\(246\) 0 0
\(247\) −29.6897 + 51.4242i −1.88911 + 3.27204i
\(248\) −4.39314 7.60915i −0.278965 0.483181i
\(249\) 0 0
\(250\) −10.2713 5.93015i −0.649615 0.375055i
\(251\) 19.8684i 1.25408i 0.778986 + 0.627042i \(0.215734\pi\)
−0.778986 + 0.627042i \(0.784266\pi\)
\(252\) 0 0
\(253\) −4.14240 + 3.12591i −0.260430 + 0.196524i
\(254\) 5.49001 + 3.16966i 0.344474 + 0.198882i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 19.1251 + 11.0419i 1.19299 + 0.688773i 0.958983 0.283463i \(-0.0914832\pi\)
0.234006 + 0.972235i \(0.424817\pi\)
\(258\) 0 0
\(259\) 7.77267 + 5.70683i 0.482970 + 0.354605i
\(260\) −14.3712 −0.891261
\(261\) 0 0
\(262\) −6.50013 11.2586i −0.401579 0.695556i
\(263\) −5.60069 9.70067i −0.345353 0.598169i 0.640065 0.768321i \(-0.278907\pi\)
−0.985418 + 0.170152i \(0.945574\pi\)
\(264\) 0 0
\(265\) 23.6164 1.45074
\(266\) 9.05308 + 20.6105i 0.555080 + 1.26371i
\(267\) 0 0
\(268\) −4.75461 + 8.23523i −0.290434 + 0.503047i
\(269\) 3.35811 1.93880i 0.204747 0.118211i −0.394121 0.919059i \(-0.628951\pi\)
0.598868 + 0.800848i \(0.295617\pi\)
\(270\) 0 0
\(271\) 2.49796 + 1.44220i 0.151740 + 0.0876073i 0.573948 0.818892i \(-0.305411\pi\)
−0.422207 + 0.906499i \(0.638745\pi\)
\(272\) 5.33030 0.323197
\(273\) 0 0
\(274\) 9.20594i 0.556151i
\(275\) −2.50026 + 0.308708i −0.150772 + 0.0186158i
\(276\) 0 0
\(277\) −18.4381 + 10.6453i −1.10784 + 0.639612i −0.938269 0.345906i \(-0.887572\pi\)
−0.169571 + 0.985518i \(0.554238\pi\)
\(278\) −16.0390 9.26012i −0.961955 0.555385i
\(279\) 0 0
\(280\) −3.22439 + 4.39161i −0.192694 + 0.262449i
\(281\) −14.7696 −0.881078 −0.440539 0.897733i \(-0.645213\pi\)
−0.440539 + 0.897733i \(0.645213\pi\)
\(282\) 0 0
\(283\) −0.509546 + 0.294187i −0.0302894 + 0.0174876i −0.515068 0.857149i \(-0.672233\pi\)
0.484779 + 0.874637i \(0.338900\pi\)
\(284\) −2.86172 + 1.65221i −0.169812 + 0.0980408i
\(285\) 0 0
\(286\) −18.4761 + 13.9423i −1.09252 + 0.824428i
\(287\) −0.702924 + 6.38054i −0.0414923 + 0.376631i
\(288\) 0 0
\(289\) −5.70605 + 9.88317i −0.335650 + 0.581363i
\(290\) 5.13082 2.96228i 0.301292 0.173951i
\(291\) 0 0
\(292\) 0.828178 + 0.478149i 0.0484654 + 0.0279815i
\(293\) 1.57886 0.0922380 0.0461190 0.998936i \(-0.485315\pi\)
0.0461190 + 0.998936i \(0.485315\pi\)
\(294\) 0 0
\(295\) −8.30318 −0.483430
\(296\) −1.82231 + 3.15633i −0.105919 + 0.183458i
\(297\) 0 0
\(298\) 6.04969 + 10.4784i 0.350449 + 0.606996i
\(299\) 5.45991 9.45683i 0.315754 0.546903i
\(300\) 0 0
\(301\) −19.8609 2.18801i −1.14476 0.126115i
\(302\) 5.16913i 0.297450i
\(303\) 0 0
\(304\) −7.36851 + 4.25421i −0.422613 + 0.243996i
\(305\) 5.22170 + 9.04425i 0.298994 + 0.517872i
\(306\) 0 0
\(307\) 14.9956i 0.855842i 0.903816 + 0.427921i \(0.140754\pi\)
−0.903816 + 0.427921i \(0.859246\pi\)
\(308\) 0.115158 + 8.77421i 0.00656171 + 0.499957i
\(309\) 0 0
\(310\) −15.6690 9.04648i −0.889937 0.513806i
\(311\) −9.46660 + 5.46555i −0.536802 + 0.309923i −0.743782 0.668422i \(-0.766970\pi\)
0.206980 + 0.978345i \(0.433637\pi\)
\(312\) 0 0
\(313\) 6.10928 10.5816i 0.345317 0.598107i −0.640094 0.768296i \(-0.721105\pi\)
0.985411 + 0.170190i \(0.0544380\pi\)
\(314\) −0.957476 −0.0540335
\(315\) 0 0
\(316\) 8.95224i 0.503603i
\(317\) 19.9526 + 11.5197i 1.12065 + 0.647008i 0.941567 0.336826i \(-0.109353\pi\)
0.179084 + 0.983834i \(0.442687\pi\)
\(318\) 0 0
\(319\) 3.72250 8.78615i 0.208420 0.491930i
\(320\) −1.78334 1.02961i −0.0996919 0.0575572i
\(321\) 0 0
\(322\) −1.66485 3.79025i −0.0927785 0.211222i
\(323\) 45.3525i 2.52348i
\(324\) 0 0
\(325\) 4.59085 2.65053i 0.254654 0.147025i
\(326\) 8.54401 + 14.7987i 0.473209 + 0.819622i
\(327\) 0 0
\(328\) −2.42621 −0.133965
\(329\) −18.5236 + 25.2291i −1.02124 + 1.39092i
\(330\) 0 0
\(331\) −0.855231 + 1.48130i −0.0470077 + 0.0814198i −0.888572 0.458737i \(-0.848302\pi\)
0.841564 + 0.540157i \(0.181635\pi\)
\(332\) 3.75353 + 6.50130i 0.206002 + 0.356805i
\(333\) 0 0
\(334\) −8.81000 + 15.2594i −0.482062 + 0.834956i
\(335\) 19.5817i 1.06986i
\(336\) 0 0
\(337\) 4.45772i 0.242828i 0.992602 + 0.121414i \(0.0387428\pi\)
−0.992602 + 0.121414i \(0.961257\pi\)
\(338\) 17.8526 30.9216i 0.971052 1.68191i
\(339\) 0 0
\(340\) 9.50576 5.48815i 0.515522 0.297637i
\(341\) −28.9212 + 3.57090i −1.56617 + 0.193375i
\(342\) 0 0
\(343\) −5.98688 + 17.5259i −0.323261 + 0.946310i
\(344\) 7.55213i 0.407183i
\(345\) 0 0
\(346\) −8.05455 13.9509i −0.433016 0.750005i
\(347\) −9.27272 16.0608i −0.497786 0.862190i 0.502211 0.864745i \(-0.332520\pi\)
−0.999997 + 0.00255476i \(0.999187\pi\)
\(348\) 0 0
\(349\) 16.0494i 0.859104i −0.903042 0.429552i \(-0.858671\pi\)
0.903042 0.429552i \(-0.141329\pi\)
\(350\) 0.220067 1.99758i 0.0117631 0.106775i
\(351\) 0 0
\(352\) −3.29163 + 0.406418i −0.175444 + 0.0216621i
\(353\) 5.81710 3.35850i 0.309613 0.178755i −0.337140 0.941454i \(-0.609460\pi\)
0.646753 + 0.762699i \(0.276126\pi\)
\(354\) 0 0
\(355\) −3.40228 + 5.89292i −0.180574 + 0.312764i
\(356\) 3.45457i 0.183092i
\(357\) 0 0
\(358\) 9.22784i 0.487707i
\(359\) −17.4909 + 30.2952i −0.923136 + 1.59892i −0.128605 + 0.991696i \(0.541050\pi\)
−0.794531 + 0.607223i \(0.792283\pi\)
\(360\) 0 0
\(361\) 26.6966 + 46.2399i 1.40509 + 2.43368i
\(362\) −2.73173 + 4.73150i −0.143577 + 0.248682i
\(363\) 0 0
\(364\) −7.42565 16.9055i −0.389210 0.886089i
\(365\) 1.96923 0.103074
\(366\) 0 0
\(367\) 1.89294 + 3.27867i 0.0988107 + 0.171145i 0.911193 0.411981i \(-0.135163\pi\)
−0.812382 + 0.583126i \(0.801830\pi\)
\(368\) 1.35506 0.782344i 0.0706374 0.0407825i
\(369\) 0 0
\(370\) 7.50508i 0.390171i
\(371\) 12.2027 + 27.7811i 0.633533 + 1.44232i
\(372\) 0 0
\(373\) −16.3482 9.43867i −0.846480 0.488716i 0.0129814 0.999916i \(-0.495868\pi\)
−0.859462 + 0.511200i \(0.829201\pi\)
\(374\) 6.89659 16.2779i 0.356614 0.841710i
\(375\) 0 0
\(376\) −10.2450 5.91497i −0.528347 0.305041i
\(377\) 20.0789i 1.03411i
\(378\) 0 0
\(379\) 14.1679 0.727755 0.363878 0.931447i \(-0.381453\pi\)
0.363878 + 0.931447i \(0.381453\pi\)
\(380\) −8.76039 + 15.1734i −0.449399 + 0.778381i
\(381\) 0 0
\(382\) 17.8512 10.3064i 0.913349 0.527322i
\(383\) 23.0987 + 13.3360i 1.18029 + 0.681439i 0.956081 0.293103i \(-0.0946879\pi\)
0.224206 + 0.974542i \(0.428021\pi\)
\(384\) 0 0
\(385\) 9.23941 + 15.5289i 0.470884 + 0.791424i
\(386\) 13.0055i 0.661961i
\(387\) 0 0
\(388\) 2.97666 + 5.15573i 0.151117 + 0.261742i
\(389\) 2.99247 1.72771i 0.151724 0.0875981i −0.422216 0.906495i \(-0.638748\pi\)
0.573940 + 0.818897i \(0.305414\pi\)
\(390\) 0 0
\(391\) 8.34026i 0.421785i
\(392\) −6.83212 1.52384i −0.345074 0.0769657i
\(393\) 0 0
\(394\) 9.24031 16.0047i 0.465520 0.806305i
\(395\) −9.21735 15.9649i −0.463775 0.803283i
\(396\) 0 0
\(397\) 11.1910 19.3833i 0.561659 0.972822i −0.435693 0.900096i \(-0.643497\pi\)
0.997352 0.0727269i \(-0.0231701\pi\)
\(398\) −11.3096 −0.566897
\(399\) 0 0
\(400\) 0.759582 0.0379791
\(401\) −5.81710 3.35850i −0.290492 0.167716i 0.347672 0.937616i \(-0.386972\pi\)
−0.638164 + 0.769901i \(0.720306\pi\)
\(402\) 0 0
\(403\) 53.1035 30.6593i 2.64528 1.52725i
\(404\) −1.95460 + 3.38547i −0.0972451 + 0.168434i
\(405\) 0 0
\(406\) 6.13580 + 4.50501i 0.304515 + 0.223580i
\(407\) 7.28114 + 9.64884i 0.360913 + 0.478275i
\(408\) 0 0
\(409\) 1.30162 0.751492i 0.0643611 0.0371589i −0.467474 0.884007i \(-0.654836\pi\)
0.531835 + 0.846848i \(0.321503\pi\)
\(410\) −4.32676 + 2.49806i −0.213683 + 0.123370i
\(411\) 0 0
\(412\) −3.44084 −0.169518
\(413\) −4.29030 9.76744i −0.211112 0.480624i
\(414\) 0 0
\(415\) 13.3877 + 7.72937i 0.657175 + 0.379420i
\(416\) 6.04391 3.48945i 0.296327 0.171085i
\(417\) 0 0
\(418\) 3.45797 + 28.0066i 0.169135 + 1.36985i
\(419\) 15.6194i 0.763058i 0.924357 + 0.381529i \(0.124602\pi\)
−0.924357 + 0.381529i \(0.875398\pi\)
\(420\) 0 0
\(421\) 9.70442 0.472965 0.236482 0.971636i \(-0.424005\pi\)
0.236482 + 0.971636i \(0.424005\pi\)
\(422\) 18.9267 + 10.9274i 0.921339 + 0.531936i
\(423\) 0 0
\(424\) −9.93207 + 5.73428i −0.482344 + 0.278481i
\(425\) −2.02440 + 3.50637i −0.0981979 + 0.170084i
\(426\) 0 0
\(427\) −7.94111 + 10.8158i −0.384297 + 0.523411i
\(428\) 2.01995 0.0976377
\(429\) 0 0
\(430\) −7.77577 13.4680i −0.374981 0.649486i
\(431\) 11.7521 + 20.3553i 0.566081 + 0.980480i 0.996948 + 0.0780652i \(0.0248742\pi\)
−0.430868 + 0.902415i \(0.641792\pi\)
\(432\) 0 0
\(433\) −18.3720 −0.882902 −0.441451 0.897285i \(-0.645536\pi\)
−0.441451 + 0.897285i \(0.645536\pi\)
\(434\) 2.54558 23.1065i 0.122192 1.10915i
\(435\) 0 0
\(436\) 3.05488 + 1.76373i 0.146302 + 0.0844675i
\(437\) −6.65651 11.5294i −0.318424 0.551527i
\(438\) 0 0
\(439\) 11.8078 + 6.81724i 0.563556 + 0.325369i 0.754571 0.656218i \(-0.227845\pi\)
−0.191016 + 0.981587i \(0.561178\pi\)
\(440\) −5.45165 + 4.11389i −0.259897 + 0.196122i
\(441\) 0 0
\(442\) 37.1997i 1.76941i
\(443\) 18.9667 + 10.9504i 0.901133 + 0.520270i 0.877568 0.479453i \(-0.159165\pi\)
0.0235656 + 0.999722i \(0.492498\pi\)
\(444\) 0 0
\(445\) −3.55687 6.16068i −0.168612 0.292044i
\(446\) 9.17207 15.8865i 0.434310 0.752247i
\(447\) 0 0
\(448\) 0.289722 2.62984i 0.0136881 0.124248i
\(449\) 34.6012i 1.63293i −0.577395 0.816465i \(-0.695931\pi\)
0.577395 0.816465i \(-0.304069\pi\)
\(450\) 0 0
\(451\) −3.13914 + 7.40926i −0.147816 + 0.348888i
\(452\) −6.58287 + 3.80062i −0.309632 + 0.178766i
\(453\) 0 0
\(454\) 1.74308 0.0818070
\(455\) −30.6486 22.5027i −1.43683 1.05494i
\(456\) 0 0
\(457\) −22.7285 13.1223i −1.06319 0.613835i −0.136879 0.990588i \(-0.543707\pi\)
−0.926314 + 0.376753i \(0.877041\pi\)
\(458\) 14.1778 + 24.5567i 0.662485 + 1.14746i
\(459\) 0 0
\(460\) 1.61102 2.79038i 0.0751144 0.130102i
\(461\) 42.1747 1.96427 0.982136 0.188175i \(-0.0602571\pi\)
0.982136 + 0.188175i \(0.0602571\pi\)
\(462\) 0 0
\(463\) 26.1308 1.21440 0.607200 0.794549i \(-0.292293\pi\)
0.607200 + 0.794549i \(0.292293\pi\)
\(464\) −1.43854 + 2.49162i −0.0667826 + 0.115671i
\(465\) 0 0
\(466\) 10.4076 + 18.0264i 0.482121 + 0.835059i
\(467\) −4.98050 2.87549i −0.230470 0.133062i 0.380319 0.924855i \(-0.375814\pi\)
−0.610789 + 0.791794i \(0.709148\pi\)
\(468\) 0 0
\(469\) −23.0349 + 10.1179i −1.06365 + 0.467203i
\(470\) −24.3605 −1.12367
\(471\) 0 0
\(472\) 3.49197 2.01609i 0.160731 0.0927981i
\(473\) −23.0630 9.77129i −1.06044 0.449285i
\(474\) 0 0
\(475\) 6.46285i 0.296536i
\(476\) 11.3677 + 8.34633i 0.521036 + 0.382553i
\(477\) 0 0
\(478\) −3.72902 + 6.45884i −0.170561 + 0.295421i
\(479\) 6.97303 + 12.0776i 0.318606 + 0.551842i 0.980197 0.198023i \(-0.0634520\pi\)
−0.661591 + 0.749865i \(0.730119\pi\)
\(480\) 0 0
\(481\) −22.0277 12.7177i −1.00438 0.579877i
\(482\) 6.65942i 0.303328i
\(483\) 0 0
\(484\) −3.01773 + 10.5780i −0.137169 + 0.480817i
\(485\) 10.6168 + 6.12962i 0.482085 + 0.278332i
\(486\) 0 0
\(487\) −7.77700 13.4702i −0.352410 0.610391i 0.634261 0.773119i \(-0.281304\pi\)
−0.986671 + 0.162727i \(0.947971\pi\)
\(488\) −4.39206 2.53576i −0.198819 0.114788i
\(489\) 0 0
\(490\) −13.7530 + 4.31691i −0.621297 + 0.195018i
\(491\) 14.7267 0.664609 0.332304 0.943172i \(-0.392174\pi\)
0.332304 + 0.943172i \(0.392174\pi\)
\(492\) 0 0
\(493\) −7.66785 13.2811i −0.345343 0.598151i
\(494\) −29.6897 51.4242i −1.33580 2.31368i
\(495\) 0 0
\(496\) 8.78629 0.394516
\(497\) −8.69011 0.957363i −0.389805 0.0429436i
\(498\) 0 0
\(499\) 3.51020 6.07984i 0.157138 0.272171i −0.776697 0.629874i \(-0.783107\pi\)
0.933835 + 0.357703i \(0.116440\pi\)
\(500\) 10.2713 5.93015i 0.459347 0.265204i
\(501\) 0 0
\(502\) −17.2066 9.93421i −0.767966 0.443385i
\(503\) 20.7055 0.923213 0.461607 0.887085i \(-0.347273\pi\)
0.461607 + 0.887085i \(0.347273\pi\)
\(504\) 0 0
\(505\) 8.04994i 0.358218i
\(506\) −0.635917 5.15037i −0.0282699 0.228962i
\(507\) 0 0
\(508\) −5.49001 + 3.16966i −0.243580 + 0.140631i
\(509\) −19.4116 11.2073i −0.860403 0.496754i 0.00374431 0.999993i \(-0.498808\pi\)
−0.864147 + 0.503239i \(0.832141\pi\)
\(510\) 0 0
\(511\) 1.01751 + 2.31651i 0.0450122 + 0.102476i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −19.1251 + 11.0419i −0.843571 + 0.487036i
\(515\) −6.13620 + 3.54273i −0.270393 + 0.156112i
\(516\) 0 0
\(517\) −31.3189 + 23.6336i −1.37740 + 1.03941i
\(518\) −8.82859 + 3.87792i −0.387906 + 0.170386i
\(519\) 0 0
\(520\) 7.18558 12.4458i 0.315108 0.545784i
\(521\) −20.0520 + 11.5770i −0.878494 + 0.507199i −0.870161 0.492767i \(-0.835986\pi\)
−0.00833225 + 0.999965i \(0.502652\pi\)
\(522\) 0 0
\(523\) −18.0181 10.4027i −0.787875 0.454880i 0.0513386 0.998681i \(-0.483651\pi\)
−0.839214 + 0.543801i \(0.816985\pi\)
\(524\) 13.0003 0.567919
\(525\) 0 0
\(526\) 11.2014 0.488403
\(527\) −23.4168 + 40.5590i −1.02005 + 1.76678i
\(528\) 0 0
\(529\) −10.2759 17.7983i −0.446777 0.773841i
\(530\) −11.8082 + 20.4524i −0.512915 + 0.888395i
\(531\) 0 0
\(532\) −22.3758 2.46507i −0.970114 0.106875i
\(533\) 16.9323i 0.733418i
\(534\) 0 0
\(535\) 3.60226 2.07976i 0.155739 0.0899160i
\(536\) −4.75461 8.23523i −0.205368 0.355708i
\(537\) 0 0
\(538\) 3.87761i 0.167175i
\(539\) −13.4933 + 18.8926i −0.581197 + 0.813763i
\(540\) 0 0
\(541\) 16.4366 + 9.48967i 0.706664 + 0.407993i 0.809825 0.586672i \(-0.199562\pi\)
−0.103160 + 0.994665i \(0.532896\pi\)
\(542\) −2.49796 + 1.44220i −0.107297 + 0.0619477i
\(543\) 0 0
\(544\) −2.66515 + 4.61618i −0.114267 + 0.197917i
\(545\) 7.26386 0.311149
\(546\) 0 0
\(547\) 27.3881i 1.17103i −0.810661 0.585515i \(-0.800892\pi\)
0.810661 0.585515i \(-0.199108\pi\)
\(548\) −7.97258 4.60297i −0.340572 0.196629i
\(549\) 0 0
\(550\) 0.982783 2.31965i 0.0419060 0.0989100i
\(551\) 21.1998 + 12.2397i 0.903142 + 0.521429i
\(552\) 0 0
\(553\) 14.0177 19.0920i 0.596092 0.811874i
\(554\) 21.2905i 0.904548i
\(555\) 0 0
\(556\) 16.0390 9.26012i 0.680205 0.392717i
\(557\) −5.98411 10.3648i −0.253555 0.439170i 0.710947 0.703245i \(-0.248266\pi\)
−0.964502 + 0.264076i \(0.914933\pi\)
\(558\) 0 0
\(559\) 52.7056 2.22921
\(560\) −2.19105 4.98821i −0.0925886 0.210790i
\(561\) 0 0
\(562\) 7.38478 12.7908i 0.311508 0.539548i
\(563\) 3.34982 + 5.80206i 0.141178 + 0.244527i 0.927940 0.372728i \(-0.121578\pi\)
−0.786762 + 0.617256i \(0.788244\pi\)
\(564\) 0 0
\(565\) −7.82635 + 13.5556i −0.329257 + 0.570290i
\(566\) 0.588373i 0.0247312i
\(567\) 0 0
\(568\) 3.30443i 0.138651i
\(569\) 7.52076 13.0263i 0.315287 0.546092i −0.664212 0.747544i \(-0.731233\pi\)
0.979498 + 0.201452i \(0.0645660\pi\)
\(570\) 0 0
\(571\) 24.3794 14.0755i 1.02025 0.589040i 0.106072 0.994358i \(-0.466173\pi\)
0.914176 + 0.405318i \(0.132839\pi\)
\(572\) −2.83635 22.9720i −0.118594 0.960507i
\(573\) 0 0
\(574\) −5.17424 3.79902i −0.215969 0.158568i
\(575\) 1.18851i 0.0495643i
\(576\) 0 0
\(577\) −11.3717 19.6964i −0.473410 0.819970i 0.526127 0.850406i \(-0.323644\pi\)
−0.999537 + 0.0304358i \(0.990310\pi\)
\(578\) −5.70605 9.88317i −0.237340 0.411086i
\(579\) 0 0
\(580\) 5.92456i 0.246004i
\(581\) −2.17496 + 19.7424i −0.0902324 + 0.819051i
\(582\) 0 0
\(583\) 4.66103 + 37.7503i 0.193040 + 1.56346i
\(584\) −0.828178 + 0.478149i −0.0342702 + 0.0197859i
\(585\) 0 0
\(586\) −0.789430 + 1.36733i −0.0326110 + 0.0564840i
\(587\) 18.9106i 0.780523i −0.920704 0.390261i \(-0.872385\pi\)
0.920704 0.390261i \(-0.127615\pi\)
\(588\) 0 0
\(589\) 74.7574i 3.08033i
\(590\) 4.15159 7.19077i 0.170918 0.296039i
\(591\) 0 0
\(592\) −1.82231 3.15633i −0.0748963 0.129724i
\(593\) 16.7412 28.9966i 0.687479 1.19075i −0.285171 0.958477i \(-0.592051\pi\)
0.972651 0.232273i \(-0.0746162\pi\)
\(594\) 0 0
\(595\) 28.8659 + 3.18007i 1.18339 + 0.130370i
\(596\) −12.0994 −0.495610
\(597\) 0 0
\(598\) 5.45991 + 9.45683i 0.223272 + 0.386719i
\(599\) 7.22458 4.17111i 0.295188 0.170427i −0.345091 0.938569i \(-0.612152\pi\)
0.640279 + 0.768142i \(0.278819\pi\)
\(600\) 0 0
\(601\) 18.8871i 0.770420i −0.922829 0.385210i \(-0.874129\pi\)
0.922829 0.385210i \(-0.125871\pi\)
\(602\) 11.8253 16.1060i 0.481964 0.656433i
\(603\) 0 0
\(604\) 4.47659 + 2.58456i 0.182150 + 0.105164i
\(605\) 5.50957 + 21.9712i 0.223996 + 0.893258i
\(606\) 0 0
\(607\) 34.0729 + 19.6720i 1.38298 + 0.798461i 0.992511 0.122157i \(-0.0389812\pi\)
0.390464 + 0.920618i \(0.372314\pi\)
\(608\) 8.50842i 0.345062i
\(609\) 0 0
\(610\) −10.4434 −0.422841
\(611\) 41.2800 71.4991i 1.67001 2.89254i
\(612\) 0 0
\(613\) −8.07950 + 4.66470i −0.326328 + 0.188405i −0.654210 0.756313i \(-0.726999\pi\)
0.327882 + 0.944719i \(0.393665\pi\)
\(614\) −12.9865 7.49778i −0.524094 0.302586i
\(615\) 0 0
\(616\) −7.65627 4.28737i −0.308480 0.172743i
\(617\) 46.3271i 1.86506i 0.361093 + 0.932530i \(0.382404\pi\)
−0.361093 + 0.932530i \(0.617596\pi\)
\(618\) 0 0
\(619\) 12.3541 + 21.3979i 0.496552 + 0.860053i 0.999992 0.00397706i \(-0.00126594\pi\)
−0.503440 + 0.864030i \(0.667933\pi\)
\(620\) 15.6690 9.04648i 0.629281 0.363315i
\(621\) 0 0
\(622\) 10.9311i 0.438297i
\(623\) 5.40925 7.36737i 0.216717 0.295168i
\(624\) 0 0
\(625\) 10.3126 17.8619i 0.412502 0.714475i
\(626\) 6.10928 + 10.5816i 0.244176 + 0.422925i
\(627\) 0 0
\(628\) 0.478738 0.829198i 0.0191037 0.0330886i
\(629\) 19.4269 0.774600
\(630\) 0 0
\(631\) −15.6824 −0.624306 −0.312153 0.950032i \(-0.601050\pi\)
−0.312153 + 0.950032i \(0.601050\pi\)
\(632\) 7.75287 + 4.47612i 0.308393 + 0.178051i
\(633\) 0 0
\(634\) −19.9526 + 11.5197i −0.792420 + 0.457504i
\(635\) −6.52705 + 11.3052i −0.259018 + 0.448632i
\(636\) 0 0
\(637\) 10.6348 47.6807i 0.421364 1.88918i
\(638\) 5.74778 + 7.61686i 0.227557 + 0.301554i
\(639\) 0 0
\(640\) 1.78334 1.02961i 0.0704928 0.0406991i
\(641\) 21.5853 12.4623i 0.852568 0.492231i −0.00894816 0.999960i \(-0.502848\pi\)
0.861517 + 0.507729i \(0.169515\pi\)
\(642\) 0 0
\(643\) −22.4327 −0.884658 −0.442329 0.896853i \(-0.645848\pi\)
−0.442329 + 0.896853i \(0.645848\pi\)
\(644\) 4.11488 + 0.453324i 0.162149 + 0.0178635i
\(645\) 0 0
\(646\) 39.2764 + 22.6762i 1.54531 + 0.892184i
\(647\) 23.0631 13.3155i 0.906705 0.523486i 0.0273356 0.999626i \(-0.491298\pi\)
0.879370 + 0.476140i \(0.157964\pi\)
\(648\) 0 0
\(649\) −1.63875 13.2725i −0.0643266 0.520989i
\(650\) 5.30106i 0.207924i
\(651\) 0 0
\(652\) −17.0880 −0.669219
\(653\) −5.78961 3.34263i −0.226565 0.130807i 0.382421 0.923988i \(-0.375090\pi\)
−0.608986 + 0.793181i \(0.708424\pi\)
\(654\) 0 0
\(655\) 23.1839 13.3852i 0.905871 0.523005i
\(656\) 1.21310 2.10116i 0.0473637 0.0820364i
\(657\) 0 0
\(658\) −12.5872 28.6565i −0.490701 1.11715i
\(659\) 1.73849 0.0677218 0.0338609 0.999427i \(-0.489220\pi\)
0.0338609 + 0.999427i \(0.489220\pi\)
\(660\) 0 0
\(661\) 13.9433 + 24.1506i 0.542333 + 0.939349i 0.998770 + 0.0495927i \(0.0157923\pi\)
−0.456436 + 0.889756i \(0.650874\pi\)
\(662\) −0.855231 1.48130i −0.0332395 0.0575725i
\(663\) 0 0
\(664\) −7.50706 −0.291330
\(665\) −42.4418 + 18.6424i −1.64582 + 0.722920i
\(666\) 0 0
\(667\) −3.89861 2.25087i −0.150955 0.0871539i
\(668\) −8.81000 15.2594i −0.340869 0.590403i
\(669\) 0 0
\(670\) −16.9582 9.79083i −0.655153 0.378253i
\(671\) −13.4265 + 10.1318i −0.518323 + 0.391133i
\(672\) 0 0
\(673\) 3.61388i 0.139305i 0.997571 + 0.0696525i \(0.0221890\pi\)
−0.997571 + 0.0696525i \(0.977811\pi\)
\(674\) −3.86050 2.22886i −0.148701 0.0858526i
\(675\) 0 0
\(676\) 17.8526 + 30.9216i 0.686637 + 1.18929i
\(677\) −7.73709 + 13.4010i −0.297361 + 0.515044i −0.975531 0.219861i \(-0.929440\pi\)
0.678171 + 0.734904i \(0.262773\pi\)
\(678\) 0 0
\(679\) −1.72480 + 15.6563i −0.0661919 + 0.600833i
\(680\) 10.9763i 0.420922i
\(681\) 0 0
\(682\) 11.3681 26.8319i 0.435307 1.02745i
\(683\) −22.4201 + 12.9442i −0.857879 + 0.495297i −0.863302 0.504688i \(-0.831607\pi\)
0.00542219 + 0.999985i \(0.498274\pi\)
\(684\) 0 0
\(685\) −18.9571 −0.724315
\(686\) −12.1844 13.9477i −0.465204 0.532527i
\(687\) 0 0
\(688\) 6.54033 + 3.77606i 0.249348 + 0.143961i
\(689\) −40.0190 69.3150i −1.52460 2.64069i
\(690\) 0 0
\(691\) 22.4617 38.9047i 0.854481 1.48001i −0.0226438 0.999744i \(-0.507208\pi\)
0.877125 0.480262i \(-0.159458\pi\)
\(692\) 16.1091 0.612376
\(693\) 0 0
\(694\) 18.5454 0.703976
\(695\) 19.0687 33.0279i 0.723317 1.25282i
\(696\) 0 0
\(697\) 6.46621 + 11.1998i 0.244925 + 0.424223i
\(698\) 13.8992 + 8.02470i 0.526092 + 0.303739i
\(699\) 0 0
\(700\) 1.61992 + 1.18937i 0.0612273 + 0.0449541i
\(701\) −10.0235 −0.378583 −0.189292 0.981921i \(-0.560619\pi\)
−0.189292 + 0.981921i \(0.560619\pi\)
\(702\) 0 0
\(703\) −26.8554 + 15.5049i −1.01287 + 0.584780i
\(704\) 1.29385 3.05384i 0.0487637 0.115096i
\(705\) 0 0
\(706\) 6.71701i 0.252798i
\(707\) −9.46954 + 4.15945i −0.356139 + 0.156432i
\(708\) 0 0
\(709\) 9.17467 15.8910i 0.344562 0.596799i −0.640712 0.767781i \(-0.721361\pi\)
0.985274 + 0.170982i \(0.0546941\pi\)
\(710\) −3.40228 5.89292i −0.127685 0.221158i
\(711\) 0 0
\(712\) 2.99174 + 1.72728i 0.112120 + 0.0647327i
\(713\) 13.7478i 0.514859i
\(714\) 0 0
\(715\) −28.7104 38.0466i −1.07371 1.42286i
\(716\) −7.99155 4.61392i −0.298658 0.172430i
\(717\) 0 0
\(718\) −17.4909 30.2952i −0.652756 1.13061i
\(719\) −40.5198 23.3941i −1.51113 0.872454i −0.999915 0.0130036i \(-0.995861\pi\)
−0.511219 0.859450i \(-0.670806\pi\)
\(720\) 0 0
\(721\) −7.33810 5.38776i −0.273285 0.200651i
\(722\) −53.3933 −1.98709
\(723\) 0 0
\(724\) −2.73173 4.73150i −0.101524 0.175845i
\(725\) −1.09269 1.89259i −0.0405815 0.0702892i
\(726\) 0 0
\(727\) −6.15090 −0.228124 −0.114062 0.993474i \(-0.536386\pi\)
−0.114062 + 0.993474i \(0.536386\pi\)
\(728\) 18.3534 + 2.02194i 0.680223 + 0.0749381i
\(729\) 0 0
\(730\) −0.984617 + 1.70541i −0.0364423 + 0.0631199i
\(731\) −34.8619 + 20.1276i −1.28942 + 0.744444i
\(732\) 0 0
\(733\) 18.6845 + 10.7875i 0.690128 + 0.398446i 0.803660 0.595089i \(-0.202883\pi\)
−0.113532 + 0.993534i \(0.536216\pi\)
\(734\) −3.78588 −0.139739
\(735\) 0 0
\(736\) 1.56469i 0.0576752i
\(737\) −31.3008 + 3.86472i −1.15298 + 0.142359i
\(738\) 0 0
\(739\) 21.3942 12.3520i 0.787000 0.454375i −0.0519053 0.998652i \(-0.516529\pi\)
0.838905 + 0.544277i \(0.183196\pi\)
\(740\) −6.49959 3.75254i −0.238930 0.137946i
\(741\) 0 0
\(742\) −30.1605 3.32269i −1.10723 0.121980i
\(743\) −10.6465 −0.390583 −0.195292 0.980745i \(-0.562565\pi\)
−0.195292 + 0.980745i \(0.562565\pi\)
\(744\) 0 0
\(745\) −21.5774 + 12.4577i −0.790533 + 0.456414i
\(746\) 16.3482 9.43867i 0.598552 0.345574i
\(747\) 0 0
\(748\) 10.6488 + 14.1116i 0.389358 + 0.515970i
\(749\) 4.30783 + 3.16288i 0.157405 + 0.115569i
\(750\) 0 0
\(751\) 15.2351 26.3879i 0.555935 0.962908i −0.441895 0.897067i \(-0.645694\pi\)
0.997830 0.0658410i \(-0.0209730\pi\)
\(752\) 10.2450 5.91497i 0.373598 0.215697i
\(753\) 0 0
\(754\) −17.3888 10.0394i −0.633263 0.365615i
\(755\) 10.6444 0.387390
\(756\) 0 0
\(757\) 43.9876 1.59876 0.799379 0.600827i \(-0.205162\pi\)
0.799379 + 0.600827i \(0.205162\pi\)
\(758\) −7.08394 + 12.2697i −0.257300 + 0.445657i
\(759\) 0 0
\(760\) −8.76039 15.1734i −0.317773 0.550399i
\(761\) −2.85261 + 4.94087i −0.103407 + 0.179106i −0.913086 0.407766i \(-0.866308\pi\)
0.809679 + 0.586873i \(0.199641\pi\)
\(762\) 0 0
\(763\) 3.75327 + 8.54483i 0.135878 + 0.309344i
\(764\) 20.6128i 0.745746i
\(765\) 0 0
\(766\) −23.0987 + 13.3360i −0.834589 + 0.481850i
\(767\) 14.0701 + 24.3702i 0.508042 + 0.879955i
\(768\) 0 0
\(769\) 4.02217i 0.145043i −0.997367 0.0725215i \(-0.976895\pi\)
0.997367 0.0725215i \(-0.0231046\pi\)
\(770\) −18.0681 + 0.237136i −0.651129 + 0.00854578i
\(771\) 0 0
\(772\) −11.2631 6.50274i −0.405367 0.234039i
\(773\) −13.6864 + 7.90184i −0.492265 + 0.284210i −0.725514 0.688208i \(-0.758398\pi\)
0.233248 + 0.972417i \(0.425064\pi\)
\(774\) 0 0
\(775\) −3.33695 + 5.77977i −0.119867 + 0.207616i
\(776\) −5.95332 −0.213712
\(777\) 0 0
\(778\) 3.45541i 0.123882i
\(779\) −17.8775 10.3216i −0.640529 0.369810i
\(780\) 0 0
\(781\) −10.0912 4.27542i −0.361091 0.152987i
\(782\) −7.22287 4.17013i −0.258289 0.149123i
\(783\) 0 0
\(784\) 4.73575 5.15487i 0.169134 0.184103i
\(785\) 1.97166i 0.0703716i
\(786\) 0 0
\(787\) 9.40102 5.42768i 0.335110 0.193476i −0.322997 0.946400i \(-0.604691\pi\)
0.658108 + 0.752924i \(0.271357\pi\)
\(788\) 9.24031 + 16.0047i 0.329172 + 0.570143i
\(789\) 0 0
\(790\) 18.4347 0.655877
\(791\) −19.9901