Properties

Label 1386.2.r.b.89.2
Level $1386$
Weight $2$
Character 1386.89
Analytic conductor $11.067$
Analytic rank $0$
Dimension $8$
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.r (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 89.2
Root \(-0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1386.89
Dual form 1386.2.r.b.1277.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.22474 - 2.12132i) q^{5} +(-1.00000 + 2.44949i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.22474 - 2.12132i) q^{5} +(-1.00000 + 2.44949i) q^{7} -1.00000i q^{8} +(-2.12132 + 1.22474i) q^{10} +(-0.866025 + 0.500000i) q^{11} +2.44949i q^{13} +(2.09077 - 1.62132i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.866025 + 1.50000i) q^{17} +(-1.50000 - 0.866025i) q^{19} +2.44949 q^{20} +1.00000 q^{22} +(-1.07616 - 0.621320i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(1.22474 - 2.12132i) q^{26} +(-2.62132 + 0.358719i) q^{28} +7.24264i q^{29} +(-7.24264 + 4.18154i) q^{31} +(0.866025 - 0.500000i) q^{32} -1.73205i q^{34} +(3.97141 + 5.12132i) q^{35} +(-2.62132 + 4.54026i) q^{37} +(0.866025 + 1.50000i) q^{38} +(-2.12132 - 1.22474i) q^{40} +8.36308 q^{41} +1.00000 q^{43} +(-0.866025 - 0.500000i) q^{44} +(0.621320 + 1.07616i) q^{46} +(-1.37333 + 2.37868i) q^{47} +(-5.00000 - 4.89898i) q^{49} +1.00000i q^{50} +(-2.12132 + 1.22474i) q^{52} +2.44949i q^{55} +(2.44949 + 1.00000i) q^{56} +(3.62132 - 6.27231i) q^{58} +(-2.30090 - 3.98528i) q^{59} +(9.00000 + 5.19615i) q^{61} +8.36308 q^{62} -1.00000 q^{64} +(5.19615 + 3.00000i) q^{65} +(-2.24264 - 3.88437i) q^{67} +(-0.866025 + 1.50000i) q^{68} +(-0.878680 - 6.42090i) q^{70} -1.24264i q^{71} +(-4.24264 + 2.44949i) q^{73} +(4.54026 - 2.62132i) q^{74} -1.73205i q^{76} +(-0.358719 - 2.62132i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(1.22474 + 2.12132i) q^{80} +(-7.24264 - 4.18154i) q^{82} -7.94282 q^{83} +4.24264 q^{85} +(-0.866025 - 0.500000i) q^{86} +(0.500000 + 0.866025i) q^{88} +(2.95680 - 5.12132i) q^{89} +(-6.00000 - 2.44949i) q^{91} -1.24264i q^{92} +(2.37868 - 1.37333i) q^{94} +(-3.67423 + 2.12132i) q^{95} +6.63103i q^{97} +(1.88064 + 6.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} - 8 q^{7} - 4 q^{16} - 12 q^{19} + 8 q^{22} - 4 q^{25} - 4 q^{28} - 24 q^{31} - 4 q^{37} + 8 q^{43} - 12 q^{46} - 40 q^{49} + 12 q^{58} + 72 q^{61} - 8 q^{64} + 16 q^{67} - 24 q^{70} - 32 q^{79} - 24 q^{82} + 4 q^{88} - 48 q^{91} + 36 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.22474 2.12132i 0.547723 0.948683i −0.450708 0.892672i \(-0.648828\pi\)
0.998430 0.0560116i \(-0.0178384\pi\)
\(6\) 0 0
\(7\) −1.00000 + 2.44949i −0.377964 + 0.925820i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −2.12132 + 1.22474i −0.670820 + 0.387298i
\(11\) −0.866025 + 0.500000i −0.261116 + 0.150756i
\(12\) 0 0
\(13\) 2.44949i 0.679366i 0.940540 + 0.339683i \(0.110320\pi\)
−0.940540 + 0.339683i \(0.889680\pi\)
\(14\) 2.09077 1.62132i 0.558782 0.433316i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.866025 + 1.50000i 0.210042 + 0.363803i 0.951727 0.306944i \(-0.0993066\pi\)
−0.741685 + 0.670748i \(0.765973\pi\)
\(18\) 0 0
\(19\) −1.50000 0.866025i −0.344124 0.198680i 0.317970 0.948101i \(-0.396999\pi\)
−0.662094 + 0.749421i \(0.730332\pi\)
\(20\) 2.44949 0.547723
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −1.07616 0.621320i −0.224395 0.129554i 0.383589 0.923504i \(-0.374688\pi\)
−0.607983 + 0.793950i \(0.708021\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 1.22474 2.12132i 0.240192 0.416025i
\(27\) 0 0
\(28\) −2.62132 + 0.358719i −0.495383 + 0.0677916i
\(29\) 7.24264i 1.34492i 0.740131 + 0.672462i \(0.234763\pi\)
−0.740131 + 0.672462i \(0.765237\pi\)
\(30\) 0 0
\(31\) −7.24264 + 4.18154i −1.30082 + 0.751027i −0.980544 0.196299i \(-0.937108\pi\)
−0.320273 + 0.947325i \(0.603774\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 1.73205i 0.297044i
\(35\) 3.97141 + 5.12132i 0.671290 + 0.865661i
\(36\) 0 0
\(37\) −2.62132 + 4.54026i −0.430942 + 0.746414i −0.996955 0.0779826i \(-0.975152\pi\)
0.566012 + 0.824397i \(0.308485\pi\)
\(38\) 0.866025 + 1.50000i 0.140488 + 0.243332i
\(39\) 0 0
\(40\) −2.12132 1.22474i −0.335410 0.193649i
\(41\) 8.36308 1.30609 0.653047 0.757317i \(-0.273490\pi\)
0.653047 + 0.757317i \(0.273490\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) −0.866025 0.500000i −0.130558 0.0753778i
\(45\) 0 0
\(46\) 0.621320 + 1.07616i 0.0916087 + 0.158671i
\(47\) −1.37333 + 2.37868i −0.200321 + 0.346966i −0.948632 0.316382i \(-0.897532\pi\)
0.748311 + 0.663348i \(0.230865\pi\)
\(48\) 0 0
\(49\) −5.00000 4.89898i −0.714286 0.699854i
\(50\) 1.00000i 0.141421i
\(51\) 0 0
\(52\) −2.12132 + 1.22474i −0.294174 + 0.169842i
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) 0 0
\(55\) 2.44949i 0.330289i
\(56\) 2.44949 + 1.00000i 0.327327 + 0.133631i
\(57\) 0 0
\(58\) 3.62132 6.27231i 0.475503 0.823595i
\(59\) −2.30090 3.98528i −0.299552 0.518839i 0.676481 0.736460i \(-0.263504\pi\)
−0.976034 + 0.217620i \(0.930171\pi\)
\(60\) 0 0
\(61\) 9.00000 + 5.19615i 1.15233 + 0.665299i 0.949454 0.313905i \(-0.101637\pi\)
0.202878 + 0.979204i \(0.434971\pi\)
\(62\) 8.36308 1.06211
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 5.19615 + 3.00000i 0.644503 + 0.372104i
\(66\) 0 0
\(67\) −2.24264 3.88437i −0.273982 0.474551i 0.695896 0.718143i \(-0.255008\pi\)
−0.969878 + 0.243592i \(0.921674\pi\)
\(68\) −0.866025 + 1.50000i −0.105021 + 0.181902i
\(69\) 0 0
\(70\) −0.878680 6.42090i −0.105022 0.767444i
\(71\) 1.24264i 0.147474i −0.997278 0.0737372i \(-0.976507\pi\)
0.997278 0.0737372i \(-0.0234926\pi\)
\(72\) 0 0
\(73\) −4.24264 + 2.44949i −0.496564 + 0.286691i −0.727293 0.686327i \(-0.759222\pi\)
0.230730 + 0.973018i \(0.425889\pi\)
\(74\) 4.54026 2.62132i 0.527795 0.304722i
\(75\) 0 0
\(76\) 1.73205i 0.198680i
\(77\) −0.358719 2.62132i −0.0408799 0.298727i
\(78\) 0 0
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) 1.22474 + 2.12132i 0.136931 + 0.237171i
\(81\) 0 0
\(82\) −7.24264 4.18154i −0.799816 0.461774i
\(83\) −7.94282 −0.871837 −0.435919 0.899986i \(-0.643576\pi\)
−0.435919 + 0.899986i \(0.643576\pi\)
\(84\) 0 0
\(85\) 4.24264 0.460179
\(86\) −0.866025 0.500000i −0.0933859 0.0539164i
\(87\) 0 0
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) 2.95680 5.12132i 0.313420 0.542859i −0.665681 0.746237i \(-0.731859\pi\)
0.979100 + 0.203378i \(0.0651920\pi\)
\(90\) 0 0
\(91\) −6.00000 2.44949i −0.628971 0.256776i
\(92\) 1.24264i 0.129554i
\(93\) 0 0
\(94\) 2.37868 1.37333i 0.245342 0.141648i
\(95\) −3.67423 + 2.12132i −0.376969 + 0.217643i
\(96\) 0 0
\(97\) 6.63103i 0.673279i 0.941634 + 0.336640i \(0.109290\pi\)
−0.941634 + 0.336640i \(0.890710\pi\)
\(98\) 1.88064 + 6.74264i 0.189973 + 0.681110i
\(99\) 0 0
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 6.98975 + 12.1066i 0.695506 + 1.20465i 0.970010 + 0.243066i \(0.0781531\pi\)
−0.274504 + 0.961586i \(0.588514\pi\)
\(102\) 0 0
\(103\) 9.87868 + 5.70346i 0.973375 + 0.561978i 0.900264 0.435345i \(-0.143374\pi\)
0.0731117 + 0.997324i \(0.476707\pi\)
\(104\) 2.44949 0.240192
\(105\) 0 0
\(106\) 0 0
\(107\) −2.15232 1.24264i −0.208072 0.120131i 0.392343 0.919819i \(-0.371665\pi\)
−0.600415 + 0.799688i \(0.704998\pi\)
\(108\) 0 0
\(109\) 9.12132 + 15.7986i 0.873664 + 1.51323i 0.858179 + 0.513350i \(0.171596\pi\)
0.0154849 + 0.999880i \(0.495071\pi\)
\(110\) 1.22474 2.12132i 0.116775 0.202260i
\(111\) 0 0
\(112\) −1.62132 2.09077i −0.153200 0.197559i
\(113\) 10.2426i 0.963547i 0.876296 + 0.481773i \(0.160007\pi\)
−0.876296 + 0.481773i \(0.839993\pi\)
\(114\) 0 0
\(115\) −2.63604 + 1.52192i −0.245812 + 0.141920i
\(116\) −6.27231 + 3.62132i −0.582369 + 0.336231i
\(117\) 0 0
\(118\) 4.60181i 0.423631i
\(119\) −4.54026 + 0.621320i −0.416205 + 0.0569563i
\(120\) 0 0
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) −5.19615 9.00000i −0.470438 0.814822i
\(123\) 0 0
\(124\) −7.24264 4.18154i −0.650408 0.375513i
\(125\) 9.79796 0.876356
\(126\) 0 0
\(127\) 21.2426 1.88498 0.942490 0.334235i \(-0.108478\pi\)
0.942490 + 0.334235i \(0.108478\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −3.00000 5.19615i −0.263117 0.455733i
\(131\) 8.15295 14.1213i 0.712326 1.23379i −0.251655 0.967817i \(-0.580975\pi\)
0.963982 0.265969i \(-0.0856917\pi\)
\(132\) 0 0
\(133\) 3.62132 2.80821i 0.314008 0.243503i
\(134\) 4.48528i 0.387469i
\(135\) 0 0
\(136\) 1.50000 0.866025i 0.128624 0.0742611i
\(137\) −8.87039 + 5.12132i −0.757848 + 0.437544i −0.828523 0.559956i \(-0.810818\pi\)
0.0706744 + 0.997499i \(0.477485\pi\)
\(138\) 0 0
\(139\) 10.0951i 0.856258i 0.903718 + 0.428129i \(0.140827\pi\)
−0.903718 + 0.428129i \(0.859173\pi\)
\(140\) −2.44949 + 6.00000i −0.207020 + 0.507093i
\(141\) 0 0
\(142\) −0.621320 + 1.07616i −0.0521400 + 0.0903092i
\(143\) −1.22474 2.12132i −0.102418 0.177394i
\(144\) 0 0
\(145\) 15.3640 + 8.87039i 1.27591 + 0.736646i
\(146\) 4.89898 0.405442
\(147\) 0 0
\(148\) −5.24264 −0.430942
\(149\) −11.4685 6.62132i −0.939533 0.542440i −0.0497192 0.998763i \(-0.515833\pi\)
−0.889814 + 0.456324i \(0.849166\pi\)
\(150\) 0 0
\(151\) −5.62132 9.73641i −0.457457 0.792338i 0.541369 0.840785i \(-0.317906\pi\)
−0.998826 + 0.0484470i \(0.984573\pi\)
\(152\) −0.866025 + 1.50000i −0.0702439 + 0.121666i
\(153\) 0 0
\(154\) −1.00000 + 2.44949i −0.0805823 + 0.197386i
\(155\) 20.4853i 1.64542i
\(156\) 0 0
\(157\) −0.621320 + 0.358719i −0.0495868 + 0.0286289i −0.524588 0.851356i \(-0.675781\pi\)
0.475002 + 0.879985i \(0.342447\pi\)
\(158\) 6.92820 4.00000i 0.551178 0.318223i
\(159\) 0 0
\(160\) 2.44949i 0.193649i
\(161\) 2.59808 2.01472i 0.204757 0.158782i
\(162\) 0 0
\(163\) −9.48528 + 16.4290i −0.742945 + 1.28682i 0.208204 + 0.978085i \(0.433238\pi\)
−0.951149 + 0.308732i \(0.900095\pi\)
\(164\) 4.18154 + 7.24264i 0.326523 + 0.565555i
\(165\) 0 0
\(166\) 6.87868 + 3.97141i 0.533889 + 0.308241i
\(167\) −14.2767 −1.10476 −0.552381 0.833592i \(-0.686281\pi\)
−0.552381 + 0.833592i \(0.686281\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) −3.67423 2.12132i −0.281801 0.162698i
\(171\) 0 0
\(172\) 0.500000 + 0.866025i 0.0381246 + 0.0660338i
\(173\) 5.91359 10.2426i 0.449602 0.778734i −0.548758 0.835981i \(-0.684899\pi\)
0.998360 + 0.0572477i \(0.0182325\pi\)
\(174\) 0 0
\(175\) 2.62132 0.358719i 0.198153 0.0271166i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) −5.12132 + 2.95680i −0.383859 + 0.221621i
\(179\) 7.79423 4.50000i 0.582568 0.336346i −0.179585 0.983742i \(-0.557476\pi\)
0.762153 + 0.647397i \(0.224142\pi\)
\(180\) 0 0
\(181\) 4.89898i 0.364138i 0.983286 + 0.182069i \(0.0582795\pi\)
−0.983286 + 0.182069i \(0.941721\pi\)
\(182\) 3.97141 + 5.12132i 0.294380 + 0.379618i
\(183\) 0 0
\(184\) −0.621320 + 1.07616i −0.0458043 + 0.0793355i
\(185\) 6.42090 + 11.1213i 0.472074 + 0.817656i
\(186\) 0 0
\(187\) −1.50000 0.866025i −0.109691 0.0633300i
\(188\) −2.74666 −0.200321
\(189\) 0 0
\(190\) 4.24264 0.307794
\(191\) −14.6969 8.48528i −1.06343 0.613973i −0.137053 0.990564i \(-0.543763\pi\)
−0.926380 + 0.376590i \(0.877096\pi\)
\(192\) 0 0
\(193\) −2.36396 4.09450i −0.170162 0.294729i 0.768315 0.640072i \(-0.221096\pi\)
−0.938476 + 0.345344i \(0.887762\pi\)
\(194\) 3.31552 5.74264i 0.238040 0.412298i
\(195\) 0 0
\(196\) 1.74264 6.77962i 0.124474 0.484258i
\(197\) 21.7279i 1.54805i 0.633155 + 0.774025i \(0.281760\pi\)
−0.633155 + 0.774025i \(0.718240\pi\)
\(198\) 0 0
\(199\) 6.36396 3.67423i 0.451129 0.260460i −0.257178 0.966364i \(-0.582793\pi\)
0.708307 + 0.705905i \(0.249459\pi\)
\(200\) −0.866025 + 0.500000i −0.0612372 + 0.0353553i
\(201\) 0 0
\(202\) 13.9795i 0.983594i
\(203\) −17.7408 7.24264i −1.24516 0.508334i
\(204\) 0 0
\(205\) 10.2426 17.7408i 0.715377 1.23907i
\(206\) −5.70346 9.87868i −0.397379 0.688280i
\(207\) 0 0
\(208\) −2.12132 1.22474i −0.147087 0.0849208i
\(209\) 1.73205 0.119808
\(210\) 0 0
\(211\) −5.51472 −0.379649 −0.189824 0.981818i \(-0.560792\pi\)
−0.189824 + 0.981818i \(0.560792\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 1.24264 + 2.15232i 0.0849452 + 0.147129i
\(215\) 1.22474 2.12132i 0.0835269 0.144673i
\(216\) 0 0
\(217\) −3.00000 21.9223i −0.203653 1.48818i
\(218\) 18.2426i 1.23555i
\(219\) 0 0
\(220\) −2.12132 + 1.22474i −0.143019 + 0.0825723i
\(221\) −3.67423 + 2.12132i −0.247156 + 0.142695i
\(222\) 0 0
\(223\) 4.47871i 0.299917i 0.988692 + 0.149958i \(0.0479140\pi\)
−0.988692 + 0.149958i \(0.952086\pi\)
\(224\) 0.358719 + 2.62132i 0.0239680 + 0.175144i
\(225\) 0 0
\(226\) 5.12132 8.87039i 0.340665 0.590049i
\(227\) 6.63103 + 11.4853i 0.440117 + 0.762305i 0.997698 0.0678178i \(-0.0216037\pi\)
−0.557581 + 0.830123i \(0.688270\pi\)
\(228\) 0 0
\(229\) −12.0000 6.92820i −0.792982 0.457829i 0.0480291 0.998846i \(-0.484706\pi\)
−0.841011 + 0.541017i \(0.818039\pi\)
\(230\) 3.04384 0.200705
\(231\) 0 0
\(232\) 7.24264 0.475503
\(233\) 0.445759 + 0.257359i 0.0292027 + 0.0168602i 0.514530 0.857472i \(-0.327966\pi\)
−0.485328 + 0.874332i \(0.661300\pi\)
\(234\) 0 0
\(235\) 3.36396 + 5.82655i 0.219441 + 0.380082i
\(236\) 2.30090 3.98528i 0.149776 0.259420i
\(237\) 0 0
\(238\) 4.24264 + 1.73205i 0.275010 + 0.112272i
\(239\) 12.7279i 0.823301i −0.911342 0.411650i \(-0.864952\pi\)
0.911342 0.411650i \(-0.135048\pi\)
\(240\) 0 0
\(241\) 22.9706 13.2621i 1.47966 0.854284i 0.479929 0.877307i \(-0.340662\pi\)
0.999735 + 0.0230229i \(0.00732905\pi\)
\(242\) −0.866025 + 0.500000i −0.0556702 + 0.0321412i
\(243\) 0 0
\(244\) 10.3923i 0.665299i
\(245\) −16.5160 + 4.60660i −1.05517 + 0.294305i
\(246\) 0 0
\(247\) 2.12132 3.67423i 0.134976 0.233786i
\(248\) 4.18154 + 7.24264i 0.265528 + 0.459908i
\(249\) 0 0
\(250\) −8.48528 4.89898i −0.536656 0.309839i
\(251\) 1.13770 0.0718113 0.0359056 0.999355i \(-0.488568\pi\)
0.0359056 + 0.999355i \(0.488568\pi\)
\(252\) 0 0
\(253\) 1.24264 0.0781242
\(254\) −18.3967 10.6213i −1.15431 0.666441i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.39167 7.60660i 0.273945 0.474487i −0.695923 0.718116i \(-0.745005\pi\)
0.969868 + 0.243629i \(0.0783380\pi\)
\(258\) 0 0
\(259\) −8.50000 10.9612i −0.528164 0.681093i
\(260\) 6.00000i 0.372104i
\(261\) 0 0
\(262\) −14.1213 + 8.15295i −0.872418 + 0.503691i
\(263\) 8.23999 4.75736i 0.508099 0.293351i −0.223953 0.974600i \(-0.571896\pi\)
0.732052 + 0.681249i \(0.238563\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −4.54026 + 0.621320i −0.278381 + 0.0380956i
\(267\) 0 0
\(268\) 2.24264 3.88437i 0.136991 0.237276i
\(269\) −10.8996 18.8787i −0.664561 1.15105i −0.979404 0.201910i \(-0.935285\pi\)
0.314843 0.949144i \(-0.398048\pi\)
\(270\) 0 0
\(271\) 10.2426 + 5.91359i 0.622196 + 0.359225i 0.777724 0.628606i \(-0.216374\pi\)
−0.155527 + 0.987832i \(0.549708\pi\)
\(272\) −1.73205 −0.105021
\(273\) 0 0
\(274\) 10.2426 0.618781
\(275\) 0.866025 + 0.500000i 0.0522233 + 0.0301511i
\(276\) 0 0
\(277\) −10.7279 18.5813i −0.644578 1.11644i −0.984399 0.175952i \(-0.943700\pi\)
0.339820 0.940490i \(-0.389634\pi\)
\(278\) 5.04757 8.74264i 0.302733 0.524349i
\(279\) 0 0
\(280\) 5.12132 3.97141i 0.306057 0.237337i
\(281\) 6.51472i 0.388636i −0.980939 0.194318i \(-0.937751\pi\)
0.980939 0.194318i \(-0.0622493\pi\)
\(282\) 0 0
\(283\) −9.51472 + 5.49333i −0.565591 + 0.326544i −0.755387 0.655279i \(-0.772551\pi\)
0.189795 + 0.981824i \(0.439218\pi\)
\(284\) 1.07616 0.621320i 0.0638583 0.0368686i
\(285\) 0 0
\(286\) 2.44949i 0.144841i
\(287\) −8.36308 + 20.4853i −0.493657 + 1.20921i
\(288\) 0 0
\(289\) 7.00000 12.1244i 0.411765 0.713197i
\(290\) −8.87039 15.3640i −0.520887 0.902203i
\(291\) 0 0
\(292\) −4.24264 2.44949i −0.248282 0.143346i
\(293\) −17.4436 −1.01907 −0.509533 0.860451i \(-0.670182\pi\)
−0.509533 + 0.860451i \(0.670182\pi\)
\(294\) 0 0
\(295\) −11.2721 −0.656286
\(296\) 4.54026 + 2.62132i 0.263897 + 0.152361i
\(297\) 0 0
\(298\) 6.62132 + 11.4685i 0.383563 + 0.664350i
\(299\) 1.52192 2.63604i 0.0880148 0.152446i
\(300\) 0 0
\(301\) −1.00000 + 2.44949i −0.0576390 + 0.141186i
\(302\) 11.2426i 0.646941i
\(303\) 0 0
\(304\) 1.50000 0.866025i 0.0860309 0.0496700i
\(305\) 22.0454 12.7279i 1.26232 0.728799i
\(306\) 0 0
\(307\) 27.1185i 1.54773i 0.633349 + 0.773866i \(0.281680\pi\)
−0.633349 + 0.773866i \(0.718320\pi\)
\(308\) 2.09077 1.62132i 0.119133 0.0923833i
\(309\) 0 0
\(310\) 10.2426 17.7408i 0.581743 1.00761i
\(311\) −5.85204 10.1360i −0.331839 0.574762i 0.651033 0.759049i \(-0.274336\pi\)
−0.982872 + 0.184287i \(0.941002\pi\)
\(312\) 0 0
\(313\) −9.98528 5.76500i −0.564401 0.325857i 0.190509 0.981685i \(-0.438986\pi\)
−0.754910 + 0.655828i \(0.772320\pi\)
\(314\) 0.717439 0.0404874
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −14.0665 8.12132i −0.790056 0.456139i 0.0499265 0.998753i \(-0.484101\pi\)
−0.839982 + 0.542614i \(0.817435\pi\)
\(318\) 0 0
\(319\) −3.62132 6.27231i −0.202755 0.351182i
\(320\) −1.22474 + 2.12132i −0.0684653 + 0.118585i
\(321\) 0 0
\(322\) −3.25736 + 0.445759i −0.181526 + 0.0248412i
\(323\) 3.00000i 0.166924i
\(324\) 0 0
\(325\) 2.12132 1.22474i 0.117670 0.0679366i
\(326\) 16.4290 9.48528i 0.909918 0.525341i
\(327\) 0 0
\(328\) 8.36308i 0.461774i
\(329\) −4.45322 5.74264i −0.245514 0.316602i
\(330\) 0 0
\(331\) 7.00000 12.1244i 0.384755 0.666415i −0.606980 0.794717i \(-0.707619\pi\)
0.991735 + 0.128302i \(0.0409527\pi\)
\(332\) −3.97141 6.87868i −0.217959 0.377517i
\(333\) 0 0
\(334\) 12.3640 + 7.13834i 0.676526 + 0.390592i
\(335\) −10.9867 −0.600265
\(336\) 0 0
\(337\) −15.7574 −0.858358 −0.429179 0.903219i \(-0.641197\pi\)
−0.429179 + 0.903219i \(0.641197\pi\)
\(338\) −6.06218 3.50000i −0.329739 0.190375i
\(339\) 0 0
\(340\) 2.12132 + 3.67423i 0.115045 + 0.199263i
\(341\) 4.18154 7.24264i 0.226443 0.392211i
\(342\) 0 0
\(343\) 17.0000 7.34847i 0.917914 0.396780i
\(344\) 1.00000i 0.0539164i
\(345\) 0 0
\(346\) −10.2426 + 5.91359i −0.550648 + 0.317917i
\(347\) −28.1331 + 16.2426i −1.51026 + 0.871951i −0.510335 + 0.859976i \(0.670478\pi\)
−0.999928 + 0.0119747i \(0.996188\pi\)
\(348\) 0 0
\(349\) 14.6969i 0.786709i 0.919387 + 0.393355i \(0.128686\pi\)
−0.919387 + 0.393355i \(0.871314\pi\)
\(350\) −2.44949 1.00000i −0.130931 0.0534522i
\(351\) 0 0
\(352\) −0.500000 + 0.866025i −0.0266501 + 0.0461593i
\(353\) 7.85578 + 13.6066i 0.418121 + 0.724206i 0.995750 0.0920926i \(-0.0293556\pi\)
−0.577630 + 0.816299i \(0.696022\pi\)
\(354\) 0 0
\(355\) −2.63604 1.52192i −0.139906 0.0807750i
\(356\) 5.91359 0.313420
\(357\) 0 0
\(358\) −9.00000 −0.475665
\(359\) −30.2854 17.4853i −1.59840 0.922838i −0.991795 0.127836i \(-0.959197\pi\)
−0.606607 0.795002i \(-0.707470\pi\)
\(360\) 0 0
\(361\) −8.00000 13.8564i −0.421053 0.729285i
\(362\) 2.44949 4.24264i 0.128742 0.222988i
\(363\) 0 0
\(364\) −0.878680 6.42090i −0.0460553 0.336546i
\(365\) 12.0000i 0.628109i
\(366\) 0 0
\(367\) 1.75736 1.01461i 0.0917334 0.0529623i −0.453432 0.891291i \(-0.649800\pi\)
0.545165 + 0.838329i \(0.316467\pi\)
\(368\) 1.07616 0.621320i 0.0560986 0.0323886i
\(369\) 0 0
\(370\) 12.8418i 0.667613i
\(371\) 0 0
\(372\) 0 0
\(373\) 17.0000 29.4449i 0.880227 1.52460i 0.0291379 0.999575i \(-0.490724\pi\)
0.851089 0.525022i \(-0.175943\pi\)
\(374\) 0.866025 + 1.50000i 0.0447811 + 0.0775632i
\(375\) 0 0
\(376\) 2.37868 + 1.37333i 0.122671 + 0.0708242i
\(377\) −17.7408 −0.913696
\(378\) 0 0
\(379\) −7.27208 −0.373542 −0.186771 0.982404i \(-0.559802\pi\)
−0.186771 + 0.982404i \(0.559802\pi\)
\(380\) −3.67423 2.12132i −0.188484 0.108821i
\(381\) 0 0
\(382\) 8.48528 + 14.6969i 0.434145 + 0.751961i
\(383\) 17.5051 30.3198i 0.894471 1.54927i 0.0600136 0.998198i \(-0.480886\pi\)
0.834458 0.551072i \(-0.185781\pi\)
\(384\) 0 0
\(385\) −6.00000 2.44949i −0.305788 0.124838i
\(386\) 4.72792i 0.240645i
\(387\) 0 0
\(388\) −5.74264 + 3.31552i −0.291538 + 0.168320i
\(389\) 9.76191 5.63604i 0.494948 0.285759i −0.231677 0.972793i \(-0.574421\pi\)
0.726625 + 0.687034i \(0.241088\pi\)
\(390\) 0 0
\(391\) 2.15232i 0.108847i
\(392\) −4.89898 + 5.00000i −0.247436 + 0.252538i
\(393\) 0 0
\(394\) 10.8640 18.8169i 0.547318 0.947983i
\(395\) 9.79796 + 16.9706i 0.492989 + 0.853882i
\(396\) 0 0
\(397\) −1.34924 0.778985i −0.0677165 0.0390962i 0.465759 0.884911i \(-0.345781\pi\)
−0.533476 + 0.845815i \(0.679115\pi\)
\(398\) −7.34847 −0.368345
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −17.1104 9.87868i −0.854451 0.493318i 0.00769892 0.999970i \(-0.497549\pi\)
−0.862150 + 0.506653i \(0.830883\pi\)
\(402\) 0 0
\(403\) −10.2426 17.7408i −0.510222 0.883731i
\(404\) −6.98975 + 12.1066i −0.347753 + 0.602326i
\(405\) 0 0
\(406\) 11.7426 + 15.1427i 0.582777 + 0.751519i
\(407\) 5.24264i 0.259868i
\(408\) 0 0
\(409\) −12.3640 + 7.13834i −0.611359 + 0.352968i −0.773497 0.633800i \(-0.781494\pi\)
0.162138 + 0.986768i \(0.448161\pi\)
\(410\) −17.7408 + 10.2426i −0.876154 + 0.505848i
\(411\) 0 0
\(412\) 11.4069i 0.561978i
\(413\) 12.0628 1.65076i 0.593572 0.0812285i
\(414\) 0 0
\(415\) −9.72792 + 16.8493i −0.477525 + 0.827097i
\(416\) 1.22474 + 2.12132i 0.0600481 + 0.104006i
\(417\) 0 0
\(418\) −1.50000 0.866025i −0.0733674 0.0423587i
\(419\) −14.9941 −0.732510 −0.366255 0.930514i \(-0.619360\pi\)
−0.366255 + 0.930514i \(0.619360\pi\)
\(420\) 0 0
\(421\) −30.6985 −1.49615 −0.748076 0.663613i \(-0.769022\pi\)
−0.748076 + 0.663613i \(0.769022\pi\)
\(422\) 4.77589 + 2.75736i 0.232487 + 0.134226i
\(423\) 0 0
\(424\) 0 0
\(425\) 0.866025 1.50000i 0.0420084 0.0727607i
\(426\) 0 0
\(427\) −21.7279 + 16.8493i −1.05149 + 0.815393i
\(428\) 2.48528i 0.120131i
\(429\) 0 0
\(430\) −2.12132 + 1.22474i −0.102299 + 0.0590624i
\(431\) 14.6969 8.48528i 0.707927 0.408722i −0.102366 0.994747i \(-0.532641\pi\)
0.810293 + 0.586025i \(0.199308\pi\)
\(432\) 0 0
\(433\) 17.8639i 0.858483i 0.903190 + 0.429241i \(0.141219\pi\)
−0.903190 + 0.429241i \(0.858781\pi\)
\(434\) −8.36308 + 20.4853i −0.401441 + 0.983325i
\(435\) 0 0
\(436\) −9.12132 + 15.7986i −0.436832 + 0.756615i
\(437\) 1.07616 + 1.86396i 0.0514796 + 0.0891653i
\(438\) 0 0
\(439\) 17.3787 + 10.0336i 0.829439 + 0.478877i 0.853661 0.520830i \(-0.174377\pi\)
−0.0242215 + 0.999707i \(0.507711\pi\)
\(440\) 2.44949 0.116775
\(441\) 0 0
\(442\) 4.24264 0.201802
\(443\) 2.59808 + 1.50000i 0.123438 + 0.0712672i 0.560448 0.828190i \(-0.310629\pi\)
−0.437009 + 0.899457i \(0.643962\pi\)
\(444\) 0 0
\(445\) −7.24264 12.5446i −0.343334 0.594672i
\(446\) 2.23936 3.87868i 0.106037 0.183661i
\(447\) 0 0
\(448\) 1.00000 2.44949i 0.0472456 0.115728i
\(449\) 37.4558i 1.76765i −0.467817 0.883825i \(-0.654959\pi\)
0.467817 0.883825i \(-0.345041\pi\)
\(450\) 0 0
\(451\) −7.24264 + 4.18154i −0.341043 + 0.196901i
\(452\) −8.87039 + 5.12132i −0.417228 + 0.240887i
\(453\) 0 0
\(454\) 13.2621i 0.622419i
\(455\) −12.5446 + 9.72792i −0.588101 + 0.456052i
\(456\) 0 0
\(457\) 12.8492 22.2555i 0.601062 1.04107i −0.391598 0.920136i \(-0.628078\pi\)
0.992661 0.120934i \(-0.0385889\pi\)
\(458\) 6.92820 + 12.0000i 0.323734 + 0.560723i
\(459\) 0 0
\(460\) −2.63604 1.52192i −0.122906 0.0709598i
\(461\) 4.77589 0.222435 0.111218 0.993796i \(-0.464525\pi\)
0.111218 + 0.993796i \(0.464525\pi\)
\(462\) 0 0
\(463\) 21.4558 0.997138 0.498569 0.866850i \(-0.333859\pi\)
0.498569 + 0.866850i \(0.333859\pi\)
\(464\) −6.27231 3.62132i −0.291185 0.168116i
\(465\) 0 0
\(466\) −0.257359 0.445759i −0.0119219 0.0206494i
\(467\) −2.59808 + 4.50000i −0.120225 + 0.208235i −0.919856 0.392256i \(-0.871695\pi\)
0.799632 + 0.600491i \(0.205028\pi\)
\(468\) 0 0
\(469\) 11.7574 1.60896i 0.542904 0.0742948i
\(470\) 6.72792i 0.310336i
\(471\) 0 0
\(472\) −3.98528 + 2.30090i −0.183437 + 0.105908i
\(473\) −0.866025 + 0.500000i −0.0398199 + 0.0229900i
\(474\) 0 0
\(475\) 1.73205i 0.0794719i
\(476\) −2.80821 3.62132i −0.128714 0.165983i
\(477\) 0 0
\(478\) −6.36396 + 11.0227i −0.291081 + 0.504167i
\(479\) 18.0379 + 31.2426i 0.824175 + 1.42751i 0.902548 + 0.430589i \(0.141694\pi\)
−0.0783735 + 0.996924i \(0.524973\pi\)
\(480\) 0 0
\(481\) −11.1213 6.42090i −0.507089 0.292768i
\(482\) −26.5241 −1.20814
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 14.0665 + 8.12132i 0.638729 + 0.368770i
\(486\) 0 0
\(487\) 20.6066 + 35.6917i 0.933774 + 1.61734i 0.776805 + 0.629741i \(0.216839\pi\)
0.156969 + 0.987604i \(0.449828\pi\)
\(488\) 5.19615 9.00000i 0.235219 0.407411i
\(489\) 0 0
\(490\) 16.6066 + 4.26858i 0.750210 + 0.192835i
\(491\) 42.7279i 1.92828i −0.265387 0.964142i \(-0.585500\pi\)
0.265387 0.964142i \(-0.414500\pi\)
\(492\) 0 0
\(493\) −10.8640 + 6.27231i −0.489288 + 0.282491i
\(494\) −3.67423 + 2.12132i −0.165312 + 0.0954427i
\(495\) 0 0
\(496\) 8.36308i 0.375513i
\(497\) 3.04384 + 1.24264i 0.136535 + 0.0557401i
\(498\) 0 0
\(499\) −18.6066 + 32.2276i −0.832946 + 1.44270i 0.0627461 + 0.998030i \(0.480014\pi\)
−0.895692 + 0.444675i \(0.853319\pi\)
\(500\) 4.89898 + 8.48528i 0.219089 + 0.379473i
\(501\) 0 0
\(502\) −0.985281 0.568852i −0.0439753 0.0253891i
\(503\) −0.594346 −0.0265006 −0.0132503 0.999912i \(-0.504218\pi\)
−0.0132503 + 0.999912i \(0.504218\pi\)
\(504\) 0 0
\(505\) 34.2426 1.52378
\(506\) −1.07616 0.621320i −0.0478411 0.0276211i
\(507\) 0 0
\(508\) 10.6213 + 18.3967i 0.471245 + 0.816220i
\(509\) −0.594346 + 1.02944i −0.0263439 + 0.0456290i −0.878897 0.477012i \(-0.841720\pi\)
0.852553 + 0.522641i \(0.175053\pi\)
\(510\) 0 0
\(511\) −1.75736 12.8418i −0.0777410 0.568088i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −7.60660 + 4.39167i −0.335513 + 0.193708i
\(515\) 24.1977 13.9706i 1.06628 0.615617i
\(516\) 0 0
\(517\) 2.74666i 0.120798i
\(518\) 1.88064 + 13.7426i 0.0826305 + 0.603817i
\(519\) 0 0
\(520\) 3.00000 5.19615i 0.131559 0.227866i
\(521\) 16.4290 + 28.4558i 0.719767 + 1.24667i 0.961092 + 0.276229i \(0.0890847\pi\)
−0.241325 + 0.970444i \(0.577582\pi\)
\(522\) 0 0
\(523\) 6.72792 + 3.88437i 0.294191 + 0.169852i 0.639831 0.768516i \(-0.279005\pi\)
−0.345639 + 0.938368i \(0.612338\pi\)
\(524\) 16.3059 0.712326
\(525\) 0 0
\(526\) −9.51472 −0.414861
\(527\) −12.5446 7.24264i −0.546452 0.315494i
\(528\) 0 0
\(529\) −10.7279 18.5813i −0.466431 0.807883i
\(530\) 0 0
\(531\) 0 0
\(532\) 4.24264 + 1.73205i 0.183942 + 0.0750939i
\(533\) 20.4853i 0.887316i
\(534\) 0 0
\(535\) −5.27208 + 3.04384i −0.227932 + 0.131596i
\(536\) −3.88437 + 2.24264i −0.167779 + 0.0968673i
\(537\) 0 0
\(538\) 21.7992i 0.939831i
\(539\) 6.77962 + 1.74264i 0.292019 + 0.0750608i
\(540\) 0 0
\(541\) 18.2426 31.5972i 0.784312 1.35847i −0.145097 0.989417i \(-0.546349\pi\)
0.929409 0.369051i \(-0.120317\pi\)
\(542\) −5.91359 10.2426i −0.254010 0.439959i
\(543\) 0 0
\(544\) 1.50000 + 0.866025i 0.0643120 + 0.0371305i
\(545\) 44.6852 1.91410
\(546\) 0 0
\(547\) −27.4853 −1.17519 −0.587593 0.809157i \(-0.699924\pi\)
−0.587593 + 0.809157i \(0.699924\pi\)
\(548\) −8.87039 5.12132i −0.378924 0.218772i
\(549\) 0 0
\(550\) −0.500000 0.866025i −0.0213201 0.0369274i
\(551\) 6.27231 10.8640i 0.267209 0.462820i
\(552\) 0 0
\(553\) −12.9706 16.7262i −0.551564 0.711269i
\(554\) 21.4558i 0.911571i
\(555\) 0 0
\(556\) −8.74264 + 5.04757i −0.370771 + 0.214064i
\(557\) 17.9254 10.3492i 0.759524 0.438511i −0.0696007 0.997575i \(-0.522173\pi\)
0.829125 + 0.559063i \(0.188839\pi\)
\(558\) 0 0
\(559\) 2.44949i 0.103602i
\(560\) −6.42090 + 0.878680i −0.271332 + 0.0371310i
\(561\) 0 0
\(562\) −3.25736 + 5.64191i −0.137403 + 0.237990i
\(563\) 14.7840 + 25.6066i 0.623070 + 1.07919i 0.988911 + 0.148512i \(0.0474483\pi\)
−0.365840 + 0.930678i \(0.619218\pi\)
\(564\) 0 0
\(565\) 21.7279 + 12.5446i 0.914101 + 0.527756i
\(566\) 10.9867 0.461803
\(567\) 0 0
\(568\) −1.24264 −0.0521400
\(569\) −19.4473 11.2279i −0.815275 0.470699i 0.0335097 0.999438i \(-0.489332\pi\)
−0.848784 + 0.528739i \(0.822665\pi\)
\(570\) 0 0
\(571\) 5.25736 + 9.10601i 0.220014 + 0.381075i 0.954812 0.297211i \(-0.0960565\pi\)
−0.734798 + 0.678286i \(0.762723\pi\)
\(572\) 1.22474 2.12132i 0.0512092 0.0886969i
\(573\) 0 0
\(574\) 17.4853 13.5592i 0.729822 0.565951i
\(575\) 1.24264i 0.0518217i
\(576\) 0 0
\(577\) 3.00000 1.73205i 0.124892 0.0721062i −0.436253 0.899824i \(-0.643695\pi\)
0.561144 + 0.827718i \(0.310361\pi\)
\(578\) −12.1244 + 7.00000i −0.504307 + 0.291162i
\(579\) 0 0
\(580\) 17.7408i 0.736646i
\(581\) 7.94282 19.4558i 0.329523 0.807164i
\(582\) 0 0
\(583\) 0 0
\(584\) 2.44949 + 4.24264i 0.101361 + 0.175562i
\(585\) 0 0
\(586\) 15.1066 + 8.72180i 0.624048 + 0.360294i
\(587\) 34.0467 1.40526 0.702628 0.711557i \(-0.252010\pi\)
0.702628 + 0.711557i \(0.252010\pi\)
\(588\) 0 0
\(589\) 14.4853 0.596856
\(590\) 9.76191 + 5.63604i 0.401891 + 0.232032i
\(591\) 0 0
\(592\) −2.62132 4.54026i −0.107736 0.186604i
\(593\) −12.6932 + 21.9853i −0.521248 + 0.902827i 0.478447 + 0.878116i \(0.341200\pi\)
−0.999695 + 0.0247109i \(0.992133\pi\)
\(594\) 0 0
\(595\) −4.24264 + 10.3923i −0.173931 + 0.426043i
\(596\) 13.2426i 0.542440i
\(597\) 0 0
\(598\) −2.63604 + 1.52192i −0.107796 + 0.0622358i
\(599\) 15.5885 9.00000i 0.636927 0.367730i −0.146503 0.989210i \(-0.546802\pi\)
0.783430 + 0.621480i \(0.213468\pi\)
\(600\) 0 0
\(601\) 17.1464i 0.699417i −0.936858 0.349709i \(-0.886281\pi\)
0.936858 0.349709i \(-0.113719\pi\)
\(602\) 2.09077 1.62132i 0.0852134 0.0660801i
\(603\) 0 0
\(604\) 5.62132 9.73641i 0.228728 0.396169i
\(605\) −1.22474 2.12132i −0.0497930 0.0862439i
\(606\) 0 0
\(607\) 12.5147 + 7.22538i 0.507957 + 0.293269i 0.731993 0.681312i \(-0.238590\pi\)
−0.224037 + 0.974581i \(0.571924\pi\)
\(608\) −1.73205 −0.0702439
\(609\) 0 0
\(610\) −25.4558 −1.03068
\(611\) −5.82655 3.36396i −0.235717 0.136091i
\(612\) 0 0
\(613\) −3.63604 6.29780i −0.146858 0.254366i 0.783206 0.621762i \(-0.213583\pi\)
−0.930065 + 0.367396i \(0.880249\pi\)
\(614\) 13.5592 23.4853i 0.547206 0.947789i
\(615\) 0 0
\(616\) −2.62132 + 0.358719i −0.105616 + 0.0144532i
\(617\) 33.2132i 1.33711i 0.743661 + 0.668557i \(0.233088\pi\)
−0.743661 + 0.668557i \(0.766912\pi\)
\(618\) 0 0
\(619\) 12.2132 7.05130i 0.490890 0.283416i −0.234054 0.972224i \(-0.575199\pi\)
0.724944 + 0.688808i \(0.241866\pi\)
\(620\) −17.7408 + 10.2426i −0.712487 + 0.411354i
\(621\) 0 0
\(622\) 11.7041i 0.469291i
\(623\) 9.58783 + 12.3640i 0.384128 + 0.495352i
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 5.76500 + 9.98528i 0.230416 + 0.399092i
\(627\) 0 0
\(628\) −0.621320 0.358719i −0.0247934 0.0143145i
\(629\) −9.08052 −0.362064
\(630\) 0 0
\(631\) −21.6985 −0.863803 −0.431902 0.901921i \(-0.642157\pi\)
−0.431902 + 0.901921i \(0.642157\pi\)
\(632\) 6.92820 + 4.00000i 0.275589 + 0.159111i
\(633\) 0 0
\(634\) 8.12132 + 14.0665i 0.322539 + 0.558654i
\(635\) 26.0168 45.0624i 1.03245 1.78825i
\(636\) 0 0
\(637\) 12.0000 12.2474i 0.475457 0.485262i
\(638\) 7.24264i 0.286739i
\(639\) 0 0
\(640\) 2.12132 1.22474i 0.0838525 0.0484123i
\(641\) 21.4150 12.3640i 0.845842 0.488347i −0.0134037 0.999910i \(-0.504267\pi\)
0.859246 + 0.511563i \(0.170933\pi\)
\(642\) 0 0
\(643\) 30.1623i 1.18949i −0.803916 0.594743i \(-0.797254\pi\)
0.803916 0.594743i \(-0.202746\pi\)
\(644\) 3.04384 + 1.24264i 0.119944 + 0.0489669i
\(645\) 0 0
\(646\) −1.50000 + 2.59808i −0.0590167 + 0.102220i
\(647\) 14.8710 + 25.7574i 0.584640 + 1.01263i 0.994920 + 0.100667i \(0.0320976\pi\)
−0.410280 + 0.911960i \(0.634569\pi\)
\(648\) 0 0
\(649\) 3.98528 + 2.30090i 0.156436 + 0.0903184i
\(650\) −2.44949 −0.0960769
\(651\) 0 0
\(652\) −18.9706 −0.742945
\(653\) 39.1558 + 22.6066i 1.53228 + 0.884665i 0.999256 + 0.0385672i \(0.0122794\pi\)
0.533028 + 0.846097i \(0.321054\pi\)
\(654\) 0 0
\(655\) −19.9706 34.5900i −0.780314 1.35154i
\(656\) −4.18154 + 7.24264i −0.163262 + 0.282778i
\(657\) 0 0
\(658\) 0.985281 + 7.19988i 0.0384103 + 0.280681i
\(659\) 7.75736i 0.302184i −0.988520 0.151092i \(-0.951721\pi\)
0.988520 0.151092i \(-0.0482789\pi\)
\(660\) 0 0
\(661\) 11.3787 6.56948i 0.442579 0.255523i −0.262112 0.965038i \(-0.584419\pi\)
0.704691 + 0.709514i \(0.251086\pi\)
\(662\) −12.1244 + 7.00000i −0.471226 + 0.272063i
\(663\) 0 0
\(664\) 7.94282i 0.308241i
\(665\) −1.52192 11.1213i −0.0590174 0.431266i
\(666\) 0 0
\(667\) 4.50000 7.79423i 0.174241 0.301794i
\(668\) −7.13834 12.3640i −0.276191 0.478376i
\(669\) 0 0
\(670\) 9.51472 + 5.49333i 0.367586 + 0.212226i
\(671\) −10.3923 −0.401190
\(672\) 0 0
\(673\) 29.7574 1.14706 0.573531 0.819184i \(-0.305573\pi\)
0.573531 + 0.819184i \(0.305573\pi\)
\(674\) 13.6463 + 7.87868i 0.525635 + 0.303475i
\(675\) 0 0
\(676\) 3.50000 + 6.06218i 0.134615 + 0.233161i
\(677\) −12.9033 + 22.3492i −0.495916 + 0.858951i −0.999989 0.00470976i \(-0.998501\pi\)
0.504073 + 0.863661i \(0.331834\pi\)
\(678\) 0 0
\(679\) −16.2426 6.63103i −0.623335 0.254476i
\(680\) 4.24264i 0.162698i
\(681\) 0 0
\(682\) −7.24264 + 4.18154i −0.277335 + 0.160119i
\(683\) 20.3389 11.7426i 0.778244 0.449320i −0.0575633 0.998342i \(-0.518333\pi\)
0.835808 + 0.549022i \(0.185000\pi\)
\(684\) 0 0
\(685\) 25.0892i 0.958611i
\(686\) −18.3967 2.13604i −0.702388 0.0815543i
\(687\) 0 0
\(688\) −0.500000 + 0.866025i −0.0190623 + 0.0330169i
\(689\) 0 0
\(690\) 0 0
\(691\) −35.4853 20.4874i −1.34992 0.779379i −0.361685 0.932300i \(-0.617799\pi\)
−0.988238 + 0.152921i \(0.951132\pi\)
\(692\) 11.8272 0.449602
\(693\) 0 0
\(694\) 32.4853 1.23312
\(695\) 21.4150 + 12.3640i 0.812318 + 0.468992i
\(696\) 0 0
\(697\) 7.24264 + 12.5446i 0.274335 + 0.475161i
\(698\) 7.34847 12.7279i 0.278144 0.481759i
\(699\) 0 0
\(700\) 1.62132 + 2.09077i 0.0612801 + 0.0790237i
\(701\) 49.2426i 1.85987i 0.367725 + 0.929934i \(0.380137\pi\)
−0.367725 + 0.929934i \(0.619863\pi\)
\(702\) 0 0
\(703\) 7.86396 4.54026i 0.296595 0.171239i
\(704\) 0.866025 0.500000i 0.0326396 0.0188445i
\(705\) 0 0
\(706\) 15.7116i 0.591312i
\(707\) −36.6447 + 5.01472i −1.37817 + 0.188598i
\(708\) 0 0
\(709\) −5.62132 + 9.73641i −0.211113 + 0.365659i −0.952063 0.305901i \(-0.901042\pi\)
0.740950 + 0.671560i \(0.234376\pi\)
\(710\) 1.52192 + 2.63604i 0.0571166 + 0.0989288i
\(711\) 0 0
\(712\) −5.12132 2.95680i −0.191930 0.110811i
\(713\) 10.3923 0.389195
\(714\) 0 0
\(715\) −6.00000 −0.224387
\(716\) 7.79423 + 4.50000i 0.291284 + 0.168173i
\(717\) 0 0
\(718\) 17.4853 + 30.2854i 0.652545 + 1.13024i
\(719\) −15.6500 + 27.1066i −0.583647 + 1.01091i 0.411396 + 0.911457i \(0.365041\pi\)
−0.995043 + 0.0994490i \(0.968292\pi\)
\(720\) 0 0
\(721\) −23.8492 + 18.4943i −0.888192 + 0.688762i
\(722\) 16.0000i 0.595458i
\(723\) 0 0
\(724\) −4.24264 + 2.44949i −0.157676 + 0.0910346i
\(725\) 6.27231 3.62132i 0.232948 0.134492i
\(726\) 0 0
\(727\) 38.1051i 1.41324i 0.707593 + 0.706620i \(0.249781\pi\)
−0.707593 + 0.706620i \(0.750219\pi\)
\(728\) −2.44949 + 6.00000i −0.0907841 + 0.222375i
\(729\) 0 0
\(730\) 6.00000 10.3923i 0.222070 0.384636i
\(731\) 0.866025 + 1.50000i 0.0320311 + 0.0554795i
\(732\) 0 0
\(733\) 46.4558 + 26.8213i 1.71589 + 0.990667i 0.926095 + 0.377291i \(0.123144\pi\)
0.789791 + 0.613376i \(0.210189\pi\)
\(734\) −2.02922 −0.0749000
\(735\) 0 0
\(736\) −1.24264 −0.0458043
\(737\) 3.88437 + 2.24264i 0.143083 + 0.0826087i
\(738\) 0 0
\(739\) 23.7279 + 41.0980i 0.872846 + 1.51181i 0.859040 + 0.511908i \(0.171061\pi\)
0.0138057 + 0.999905i \(0.495605\pi\)
\(740\) −6.42090 + 11.1213i −0.236037 + 0.408828i
\(741\) 0 0
\(742\) 0 0
\(743\) 23.6985i 0.869413i 0.900572 + 0.434707i \(0.143148\pi\)
−0.900572 + 0.434707i \(0.856852\pi\)
\(744\) 0 0
\(745\) −28.0919 + 16.2189i −1.02921 + 0.594213i
\(746\) −29.4449 + 17.0000i −1.07805 + 0.622414i
\(747\) 0 0
\(748\) 1.73205i 0.0633300i
\(749\) 5.19615 4.02944i 0.189863 0.147232i
\(750\) 0 0
\(751\) 15.1213 26.1909i 0.551785 0.955719i −0.446361 0.894853i \(-0.647280\pi\)
0.998146 0.0608664i \(-0.0193864\pi\)
\(752\) −1.37333 2.37868i −0.0500802 0.0867415i
\(753\) 0 0
\(754\) 15.3640 + 8.87039i 0.559522 + 0.323040i
\(755\) −27.5387 −1.00224
\(756\) 0 0
\(757\) −51.6690 −1.87794 −0.938972 0.343994i \(-0.888220\pi\)
−0.938972 + 0.343994i \(0.888220\pi\)
\(758\) 6.29780 + 3.63604i 0.228747 + 0.132067i
\(759\) 0 0
\(760\) 2.12132 + 3.67423i 0.0769484 + 0.133278i
\(761\) −13.1390 + 22.7574i −0.476287 + 0.824954i −0.999631 0.0271681i \(-0.991351\pi\)
0.523344 + 0.852122i \(0.324684\pi\)
\(762\) 0 0
\(763\) −47.8198 + 6.54399i −1.73119 + 0.236908i
\(764\) 16.9706i 0.613973i
\(765\) 0 0
\(766\) −30.3198 + 17.5051i −1.09550 + 0.632487i
\(767\) 9.76191 5.63604i 0.352482 0.203506i
\(768\) 0 0
\(769\) 33.0321i 1.19117i −0.803294 0.595583i \(-0.796921\pi\)
0.803294 0.595583i \(-0.203079\pi\)
\(770\) 3.97141 + 5.12132i 0.143120 + 0.184560i
\(771\) 0 0
\(772\) 2.36396 4.09450i 0.0850808 0.147364i
\(773\) −8.45012 14.6360i −0.303930 0.526422i 0.673093 0.739558i \(-0.264965\pi\)
−0.977022 + 0.213136i \(0.931632\pi\)
\(774\) 0 0
\(775\) 7.24264 + 4.18154i 0.260163 + 0.150205i
\(776\) 6.63103 0.238040
\(777\) 0 0
\(778\) −11.2721 −0.404124
\(779\) −12.5446 7.24264i −0.449458 0.259495i
\(780\) 0 0
\(781\) 0.621320 + 1.07616i 0.0222326 + 0.0385080i
\(782\) −1.07616 + 1.86396i −0.0384833 + 0.0666551i
\(783\) 0 0
\(784\) 6.74264 1.88064i 0.240809 0.0671656i
\(785\) 1.75736i 0.0627228i
\(786\) 0 0
\(787\) −27.4706 + 15.8601i −0.979220 + 0.565353i −0.902034 0.431664i \(-0.857927\pi\)
−0.0771853 + 0.997017i \(0.524593\pi\)
\(788\) −18.8169 + 10.8640i −0.670325 + 0.387013i