Properties

Label 1386.2.r.b.1277.4
Level $1386$
Weight $2$
Character 1386.1277
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: \(x^{8} - x^{4} + 1\)
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 1277.4
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1386.1277
Dual form 1386.2.r.b.89.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.22474 + 2.12132i) q^{5} +(-1.00000 + 2.44949i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(1.22474 + 2.12132i) q^{5} +(-1.00000 + 2.44949i) q^{7} -1.00000i q^{8} +(2.12132 + 1.22474i) q^{10} +(0.866025 + 0.500000i) q^{11} +2.44949i q^{13} +(0.358719 + 2.62132i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.866025 + 1.50000i) q^{17} +(-1.50000 + 0.866025i) q^{19} +2.44949 q^{20} +1.00000 q^{22} +(-6.27231 + 3.62132i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(1.22474 + 2.12132i) q^{26} +(1.62132 + 2.09077i) q^{28} -1.24264i q^{29} +(1.24264 + 0.717439i) q^{31} +(-0.866025 - 0.500000i) q^{32} +1.73205i q^{34} +(-6.42090 + 0.878680i) q^{35} +(1.62132 + 2.80821i) q^{37} +(-0.866025 + 1.50000i) q^{38} +(2.12132 - 1.22474i) q^{40} +1.43488 q^{41} +1.00000 q^{43} +(0.866025 - 0.500000i) q^{44} +(-3.62132 + 6.27231i) q^{46} +(3.82282 + 6.62132i) q^{47} +(-5.00000 - 4.89898i) q^{49} +1.00000i q^{50} +(2.12132 + 1.22474i) q^{52} +2.44949i q^{55} +(2.44949 + 1.00000i) q^{56} +(-0.621320 - 1.07616i) q^{58} +(-7.49706 + 12.9853i) q^{59} +(9.00000 - 5.19615i) q^{61} +1.43488 q^{62} -1.00000 q^{64} +(-5.19615 + 3.00000i) q^{65} +(6.24264 - 10.8126i) q^{67} +(0.866025 + 1.50000i) q^{68} +(-5.12132 + 3.97141i) q^{70} +7.24264i q^{71} +(4.24264 + 2.44949i) q^{73} +(2.80821 + 1.62132i) q^{74} +1.73205i q^{76} +(-2.09077 + 1.62132i) q^{77} +(-4.00000 - 6.92820i) q^{79} +(1.22474 - 2.12132i) q^{80} +(1.24264 - 0.717439i) q^{82} +12.8418 q^{83} -4.24264 q^{85} +(0.866025 - 0.500000i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-0.507306 - 0.878680i) q^{89} +(-6.00000 - 2.44949i) q^{91} +7.24264i q^{92} +(6.62132 + 3.82282i) q^{94} +(-3.67423 - 2.12132i) q^{95} +3.16693i q^{97} +(-6.77962 - 1.74264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} - 8 q^{7} + O(q^{10}) \) \( 8 q + 4 q^{4} - 8 q^{7} - 4 q^{16} - 12 q^{19} + 8 q^{22} - 4 q^{25} - 4 q^{28} - 24 q^{31} - 4 q^{37} + 8 q^{43} - 12 q^{46} - 40 q^{49} + 12 q^{58} + 72 q^{61} - 8 q^{64} + 16 q^{67} - 24 q^{70} - 32 q^{79} - 24 q^{82} + 4 q^{88} - 48 q^{91} + 36 q^{94} + O(q^{100}) \)

Character values

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

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

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 0.998430 + 0.0560116i \(0.0178384\pi\)
−0.450708 + 0.892672i \(0.648828\pi\)
\(6\) 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 \(0.889680\pi\)
\(14\) 0.358719 + 2.62132i 0.0958718 + 0.700577i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.866025 + 1.50000i −0.210042 + 0.363803i −0.951727 0.306944i \(-0.900693\pi\)
0.741685 + 0.670748i \(0.234027\pi\)
\(18\) 0 0
\(19\) −1.50000 + 0.866025i −0.344124 + 0.198680i −0.662094 0.749421i \(-0.730332\pi\)
0.317970 + 0.948101i \(0.396999\pi\)
\(20\) 2.44949 0.547723
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −6.27231 + 3.62132i −1.30787 + 0.755097i −0.981740 0.190228i \(-0.939077\pi\)
−0.326127 + 0.945326i \(0.605744\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 1.22474 + 2.12132i 0.240192 + 0.416025i
\(27\) 0 0
\(28\) 1.62132 + 2.09077i 0.306401 + 0.395118i
\(29\) 1.24264i 0.230753i −0.993322 0.115376i \(-0.963193\pi\)
0.993322 0.115376i \(-0.0368074\pi\)
\(30\) 0 0
\(31\) 1.24264 + 0.717439i 0.223185 + 0.128856i 0.607424 0.794378i \(-0.292203\pi\)
−0.384239 + 0.923234i \(0.625536\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 1.73205i 0.297044i
\(35\) −6.42090 + 0.878680i −1.08533 + 0.148524i
\(36\) 0 0
\(37\) 1.62132 + 2.80821i 0.266543 + 0.461667i 0.967967 0.251078i \(-0.0807851\pi\)
−0.701423 + 0.712745i \(0.747452\pi\)
\(38\) −0.866025 + 1.50000i −0.140488 + 0.243332i
\(39\) 0 0
\(40\) 2.12132 1.22474i 0.335410 0.193649i
\(41\) 1.43488 0.224090 0.112045 0.993703i \(-0.464260\pi\)
0.112045 + 0.993703i \(0.464260\pi\)
\(42\) 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
\(46\) −3.62132 + 6.27231i −0.533935 + 0.924802i
\(47\) 3.82282 + 6.62132i 0.557616 + 0.965819i 0.997695 + 0.0678598i \(0.0216171\pi\)
−0.440079 + 0.897959i \(0.645050\pi\)
\(48\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) 0 0
\(55\) 2.44949i 0.330289i
\(56\) 2.44949 + 1.00000i 0.327327 + 0.133631i
\(57\) 0 0
\(58\) −0.621320 1.07616i −0.0815834 0.141307i
\(59\) −7.49706 + 12.9853i −0.976034 + 1.69054i −0.299552 + 0.954080i \(0.596837\pi\)
−0.676481 + 0.736460i \(0.736496\pi\)
\(60\) 0 0
\(61\) 9.00000 5.19615i 1.15233 0.665299i 0.202878 0.979204i \(-0.434971\pi\)
0.949454 + 0.313905i \(0.101637\pi\)
\(62\) 1.43488 0.182230
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −5.19615 + 3.00000i −0.644503 + 0.372104i
\(66\) 0 0
\(67\) 6.24264 10.8126i 0.762660 1.32097i −0.178815 0.983883i \(-0.557226\pi\)
0.941475 0.337083i \(-0.109440\pi\)
\(68\) 0.866025 + 1.50000i 0.105021 + 0.181902i
\(69\) 0 0
\(70\) −5.12132 + 3.97141i −0.612115 + 0.474674i
\(71\) 7.24264i 0.859543i 0.902938 + 0.429772i \(0.141406\pi\)
−0.902938 + 0.429772i \(0.858594\pi\)
\(72\) 0 0
\(73\) 4.24264 + 2.44949i 0.496564 + 0.286691i 0.727293 0.686327i \(-0.240778\pi\)
−0.230730 + 0.973018i \(0.574111\pi\)
\(74\) 2.80821 + 1.62132i 0.326448 + 0.188475i
\(75\) 0 0
\(76\) 1.73205i 0.198680i
\(77\) −2.09077 + 1.62132i −0.238265 + 0.184767i
\(78\) 0 0
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) 1.22474 2.12132i 0.136931 0.237171i
\(81\) 0 0
\(82\) 1.24264 0.717439i 0.137227 0.0792279i
\(83\) 12.8418 1.40957 0.704785 0.709421i \(-0.251043\pi\)
0.704785 + 0.709421i \(0.251043\pi\)
\(84\) 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
\(89\) −0.507306 0.878680i −0.0537743 0.0931399i 0.837885 0.545846i \(-0.183792\pi\)
−0.891660 + 0.452707i \(0.850458\pi\)
\(90\) 0 0
\(91\) −6.00000 2.44949i −0.628971 0.256776i
\(92\) 7.24264i 0.755097i
\(93\) 0 0
\(94\) 6.62132 + 3.82282i 0.682937 + 0.394294i
\(95\) −3.67423 2.12132i −0.376969 0.217643i
\(96\) 0 0
\(97\) 3.16693i 0.321553i 0.986991 + 0.160776i \(0.0513998\pi\)
−0.986991 + 0.160776i \(0.948600\pi\)
\(98\) −6.77962 1.74264i −0.684845 0.176033i
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) 5.25770 9.10660i 0.523161 0.906141i −0.476476 0.879187i \(-0.658086\pi\)
0.999637 0.0269533i \(-0.00858054\pi\)
\(102\) 0 0
\(103\) 14.1213 8.15295i 1.39142 0.803334i 0.397943 0.917410i \(-0.369724\pi\)
0.993472 + 0.114076i \(0.0363908\pi\)
\(104\) 2.44949 0.240192
\(105\) 0 0
\(106\) 0 0
\(107\) −12.5446 + 7.24264i −1.21273 + 0.700173i −0.963354 0.268233i \(-0.913560\pi\)
−0.249380 + 0.968406i \(0.580227\pi\)
\(108\) 0 0
\(109\) 4.87868 8.45012i 0.467293 0.809375i −0.532009 0.846739i \(-0.678563\pi\)
0.999302 + 0.0373639i \(0.0118961\pi\)
\(110\) 1.22474 + 2.12132i 0.116775 + 0.202260i
\(111\) 0 0
\(112\) 2.62132 0.358719i 0.247691 0.0338958i
\(113\) 1.75736i 0.165318i 0.996578 + 0.0826592i \(0.0263413\pi\)
−0.996578 + 0.0826592i \(0.973659\pi\)
\(114\) 0 0
\(115\) −15.3640 8.87039i −1.43270 0.827168i
\(116\) −1.07616 0.621320i −0.0999188 0.0576881i
\(117\) 0 0
\(118\) 14.9941i 1.38032i
\(119\) −2.80821 3.62132i −0.257428 0.331966i
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) 5.19615 9.00000i 0.470438 0.814822i
\(123\) 0 0
\(124\) 1.24264 0.717439i 0.111592 0.0644279i
\(125\) 9.79796 0.876356
\(126\) 0 0
\(127\) 12.7574 1.13203 0.566016 0.824394i \(-0.308484\pi\)
0.566016 + 0.824394i \(0.308484\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −3.00000 + 5.19615i −0.263117 + 0.455733i
\(131\) −5.70346 9.87868i −0.498313 0.863104i 0.501685 0.865051i \(-0.332714\pi\)
−0.999998 + 0.00194634i \(0.999380\pi\)
\(132\) 0 0
\(133\) −0.621320 4.54026i −0.0538753 0.393690i
\(134\) 12.4853i 1.07856i
\(135\) 0 0
\(136\) 1.50000 + 0.866025i 0.128624 + 0.0742611i
\(137\) 1.52192 + 0.878680i 0.130026 + 0.0750707i 0.563602 0.826046i \(-0.309415\pi\)
−0.433576 + 0.901117i \(0.642748\pi\)
\(138\) 0 0
\(139\) 0.297173i 0.0252059i −0.999921 0.0126029i \(-0.995988\pi\)
0.999921 0.0126029i \(-0.00401175\pi\)
\(140\) −2.44949 + 6.00000i −0.207020 + 0.507093i
\(141\) 0 0
\(142\) 3.62132 + 6.27231i 0.303894 + 0.526361i
\(143\) −1.22474 + 2.12132i −0.102418 + 0.177394i
\(144\) 0 0
\(145\) 2.63604 1.52192i 0.218911 0.126388i
\(146\) 4.89898 0.405442
\(147\) 0 0
\(148\) 3.24264 0.266543
\(149\) 4.11999 2.37868i 0.337523 0.194869i −0.321653 0.946858i \(-0.604238\pi\)
0.659176 + 0.751989i \(0.270905\pi\)
\(150\) 0 0
\(151\) −1.37868 + 2.38794i −0.112195 + 0.194328i −0.916655 0.399679i \(-0.869122\pi\)
0.804460 + 0.594007i \(0.202455\pi\)
\(152\) 0.866025 + 1.50000i 0.0702439 + 0.121666i
\(153\) 0 0
\(154\) −1.00000 + 2.44949i −0.0805823 + 0.197386i
\(155\) 3.51472i 0.282309i
\(156\) 0 0
\(157\) 3.62132 + 2.09077i 0.289013 + 0.166862i 0.637497 0.770453i \(-0.279970\pi\)
−0.348484 + 0.937315i \(0.613303\pi\)
\(158\) −6.92820 4.00000i −0.551178 0.318223i
\(159\) 0 0
\(160\) 2.44949i 0.193649i
\(161\) −2.59808 18.9853i −0.204757 1.49625i
\(162\) 0 0
\(163\) 7.48528 + 12.9649i 0.586292 + 1.01549i 0.994713 + 0.102694i \(0.0327464\pi\)
−0.408420 + 0.912794i \(0.633920\pi\)
\(164\) 0.717439 1.24264i 0.0560226 0.0970339i
\(165\) 0 0
\(166\) 11.1213 6.42090i 0.863182 0.498358i
\(167\) −0.420266 −0.0325212 −0.0162606 0.999868i \(-0.505176\pi\)
−0.0162606 + 0.999868i \(0.505176\pi\)
\(168\) 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
\(173\) −1.01461 1.75736i −0.0771395 0.133610i 0.824875 0.565315i \(-0.191245\pi\)
−0.902015 + 0.431705i \(0.857912\pi\)
\(174\) 0 0
\(175\) −1.62132 2.09077i −0.122560 0.158047i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) −0.878680 0.507306i −0.0658598 0.0380242i
\(179\) −7.79423 4.50000i −0.582568 0.336346i 0.179585 0.983742i \(-0.442524\pi\)
−0.762153 + 0.647397i \(0.775858\pi\)
\(180\) 0 0
\(181\) 4.89898i 0.364138i 0.983286 + 0.182069i \(0.0582795\pi\)
−0.983286 + 0.182069i \(0.941721\pi\)
\(182\) −6.42090 + 0.878680i −0.475949 + 0.0651321i
\(183\) 0 0
\(184\) 3.62132 + 6.27231i 0.266967 + 0.462401i
\(185\) −3.97141 + 6.87868i −0.291984 + 0.505731i
\(186\) 0 0
\(187\) −1.50000 + 0.866025i −0.109691 + 0.0633300i
\(188\) 7.64564 0.557616
\(189\) 0 0
\(190\) −4.24264 −0.307794
\(191\) −14.6969 + 8.48528i −1.06343 + 0.613973i −0.926380 0.376590i \(-0.877096\pi\)
−0.137053 + 0.990564i \(0.543763\pi\)
\(192\) 0 0
\(193\) 10.3640 17.9509i 0.746014 1.29213i −0.203705 0.979032i \(-0.565298\pi\)
0.949719 0.313102i \(-0.101368\pi\)
\(194\) 1.58346 + 2.74264i 0.113686 + 0.196910i
\(195\) 0 0
\(196\) −6.74264 + 1.88064i −0.481617 + 0.134331i
\(197\) 3.72792i 0.265603i −0.991143 0.132802i \(-0.957603\pi\)
0.991143 0.132802i \(-0.0423974\pi\)
\(198\) 0 0
\(199\) −6.36396 3.67423i −0.451129 0.260460i 0.257178 0.966364i \(-0.417207\pi\)
−0.708307 + 0.705905i \(0.750541\pi\)
\(200\) 0.866025 + 0.500000i 0.0612372 + 0.0353553i
\(201\) 0 0
\(202\) 10.5154i 0.739861i
\(203\) 3.04384 + 1.24264i 0.213635 + 0.0872163i
\(204\) 0 0
\(205\) 1.75736 + 3.04384i 0.122739 + 0.212591i
\(206\) 8.15295 14.1213i 0.568043 0.983879i
\(207\) 0 0
\(208\) 2.12132 1.22474i 0.147087 0.0849208i
\(209\) −1.73205 −0.119808
\(210\) 0 0
\(211\) −22.4853 −1.54795 −0.773975 0.633216i \(-0.781735\pi\)
−0.773975 + 0.633216i \(0.781735\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −7.24264 + 12.5446i −0.495097 + 0.857533i
\(215\) 1.22474 + 2.12132i 0.0835269 + 0.144673i
\(216\) 0 0
\(217\) −3.00000 + 2.32640i −0.203653 + 0.157926i
\(218\) 9.75736i 0.660852i
\(219\) 0 0
\(220\) 2.12132 + 1.22474i 0.143019 + 0.0825723i
\(221\) −3.67423 2.12132i −0.247156 0.142695i
\(222\) 0 0
\(223\) 9.37769i 0.627977i −0.949427 0.313988i \(-0.898335\pi\)
0.949427 0.313988i \(-0.101665\pi\)
\(224\) 2.09077 1.62132i 0.139695 0.108329i
\(225\) 0 0
\(226\) 0.878680 + 1.52192i 0.0584489 + 0.101236i
\(227\) 3.16693 5.48528i 0.210196 0.364071i −0.741579 0.670865i \(-0.765923\pi\)
0.951776 + 0.306794i \(0.0992563\pi\)
\(228\) 0 0
\(229\) −12.0000 + 6.92820i −0.792982 + 0.457829i −0.841011 0.541017i \(-0.818039\pi\)
0.0480291 + 0.998846i \(0.484706\pi\)
\(230\) −17.7408 −1.16979
\(231\) 0 0
\(232\) −1.24264 −0.0815834
\(233\) −15.1427 + 8.74264i −0.992031 + 0.572749i −0.905881 0.423533i \(-0.860790\pi\)
−0.0861503 + 0.996282i \(0.527457\pi\)
\(234\) 0 0
\(235\) −9.36396 + 16.2189i −0.610837 + 1.05800i
\(236\) 7.49706 + 12.9853i 0.488017 + 0.845270i
\(237\) 0 0
\(238\) −4.24264 1.73205i −0.275010 0.112272i
\(239\) 12.7279i 0.823301i 0.911342 + 0.411650i \(0.135048\pi\)
−0.911342 + 0.411650i \(0.864952\pi\)
\(240\) 0 0
\(241\) −10.9706 6.33386i −0.706676 0.408000i 0.103153 0.994665i \(-0.467107\pi\)
−0.809829 + 0.586666i \(0.800440\pi\)
\(242\) 0.866025 + 0.500000i 0.0556702 + 0.0321412i
\(243\) 0 0
\(244\) 10.3923i 0.665299i
\(245\) 4.26858 16.6066i 0.272710 1.06096i
\(246\) 0 0
\(247\) −2.12132 3.67423i −0.134976 0.233786i
\(248\) 0.717439 1.24264i 0.0455574 0.0789078i
\(249\) 0 0
\(250\) 8.48528 4.89898i 0.536656 0.309839i
\(251\) 18.4582 1.16507 0.582536 0.812805i \(-0.302060\pi\)
0.582536 + 0.812805i \(0.302060\pi\)
\(252\) 0 0
\(253\) −7.24264 −0.455341
\(254\) 11.0482 6.37868i 0.693226 0.400234i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.85578 + 13.6066i 0.490030 + 0.848756i 0.999934 0.0114746i \(-0.00365256\pi\)
−0.509904 + 0.860231i \(0.670319\pi\)
\(258\) 0 0
\(259\) −8.50000 + 1.16320i −0.528164 + 0.0722776i
\(260\) 6.00000i 0.372104i
\(261\) 0 0
\(262\) −9.87868 5.70346i −0.610307 0.352361i
\(263\) −22.9369 13.2426i −1.41435 0.816576i −0.418557 0.908191i \(-0.637464\pi\)
−0.995795 + 0.0916144i \(0.970797\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −2.80821 3.62132i −0.172182 0.222037i
\(267\) 0 0
\(268\) −6.24264 10.8126i −0.381330 0.660483i
\(269\) 13.3491 23.1213i 0.813909 1.40973i −0.0961996 0.995362i \(-0.530669\pi\)
0.910109 0.414370i \(-0.135998\pi\)
\(270\) 0 0
\(271\) 1.75736 1.01461i 0.106752 0.0616333i −0.445673 0.895196i \(-0.647036\pi\)
0.552425 + 0.833562i \(0.313702\pi\)
\(272\) 1.73205 0.105021
\(273\) 0 0
\(274\) 1.75736 0.106166
\(275\) −0.866025 + 0.500000i −0.0522233 + 0.0301511i
\(276\) 0 0
\(277\) 14.7279 25.5095i 0.884915 1.53272i 0.0391041 0.999235i \(-0.487550\pi\)
0.845811 0.533483i \(-0.179117\pi\)
\(278\) −0.148586 0.257359i −0.00891162 0.0154354i
\(279\) 0 0
\(280\) 0.878680 + 6.42090i 0.0525112 + 0.383722i
\(281\) 23.4853i 1.40101i −0.713645 0.700507i \(-0.752957\pi\)
0.713645 0.700507i \(-0.247043\pi\)
\(282\) 0 0
\(283\) −26.4853 15.2913i −1.57439 0.908973i −0.995621 0.0934783i \(-0.970201\pi\)
−0.578765 0.815494i \(-0.696465\pi\)
\(284\) 6.27231 + 3.62132i 0.372193 + 0.214886i
\(285\) 0 0
\(286\) 2.44949i 0.144841i
\(287\) −1.43488 + 3.51472i −0.0846982 + 0.207467i
\(288\) 0 0
\(289\) 7.00000 + 12.1244i 0.411765 + 0.713197i
\(290\) 1.52192 2.63604i 0.0893701 0.154794i
\(291\) 0 0
\(292\) 4.24264 2.44949i 0.248282 0.143346i
\(293\) −7.05130 −0.411941 −0.205971 0.978558i \(-0.566035\pi\)
−0.205971 + 0.978558i \(0.566035\pi\)
\(294\) 0 0
\(295\) −36.7279 −2.13838
\(296\) 2.80821 1.62132i 0.163224 0.0942373i
\(297\) 0 0
\(298\) 2.37868 4.11999i 0.137793 0.238665i
\(299\) −8.87039 15.3640i −0.512988 0.888521i
\(300\) 0 0
\(301\) −1.00000 + 2.44949i −0.0576390 + 0.141186i
\(302\) 2.75736i 0.158668i
\(303\) 0 0
\(304\) 1.50000 + 0.866025i 0.0860309 + 0.0496700i
\(305\) 22.0454 + 12.7279i 1.26232 + 0.728799i
\(306\) 0 0
\(307\) 7.52255i 0.429335i −0.976687 0.214667i \(-0.931133\pi\)
0.976687 0.214667i \(-0.0688667\pi\)
\(308\) 0.358719 + 2.62132i 0.0204399 + 0.149364i
\(309\) 0 0
\(310\) 1.75736 + 3.04384i 0.0998113 + 0.172878i
\(311\) 13.2005 22.8640i 0.748532 1.29650i −0.199994 0.979797i \(-0.564092\pi\)
0.948526 0.316699i \(-0.102575\pi\)
\(312\) 0 0
\(313\) 6.98528 4.03295i 0.394831 0.227956i −0.289420 0.957202i \(-0.593462\pi\)
0.684251 + 0.729246i \(0.260129\pi\)
\(314\) 4.18154 0.235978
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 6.71807 3.87868i 0.377324 0.217848i −0.299329 0.954150i \(-0.596763\pi\)
0.676654 + 0.736302i \(0.263430\pi\)
\(318\) 0 0
\(319\) 0.621320 1.07616i 0.0347873 0.0602533i
\(320\) −1.22474 2.12132i −0.0684653 0.118585i
\(321\) 0 0
\(322\) −11.7426 15.1427i −0.654392 0.843870i
\(323\) 3.00000i 0.166924i
\(324\) 0 0
\(325\) −2.12132 1.22474i −0.117670 0.0679366i
\(326\) 12.9649 + 7.48528i 0.718059 + 0.414571i
\(327\) 0 0
\(328\) 1.43488i 0.0792279i
\(329\) −20.0417 + 2.74264i −1.10493 + 0.151207i
\(330\) 0 0
\(331\) 7.00000 + 12.1244i 0.384755 + 0.666415i 0.991735 0.128302i \(-0.0409527\pi\)
−0.606980 + 0.794717i \(0.707619\pi\)
\(332\) 6.42090 11.1213i 0.352393 0.610362i
\(333\) 0 0
\(334\) −0.363961 + 0.210133i −0.0199151 + 0.0114980i
\(335\) 30.5826 1.67090
\(336\) 0 0
\(337\) −24.2426 −1.32058 −0.660290 0.751010i \(-0.729567\pi\)
−0.660290 + 0.751010i \(0.729567\pi\)
\(338\) 6.06218 3.50000i 0.329739 0.190375i
\(339\) 0 0
\(340\) −2.12132 + 3.67423i −0.115045 + 0.199263i
\(341\) 0.717439 + 1.24264i 0.0388515 + 0.0672928i
\(342\) 0 0
\(343\) 17.0000 7.34847i 0.917914 0.396780i
\(344\) 1.00000i 0.0539164i
\(345\) 0 0
\(346\) −1.75736 1.01461i −0.0944762 0.0545459i
\(347\) 13.4361 + 7.75736i 0.721290 + 0.416437i 0.815227 0.579141i \(-0.196612\pi\)
−0.0939374 + 0.995578i \(0.529945\pi\)
\(348\) 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
\(353\) 4.39167 7.60660i 0.233745 0.404859i −0.725162 0.688578i \(-0.758235\pi\)
0.958907 + 0.283720i \(0.0915685\pi\)
\(354\) 0 0
\(355\) −15.3640 + 8.87039i −0.815434 + 0.470791i
\(356\) −1.01461 −0.0537743
\(357\) 0 0
\(358\) −9.00000 −0.475665
\(359\) 0.891519 0.514719i 0.0470526 0.0271658i −0.476289 0.879289i \(-0.658018\pi\)
0.523342 + 0.852123i \(0.324685\pi\)
\(360\) 0 0
\(361\) −8.00000 + 13.8564i −0.421053 + 0.729285i
\(362\) 2.44949 + 4.24264i 0.128742 + 0.222988i
\(363\) 0 0
\(364\) −5.12132 + 3.97141i −0.268430 + 0.208158i
\(365\) 12.0000i 0.628109i
\(366\) 0 0
\(367\) 10.2426 + 5.91359i 0.534661 + 0.308687i 0.742913 0.669388i \(-0.233444\pi\)
−0.208251 + 0.978075i \(0.566777\pi\)
\(368\) 6.27231 + 3.62132i 0.326967 + 0.188774i
\(369\) 0 0
\(370\) 7.94282i 0.412927i
\(371\) 0 0
\(372\) 0 0
\(373\) 17.0000 + 29.4449i 0.880227 + 1.52460i 0.851089 + 0.525022i \(0.175943\pi\)
0.0291379 + 0.999575i \(0.490724\pi\)
\(374\) −0.866025 + 1.50000i −0.0447811 + 0.0775632i
\(375\) 0 0
\(376\) 6.62132 3.82282i 0.341469 0.197147i
\(377\) 3.04384 0.156766
\(378\) 0 0
\(379\) −32.7279 −1.68112 −0.840560 0.541718i \(-0.817774\pi\)
−0.840560 + 0.541718i \(0.817774\pi\)
\(380\) −3.67423 + 2.12132i −0.188484 + 0.108821i
\(381\) 0 0
\(382\) −8.48528 + 14.6969i −0.434145 + 0.751961i
\(383\) 19.2372 + 33.3198i 0.982975 + 1.70256i 0.650611 + 0.759411i \(0.274513\pi\)
0.332364 + 0.943151i \(0.392154\pi\)
\(384\) 0 0
\(385\) −6.00000 2.44949i −0.305788 0.124838i
\(386\) 20.7279i 1.05502i
\(387\) 0 0
\(388\) 2.74264 + 1.58346i 0.139236 + 0.0803882i
\(389\) −31.8073 18.3640i −1.61269 0.931090i −0.988742 0.149627i \(-0.952193\pi\)
−0.623952 0.781462i \(-0.714474\pi\)
\(390\) 0 0
\(391\) 12.5446i 0.634409i
\(392\) −4.89898 + 5.00000i −0.247436 + 0.252538i
\(393\) 0 0
\(394\) −1.86396 3.22848i −0.0939050 0.162648i
\(395\) 9.79796 16.9706i 0.492989 0.853882i
\(396\) 0 0
\(397\) 28.3492 16.3674i 1.42281 0.821458i 0.426270 0.904596i \(-0.359827\pi\)
0.996538 + 0.0831378i \(0.0264941\pi\)
\(398\) −7.34847 −0.368345
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 24.4588 14.1213i 1.22142 0.705185i 0.256197 0.966625i \(-0.417531\pi\)
0.965220 + 0.261440i \(0.0841972\pi\)
\(402\) 0 0
\(403\) −1.75736 + 3.04384i −0.0875403 + 0.151624i
\(404\) −5.25770 9.10660i −0.261580 0.453070i
\(405\) 0 0
\(406\) 3.25736 0.445759i 0.161660 0.0221227i
\(407\) 3.24264i 0.160732i
\(408\) 0 0
\(409\) 0.363961 + 0.210133i 0.0179967 + 0.0103904i 0.508971 0.860783i \(-0.330026\pi\)
−0.490975 + 0.871174i \(0.663359\pi\)
\(410\) 3.04384 + 1.75736i 0.150324 + 0.0867898i
\(411\) 0 0
\(412\) 16.3059i 0.803334i
\(413\) −24.3103 31.3492i −1.19623 1.54260i
\(414\) 0 0
\(415\) 15.7279 + 27.2416i 0.772053 + 1.33724i
\(416\) 1.22474 2.12132i 0.0600481 0.104006i
\(417\) 0 0
\(418\) −1.50000 + 0.866025i −0.0733674 + 0.0423587i
\(419\) −4.60181 −0.224813 −0.112406 0.993662i \(-0.535856\pi\)
−0.112406 + 0.993662i \(0.535856\pi\)
\(420\) 0 0
\(421\) 28.6985 1.39868 0.699339 0.714790i \(-0.253478\pi\)
0.699339 + 0.714790i \(0.253478\pi\)
\(422\) −19.4728 + 11.2426i −0.947922 + 0.547283i
\(423\) 0 0
\(424\) 0 0
\(425\) −0.866025 1.50000i −0.0420084 0.0727607i
\(426\) 0 0
\(427\) 3.72792 + 27.2416i 0.180407 + 1.31831i
\(428\) 14.4853i 0.700173i
\(429\) 0 0
\(430\) 2.12132 + 1.22474i 0.102299 + 0.0590624i
\(431\) 14.6969 + 8.48528i 0.707927 + 0.408722i 0.810293 0.586025i \(-0.199308\pi\)
−0.102366 + 0.994747i \(0.532641\pi\)
\(432\) 0 0
\(433\) 21.3280i 1.02496i 0.858700 + 0.512478i \(0.171273\pi\)
−0.858700 + 0.512478i \(0.828727\pi\)
\(434\) −1.43488 + 3.51472i −0.0688763 + 0.168712i
\(435\) 0 0
\(436\) −4.87868 8.45012i −0.233646 0.404687i
\(437\) 6.27231 10.8640i 0.300045 0.519694i
\(438\) 0 0
\(439\) 21.6213 12.4831i 1.03193 0.595785i 0.114393 0.993436i \(-0.463508\pi\)
0.917537 + 0.397651i \(0.130175\pi\)
\(440\) 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 \(-0.689371\pi\)
0.437009 + 0.899457i \(0.356038\pi\)
\(444\) 0 0
\(445\) 1.24264 2.15232i 0.0589068 0.102030i
\(446\) −4.68885 8.12132i −0.222023 0.384556i
\(447\) 0 0
\(448\) 1.00000 2.44949i 0.0472456 0.115728i
\(449\) 13.4558i 0.635021i 0.948255 + 0.317510i \(0.102847\pi\)
−0.948255 + 0.317510i \(0.897153\pi\)
\(450\) 0 0
\(451\) 1.24264 + 0.717439i 0.0585137 + 0.0337829i
\(452\) 1.52192 + 0.878680i 0.0715850 + 0.0413296i
\(453\) 0 0
\(454\) 6.33386i 0.297263i
\(455\) −2.15232 15.7279i −0.100902 0.737336i
\(456\) 0 0
\(457\) −16.8492 29.1837i −0.788174 1.36516i −0.927084 0.374853i \(-0.877693\pi\)
0.138910 0.990305i \(-0.455640\pi\)
\(458\) −6.92820 + 12.0000i −0.323734 + 0.560723i
\(459\) 0 0
\(460\) −15.3640 + 8.87039i −0.716348 + 0.413584i
\(461\) −19.4728 −0.906940 −0.453470 0.891272i \(-0.649814\pi\)
−0.453470 + 0.891272i \(0.649814\pi\)
\(462\) 0 0
\(463\) −29.4558 −1.36893 −0.684465 0.729046i \(-0.739964\pi\)
−0.684465 + 0.729046i \(0.739964\pi\)
\(464\) −1.07616 + 0.621320i −0.0499594 + 0.0288441i
\(465\) 0 0
\(466\) −8.74264 + 15.1427i −0.404995 + 0.701472i
\(467\) 2.59808 + 4.50000i 0.120225 + 0.208235i 0.919856 0.392256i \(-0.128305\pi\)
−0.799632 + 0.600491i \(0.794972\pi\)
\(468\) 0 0
\(469\) 20.2426 + 26.1039i 0.934718 + 1.20536i
\(470\) 18.7279i 0.863855i
\(471\) 0 0
\(472\) 12.9853 + 7.49706i 0.597696 + 0.345080i
\(473\) 0.866025 + 0.500000i 0.0398199 + 0.0229900i
\(474\) 0 0
\(475\) 1.73205i 0.0794719i
\(476\) −4.54026 + 0.621320i −0.208102 + 0.0284782i
\(477\) 0 0
\(478\) 6.36396 + 11.0227i 0.291081 + 0.504167i
\(479\) −13.1390 + 22.7574i −0.600335 + 1.03981i 0.392435 + 0.919780i \(0.371633\pi\)
−0.992770 + 0.120031i \(0.961701\pi\)
\(480\) 0 0
\(481\) −6.87868 + 3.97141i −0.313641 + 0.181081i
\(482\) −12.6677 −0.576999
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −6.71807 + 3.87868i −0.305052 + 0.176122i
\(486\) 0 0
\(487\) −0.606602 + 1.05066i −0.0274877 + 0.0476102i −0.879442 0.476006i \(-0.842084\pi\)
0.851954 + 0.523616i \(0.175417\pi\)
\(488\) −5.19615 9.00000i −0.235219 0.407411i
\(489\) 0 0
\(490\) −4.60660 16.5160i −0.208105 0.746118i
\(491\) 17.2721i 0.779478i −0.920925 0.389739i \(-0.872565\pi\)
0.920925 0.389739i \(-0.127435\pi\)
\(492\) 0 0
\(493\) 1.86396 + 1.07616i 0.0839486 + 0.0484677i
\(494\) −3.67423 2.12132i −0.165312 0.0954427i
\(495\) 0 0
\(496\) 1.43488i 0.0644279i
\(497\) −17.7408 7.24264i −0.795782 0.324877i
\(498\) 0 0
\(499\) 2.60660 + 4.51477i 0.116688 + 0.202109i 0.918453 0.395530i \(-0.129439\pi\)
−0.801766 + 0.597639i \(0.796106\pi\)
\(500\) 4.89898 8.48528i 0.219089 0.379473i
\(501\) 0 0
\(502\) 15.9853 9.22911i 0.713458 0.411915i
\(503\) 20.1903 0.900239 0.450120 0.892968i \(-0.351381\pi\)
0.450120 + 0.892968i \(0.351381\pi\)
\(504\) 0 0
\(505\) 25.7574 1.14619
\(506\) −6.27231 + 3.62132i −0.278838 + 0.160987i
\(507\) 0 0
\(508\) 6.37868 11.0482i 0.283008 0.490184i
\(509\) 20.1903 + 34.9706i 0.894918 + 1.55004i 0.833906 + 0.551906i \(0.186099\pi\)
0.0610113 + 0.998137i \(0.480567\pi\)
\(510\) 0 0
\(511\) −10.2426 + 7.94282i −0.453108 + 0.351369i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 13.6066 + 7.85578i 0.600161 + 0.346503i
\(515\) 34.5900 + 19.9706i 1.52422 + 0.880008i
\(516\) 0 0
\(517\) 7.64564i 0.336255i
\(518\) −6.77962 + 5.25736i −0.297879 + 0.230995i
\(519\) 0 0
\(520\) 3.00000 + 5.19615i 0.131559 + 0.227866i
\(521\) 12.9649 22.4558i 0.568002 0.983808i −0.428761 0.903418i \(-0.641050\pi\)
0.996763 0.0803906i \(-0.0256168\pi\)
\(522\) 0 0
\(523\) −18.7279 + 10.8126i −0.818915 + 0.472801i −0.850042 0.526715i \(-0.823424\pi\)
0.0311273 + 0.999515i \(0.490090\pi\)
\(524\) −11.4069 −0.498313
\(525\) 0 0
\(526\) −26.4853 −1.15481
\(527\) −2.15232 + 1.24264i −0.0937564 + 0.0541303i
\(528\) 0 0
\(529\) 14.7279 25.5095i 0.640344 1.10911i
\(530\) 0 0
\(531\) 0 0
\(532\) −4.24264 1.73205i −0.183942 0.0750939i
\(533\) 3.51472i 0.152239i
\(534\) 0 0
\(535\) −30.7279 17.7408i −1.32848 0.767001i
\(536\) −10.8126 6.24264i −0.467032 0.269641i
\(537\) 0 0
\(538\) 26.6982i 1.15104i
\(539\) −1.88064 6.74264i −0.0810048 0.290426i
\(540\) 0 0
\(541\) 9.75736 + 16.9002i 0.419502 + 0.726598i 0.995889 0.0905782i \(-0.0288715\pi\)
−0.576388 + 0.817176i \(0.695538\pi\)
\(542\) 1.01461 1.75736i 0.0435813 0.0754850i
\(543\) 0 0
\(544\) 1.50000 0.866025i 0.0643120 0.0371305i
\(545\) 23.9006 1.02379
\(546\) 0 0
\(547\) −10.5147 −0.449577 −0.224788 0.974408i \(-0.572169\pi\)
−0.224788 + 0.974408i \(0.572169\pi\)
\(548\) 1.52192 0.878680i 0.0650131 0.0375353i
\(549\) 0 0
\(550\) −0.500000 + 0.866025i −0.0213201 + 0.0369274i
\(551\) 1.07616 + 1.86396i 0.0458459 + 0.0794074i
\(552\) 0 0
\(553\) 20.9706 2.86976i 0.891759 0.122034i
\(554\) 29.4558i 1.25146i
\(555\) 0 0
\(556\) −0.257359 0.148586i −0.0109145 0.00630147i
\(557\) 33.5139 + 19.3492i 1.42003 + 0.819854i 0.996301 0.0859359i \(-0.0273880\pi\)
0.423728 + 0.905790i \(0.360721\pi\)
\(558\) 0 0
\(559\) 2.44949i 0.103602i
\(560\) 3.97141 + 5.12132i 0.167823 + 0.216415i
\(561\) 0 0
\(562\) −11.7426 20.3389i −0.495333 0.857943i
\(563\) −2.53653 + 4.39340i −0.106902 + 0.185160i −0.914514 0.404555i \(-0.867426\pi\)
0.807612 + 0.589715i \(0.200760\pi\)
\(564\) 0 0
\(565\) −3.72792 + 2.15232i −0.156835 + 0.0905486i
\(566\) −30.5826 −1.28548
\(567\) 0 0
\(568\) 7.24264 0.303894
\(569\) −24.6435 + 14.2279i −1.03311 + 0.596466i −0.917874 0.396873i \(-0.870095\pi\)
−0.115235 + 0.993338i \(0.536762\pi\)
\(570\) 0 0
\(571\) 13.7426 23.8030i 0.575112 0.996123i −0.420918 0.907099i \(-0.638292\pi\)
0.996030 0.0890238i \(-0.0283747\pi\)
\(572\) 1.22474 + 2.12132i 0.0512092 + 0.0886969i
\(573\) 0 0
\(574\) 0.514719 + 3.76127i 0.0214839 + 0.156993i
\(575\) 7.24264i 0.302039i
\(576\) 0 0
\(577\) 3.00000 + 1.73205i 0.124892 + 0.0721062i 0.561144 0.827718i \(-0.310361\pi\)
−0.436253 + 0.899824i \(0.643695\pi\)
\(578\) 12.1244 + 7.00000i 0.504307 + 0.291162i
\(579\) 0 0
\(580\) 3.04384i 0.126388i
\(581\) −12.8418 + 31.4558i −0.532767 + 1.30501i
\(582\) 0 0
\(583\) 0 0
\(584\) 2.44949 4.24264i 0.101361 0.175562i
\(585\) 0 0
\(586\) −6.10660 + 3.52565i −0.252261 + 0.145643i
\(587\) −14.4508 −0.596446 −0.298223 0.954496i \(-0.596394\pi\)
−0.298223 + 0.954496i \(0.596394\pi\)
\(588\) 0 0
\(589\) −2.48528 −0.102404
\(590\) −31.8073 + 18.3640i −1.30949 + 0.756032i
\(591\) 0 0
\(592\) 1.62132 2.80821i 0.0666359 0.115417i
\(593\) 2.89525 + 5.01472i 0.118894 + 0.205930i 0.919329 0.393489i \(-0.128732\pi\)
−0.800436 + 0.599418i \(0.795399\pi\)
\(594\) 0 0
\(595\) 4.24264 10.3923i 0.173931 0.426043i
\(596\) 4.75736i 0.194869i
\(597\) 0 0
\(598\) −15.3640 8.87039i −0.628279 0.362737i
\(599\) −15.5885 9.00000i −0.636927 0.367730i 0.146503 0.989210i \(-0.453198\pi\)
−0.783430 + 0.621480i \(0.786532\pi\)
\(600\) 0 0
\(601\) 17.1464i 0.699417i −0.936858 0.349709i \(-0.886281\pi\)
0.936858 0.349709i \(-0.113719\pi\)
\(602\) 0.358719 + 2.62132i 0.0146203 + 0.106837i
\(603\) 0 0
\(604\) 1.37868 + 2.38794i 0.0560977 + 0.0971640i
\(605\) −1.22474 + 2.12132i −0.0497930 + 0.0862439i
\(606\) 0 0
\(607\) 29.4853 17.0233i 1.19677 0.690956i 0.236937 0.971525i \(-0.423857\pi\)
0.959834 + 0.280569i \(0.0905232\pi\)
\(608\) 1.73205 0.0702439
\(609\) 0 0
\(610\) 25.4558 1.03068
\(611\) −16.2189 + 9.36396i −0.656145 + 0.378825i
\(612\) 0 0
\(613\) −16.3640 + 28.3432i −0.660934 + 1.14477i 0.319436 + 0.947608i \(0.396506\pi\)
−0.980371 + 0.197164i \(0.936827\pi\)
\(614\) −3.76127 6.51472i −0.151793 0.262913i
\(615\) 0 0
\(616\) 1.62132 + 2.09077i 0.0653249 + 0.0842395i
\(617\) 9.21320i 0.370910i −0.982653 0.185455i \(-0.940624\pi\)
0.982653 0.185455i \(-0.0593758\pi\)
\(618\) 0 0
\(619\) −30.2132 17.4436i −1.21437 0.701118i −0.250663 0.968074i \(-0.580649\pi\)
−0.963708 + 0.266957i \(0.913982\pi\)
\(620\) 3.04384 + 1.75736i 0.122243 + 0.0705772i
\(621\) 0 0
\(622\) 26.4010i 1.05858i
\(623\) 2.65962 0.363961i 0.106556 0.0145818i
\(624\) 0 0
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 4.03295 6.98528i 0.161189 0.279188i
\(627\) 0 0
\(628\) 3.62132 2.09077i 0.144506 0.0834308i
\(629\) −5.61642 −0.223941
\(630\) 0 0
\(631\) 37.6985 1.50075 0.750376 0.661011i \(-0.229872\pi\)
0.750376 + 0.661011i \(0.229872\pi\)
\(632\) −6.92820 + 4.00000i −0.275589 + 0.159111i
\(633\) 0 0
\(634\) 3.87868 6.71807i 0.154042 0.266809i
\(635\) 15.6245 + 27.0624i 0.620040 + 1.07394i
\(636\) 0 0
\(637\) 12.0000 12.2474i 0.475457 0.485262i
\(638\) 1.24264i 0.0491966i
\(639\) 0 0
\(640\) −2.12132 1.22474i −0.0838525 0.0484123i
\(641\) 0.630399 + 0.363961i 0.0248993 + 0.0143756i 0.512398 0.858748i \(-0.328757\pi\)
−0.487499 + 0.873124i \(0.662091\pi\)
\(642\) 0 0
\(643\) 25.2633i 0.996288i 0.867094 + 0.498144i \(0.165985\pi\)
−0.867094 + 0.498144i \(0.834015\pi\)
\(644\) −17.7408 7.24264i −0.699084 0.285400i
\(645\) 0 0
\(646\) −1.50000 2.59808i −0.0590167 0.102220i
\(647\) −19.7700 + 34.2426i −0.777239 + 1.34622i 0.156289 + 0.987711i \(0.450047\pi\)
−0.933528 + 0.358506i \(0.883286\pi\)
\(648\) 0 0
\(649\) −12.9853 + 7.49706i −0.509717 + 0.294285i
\(650\) −2.44949 −0.0960769
\(651\) 0 0
\(652\) 14.9706 0.586292
\(653\) −2.41344 + 1.39340i −0.0944451 + 0.0545279i −0.546479 0.837473i \(-0.684032\pi\)
0.452034 + 0.892001i \(0.350699\pi\)
\(654\) 0 0
\(655\) 13.9706 24.1977i 0.545875 0.945483i
\(656\) −0.717439 1.24264i −0.0280113 0.0485170i
\(657\) 0 0
\(658\) −15.9853 + 12.3960i −0.623171 + 0.483248i
\(659\) 16.2426i 0.632723i −0.948639 0.316362i \(-0.897539\pi\)
0.948639 0.316362i \(-0.102461\pi\)
\(660\) 0 0
\(661\) 15.6213 + 9.01897i 0.607599 + 0.350797i 0.772025 0.635592i \(-0.219244\pi\)
−0.164426 + 0.986389i \(0.552577\pi\)
\(662\) 12.1244 + 7.00000i 0.471226 + 0.272063i
\(663\) 0 0
\(664\) 12.8418i 0.498358i
\(665\) 8.87039 6.87868i 0.343979 0.266744i
\(666\) 0 0
\(667\) 4.50000 + 7.79423i 0.174241 + 0.301794i
\(668\) −0.210133 + 0.363961i −0.00813029 + 0.0140821i
\(669\) 0 0
\(670\) 26.4853 15.2913i 1.02322 0.590754i
\(671\) 10.3923 0.401190
\(672\) 0 0
\(673\) 38.2426 1.47415 0.737073 0.675813i \(-0.236207\pi\)
0.737073 + 0.675813i \(0.236207\pi\)
\(674\) −20.9947 + 12.1213i −0.808687 + 0.466896i
\(675\) 0 0
\(676\) 3.50000 6.06218i 0.134615 0.233161i
\(677\) −4.24309 7.34924i −0.163075 0.282454i 0.772895 0.634534i \(-0.218808\pi\)
−0.935970 + 0.352080i \(0.885475\pi\)
\(678\) 0 0
\(679\) −7.75736 3.16693i −0.297700 0.121536i
\(680\) 4.24264i 0.162698i
\(681\) 0 0
\(682\) 1.24264 + 0.717439i 0.0475832 + 0.0274722i
\(683\) −5.64191 3.25736i −0.215882 0.124639i 0.388160 0.921592i \(-0.373111\pi\)
−0.604042 + 0.796953i \(0.706444\pi\)
\(684\) 0 0
\(685\) 4.30463i 0.164472i
\(686\) 11.0482 14.8640i 0.421822 0.567509i
\(687\) 0 0
\(688\) −0.500000 0.866025i −0.0190623 0.0330169i
\(689\) 0 0
\(690\) 0 0
\(691\) −18.5147 + 10.6895i −0.704333 + 0.406647i −0.808959 0.587865i \(-0.799969\pi\)
0.104626 + 0.994512i \(0.466635\pi\)
\(692\) −2.02922 −0.0771395
\(693\) 0 0
\(694\) 15.5147 0.588931
\(695\) 0.630399 0.363961i 0.0239124 0.0138058i
\(696\) 0 0
\(697\) −1.24264 + 2.15232i −0.0470684 + 0.0815248i
\(698\) 7.34847 + 12.7279i 0.278144 + 0.481759i
\(699\) 0 0
\(700\) −2.62132 + 0.358719i −0.0990766 + 0.0135583i
\(701\) 40.7574i 1.53938i 0.638415 + 0.769692i \(0.279590\pi\)
−0.638415 + 0.769692i \(0.720410\pi\)
\(702\) 0 0
\(703\) −4.86396 2.80821i −0.183448 0.105914i
\(704\) −0.866025 0.500000i −0.0326396 0.0188445i
\(705\) 0 0
\(706\) 8.78335i 0.330566i
\(707\) 17.0488 + 21.9853i 0.641187 + 0.826842i
\(708\) 0 0
\(709\) −1.37868 2.38794i −0.0517774 0.0896811i 0.838975 0.544170i \(-0.183155\pi\)
−0.890752 + 0.454489i \(0.849822\pi\)
\(710\) −8.87039 + 15.3640i −0.332900 + 0.576599i
\(711\) 0 0
\(712\) −0.878680 + 0.507306i −0.0329299 + 0.0190121i
\(713\) −10.3923 −0.389195
\(714\) 0 0
\(715\) −6.00000 −0.224387
\(716\) −7.79423 + 4.50000i −0.291284 + 0.168173i
\(717\) 0 0
\(718\) 0.514719 0.891519i 0.0192091 0.0332712i
\(719\) 3.40256 + 5.89340i 0.126894 + 0.219787i 0.922472 0.386065i \(-0.126166\pi\)
−0.795578 + 0.605851i \(0.792833\pi\)
\(720\) 0 0
\(721\) 5.84924 + 42.7430i 0.217837 + 1.59183i
\(722\) 16.0000i 0.595458i
\(723\) 0 0
\(724\) 4.24264 + 2.44949i 0.157676 + 0.0910346i
\(725\) 1.07616 + 0.621320i 0.0399675 + 0.0230753i
\(726\) 0 0
\(727\) 38.1051i 1.41324i −0.707593 0.706620i \(-0.750219\pi\)
0.707593 0.706620i \(-0.249781\pi\)
\(728\) −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
\(733\) −4.45584 + 2.57258i −0.164580 + 0.0950205i −0.580028 0.814597i \(-0.696958\pi\)
0.415447 + 0.909617i \(0.363625\pi\)
\(734\) 11.8272 0.436549
\(735\) 0 0
\(736\) 7.24264 0.266967
\(737\) 10.8126 6.24264i 0.398286 0.229951i
\(738\) 0 0
\(739\) −1.72792 + 2.99285i −0.0635626 + 0.110094i −0.896055 0.443942i \(-0.853580\pi\)
0.832493 + 0.554036i \(0.186913\pi\)
\(740\) 3.97141 + 6.87868i 0.145992 + 0.252865i
\(741\) 0 0
\(742\) 0 0
\(743\) 35.6985i 1.30965i −0.755780 0.654825i \(-0.772742\pi\)
0.755780 0.654825i \(-0.227258\pi\)
\(744\) 0 0
\(745\) 10.0919 + 5.82655i 0.369738 + 0.213468i
\(746\) 29.4449 + 17.0000i 1.07805 + 0.622414i
\(747\) 0 0
\(748\) 1.73205i 0.0633300i
\(749\) −5.19615 37.9706i −0.189863 1.38741i
\(750\) 0 0
\(751\) 10.8787 + 18.8424i 0.396969 + 0.687570i 0.993350 0.115131i \(-0.0367288\pi\)
−0.596382 + 0.802701i \(0.703395\pi\)
\(752\) 3.82282 6.62132i 0.139404 0.241455i
\(753\) 0 0
\(754\) 2.63604 1.52192i 0.0959989 0.0554250i
\(755\) −6.75412 −0.245808
\(756\) 0 0
\(757\) 41.6690 1.51449 0.757244 0.653132i \(-0.226546\pi\)
0.757244 + 0.653132i \(0.226546\pi\)
\(758\) −28.3432 + 16.3640i −1.02947 + 0.594366i
\(759\) 0 0
\(760\) −2.12132 + 3.67423i −0.0769484 + 0.133278i
\(761\) 18.0379 + 31.2426i 0.653875 + 1.13254i 0.982175 + 0.187971i \(0.0601911\pi\)
−0.328299 + 0.944574i \(0.606476\pi\)
\(762\) 0 0
\(763\) 15.8198 + 20.4004i 0.572715 + 0.738544i
\(764\) 16.9706i 0.613973i
\(765\) 0 0
\(766\) 33.3198 + 19.2372i 1.20389 + 0.695068i
\(767\) −31.8073 18.3640i −1.14850 0.663084i
\(768\) 0 0
\(769\) 8.53716i 0.307858i 0.988082 + 0.153929i \(0.0491927\pi\)
−0.988082 + 0.153929i \(0.950807\pi\)
\(770\) −6.42090 + 0.878680i −0.231393 + 0.0316654i
\(771\) 0 0
\(772\) −10.3640 17.9509i −0.373007 0.646067i
\(773\) 15.7986 27.3640i 0.568236 0.984213i −0.428505 0.903540i \(-0.640959\pi\)
0.996741 0.0806737i \(-0.0257072\pi\)
\(774\) 0 0
\(775\) −1.24264 + 0.717439i −0.0446370 + 0.0257712i
\(776\) 3.16693 0.113686
\(777\) 0 0
\(778\) −36.7279 −1.31676
\(779\) −2.15232 + 1.24264i −0.0771148 + 0.0445222i
\(780\) 0 0
\(781\) −3.62132 + 6.27231i −0.129581 + 0.224441i
\(782\) −6.27231 10.8640i −0.224297 0.388494i
\(783\) 0 0
\(784\) −1.74264 + 6.77962i −0.0622372 + 0.242129i
\(785\) 10.2426i 0.365576i
\(786\) 0 0
\(787\) 6.47056 + 3.73578i 0.230651 + 0.133166i 0.610872 0.791729i \(-0.290819\pi\)
−0.380222 + 0.924895i \(0.624152\pi\)
\(788\) −3.22848 1.86396i −0.115010 0.0664009i
\(789\) 0 0
\(790\)