Properties

Label 1386.2.r.b.89.1
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: \(x^{8} - x^{4} + 1\)
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 89.1
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 1386.89
Dual form 1386.2.r.b.1277.1

$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

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

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 \(0.351172\pi\)
−0.998430 + 0.0560116i \(0.982162\pi\)
\(6\) 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 \(-0.889680\pi\)
0.940540 0.339683i \(-0.110320\pi\)
\(14\) −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 \(-0.0993066\pi\)
−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
\(23\) 6.27231 + 3.62132i 1.30787 + 0.755097i 0.981740 0.190228i \(-0.0609228\pi\)
0.326127 + 0.945326i \(0.394256\pi\)
\(24\) 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 −0.384239 0.923234i \(-0.625536\pi\)
0.607424 + 0.794378i \(0.292203\pi\)
\(32\) 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 −0.701423 0.712745i \(-0.747452\pi\)
0.967967 + 0.251078i \(0.0807851\pi\)
\(38\) 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 \(-0.535740\pi\)
−0.112045 + 0.993703i \(0.535740\pi\)
\(42\) 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 0.440079 + 0.897959i \(0.354950\pi\)
−0.997695 + 0.0678598i \(0.978383\pi\)
\(48\) 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
\(58\) −0.621320 + 1.07616i −0.0815834 + 0.141307i
\(59\) 7.49706 + 12.9853i 0.976034 + 1.69054i 0.676481 + 0.736460i \(0.263504\pi\)
0.299552 + 0.954080i \(0.403163\pi\)
\(60\) 0 0
\(61\) 9.00000 + 5.19615i 1.15233 + 0.665299i 0.949454 0.313905i \(-0.101637\pi\)
0.202878 + 0.979204i \(0.434971\pi\)
\(62\) −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 0.941475 + 0.337083i \(0.109440\pi\)
−0.178815 + 0.983883i \(0.557226\pi\)
\(68\) −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 −0.230730 0.973018i \(-0.574111\pi\)
0.727293 + 0.686327i \(0.240778\pi\)
\(74\) −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 −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) −1.22474 2.12132i −0.136931 0.237171i
\(81\) 0 0
\(82\) 1.24264 + 0.717439i 0.137227 + 0.0792279i
\(83\) −12.8418 −1.40957 −0.704785 0.709421i \(-0.748957\pi\)
−0.704785 + 0.709421i \(0.748957\pi\)
\(84\) 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 \(-0.816208\pi\)
0.891660 + 0.452707i \(0.149542\pi\)
\(90\) 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 \(-0.948600\pi\)
0.986991 0.160776i \(-0.0513998\pi\)
\(98\) 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 −0.999637 0.0269533i \(-0.991419\pi\)
0.476476 0.879187i \(-0.341914\pi\)
\(102\) 0 0
\(103\) 14.1213 + 8.15295i 1.39142 + 0.803334i 0.993472 0.114076i \(-0.0363908\pi\)
0.397943 + 0.917410i \(0.369724\pi\)
\(104\) −2.44949 −0.240192
\(105\) 0 0
\(106\) 0 0
\(107\) 12.5446 + 7.24264i 1.21273 + 0.700173i 0.963354 0.268233i \(-0.0864397\pi\)
0.249380 + 0.968406i \(0.419773\pi\)
\(108\) 0 0
\(109\) 4.87868 + 8.45012i 0.467293 + 0.809375i 0.999302 0.0373639i \(-0.0118961\pi\)
−0.532009 + 0.846739i \(0.678563\pi\)
\(110\) −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 \(-0.667286\pi\)
0.999998 + 0.00194634i \(0.000619541\pi\)
\(132\) 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 \(-0.690585\pi\)
0.433576 + 0.901117i \(0.357252\pi\)
\(138\) 0 0
\(139\) 0.297173i 0.0252059i 0.999921 + 0.0126029i \(0.00401175\pi\)
−0.999921 + 0.0126029i \(0.995988\pi\)
\(140\) 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 \(-0.395762\pi\)
−0.659176 + 0.751989i \(0.729095\pi\)
\(150\) 0 0
\(151\) −1.37868 2.38794i −0.112195 0.194328i 0.804460 0.594007i \(-0.202455\pi\)
−0.916655 + 0.399679i \(0.869122\pi\)
\(152\) −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 −0.348484 0.937315i \(-0.613303\pi\)
0.637497 + 0.770453i \(0.279970\pi\)
\(158\) 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 −0.408420 0.912794i \(-0.633920\pi\)
0.994713 0.102694i \(-0.0327464\pi\)
\(164\) −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 \(-0.494824\pi\)
0.0162606 + 0.999868i \(0.494824\pi\)
\(168\) 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 \(-0.808755\pi\)
0.902015 + 0.431705i \(0.142088\pi\)
\(174\) 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 \(-0.557476\pi\)
0.762153 + 0.647397i \(0.224142\pi\)
\(180\) 0 0
\(181\) 4.89898i 0.364138i −0.983286 0.182069i \(-0.941721\pi\)
0.983286 0.182069i \(-0.0582795\pi\)
\(182\) 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 \(-0.122904\pi\)
0.137053 + 0.990564i \(0.456237\pi\)
\(192\) 0 0
\(193\) 10.3640 + 17.9509i 0.746014 + 1.29213i 0.949719 + 0.313102i \(0.101368\pi\)
−0.203705 + 0.979032i \(0.565298\pi\)
\(194\) −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 −0.708307 0.705905i \(-0.750541\pi\)
0.257178 + 0.966364i \(0.417207\pi\)
\(200\) −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 \(0.101665\pi\)
−0.949427 + 0.313988i \(0.898335\pi\)
\(224\) −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 \(-0.234077\pi\)
−0.951776 + 0.306794i \(0.900744\pi\)
\(228\) 0 0
\(229\) −12.0000 6.92820i −0.792982 0.457829i 0.0480291 0.998846i \(-0.484706\pi\)
−0.841011 + 0.541017i \(0.818039\pi\)
\(230\) 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 \(-0.139210\pi\)
0.0861503 + 0.996282i \(0.472543\pi\)
\(234\) 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 −0.809829 0.586666i \(-0.800440\pi\)
0.103153 + 0.994665i \(0.467107\pi\)
\(242\) −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 \(-0.697940\pi\)
−0.582536 + 0.812805i \(0.697940\pi\)
\(252\) 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 \(-0.996347\pi\)
0.509904 + 0.860231i \(0.329681\pi\)
\(258\) 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 \(-0.362536\pi\)
0.995795 + 0.0916144i \(0.0292027\pi\)
\(264\) 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 −0.910109 0.414370i \(-0.864002\pi\)
0.0961996 0.995362i \(-0.469331\pi\)
\(270\) 0 0
\(271\) 1.75736 + 1.01461i 0.106752 + 0.0616333i 0.552425 0.833562i \(-0.313702\pi\)
−0.445673 + 0.895196i \(0.647036\pi\)
\(272\) −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 0.845811 + 0.533483i \(0.179117\pi\)
0.0391041 + 0.999235i \(0.487550\pi\)
\(278\) 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 −0.578765 + 0.815494i \(0.696465\pi\)
−0.995621 + 0.0934783i \(0.970201\pi\)
\(284\) −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 \(-0.433965\pi\)
0.205971 + 0.978558i \(0.433965\pi\)
\(294\) 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 \(0.0688667\pi\)
−0.976687 + 0.214667i \(0.931133\pi\)
\(308\) −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 −0.948526 0.316699i \(-0.897425\pi\)
0.199994 0.979797i \(-0.435908\pi\)
\(312\) 0 0
\(313\) 6.98528 + 4.03295i 0.394831 + 0.227956i 0.684251 0.729246i \(-0.260129\pi\)
−0.289420 + 0.957202i \(0.593462\pi\)
\(314\) −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 \(-0.403237\pi\)
−0.676654 + 0.736302i \(0.736570\pi\)
\(318\) 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 −0.606980 0.794717i \(-0.707619\pi\)
0.991735 + 0.128302i \(0.0409527\pi\)
\(332\) −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 \(-0.803388\pi\)
0.0939374 + 0.995578i \(0.470055\pi\)
\(348\) 0 0
\(349\) 14.6969i 0.786709i −0.919387 0.393355i \(-0.871314\pi\)
0.919387 0.393355i \(-0.128686\pi\)
\(350\) 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 \(-0.241765\pi\)
−0.958907 + 0.283720i \(0.908431\pi\)
\(354\) 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 \(-0.341982\pi\)
−0.523342 + 0.852123i \(0.675315\pi\)
\(360\) 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 −0.208251 0.978075i \(-0.566777\pi\)
0.742913 + 0.669388i \(0.233444\pi\)
\(368\) −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 0.0291379 0.999575i \(-0.490724\pi\)
0.851089 0.525022i \(-0.175943\pi\)
\(374\) 0.866025 + 1.50000i 0.0447811 + 0.0775632i
\(375\) 0 0
\(376\) 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 −0.332364 + 0.943151i \(0.607846\pi\)
−0.650611 + 0.759411i \(0.725487\pi\)
\(384\) 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 0.623952 0.781462i \(-0.285526\pi\)
0.988742 0.149627i \(-0.0478074\pi\)
\(390\) 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 0.996538 0.0831378i \(-0.0264941\pi\)
0.426270 + 0.904596i \(0.359827\pi\)
\(398\) 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 \(-0.582469\pi\)
−0.965220 + 0.261440i \(0.915803\pi\)
\(402\) 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 −0.490975 0.871174i \(-0.663359\pi\)
0.508971 + 0.860783i \(0.330026\pi\)
\(410\) −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 \(-0.464144\pi\)
0.112406 + 0.993662i \(0.464144\pi\)
\(420\) 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 \(-0.800692\pi\)
0.102366 + 0.994747i \(0.467359\pi\)
\(432\) 0 0
\(433\) 21.3280i 1.02496i −0.858700 0.512478i \(-0.828727\pi\)
0.858700 0.512478i \(-0.171273\pi\)
\(434\) 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 0.917537 0.397651i \(-0.130175\pi\)
0.114393 + 0.993436i \(0.463508\pi\)
\(440\) −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
\(445\) 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 0.138910 + 0.990305i \(0.455640\pi\)
−0.927084 + 0.374853i \(0.877693\pi\)
\(458\) 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 \(-0.350186\pi\)
0.453470 + 0.891272i \(0.350186\pi\)
\(462\) 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 \(-0.871695\pi\)
0.799632 + 0.600491i \(0.205028\pi\)
\(468\) 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 0.992770 + 0.120031i \(0.0382993\pi\)
−0.392435 + 0.919780i \(0.628367\pi\)
\(480\) 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 0.851954 0.523616i \(-0.175417\pi\)
−0.879442 + 0.476006i \(0.842084\pi\)
\(488\) 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 −0.801766 0.597639i \(-0.796106\pi\)
0.918453 + 0.395530i \(0.129439\pi\)
\(500\) −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 \(-0.648619\pi\)
−0.450120 + 0.892968i \(0.648619\pi\)
\(504\) 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 −0.0610113 + 0.998137i \(0.519433\pi\)
−0.833906 + 0.551906i \(0.813901\pi\)
\(510\) 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 −0.996763 0.0803906i \(-0.974383\pi\)
0.428761 0.903418i \(-0.358950\pi\)
\(522\) 0 0
\(523\) −18.7279 10.8126i −0.818915 0.472801i 0.0311273 0.999515i \(-0.490090\pi\)
−0.850042 + 0.526715i \(0.823424\pi\)
\(524\) 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 −0.576388 0.817176i \(-0.695538\pi\)
0.995889 + 0.0905782i \(0.0288715\pi\)
\(542\) −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 \(-0.972612\pi\)
−0.423728 + 0.905790i \(0.639279\pi\)
\(558\) 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 \(-0.132574\pi\)
−0.807612 + 0.589715i \(0.799240\pi\)
\(564\) 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 \(-0.129905\pi\)
0.115235 + 0.993338i \(0.463238\pi\)
\(570\) 0 0
\(571\) 13.7426 + 23.8030i 0.575112 + 0.996123i 0.996030 + 0.0890238i \(0.0283747\pi\)
−0.420918 + 0.907099i \(0.638292\pi\)
\(572\) −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 −0.436253 0.899824i \(-0.643695\pi\)
0.561144 + 0.827718i \(0.310361\pi\)
\(578\) −12.1244 + 7.00000i −0.504307 + 0.291162i
\(579\) 0 0
\(580\) 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 \(-0.403606\pi\)
0.298223 + 0.954496i \(0.403606\pi\)
\(588\) 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 \(-0.871268\pi\)
0.800436 + 0.599418i \(0.204601\pi\)
\(594\) 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 \(-0.546802\pi\)
0.783430 + 0.621480i \(0.213468\pi\)
\(600\) 0 0
\(601\) 17.1464i 0.699417i 0.936858 + 0.349709i \(0.113719\pi\)
−0.936858 + 0.349709i \(0.886281\pi\)
\(602\) −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 0.959834 0.280569i \(-0.0905232\pi\)
0.236937 + 0.971525i \(0.423857\pi\)
\(608\) −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 −0.980371 0.197164i \(-0.936827\pi\)
0.319436 0.947608i \(-0.396506\pi\)
\(614\) 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 −0.963708 0.266957i \(-0.913982\pi\)
−0.250663 + 0.968074i \(0.580649\pi\)
\(620\) −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 \(-0.671243\pi\)
0.487499 + 0.873124i \(0.337909\pi\)
\(642\) 0 0
\(643\) 25.2633i 0.996288i −0.867094 0.498144i \(-0.834015\pi\)
0.867094 0.498144i \(-0.165985\pi\)
\(644\) 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 0.933528 + 0.358506i \(0.116714\pi\)
−0.156289 + 0.987711i \(0.549953\pi\)
\(648\) 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 \(-0.315968\pi\)
−0.452034 + 0.892001i \(0.649301\pi\)
\(654\) 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 −0.164426 0.986389i \(-0.552577\pi\)
0.772025 + 0.635592i \(0.219244\pi\)
\(662\) −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 \(-0.781192\pi\)
0.935970 + 0.352080i \(0.114525\pi\)
\(678\) 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 \(-0.626889\pi\)
0.604042 + 0.796953i \(0.293556\pi\)
\(684\) 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 0.104626 0.994512i \(-0.466635\pi\)
−0.808959 + 0.587865i \(0.799969\pi\)
\(692\) 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 −0.890752 0.454489i \(-0.849822\pi\)
0.838975 + 0.544170i \(0.183155\pi\)
\(710\) 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 \(-0.873834\pi\)
0.795578 + 0.605851i \(0.207167\pi\)
\(720\) 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 \(0.249781\pi\)
−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
\(733\) −4.45584 2.57258i −0.164580 0.0950205i 0.415447 0.909617i \(-0.363625\pi\)
−0.580028 + 0.814597i \(0.696958\pi\)
\(734\) −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 0.832493 0.554036i \(-0.186913\pi\)
−0.896055 + 0.443942i \(0.853580\pi\)
\(740\) −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 −0.596382 0.802701i \(-0.703395\pi\)
0.993350 + 0.115131i \(0.0367288\pi\)
\(752\) −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 0.328299 + 0.944574i \(0.393524\pi\)
−0.982175 + 0.187971i \(0.939809\pi\)
\(762\) 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 \(-0.950807\pi\)
0.988082 0.153929i \(-0.0491927\pi\)
\(770\) 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 −0.996741 0.0806737i \(-0.974293\pi\)
0.428505 0.903540i \(-0.359041\pi\)
\(774\) 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 −0.380222 0.924895i \(-0.624152\pi\)
0.610872 + 0.791729i \(0.290819\pi\)
\(788\) 3.22848 1.86396i 0.115010 0.0664009i
\(789\) 0 0
\(790\)