Properties

Label 855.2.k.b.676.1
Level $855$
Weight $2$
Character 855.676
Analytic conductor $6.827$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.82720937282\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 676.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 855.676
Dual form 855.2.k.b.406.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} -4.00000 q^{7} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} -4.00000 q^{7} -3.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(-2.00000 + 3.46410i) q^{16} +(3.00000 - 5.19615i) q^{17} +(-3.50000 - 2.59808i) q^{19} -2.00000 q^{20} +(-0.500000 - 0.866025i) q^{25} +(-4.00000 - 6.92820i) q^{28} +(-1.50000 - 2.59808i) q^{29} -7.00000 q^{31} +(2.00000 - 3.46410i) q^{35} +8.00000 q^{37} +(-3.00000 + 5.19615i) q^{41} +(2.00000 - 3.46410i) q^{43} +(-3.00000 - 5.19615i) q^{44} +(3.00000 + 5.19615i) q^{47} +9.00000 q^{49} +(2.00000 - 3.46410i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(1.50000 - 2.59808i) q^{55} +(-7.50000 + 12.9904i) q^{59} +(-2.50000 - 4.33013i) q^{61} -8.00000 q^{64} +2.00000 q^{65} +(-1.00000 - 1.73205i) q^{67} +12.0000 q^{68} +(-1.50000 + 2.59808i) q^{71} +(-4.00000 + 6.92820i) q^{73} +(1.00000 - 8.66025i) q^{76} +12.0000 q^{77} +(-2.50000 + 4.33013i) q^{79} +(-2.00000 - 3.46410i) q^{80} -12.0000 q^{83} +(3.00000 + 5.19615i) q^{85} +(-7.50000 - 12.9904i) q^{89} +(4.00000 + 6.92820i) q^{91} +(4.00000 - 1.73205i) q^{95} +(-4.00000 + 6.92820i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{4} - q^{5} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{4} - q^{5} - 8 q^{7} - 6 q^{11} - 2 q^{13} - 4 q^{16} + 6 q^{17} - 7 q^{19} - 4 q^{20} - q^{25} - 8 q^{28} - 3 q^{29} - 14 q^{31} + 4 q^{35} + 16 q^{37} - 6 q^{41} + 4 q^{43} - 6 q^{44} + 6 q^{47} + 18 q^{49} + 4 q^{52} - 6 q^{53} + 3 q^{55} - 15 q^{59} - 5 q^{61} - 16 q^{64} + 4 q^{65} - 2 q^{67} + 24 q^{68} - 3 q^{71} - 8 q^{73} + 2 q^{76} + 24 q^{77} - 5 q^{79} - 4 q^{80} - 24 q^{83} + 6 q^{85} - 15 q^{89} + 8 q^{91} + 8 q^{95} - 8 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(3\) 0 0
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −4.00000 −1.51186 −0.755929 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 0 0
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i \(-0.573966\pi\)
0.957892 0.287129i \(-0.0927008\pi\)
\(18\) 0 0
\(19\) −3.50000 2.59808i −0.802955 0.596040i
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) −4.00000 6.92820i −0.755929 1.30931i
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.00000 3.46410i 0.338062 0.585540i
\(36\) 0 0
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i \(-0.988546\pi\)
0.530831 + 0.847477i \(0.321880\pi\)
\(42\) 0 0
\(43\) 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i \(-0.734678\pi\)
0.977261 + 0.212041i \(0.0680112\pi\)
\(44\) −3.00000 5.19615i −0.452267 0.783349i
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) 0 0
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) 0 0
\(52\) 2.00000 3.46410i 0.277350 0.480384i
\(53\) −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 0 0
\(55\) 1.50000 2.59808i 0.202260 0.350325i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −7.50000 + 12.9904i −0.976417 + 1.69120i −0.301239 + 0.953549i \(0.597400\pi\)
−0.675178 + 0.737655i \(0.735933\pi\)
\(60\) 0 0
\(61\) −2.50000 4.33013i −0.320092 0.554416i 0.660415 0.750901i \(-0.270381\pi\)
−0.980507 + 0.196485i \(0.937047\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) 12.0000 1.45521
\(69\) 0 0
\(70\) 0 0
\(71\) −1.50000 + 2.59808i −0.178017 + 0.308335i −0.941201 0.337846i \(-0.890302\pi\)
0.763184 + 0.646181i \(0.223635\pi\)
\(72\) 0 0
\(73\) −4.00000 + 6.92820i −0.468165 + 0.810885i −0.999338 0.0363782i \(-0.988418\pi\)
0.531174 + 0.847263i \(0.321751\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 1.00000 8.66025i 0.114708 0.993399i
\(77\) 12.0000 1.36753
\(78\) 0 0
\(79\) −2.50000 + 4.33013i −0.281272 + 0.487177i −0.971698 0.236225i \(-0.924090\pi\)
0.690426 + 0.723403i \(0.257423\pi\)
\(80\) −2.00000 3.46410i −0.223607 0.387298i
\(81\) 0 0
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 3.00000 + 5.19615i 0.325396 + 0.563602i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −7.50000 12.9904i −0.794998 1.37698i −0.922840 0.385183i \(-0.874138\pi\)
0.127842 0.991795i \(-0.459195\pi\)
\(90\) 0 0
\(91\) 4.00000 + 6.92820i 0.419314 + 0.726273i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.00000 1.73205i 0.410391 0.177705i
\(96\) 0 0
\(97\) −4.00000 + 6.92820i −0.406138 + 0.703452i −0.994453 0.105180i \(-0.966458\pi\)
0.588315 + 0.808632i \(0.299792\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.00000 1.73205i 0.100000 0.173205i
\(101\) 7.50000 + 12.9904i 0.746278 + 1.29259i 0.949595 + 0.313478i \(0.101494\pi\)
−0.203317 + 0.979113i \(0.565172\pi\)
\(102\) 0 0
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −5.50000 + 9.52628i −0.526804 + 0.912452i 0.472708 + 0.881219i \(0.343277\pi\)
−0.999512 + 0.0312328i \(0.990057\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 8.00000 13.8564i 0.755929 1.30931i
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) 0 0
\(118\) 0 0
\(119\) −12.0000 + 20.7846i −1.10004 + 1.90532i
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) 0 0
\(124\) −7.00000 12.1244i −0.628619 1.08880i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −1.00000 1.73205i −0.0887357 0.153695i 0.818241 0.574875i \(-0.194949\pi\)
−0.906977 + 0.421180i \(0.861616\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.00000 10.3923i 0.524222 0.907980i −0.475380 0.879781i \(-0.657689\pi\)
0.999602 0.0281993i \(-0.00897729\pi\)
\(132\) 0 0
\(133\) 14.0000 + 10.3923i 1.21395 + 0.901127i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.00000 10.3923i −0.512615 0.887875i −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) 0 0
\(139\) 8.00000 + 13.8564i 0.678551 + 1.17529i 0.975417 + 0.220366i \(0.0707252\pi\)
−0.296866 + 0.954919i \(0.595942\pi\)
\(140\) 8.00000 0.676123
\(141\) 0 0
\(142\) 0 0
\(143\) 3.00000 + 5.19615i 0.250873 + 0.434524i
\(144\) 0 0
\(145\) 3.00000 0.249136
\(146\) 0 0
\(147\) 0 0
\(148\) 8.00000 + 13.8564i 0.657596 + 1.13899i
\(149\) 1.50000 2.59808i 0.122885 0.212843i −0.798019 0.602632i \(-0.794119\pi\)
0.920904 + 0.389789i \(0.127452\pi\)
\(150\) 0 0
\(151\) 17.0000 1.38344 0.691720 0.722166i \(-0.256853\pi\)
0.691720 + 0.722166i \(0.256853\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3.50000 6.06218i 0.281127 0.486926i
\(156\) 0 0
\(157\) −1.00000 + 1.73205i −0.0798087 + 0.138233i −0.903167 0.429289i \(-0.858764\pi\)
0.823359 + 0.567521i \(0.192098\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −10.0000 −0.783260 −0.391630 0.920123i \(-0.628089\pi\)
−0.391630 + 0.920123i \(0.628089\pi\)
\(164\) −12.0000 −0.937043
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) 0 0
\(172\) 8.00000 0.609994
\(173\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) 2.00000 + 3.46410i 0.151186 + 0.261861i
\(176\) 6.00000 10.3923i 0.452267 0.783349i
\(177\) 0 0
\(178\) 0 0
\(179\) 9.00000 0.672692 0.336346 0.941739i \(-0.390809\pi\)
0.336346 + 0.941739i \(0.390809\pi\)
\(180\) 0 0
\(181\) −1.00000 1.73205i −0.0743294 0.128742i 0.826465 0.562988i \(-0.190348\pi\)
−0.900794 + 0.434246i \(0.857015\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.00000 + 6.92820i −0.294086 + 0.509372i
\(186\) 0 0
\(187\) −9.00000 + 15.5885i −0.658145 + 1.13994i
\(188\) −6.00000 + 10.3923i −0.437595 + 0.757937i
\(189\) 0 0
\(190\) 0 0
\(191\) 15.0000 1.08536 0.542681 0.839939i \(-0.317409\pi\)
0.542681 + 0.839939i \(0.317409\pi\)
\(192\) 0 0
\(193\) 8.00000 13.8564i 0.575853 0.997406i −0.420096 0.907480i \(-0.638004\pi\)
0.995948 0.0899262i \(-0.0286631\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 9.00000 + 15.5885i 0.642857 + 1.11346i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) 9.50000 + 16.4545i 0.673437 + 1.16643i 0.976923 + 0.213591i \(0.0685161\pi\)
−0.303486 + 0.952836i \(0.598151\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 6.00000 + 10.3923i 0.421117 + 0.729397i
\(204\) 0 0
\(205\) −3.00000 5.19615i −0.209529 0.362915i
\(206\) 0 0
\(207\) 0 0
\(208\) 8.00000 0.554700
\(209\) 10.5000 + 7.79423i 0.726300 + 0.539138i
\(210\) 0 0
\(211\) 3.50000 6.06218i 0.240950 0.417338i −0.720035 0.693938i \(-0.755874\pi\)
0.960985 + 0.276600i \(0.0892077\pi\)
\(212\) 6.00000 10.3923i 0.412082 0.713746i
\(213\) 0 0
\(214\) 0 0
\(215\) 2.00000 + 3.46410i 0.136399 + 0.236250i
\(216\) 0 0
\(217\) 28.0000 1.90076
\(218\) 0 0
\(219\) 0 0
\(220\) 6.00000 0.404520
\(221\) −12.0000 −0.807207
\(222\) 0 0
\(223\) 2.00000 3.46410i 0.133930 0.231973i −0.791258 0.611482i \(-0.790574\pi\)
0.925188 + 0.379509i \(0.123907\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 24.0000 1.59294 0.796468 0.604681i \(-0.206699\pi\)
0.796468 + 0.604681i \(0.206699\pi\)
\(228\) 0 0
\(229\) −7.00000 −0.462573 −0.231287 0.972886i \(-0.574293\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) −30.0000 −1.95283
\(237\) 0 0
\(238\) 0 0
\(239\) 3.00000 0.194054 0.0970269 0.995282i \(-0.469067\pi\)
0.0970269 + 0.995282i \(0.469067\pi\)
\(240\) 0 0
\(241\) −2.50000 4.33013i −0.161039 0.278928i 0.774202 0.632938i \(-0.218151\pi\)
−0.935242 + 0.354010i \(0.884818\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 5.00000 8.66025i 0.320092 0.554416i
\(245\) −4.50000 + 7.79423i −0.287494 + 0.497955i
\(246\) 0 0
\(247\) −1.00000 + 8.66025i −0.0636285 + 0.551039i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −7.50000 12.9904i −0.473396 0.819946i 0.526140 0.850398i \(-0.323639\pi\)
−0.999536 + 0.0304521i \(0.990305\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −9.00000 15.5885i −0.561405 0.972381i −0.997374 0.0724199i \(-0.976928\pi\)
0.435970 0.899961i \(-0.356405\pi\)
\(258\) 0 0
\(259\) −32.0000 −1.98838
\(260\) 2.00000 + 3.46410i 0.124035 + 0.214834i
\(261\) 0 0
\(262\) 0 0
\(263\) −9.00000 + 15.5885i −0.554964 + 0.961225i 0.442943 + 0.896550i \(0.353935\pi\)
−0.997906 + 0.0646755i \(0.979399\pi\)
\(264\) 0 0
\(265\) 6.00000 0.368577
\(266\) 0 0
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) −10.5000 + 18.1865i −0.640196 + 1.10885i 0.345192 + 0.938532i \(0.387814\pi\)
−0.985389 + 0.170321i \(0.945520\pi\)
\(270\) 0 0
\(271\) −5.50000 + 9.52628i −0.334101 + 0.578680i −0.983312 0.181928i \(-0.941766\pi\)
0.649211 + 0.760609i \(0.275099\pi\)
\(272\) 12.0000 + 20.7846i 0.727607 + 1.26025i
\(273\) 0 0
\(274\) 0 0
\(275\) 1.50000 + 2.59808i 0.0904534 + 0.156670i
\(276\) 0 0
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3.00000 + 5.19615i 0.178965 + 0.309976i 0.941526 0.336939i \(-0.109392\pi\)
−0.762561 + 0.646916i \(0.776058\pi\)
\(282\) 0 0
\(283\) −7.00000 + 12.1244i −0.416107 + 0.720718i −0.995544 0.0942988i \(-0.969939\pi\)
0.579437 + 0.815017i \(0.303272\pi\)
\(284\) −6.00000 −0.356034
\(285\) 0 0
\(286\) 0 0
\(287\) 12.0000 20.7846i 0.708338 1.22688i
\(288\) 0 0
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 0 0
\(291\) 0 0
\(292\) −16.0000 −0.936329
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 0 0
\(295\) −7.50000 12.9904i −0.436667 0.756329i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −8.00000 + 13.8564i −0.461112 + 0.798670i
\(302\) 0 0
\(303\) 0 0
\(304\) 16.0000 6.92820i 0.917663 0.397360i
\(305\) 5.00000 0.286299
\(306\) 0 0
\(307\) 17.0000 29.4449i 0.970241 1.68051i 0.275421 0.961324i \(-0.411183\pi\)
0.694820 0.719183i \(-0.255484\pi\)
\(308\) 12.0000 + 20.7846i 0.683763 + 1.18431i
\(309\) 0 0
\(310\) 0 0
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 0 0
\(313\) 5.00000 + 8.66025i 0.282617 + 0.489506i 0.972028 0.234863i \(-0.0754642\pi\)
−0.689412 + 0.724370i \(0.742131\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 12.0000 + 20.7846i 0.673987 + 1.16738i 0.976764 + 0.214318i \(0.0687530\pi\)
−0.302777 + 0.953062i \(0.597914\pi\)
\(318\) 0 0
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) 4.00000 6.92820i 0.223607 0.387298i
\(321\) 0 0
\(322\) 0 0
\(323\) −24.0000 + 10.3923i −1.33540 + 0.578243i
\(324\) 0 0
\(325\) −1.00000 + 1.73205i −0.0554700 + 0.0960769i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −12.0000 20.7846i −0.661581 1.14589i
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) −12.0000 20.7846i −0.658586 1.14070i
\(333\) 0 0
\(334\) 0 0
\(335\) 2.00000 0.109272
\(336\) 0 0
\(337\) 8.00000 13.8564i 0.435788 0.754807i −0.561572 0.827428i \(-0.689803\pi\)
0.997360 + 0.0726214i \(0.0231365\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) −6.00000 + 10.3923i −0.325396 + 0.563602i
\(341\) 21.0000 1.13721
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −12.0000 −0.638696 −0.319348 0.947638i \(-0.603464\pi\)
−0.319348 + 0.947638i \(0.603464\pi\)
\(354\) 0 0
\(355\) −1.50000 2.59808i −0.0796117 0.137892i
\(356\) 15.0000 25.9808i 0.794998 1.37698i
\(357\) 0 0
\(358\) 0 0
\(359\) 12.0000 20.7846i 0.633336 1.09697i −0.353529 0.935423i \(-0.615019\pi\)
0.986865 0.161546i \(-0.0516481\pi\)
\(360\) 0 0
\(361\) 5.50000 + 18.1865i 0.289474 + 0.957186i
\(362\) 0 0
\(363\) 0 0
\(364\) −8.00000 + 13.8564i −0.419314 + 0.726273i
\(365\) −4.00000 6.92820i −0.209370 0.362639i
\(366\) 0 0
\(367\) 2.00000 + 3.46410i 0.104399 + 0.180825i 0.913493 0.406855i \(-0.133375\pi\)
−0.809093 + 0.587680i \(0.800041\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 12.0000 + 20.7846i 0.623009 + 1.07908i
\(372\) 0 0
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.00000 + 5.19615i −0.154508 + 0.267615i
\(378\) 0 0
\(379\) −37.0000 −1.90056 −0.950281 0.311393i \(-0.899204\pi\)
−0.950281 + 0.311393i \(0.899204\pi\)
\(380\) 7.00000 + 5.19615i 0.359092 + 0.266557i
\(381\) 0 0
\(382\) 0 0
\(383\) 15.0000 25.9808i 0.766464 1.32755i −0.173005 0.984921i \(-0.555348\pi\)
0.939469 0.342634i \(-0.111319\pi\)
\(384\) 0 0
\(385\) −6.00000 + 10.3923i −0.305788 + 0.529641i
\(386\) 0 0
\(387\) 0 0
\(388\) −16.0000 −0.812277
\(389\) 7.50000 + 12.9904i 0.380265 + 0.658638i 0.991100 0.133120i \(-0.0424994\pi\)
−0.610835 + 0.791758i \(0.709166\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.50000 4.33013i −0.125789 0.217872i
\(396\) 0 0
\(397\) −4.00000 + 6.92820i −0.200754 + 0.347717i −0.948772 0.315963i \(-0.897673\pi\)
0.748017 + 0.663679i \(0.231006\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 4.00000 0.200000
\(401\) −16.5000 + 28.5788i −0.823971 + 1.42716i 0.0787327 + 0.996896i \(0.474913\pi\)
−0.902703 + 0.430263i \(0.858421\pi\)
\(402\) 0 0
\(403\) 7.00000 + 12.1244i 0.348695 + 0.603957i
\(404\) −15.0000 + 25.9808i −0.746278 + 1.29259i
\(405\) 0 0
\(406\) 0 0
\(407\) −24.0000 −1.18964
\(408\) 0 0
\(409\) −11.5000 19.9186i −0.568638 0.984911i −0.996701 0.0811615i \(-0.974137\pi\)
0.428063 0.903749i \(-0.359196\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −16.0000 27.7128i −0.788263 1.36531i
\(413\) 30.0000 51.9615i 1.47620 2.55686i
\(414\) 0 0
\(415\) 6.00000 10.3923i 0.294528 0.510138i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 3.00000 0.146560 0.0732798 0.997311i \(-0.476653\pi\)
0.0732798 + 0.997311i \(0.476653\pi\)
\(420\) 0 0
\(421\) 9.50000 16.4545i 0.463002 0.801942i −0.536107 0.844150i \(-0.680106\pi\)
0.999109 + 0.0422075i \(0.0134391\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −6.00000 −0.291043
\(426\) 0 0
\(427\) 10.0000 + 17.3205i 0.483934 + 0.838198i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −7.50000 12.9904i −0.361262 0.625725i 0.626907 0.779094i \(-0.284321\pi\)
−0.988169 + 0.153370i \(0.950987\pi\)
\(432\) 0 0
\(433\) −4.00000 6.92820i −0.192228 0.332948i 0.753760 0.657149i \(-0.228238\pi\)
−0.945988 + 0.324201i \(0.894905\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −22.0000 −1.05361
\(437\) 0 0
\(438\) 0 0
\(439\) 6.50000 11.2583i 0.310228 0.537331i −0.668184 0.743996i \(-0.732928\pi\)
0.978412 + 0.206666i \(0.0662612\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i \(-0.258683\pi\)
−0.972626 + 0.232377i \(0.925350\pi\)
\(444\) 0 0
\(445\) 15.0000 0.711068
\(446\) 0 0
\(447\) 0 0
\(448\) 32.0000 1.51186
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) 0 0
\(451\) 9.00000 15.5885i 0.423793 0.734032i
\(452\) −6.00000 10.3923i −0.282216 0.488813i
\(453\) 0 0
\(454\) 0 0
\(455\) −8.00000 −0.375046
\(456\) 0 0
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4.50000 + 7.79423i −0.209586 + 0.363013i −0.951584 0.307388i \(-0.900545\pi\)
0.741998 + 0.670402i \(0.233878\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 12.0000 0.557086
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 4.00000 + 6.92820i 0.184703 + 0.319915i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −6.00000 + 10.3923i −0.275880 + 0.477839i
\(474\) 0 0
\(475\) −0.500000 + 4.33013i −0.0229416 + 0.198680i
\(476\) −48.0000 −2.20008
\(477\) 0 0
\(478\) 0 0
\(479\) 7.50000 + 12.9904i 0.342684 + 0.593546i 0.984930 0.172953i \(-0.0553307\pi\)
−0.642246 + 0.766498i \(0.721997\pi\)
\(480\) 0 0
\(481\) −8.00000 13.8564i −0.364769 0.631798i
\(482\) 0 0
\(483\) 0 0
\(484\) −2.00000 3.46410i −0.0909091 0.157459i
\(485\) −4.00000 6.92820i −0.181631 0.314594i
\(486\) 0 0
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.50000 + 12.9904i −0.338470 + 0.586248i −0.984145 0.177365i \(-0.943243\pi\)
0.645675 + 0.763612i \(0.276576\pi\)
\(492\) 0 0
\(493\) −18.0000 −0.810679
\(494\) 0 0
\(495\) 0 0
\(496\) 14.0000 24.2487i 0.628619 1.08880i
\(497\) 6.00000 10.3923i 0.269137 0.466159i
\(498\) 0 0
\(499\) −10.0000 + 17.3205i −0.447661 + 0.775372i −0.998233 0.0594153i \(-0.981076\pi\)
0.550572 + 0.834788i \(0.314410\pi\)
\(500\) 1.00000 + 1.73205i 0.0447214 + 0.0774597i
\(501\) 0 0
\(502\) 0 0
\(503\) −21.0000 36.3731i −0.936344 1.62179i −0.772220 0.635355i \(-0.780854\pi\)
−0.164124 0.986440i \(-0.552480\pi\)
\(504\) 0 0
\(505\) −15.0000 −0.667491
\(506\) 0 0
\(507\) 0 0
\(508\) 2.00000 3.46410i 0.0887357 0.153695i
\(509\) −9.00000 15.5885i −0.398918 0.690946i 0.594675 0.803966i \(-0.297281\pi\)
−0.993593 + 0.113020i \(0.963948\pi\)
\(510\) 0 0
\(511\) 16.0000 27.7128i 0.707798 1.22594i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 8.00000 13.8564i 0.352522 0.610586i
\(516\) 0 0
\(517\) −9.00000 15.5885i −0.395820 0.685580i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 45.0000 1.97149 0.985743 0.168259i \(-0.0538144\pi\)
0.985743 + 0.168259i \(0.0538144\pi\)
\(522\) 0 0
\(523\) −13.0000 22.5167i −0.568450 0.984585i −0.996719 0.0809336i \(-0.974210\pi\)
0.428269 0.903651i \(-0.359124\pi\)
\(524\) 24.0000 1.04844
\(525\) 0 0
\(526\) 0 0
\(527\) −21.0000 + 36.3731i −0.914774 + 1.58444i
\(528\) 0 0
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) −4.00000 + 34.6410i −0.173422 + 1.50188i
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −27.0000 −1.16297
\(540\) 0 0
\(541\) 18.5000 + 32.0429i 0.795377 + 1.37763i 0.922599 + 0.385759i \(0.126061\pi\)
−0.127222 + 0.991874i \(0.540606\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5.50000 9.52628i −0.235594 0.408061i
\(546\) 0 0
\(547\) 2.00000 + 3.46410i 0.0855138 + 0.148114i 0.905610 0.424111i \(-0.139413\pi\)
−0.820096 + 0.572226i \(0.806080\pi\)
\(548\) 12.0000 20.7846i 0.512615 0.887875i
\(549\) 0 0
\(550\) 0 0
\(551\) −1.50000 + 12.9904i −0.0639021 + 0.553409i
\(552\) 0 0
\(553\) 10.0000 17.3205i 0.425243 0.736543i
\(554\) 0 0
\(555\) 0 0
\(556\) −16.0000 + 27.7128i −0.678551 + 1.17529i
\(557\) 6.00000 + 10.3923i 0.254228 + 0.440336i 0.964686 0.263404i \(-0.0848453\pi\)
−0.710457 + 0.703740i \(0.751512\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 8.00000 + 13.8564i 0.338062 + 0.585540i
\(561\) 0 0
\(562\) 0 0
\(563\) −6.00000 −0.252870 −0.126435 0.991975i \(-0.540353\pi\)
−0.126435 + 0.991975i \(0.540353\pi\)
\(564\) 0 0
\(565\) 3.00000 5.19615i 0.126211 0.218604i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −39.0000 −1.63497 −0.817483 0.575953i \(-0.804631\pi\)
−0.817483 + 0.575953i \(0.804631\pi\)
\(570\) 0 0
\(571\) −7.00000 −0.292941 −0.146470 0.989215i \(-0.546791\pi\)
−0.146470 + 0.989215i \(0.546791\pi\)
\(572\) −6.00000 + 10.3923i −0.250873 + 0.434524i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −16.0000 −0.666089 −0.333044 0.942911i \(-0.608076\pi\)
−0.333044 + 0.942911i \(0.608076\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 3.00000 + 5.19615i 0.124568 + 0.215758i
\(581\) 48.0000 1.99138
\(582\) 0 0
\(583\) 9.00000 + 15.5885i 0.372742 + 0.645608i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18.0000 + 31.1769i −0.742940 + 1.28681i 0.208212 + 0.978084i \(0.433236\pi\)
−0.951151 + 0.308725i \(0.900098\pi\)
\(588\) 0 0
\(589\) 24.5000 + 18.1865i 1.00950 + 0.749363i
\(590\) 0 0
\(591\) 0 0
\(592\) −16.0000 + 27.7128i −0.657596 + 1.13899i
\(593\) 6.00000 + 10.3923i 0.246390 + 0.426761i 0.962522 0.271205i \(-0.0874221\pi\)
−0.716131 + 0.697966i \(0.754089\pi\)
\(594\) 0 0
\(595\) −12.0000 20.7846i −0.491952 0.852086i
\(596\) 6.00000 0.245770
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 0 0
\(601\) −31.0000 −1.26452 −0.632258 0.774758i \(-0.717872\pi\)
−0.632258 + 0.774758i \(0.717872\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 17.0000 + 29.4449i 0.691720 + 1.19809i
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) 0 0
\(607\) 2.00000 0.0811775 0.0405887 0.999176i \(-0.487077\pi\)
0.0405887 + 0.999176i \(0.487077\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.00000 10.3923i 0.242734 0.420428i
\(612\) 0 0
\(613\) −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0000 + 31.1769i 0.724653 + 1.25514i 0.959117 + 0.283011i \(0.0913331\pi\)
−0.234464 + 0.972125i \(0.575334\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 14.0000 0.562254
\(621\) 0 0
\(622\) 0 0
\(623\) 30.0000 + 51.9615i 1.20192 + 2.08179i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) −4.00000 −0.159617
\(629\) 24.0000 41.5692i 0.956943 1.65747i
\(630\) 0 0
\(631\) 9.50000 + 16.4545i 0.378189 + 0.655043i 0.990799 0.135343i \(-0.0432136\pi\)
−0.612610 + 0.790386i \(0.709880\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.00000 0.0793676
\(636\) 0 0
\(637\) −9.00000 15.5885i −0.356593 0.617637i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4.50000 7.79423i 0.177739 0.307854i −0.763367 0.645966i \(-0.776455\pi\)
0.941106 + 0.338112i \(0.109788\pi\)
\(642\) 0 0
\(643\) 17.0000 29.4449i 0.670415 1.16119i −0.307372 0.951589i \(-0.599450\pi\)
0.977787 0.209603i \(-0.0672170\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −18.0000 −0.707653 −0.353827 0.935311i \(-0.615120\pi\)
−0.353827 + 0.935311i \(0.615120\pi\)
\(648\) 0 0
\(649\) 22.5000 38.9711i 0.883202 1.52975i
\(650\) 0 0
\(651\) 0 0
\(652\) −10.0000 17.3205i −0.391630 0.678323i
\(653\) −24.0000 −0.939193 −0.469596 0.882881i \(-0.655601\pi\)
−0.469596 + 0.882881i \(0.655601\pi\)
\(654\) 0 0
\(655\) 6.00000 + 10.3923i 0.234439 + 0.406061i
\(656\) −12.0000 20.7846i −0.468521 0.811503i
\(657\) 0 0
\(658\) 0 0
\(659\) −6.00000 10.3923i −0.233727 0.404827i 0.725175 0.688565i \(-0.241759\pi\)
−0.958902 + 0.283738i \(0.908425\pi\)
\(660\) 0 0
\(661\) −2.50000 4.33013i −0.0972387 0.168422i 0.813302 0.581842i \(-0.197668\pi\)
−0.910541 + 0.413419i \(0.864334\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −16.0000 + 6.92820i −0.620453 + 0.268664i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 7.50000 + 12.9904i 0.289534 + 0.501488i
\(672\) 0 0
\(673\) −4.00000 −0.154189 −0.0770943 0.997024i \(-0.524564\pi\)
−0.0770943 + 0.997024i \(0.524564\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 18.0000 0.692308
\(677\) −48.0000 −1.84479 −0.922395 0.386248i \(-0.873771\pi\)
−0.922395 + 0.386248i \(0.873771\pi\)
\(678\) 0 0
\(679\) 16.0000 27.7128i 0.614024 1.06352i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 18.0000 0.688751 0.344375 0.938832i \(-0.388091\pi\)
0.344375 + 0.938832i \(0.388091\pi\)
\(684\) 0 0
\(685\) 12.0000 0.458496
\(686\) 0 0
\(687\) 0 0
\(688\) 8.00000 + 13.8564i 0.304997 + 0.528271i
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) 0 0
\(691\) −37.0000 −1.40755 −0.703773 0.710425i \(-0.748503\pi\)
−0.703773 + 0.710425i \(0.748503\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −16.0000 −0.606915
\(696\) 0 0
\(697\) 18.0000 + 31.1769i 0.681799 + 1.18091i
\(698\) 0 0
\(699\) 0 0
\(700\) −4.00000 + 6.92820i −0.151186 + 0.261861i
\(701\) 3.00000 5.19615i 0.113308 0.196256i −0.803794 0.594908i \(-0.797189\pi\)
0.917102 + 0.398652i \(0.130522\pi\)
\(702\) 0 0
\(703\) −28.0000 20.7846i −1.05604 0.783906i
\(704\) 24.0000 0.904534
\(705\) 0 0
\(706\) 0 0
\(707\) −30.0000 51.9615i −1.12827 1.95421i
\(708\) 0 0
\(709\) 15.5000 + 26.8468i 0.582115 + 1.00825i 0.995228 + 0.0975728i \(0.0311079\pi\)
−0.413114 + 0.910679i \(0.635559\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −6.00000 −0.224387
\(716\) 9.00000 + 15.5885i 0.336346 + 0.582568i
\(717\) 0 0
\(718\) 0 0
\(719\) 7.50000 12.9904i 0.279703 0.484459i −0.691608 0.722273i \(-0.743097\pi\)
0.971311 + 0.237814i \(0.0764307\pi\)
\(720\) 0 0
\(721\) 64.0000 2.38348
\(722\) 0 0
\(723\) 0 0
\(724\) 2.00000 3.46410i 0.0743294 0.128742i
\(725\) −1.50000 + 2.59808i −0.0557086 + 0.0964901i
\(726\) 0 0
\(727\) −7.00000 + 12.1244i −0.259616 + 0.449667i −0.966139 0.258022i \(-0.916929\pi\)
0.706523 + 0.707690i \(0.250263\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) 0 0
\(733\) 32.0000 1.18195 0.590973 0.806691i \(-0.298744\pi\)
0.590973 + 0.806691i \(0.298744\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.00000 + 5.19615i 0.110506 + 0.191403i
\(738\) 0 0
\(739\) −17.5000 + 30.3109i −0.643748 + 1.11500i 0.340841 + 0.940121i \(0.389288\pi\)
−0.984589 + 0.174883i \(0.944045\pi\)
\(740\) −16.0000 −0.588172
\(741\) 0 0
\(742\) 0 0
\(743\) −12.0000 + 20.7846i −0.440237 + 0.762513i −0.997707 0.0676840i \(-0.978439\pi\)
0.557470 + 0.830197i \(0.311772\pi\)
\(744\) 0 0
\(745\) 1.50000 + 2.59808i 0.0549557 + 0.0951861i
\(746\) 0 0
\(747\) 0 0
\(748\) −36.0000 −1.31629
\(749\) 0 0
\(750\) 0 0
\(751\) 3.50000 + 6.06218i 0.127717 + 0.221212i 0.922792 0.385299i \(-0.125902\pi\)
−0.795075 + 0.606511i \(0.792568\pi\)
\(752\) −24.0000 −0.875190
\(753\) 0 0
\(754\) 0 0
\(755\) −8.50000 + 14.7224i −0.309347 + 0.535804i
\(756\) 0 0
\(757\) 5.00000 8.66025i 0.181728 0.314762i −0.760741 0.649056i \(-0.775164\pi\)
0.942469 + 0.334293i \(0.108498\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −6.00000 −0.217500 −0.108750 0.994069i \(-0.534685\pi\)
−0.108750 + 0.994069i \(0.534685\pi\)
\(762\) 0 0
\(763\) 22.0000 38.1051i 0.796453 1.37950i
\(764\) 15.0000 + 25.9808i 0.542681 + 0.939951i
\(765\) 0 0
\(766\) 0 0
\(767\) 30.0000 1.08324
\(768\) 0 0
\(769\) −14.5000 25.1147i −0.522883 0.905661i −0.999645 0.0266282i \(-0.991523\pi\)
0.476762 0.879032i \(-0.341810\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 32.0000 1.15171
\(773\) 15.0000 + 25.9808i 0.539513 + 0.934463i 0.998930 + 0.0462427i \(0.0147248\pi\)
−0.459418 + 0.888220i \(0.651942\pi\)
\(774\) 0 0
\(775\) 3.50000 + 6.06218i 0.125724 + 0.217760i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 24.0000 10.3923i 0.859889 0.372343i
\(780\) 0 0
\(781\) 4.50000 7.79423i 0.161023 0.278899i
\(782\) 0 0
\(783\) 0 0
\(784\) −18.0000 + 31.1769i −0.642857 + 1.11346i
\(785\) −1.00000 1.73205i −0.0356915 0.0618195i
\(786\) 0 0
\(787\) −34.0000 −1.21197 −0.605985 0.795476i \(-0.707221\pi\)
−0.605985 + 0.795476i \(0.707221\pi\)
\(788\) 18.0000 + 31.1769i 0.641223 + 1.11063i
\(789\) 0 0
\(790\) 0 0
\(791\) 24.0000 0.853342
\(792\) 0 0
\(793\) −5.00000 + 8.66025i −0.177555 + 0.307535i
\(794\) 0 0
\(795\) 0 0
\(796\) −19.0000 + 32.9090i −0.673437 + 1.16643i
\(797\) 30.0000 1.06265