Properties

Label 475.2.e.b.26.1
Level $475$
Weight $2$
Character 475.26
Analytic conductor $3.793$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 26.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 475.26
Dual form 475.2.e.b.201.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{3} +(1.00000 - 1.73205i) q^{4} +4.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{3} +(1.00000 - 1.73205i) q^{4} +4.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +3.00000 q^{11} -4.00000 q^{12} +(1.00000 - 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{16} +(3.00000 + 5.19615i) q^{17} +(-3.50000 + 2.59808i) q^{19} +(-4.00000 - 6.92820i) q^{21} -4.00000 q^{27} +(4.00000 - 6.92820i) q^{28} +(1.50000 - 2.59808i) q^{29} -7.00000 q^{31} +(-3.00000 - 5.19615i) q^{33} +(1.00000 + 1.73205i) q^{36} -8.00000 q^{37} -4.00000 q^{39} +(3.00000 + 5.19615i) q^{41} +(-2.00000 - 3.46410i) q^{43} +(3.00000 - 5.19615i) q^{44} +(3.00000 - 5.19615i) q^{47} +(-4.00000 + 6.92820i) q^{48} +9.00000 q^{49} +(6.00000 - 10.3923i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(-3.00000 + 5.19615i) q^{53} +(8.00000 + 3.46410i) q^{57} +(7.50000 + 12.9904i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(-2.00000 + 3.46410i) q^{63} -8.00000 q^{64} +(1.00000 - 1.73205i) q^{67} +12.0000 q^{68} +(1.50000 + 2.59808i) q^{71} +(4.00000 + 6.92820i) q^{73} +(1.00000 + 8.66025i) q^{76} +12.0000 q^{77} +(-2.50000 - 4.33013i) q^{79} +(5.50000 + 9.52628i) q^{81} -12.0000 q^{83} -16.0000 q^{84} -6.00000 q^{87} +(7.50000 - 12.9904i) q^{89} +(4.00000 - 6.92820i) q^{91} +(7.00000 + 12.1244i) q^{93} +(4.00000 + 6.92820i) q^{97} +(-1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} + 2 q^{4} + 8 q^{7} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{3} + 2 q^{4} + 8 q^{7} - q^{9} + 6 q^{11} - 8 q^{12} + 2 q^{13} - 4 q^{16} + 6 q^{17} - 7 q^{19} - 8 q^{21} - 8 q^{27} + 8 q^{28} + 3 q^{29} - 14 q^{31} - 6 q^{33} + 2 q^{36} - 16 q^{37} - 8 q^{39} + 6 q^{41} - 4 q^{43} + 6 q^{44} + 6 q^{47} - 8 q^{48} + 18 q^{49} + 12 q^{51} - 4 q^{52} - 6 q^{53} + 16 q^{57} + 15 q^{59} - 5 q^{61} - 4 q^{63} - 16 q^{64} + 2 q^{67} + 24 q^{68} + 3 q^{71} + 8 q^{73} + 2 q^{76} + 24 q^{77} - 5 q^{79} + 11 q^{81} - 24 q^{83} - 32 q^{84} - 12 q^{87} + 15 q^{89} + 8 q^{91} + 14 q^{93} + 8 q^{97} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(3\) −1.00000 1.73205i −0.577350 1.00000i −0.995782 0.0917517i \(-0.970753\pi\)
0.418432 0.908248i \(-0.362580\pi\)
\(4\) 1.00000 1.73205i 0.500000 0.866025i
\(5\) 0 0
\(6\) 0 0
\(7\) 4.00000 1.51186 0.755929 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) −4.00000 −1.15470
\(13\) 1.00000 1.73205i 0.277350 0.480384i −0.693375 0.720577i \(-0.743877\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.500000 0.866025i
\(17\) 3.00000 + 5.19615i 0.727607 + 1.26025i 0.957892 + 0.287129i \(0.0927008\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) 0 0
\(19\) −3.50000 + 2.59808i −0.802955 + 0.596040i
\(20\) 0 0
\(21\) −4.00000 6.92820i −0.872872 1.51186i
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −4.00000 −0.769800
\(28\) 4.00000 6.92820i 0.755929 1.30931i
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0 0
\(33\) −3.00000 5.19615i −0.522233 0.904534i
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 + 1.73205i 0.166667 + 0.288675i
\(37\) −8.00000 −1.31519 −0.657596 0.753371i \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) 0 0
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) 3.00000 + 5.19615i 0.468521 + 0.811503i 0.999353 0.0359748i \(-0.0114536\pi\)
−0.530831 + 0.847477i \(0.678120\pi\)
\(42\) 0 0
\(43\) −2.00000 3.46410i −0.304997 0.528271i 0.672264 0.740312i \(-0.265322\pi\)
−0.977261 + 0.212041i \(0.931989\pi\)
\(44\) 3.00000 5.19615i 0.452267 0.783349i
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) −4.00000 + 6.92820i −0.577350 + 1.00000i
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) 6.00000 10.3923i 0.840168 1.45521i
\(52\) −2.00000 3.46410i −0.277350 0.480384i
\(53\) −3.00000 + 5.19615i −0.412082 + 0.713746i −0.995117 0.0987002i \(-0.968532\pi\)
0.583036 + 0.812447i \(0.301865\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 8.00000 + 3.46410i 1.05963 + 0.458831i
\(58\) 0 0
\(59\) 7.50000 + 12.9904i 0.976417 + 1.69120i 0.675178 + 0.737655i \(0.264067\pi\)
0.301239 + 0.953549i \(0.402600\pi\)
\(60\) 0 0
\(61\) −2.50000 + 4.33013i −0.320092 + 0.554416i −0.980507 0.196485i \(-0.937047\pi\)
0.660415 + 0.750901i \(0.270381\pi\)
\(62\) 0 0
\(63\) −2.00000 + 3.46410i −0.251976 + 0.436436i
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 1.00000 1.73205i 0.122169 0.211604i −0.798454 0.602056i \(-0.794348\pi\)
0.920623 + 0.390453i \(0.127682\pi\)
\(68\) 12.0000 1.45521
\(69\) 0 0
\(70\) 0 0
\(71\) 1.50000 + 2.59808i 0.178017 + 0.308335i 0.941201 0.337846i \(-0.109698\pi\)
−0.763184 + 0.646181i \(0.776365\pi\)
\(72\) 0 0
\(73\) 4.00000 + 6.92820i 0.468165 + 0.810885i 0.999338 0.0363782i \(-0.0115821\pi\)
−0.531174 + 0.847263i \(0.678249\pi\)
\(74\) 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 0.690426 0.723403i \(-0.257423\pi\)
−0.971698 + 0.236225i \(0.924090\pi\)
\(80\) 0 0
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) −16.0000 −1.74574
\(85\) 0 0
\(86\) 0 0
\(87\) −6.00000 −0.643268
\(88\) 0 0
\(89\) 7.50000 12.9904i 0.794998 1.37698i −0.127842 0.991795i \(-0.540805\pi\)
0.922840 0.385183i \(-0.125862\pi\)
\(90\) 0 0
\(91\) 4.00000 6.92820i 0.419314 0.726273i
\(92\) 0 0
\(93\) 7.00000 + 12.1244i 0.725866 + 1.25724i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 4.00000 + 6.92820i 0.406138 + 0.703452i 0.994453 0.105180i \(-0.0335417\pi\)
−0.588315 + 0.808632i \(0.700208\pi\)
\(98\) 0 0
\(99\) −1.50000 + 2.59808i −0.150756 + 0.261116i
\(100\) 0 0
\(101\) −7.50000 + 12.9904i −0.746278 + 1.29259i 0.203317 + 0.979113i \(0.434828\pi\)
−0.949595 + 0.313478i \(0.898506\pi\)
\(102\) 0 0
\(103\) 16.0000 1.57653 0.788263 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −4.00000 + 6.92820i −0.384900 + 0.666667i
\(109\) −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i \(-0.990057\pi\)
0.472708 0.881219i \(-0.343277\pi\)
\(110\) 0 0
\(111\) 8.00000 + 13.8564i 0.759326 + 1.31519i
\(112\) −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
\(117\) 1.00000 + 1.73205i 0.0924500 + 0.160128i
\(118\) 0 0
\(119\) 12.0000 + 20.7846i 1.10004 + 1.90532i
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) 6.00000 10.3923i 0.541002 0.937043i
\(124\) −7.00000 + 12.1244i −0.628619 + 1.08880i
\(125\) 0 0
\(126\) 0 0
\(127\) 1.00000 1.73205i 0.0887357 0.153695i −0.818241 0.574875i \(-0.805051\pi\)
0.906977 + 0.421180i \(0.138384\pi\)
\(128\) 0 0
\(129\) −4.00000 + 6.92820i −0.352180 + 0.609994i
\(130\) 0 0
\(131\) −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i \(-0.991023\pi\)
0.475380 0.879781i \(-0.342311\pi\)
\(132\) −12.0000 −1.04447
\(133\) −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 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) 8.00000 13.8564i 0.678551 1.17529i −0.296866 0.954919i \(-0.595942\pi\)
0.975417 0.220366i \(-0.0707252\pi\)
\(140\) 0 0
\(141\) −12.0000 −1.01058
\(142\) 0 0
\(143\) 3.00000 5.19615i 0.250873 0.434524i
\(144\) 4.00000 0.333333
\(145\) 0 0
\(146\) 0 0
\(147\) −9.00000 15.5885i −0.742307 1.28571i
\(148\) −8.00000 + 13.8564i −0.657596 + 1.13899i
\(149\) −1.50000 2.59808i −0.122885 0.212843i 0.798019 0.602632i \(-0.205881\pi\)
−0.920904 + 0.389789i \(0.872548\pi\)
\(150\) 0 0
\(151\) 17.0000 1.38344 0.691720 0.722166i \(-0.256853\pi\)
0.691720 + 0.722166i \(0.256853\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) −4.00000 + 6.92820i −0.320256 + 0.554700i
\(157\) 1.00000 + 1.73205i 0.0798087 + 0.138233i 0.903167 0.429289i \(-0.141236\pi\)
−0.823359 + 0.567521i \(0.807902\pi\)
\(158\) 0 0
\(159\) 12.0000 0.951662
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 10.0000 0.783260 0.391630 0.920123i \(-0.371911\pi\)
0.391630 + 0.920123i \(0.371911\pi\)
\(164\) 12.0000 0.937043
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(168\) 0 0
\(169\) 4.50000 + 7.79423i 0.346154 + 0.599556i
\(170\) 0 0
\(171\) −0.500000 4.33013i −0.0382360 0.331133i
\(172\) −8.00000 −0.609994
\(173\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −6.00000 10.3923i −0.452267 0.783349i
\(177\) 15.0000 25.9808i 1.12747 1.95283i
\(178\) 0 0
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) 0 0
\(181\) −1.00000 + 1.73205i −0.0743294 + 0.128742i −0.900794 0.434246i \(-0.857015\pi\)
0.826465 + 0.562988i \(0.190348\pi\)
\(182\) 0 0
\(183\) 10.0000 0.739221
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 9.00000 + 15.5885i 0.658145 + 1.13994i
\(188\) −6.00000 10.3923i −0.437595 0.757937i
\(189\) −16.0000 −1.16383
\(190\) 0 0
\(191\) −15.0000 −1.08536 −0.542681 0.839939i \(-0.682591\pi\)
−0.542681 + 0.839939i \(0.682591\pi\)
\(192\) 8.00000 + 13.8564i 0.577350 + 1.00000i
\(193\) −8.00000 13.8564i −0.575853 0.997406i −0.995948 0.0899262i \(-0.971337\pi\)
0.420096 0.907480i \(-0.361996\pi\)
\(194\) 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 −0.303486 0.952836i \(-0.598151\pi\)
0.976923 0.213591i \(-0.0685161\pi\)
\(200\) 0 0
\(201\) −4.00000 −0.282138
\(202\) 0 0
\(203\) 6.00000 10.3923i 0.421117 0.729397i
\(204\) −12.0000 20.7846i −0.840168 1.45521i
\(205\) 0 0
\(206\) 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 0.960985 0.276600i \(-0.0892077\pi\)
−0.720035 + 0.693938i \(0.755874\pi\)
\(212\) 6.00000 + 10.3923i 0.412082 + 0.713746i
\(213\) 3.00000 5.19615i 0.205557 0.356034i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −28.0000 −1.90076
\(218\) 0 0
\(219\) 8.00000 13.8564i 0.540590 0.936329i
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) −2.00000 3.46410i −0.133930 0.231973i 0.791258 0.611482i \(-0.209426\pi\)
−0.925188 + 0.379509i \(0.876093\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 24.0000 1.59294 0.796468 0.604681i \(-0.206699\pi\)
0.796468 + 0.604681i \(0.206699\pi\)
\(228\) 14.0000 10.3923i 0.927173 0.688247i
\(229\) −7.00000 −0.462573 −0.231287 0.972886i \(-0.574293\pi\)
−0.231287 + 0.972886i \(0.574293\pi\)
\(230\) 0 0
\(231\) −12.0000 20.7846i −0.789542 1.36753i
\(232\) 0 0
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 30.0000 1.95283
\(237\) −5.00000 + 8.66025i −0.324785 + 0.562544i
\(238\) 0 0
\(239\) −3.00000 −0.194054 −0.0970269 0.995282i \(-0.530933\pi\)
−0.0970269 + 0.995282i \(0.530933\pi\)
\(240\) 0 0
\(241\) −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i \(-0.884818\pi\)
0.774202 + 0.632938i \(0.218151\pi\)
\(242\) 0 0
\(243\) 5.00000 8.66025i 0.320750 0.555556i
\(244\) 5.00000 + 8.66025i 0.320092 + 0.554416i
\(245\) 0 0
\(246\) 0 0
\(247\) 1.00000 + 8.66025i 0.0636285 + 0.551039i
\(248\) 0 0
\(249\) 12.0000 + 20.7846i 0.760469 + 1.31717i
\(250\) 0 0
\(251\) 7.50000 12.9904i 0.473396 0.819946i −0.526140 0.850398i \(-0.676361\pi\)
0.999536 + 0.0304521i \(0.00969471\pi\)
\(252\) 4.00000 + 6.92820i 0.251976 + 0.436436i
\(253\) 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 0.435970 + 0.899961i \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 0 0
\(259\) −32.0000 −1.98838
\(260\) 0 0
\(261\) 1.50000 + 2.59808i 0.0928477 + 0.160817i
\(262\) 0 0
\(263\) −9.00000 15.5885i −0.554964 0.961225i −0.997906 0.0646755i \(-0.979399\pi\)
0.442943 0.896550i \(-0.353935\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −30.0000 −1.83597
\(268\) −2.00000 3.46410i −0.122169 0.211604i
\(269\) 10.5000 + 18.1865i 0.640196 + 1.10885i 0.985389 + 0.170321i \(0.0544803\pi\)
−0.345192 + 0.938532i \(0.612186\pi\)
\(270\) 0 0
\(271\) −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i \(-0.275099\pi\)
−0.983312 + 0.181928i \(0.941766\pi\)
\(272\) 12.0000 20.7846i 0.727607 1.26025i
\(273\) −16.0000 −0.968364
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −8.00000 −0.480673 −0.240337 0.970690i \(-0.577258\pi\)
−0.240337 + 0.970690i \(0.577258\pi\)
\(278\) 0 0
\(279\) 3.50000 6.06218i 0.209540 0.362933i
\(280\) 0 0
\(281\) −3.00000 + 5.19615i −0.178965 + 0.309976i −0.941526 0.336939i \(-0.890608\pi\)
0.762561 + 0.646916i \(0.223942\pi\)
\(282\) 0 0
\(283\) 7.00000 + 12.1244i 0.416107 + 0.720718i 0.995544 0.0942988i \(-0.0300609\pi\)
−0.579437 + 0.815017i \(0.696728\pi\)
\(284\) 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
\(291\) 8.00000 13.8564i 0.468968 0.812277i
\(292\) 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
\(295\) 0 0
\(296\) 0 0
\(297\) −12.0000 −0.696311
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −8.00000 13.8564i −0.461112 0.798670i
\(302\) 0 0
\(303\) 30.0000 1.72345
\(304\) 16.0000 + 6.92820i 0.917663 + 0.397360i
\(305\) 0 0
\(306\) 0 0
\(307\) −17.0000 29.4449i −0.970241 1.68051i −0.694820 0.719183i \(-0.744516\pi\)
−0.275421 0.961324i \(-0.588817\pi\)
\(308\) 12.0000 20.7846i 0.683763 1.18431i
\(309\) −16.0000 27.7128i −0.910208 1.57653i
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) −5.00000 + 8.66025i −0.282617 + 0.489506i −0.972028 0.234863i \(-0.924536\pi\)
0.689412 + 0.724370i \(0.257869\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 12.0000 20.7846i 0.673987 1.16738i −0.302777 0.953062i \(-0.597914\pi\)
0.976764 0.214318i \(-0.0687530\pi\)
\(318\) 0 0
\(319\) 4.50000 7.79423i 0.251952 0.436393i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −24.0000 10.3923i −1.33540 0.578243i
\(324\) 22.0000 1.22222
\(325\) 0 0
\(326\) 0 0
\(327\) −11.0000 + 19.0526i −0.608301 + 1.05361i
\(328\) 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
\(333\) 4.00000 6.92820i 0.219199 0.379663i
\(334\) 0 0
\(335\) 0 0
\(336\) −16.0000 + 27.7128i −0.872872 + 1.51186i
\(337\) −8.00000 13.8564i −0.435788 0.754807i 0.561572 0.827428i \(-0.310197\pi\)
−0.997360 + 0.0726214i \(0.976864\pi\)
\(338\) 0 0
\(339\) 6.00000 + 10.3923i 0.325875 + 0.564433i
\(340\) 0 0
\(341\) −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 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) −6.00000 + 10.3923i −0.321634 + 0.557086i
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) −4.00000 + 6.92820i −0.213504 + 0.369800i
\(352\) 0 0
\(353\) −12.0000 −0.638696 −0.319348 0.947638i \(-0.603464\pi\)
−0.319348 + 0.947638i \(0.603464\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −15.0000 25.9808i −0.794998 1.37698i
\(357\) 24.0000 41.5692i 1.27021 2.20008i
\(358\) 0 0
\(359\) −12.0000 20.7846i −0.633336 1.09697i −0.986865 0.161546i \(-0.948352\pi\)
0.353529 0.935423i \(-0.384981\pi\)
\(360\) 0 0
\(361\) 5.50000 18.1865i 0.289474 0.957186i
\(362\) 0 0
\(363\) 2.00000 + 3.46410i 0.104973 + 0.181818i
\(364\) −8.00000 13.8564i −0.419314 0.726273i
\(365\) 0 0
\(366\) 0 0
\(367\) −2.00000 + 3.46410i −0.104399 + 0.180825i −0.913493 0.406855i \(-0.866625\pi\)
0.809093 + 0.587680i \(0.199959\pi\)
\(368\) 0 0
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) −12.0000 + 20.7846i −0.623009 + 1.07908i
\(372\) 28.0000 1.45173
\(373\) 4.00000 0.207112 0.103556 0.994624i \(-0.466978\pi\)
0.103556 + 0.994624i \(0.466978\pi\)
\(374\) 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 \(0.899204\pi\)
\(380\) 0 0
\(381\) −4.00000 −0.204926
\(382\) 0 0
\(383\) 15.0000 + 25.9808i 0.766464 + 1.32755i 0.939469 + 0.342634i \(0.111319\pi\)
−0.173005 + 0.984921i \(0.555348\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4.00000 0.203331
\(388\) 16.0000 0.812277
\(389\) −7.50000 + 12.9904i −0.380265 + 0.658638i −0.991100 0.133120i \(-0.957501\pi\)
0.610835 + 0.791758i \(0.290834\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −12.0000 + 20.7846i −0.605320 + 1.04844i
\(394\) 0 0
\(395\) 0 0
\(396\) 3.00000 + 5.19615i 0.150756 + 0.261116i
\(397\) 4.00000 + 6.92820i 0.200754 + 0.347717i 0.948772 0.315963i \(-0.102327\pi\)
−0.748017 + 0.663679i \(0.768994\pi\)
\(398\) 0 0
\(399\) 32.0000 + 13.8564i 1.60200 + 0.693688i
\(400\) 0 0
\(401\) 16.5000 + 28.5788i 0.823971 + 1.42716i 0.902703 + 0.430263i \(0.141579\pi\)
−0.0787327 + 0.996896i \(0.525087\pi\)
\(402\) 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 0.428063 + 0.903749i \(0.359196\pi\)
−0.996701 + 0.0811615i \(0.974137\pi\)
\(410\) 0 0
\(411\) 24.0000 1.18383
\(412\) 16.0000 27.7128i 0.788263 1.36531i
\(413\) 30.0000 + 51.9615i 1.47620 + 2.55686i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −32.0000 −1.56705
\(418\) 0 0
\(419\) −3.00000 −0.146560 −0.0732798 0.997311i \(-0.523347\pi\)
−0.0732798 + 0.997311i \(0.523347\pi\)
\(420\) 0 0
\(421\) 9.50000 + 16.4545i 0.463002 + 0.801942i 0.999109 0.0422075i \(-0.0134391\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 0 0
\(423\) 3.00000 + 5.19615i 0.145865 + 0.252646i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −10.0000 + 17.3205i −0.483934 + 0.838198i
\(428\) 0 0
\(429\) −12.0000 −0.579365
\(430\) 0 0
\(431\) 7.50000 12.9904i 0.361262 0.625725i −0.626907 0.779094i \(-0.715679\pi\)
0.988169 + 0.153370i \(0.0490126\pi\)
\(432\) 8.00000 + 13.8564i 0.384900 + 0.666667i
\(433\) 4.00000 6.92820i 0.192228 0.332948i −0.753760 0.657149i \(-0.771762\pi\)
0.945988 + 0.324201i \(0.105095\pi\)
\(434\) 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 0.978412 0.206666i \(-0.0662612\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 0 0
\(441\) −4.50000 + 7.79423i −0.214286 + 0.371154i
\(442\) 0 0
\(443\) −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i \(-0.925350\pi\)
0.687557 + 0.726130i \(0.258683\pi\)
\(444\) 32.0000 1.51865
\(445\) 0 0
\(446\) 0 0
\(447\) −3.00000 + 5.19615i −0.141895 + 0.245770i
\(448\) −32.0000 −1.51186
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) 9.00000 + 15.5885i 0.423793 + 0.734032i
\(452\) −6.00000 + 10.3923i −0.282216 + 0.488813i
\(453\) −17.0000 29.4449i −0.798730 1.38344i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 22.0000 1.02912 0.514558 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) 0 0
\(459\) −12.0000 20.7846i −0.560112 0.970143i
\(460\) 0 0
\(461\) 4.50000 + 7.79423i 0.209586 + 0.363013i 0.951584 0.307388i \(-0.0994551\pi\)
−0.741998 + 0.670402i \(0.766122\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) −12.0000 −0.557086
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 4.00000 0.184900
\(469\) 4.00000 6.92820i 0.184703 0.319915i
\(470\) 0 0
\(471\) 2.00000 3.46410i 0.0921551 0.159617i
\(472\) 0 0
\(473\) −6.00000 10.3923i −0.275880 0.477839i
\(474\) 0 0
\(475\) 0 0
\(476\) 48.0000 2.20008
\(477\) −3.00000 5.19615i −0.137361 0.237915i
\(478\) 0 0
\(479\) −7.50000 + 12.9904i −0.342684 + 0.593546i −0.984930 0.172953i \(-0.944669\pi\)
0.642246 + 0.766498i \(0.278003\pi\)
\(480\) 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
\(485\) 0 0
\(486\) 0 0
\(487\) −2.00000 −0.0906287 −0.0453143 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) 0 0
\(489\) −10.0000 17.3205i −0.452216 0.783260i
\(490\) 0 0
\(491\) 7.50000 + 12.9904i 0.338470 + 0.586248i 0.984145 0.177365i \(-0.0567572\pi\)
−0.645675 + 0.763612i \(0.723424\pi\)
\(492\) −12.0000 20.7846i −0.541002 0.937043i
\(493\) 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 0.550572 0.834788i \(-0.314410\pi\)
−0.998233 + 0.0594153i \(0.981076\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −21.0000 + 36.3731i −0.936344 + 1.62179i −0.164124 + 0.986440i \(0.552480\pi\)
−0.772220 + 0.635355i \(0.780854\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 9.00000 15.5885i 0.399704 0.692308i
\(508\) −2.00000 3.46410i −0.0887357 0.153695i
\(509\) 9.00000 15.5885i 0.398918 0.690946i −0.594675 0.803966i \(-0.702719\pi\)
0.993593 + 0.113020i \(0.0360525\pi\)
\(510\) 0 0
\(511\) 16.0000 + 27.7128i 0.707798 + 1.22594i
\(512\) 0 0
\(513\) 14.0000 10.3923i 0.618115 0.458831i
\(514\) 0 0
\(515\) 0 0
\(516\) 8.00000 + 13.8564i 0.352180 + 0.609994i
\(517\) 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 \(-0.946186\pi\)
−0.985743 + 0.168259i \(0.946186\pi\)
\(522\) 0 0
\(523\) 13.0000 22.5167i 0.568450 0.984585i −0.428269 0.903651i \(-0.640876\pi\)
0.996719 0.0809336i \(-0.0257902\pi\)
\(524\) −24.0000 −1.04844
\(525\) 0 0
\(526\) 0 0
\(527\) −21.0000 36.3731i −0.914774 1.58444i
\(528\) −12.0000 + 20.7846i −0.522233 + 0.904534i
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) −15.0000 −0.650945
\(532\) 4.00000 + 34.6410i 0.173422 + 1.50188i
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 9.00000 + 15.5885i 0.388379 + 0.672692i
\(538\) 0 0
\(539\) 27.0000 1.16297
\(540\) 0 0
\(541\) 18.5000 32.0429i 0.795377 1.37763i −0.127222 0.991874i \(-0.540606\pi\)
0.922599 0.385759i \(-0.126061\pi\)
\(542\) 0 0
\(543\) 4.00000 0.171656
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −2.00000 + 3.46410i −0.0855138 + 0.148114i −0.905610 0.424111i \(-0.860587\pi\)
0.820096 + 0.572226i \(0.193920\pi\)
\(548\) 12.0000 + 20.7846i 0.512615 + 0.887875i
\(549\) −2.50000 4.33013i −0.106697 0.184805i
\(550\) 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 −0.710457 0.703740i \(-0.751512\pi\)
0.964686 + 0.263404i \(0.0848453\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 18.0000 31.1769i 0.759961 1.31629i
\(562\) 0 0
\(563\) −6.00000 −0.252870 −0.126435 0.991975i \(-0.540353\pi\)
−0.126435 + 0.991975i \(0.540353\pi\)
\(564\) −12.0000 + 20.7846i −0.505291 + 0.875190i
\(565\) 0 0
\(566\) 0 0
\(567\) 22.0000 + 38.1051i 0.923913 + 1.60026i
\(568\) 0 0
\(569\) 39.0000 1.63497 0.817483 0.575953i \(-0.195369\pi\)
0.817483 + 0.575953i \(0.195369\pi\)
\(570\) 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
\(573\) 15.0000 + 25.9808i 0.626634 + 1.08536i
\(574\) 0 0
\(575\) 0 0
\(576\) 4.00000 6.92820i 0.166667 0.288675i
\(577\) 16.0000 0.666089 0.333044 0.942911i \(-0.391924\pi\)
0.333044 + 0.942911i \(0.391924\pi\)
\(578\) 0 0
\(579\) −16.0000 + 27.7128i −0.664937 + 1.15171i
\(580\) 0 0
\(581\) −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 −0.951151 0.308725i \(-0.900098\pi\)
0.208212 0.978084i \(-0.433236\pi\)
\(588\) −36.0000 −1.48461
\(589\) 24.5000 18.1865i 1.00950 0.749363i
\(590\) 0 0
\(591\) −18.0000 31.1769i −0.740421 1.28245i
\(592\) 16.0000 + 27.7128i 0.657596 + 1.13899i
\(593\) 6.00000 10.3923i 0.246390 0.426761i −0.716131 0.697966i \(-0.754089\pi\)
0.962522 + 0.271205i \(0.0874221\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −38.0000 −1.55524
\(598\) 0 0
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) −31.0000 −1.26452 −0.632258 0.774758i \(-0.717872\pi\)
−0.632258 + 0.774758i \(0.717872\pi\)
\(602\) 0 0
\(603\) 1.00000 + 1.73205i 0.0407231 + 0.0705346i
\(604\) 17.0000 29.4449i 0.691720 1.19809i
\(605\) 0 0
\(606\) 0 0
\(607\) −2.00000 −0.0811775 −0.0405887 0.999176i \(-0.512923\pi\)
−0.0405887 + 0.999176i \(0.512923\pi\)
\(608\) 0 0
\(609\) −24.0000 −0.972529
\(610\) 0 0
\(611\) −6.00000 10.3923i −0.242734 0.420428i
\(612\) −6.00000 + 10.3923i −0.242536 + 0.420084i
\(613\) 1.00000 + 1.73205i 0.0403896 + 0.0699569i 0.885514 0.464614i \(-0.153807\pi\)
−0.845124 + 0.534570i \(0.820473\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0000 31.1769i 0.724653 1.25514i −0.234464 0.972125i \(-0.575334\pi\)
0.959117 0.283011i \(-0.0913331\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 30.0000 51.9615i 1.20192 2.08179i
\(624\) 8.00000 + 13.8564i 0.320256 + 0.554700i
\(625\) 0 0
\(626\) 0 0
\(627\) 24.0000 + 10.3923i 0.958468 + 0.415029i
\(628\) 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 −0.612610 0.790386i \(-0.709880\pi\)
0.990799 + 0.135343i \(0.0432136\pi\)
\(632\) 0 0
\(633\) 7.00000 12.1244i 0.278225 0.481900i
\(634\) 0 0
\(635\) 0 0
\(636\) 12.0000 20.7846i 0.475831 0.824163i
\(637\) 9.00000 15.5885i 0.356593 0.617637i
\(638\) 0 0
\(639\) −3.00000 −0.118678
\(640\) 0 0
\(641\) −4.50000 7.79423i −0.177739 0.307854i 0.763367 0.645966i \(-0.223545\pi\)
−0.941106 + 0.338112i \(0.890212\pi\)
\(642\) 0 0
\(643\) −17.0000 29.4449i −0.670415 1.16119i −0.977787 0.209603i \(-0.932783\pi\)
0.307372 0.951589i \(-0.400550\pi\)
\(644\) 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
\(651\) 28.0000 + 48.4974i 1.09741 + 1.90076i
\(652\) 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
\(655\) 0 0
\(656\) 12.0000 20.7846i 0.468521 0.811503i
\(657\) −8.00000 −0.312110
\(658\) 0 0
\(659\) 6.00000 10.3923i 0.233727 0.404827i −0.725175 0.688565i \(-0.758241\pi\)
0.958902 + 0.283738i \(0.0915745\pi\)
\(660\) 0 0
\(661\) −2.50000 + 4.33013i −0.0972387 + 0.168422i −0.910541 0.413419i \(-0.864334\pi\)
0.813302 + 0.581842i \(0.197668\pi\)
\(662\) 0 0
\(663\) −12.0000 20.7846i −0.466041 0.807207i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −4.00000 + 6.92820i −0.154649 + 0.267860i
\(670\) 0 0
\(671\) −7.50000 + 12.9904i −0.289534 + 0.501488i
\(672\) 0 0
\(673\) 4.00000 0.154189 0.0770943 0.997024i \(-0.475436\pi\)
0.0770943 + 0.997024i \(0.475436\pi\)
\(674\) 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
\(681\) −24.0000 41.5692i −0.919682 1.59294i
\(682\) 0 0
\(683\) 18.0000 0.688751 0.344375 0.938832i \(-0.388091\pi\)
0.344375 + 0.938832i \(0.388091\pi\)
\(684\) −8.00000 3.46410i −0.305888 0.132453i
\(685\) 0 0
\(686\) 0 0
\(687\) 7.00000 + 12.1244i 0.267067 + 0.462573i
\(688\) −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
\(693\) −6.00000 + 10.3923i −0.227921 + 0.394771i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −18.0000 + 31.1769i −0.681799 + 1.18091i
\(698\) 0 0
\(699\) 6.00000 10.3923i 0.226941 0.393073i
\(700\) 0 0
\(701\) −3.00000 5.19615i −0.113308 0.196256i 0.803794 0.594908i \(-0.202811\pi\)
−0.917102 + 0.398652i \(0.869478\pi\)
\(702\) 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
\(708\) −30.0000 51.9615i −1.12747 1.95283i
\(709\) 15.5000 26.8468i 0.582115 1.00825i −0.413114 0.910679i \(-0.635559\pi\)
0.995228 0.0975728i \(-0.0311079\pi\)
\(710\) 0 0
\(711\) 5.00000 0.187515
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −9.00000 + 15.5885i −0.336346 + 0.582568i
\(717\) 3.00000 + 5.19615i 0.112037 + 0.194054i
\(718\) 0 0
\(719\) −7.50000 12.9904i −0.279703 0.484459i 0.691608 0.722273i \(-0.256903\pi\)
−0.971311 + 0.237814i \(0.923569\pi\)
\(720\) 0 0
\(721\) 64.0000 2.38348
\(722\) 0 0
\(723\) 10.0000 0.371904
\(724\) 2.00000 + 3.46410i 0.0743294 + 0.128742i
\(725\) 0 0
\(726\) 0 0
\(727\) 7.00000 + 12.1244i 0.259616 + 0.449667i 0.966139 0.258022i \(-0.0830708\pi\)
−0.706523 + 0.707690i \(0.749737\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) 10.0000 17.3205i 0.369611 0.640184i
\(733\) −32.0000 −1.18195 −0.590973 0.806691i \(-0.701256\pi\)
−0.590973 + 0.806691i \(0.701256\pi\)
\(734\) 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 −0.984589 0.174883i \(-0.944045\pi\)
0.340841 0.940121i \(-0.389288\pi\)
\(740\) 0 0
\(741\) 14.0000 10.3923i 0.514303 0.381771i
\(742\) 0 0
\(743\) −12.0000 20.7846i −0.440237 0.762513i 0.557470 0.830197i \(-0.311772\pi\)
−0.997707 + 0.0676840i \(0.978439\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) 36.0000 1.31629
\(749\) 0 0
\(750\) 0 0
\(751\) 3.50000 6.06218i 0.127717 0.221212i −0.795075 0.606511i \(-0.792568\pi\)
0.922792 + 0.385299i \(0.125902\pi\)
\(752\) −24.0000 −0.875190
\(753\) −30.0000 −1.09326
\(754\) 0 0
\(755\) 0 0
\(756\) −16.0000 + 27.7128i −0.581914 + 1.00791i
\(757\) −5.00000 8.66025i −0.181728 0.314762i 0.760741 0.649056i \(-0.224836\pi\)
−0.942469 + 0.334293i \(0.891502\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 6.00000 0.217500 0.108750 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 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
\(768\) 32.0000 1.15470
\(769\) −14.5000 + 25.1147i −0.522883 + 0.905661i 0.476762 + 0.879032i \(0.341810\pi\)
−0.999645 + 0.0266282i \(0.991523\pi\)
\(770\) 0 0
\(771\) 36.0000 1.29651
\(772\) −32.0000 −1.15171
\(773\) 15.0000 25.9808i 0.539513 0.934463i −0.459418 0.888220i \(-0.651942\pi\)
0.998930 0.0462427i \(-0.0147248\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 32.0000 + 55.4256i 1.14799 + 1.98838i
\(778\) 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
\(783\) −6.00000 + 10.3923i −0.214423 + 0.371391i
\(784\) −18.0000 31.1769i −0.642857 1.11346i
\(785\) 0 0
\(786\) 0 0
\(787\) 34.0000 1.21197 0.605985 0.795476i \(-0.292779\pi\)
0.605985 + 0.795476i \(0.292779\pi\)
\(788\) 18.0000 31.1769i 0.641223 1.11063i
\(789\) −18.0000 + 31.1769i −0.640817 + 1.10993i
\(790\) 0 0
\(791\) −24.0000 −0.853342
\(792\) 0 0
\(793\) 5.00000 + 8.66025i 0.177555 + 0.307535i