Properties

Label 475.2.j.a.349.1
Level $475$
Weight $2$
Character 475.349
Analytic conductor $3.793$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 349.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 475.349
Dual form 475.2.j.a.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.73205 + 1.00000i) q^{3} +(-1.00000 + 1.73205i) q^{4} +4.00000i q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.73205 + 1.00000i) q^{3} +(-1.00000 + 1.73205i) q^{4} +4.00000i q^{7} +(0.500000 - 0.866025i) q^{9} +3.00000 q^{11} -4.00000i q^{12} +(-1.73205 - 1.00000i) q^{13} +(-2.00000 - 3.46410i) q^{16} +(-5.19615 + 3.00000i) q^{17} +(3.50000 - 2.59808i) q^{19} +(-4.00000 - 6.92820i) q^{21} -4.00000i q^{27} +(-6.92820 - 4.00000i) q^{28} +(-1.50000 + 2.59808i) q^{29} -7.00000 q^{31} +(-5.19615 + 3.00000i) q^{33} +(1.00000 + 1.73205i) q^{36} -8.00000i q^{37} +4.00000 q^{39} +(3.00000 + 5.19615i) q^{41} +(-3.46410 + 2.00000i) q^{43} +(-3.00000 + 5.19615i) q^{44} +(5.19615 + 3.00000i) q^{47} +(6.92820 + 4.00000i) q^{48} -9.00000 q^{49} +(6.00000 - 10.3923i) q^{51} +(3.46410 - 2.00000i) q^{52} +(5.19615 + 3.00000i) q^{53} +(-3.46410 + 8.00000i) q^{57} +(-7.50000 - 12.9904i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(3.46410 + 2.00000i) q^{63} +8.00000 q^{64} +(1.73205 + 1.00000i) q^{67} -12.0000i q^{68} +(1.50000 + 2.59808i) q^{71} +(6.92820 - 4.00000i) q^{73} +(1.00000 + 8.66025i) q^{76} +12.0000i q^{77} +(2.50000 + 4.33013i) q^{79} +(5.50000 + 9.52628i) q^{81} +12.0000i q^{83} +16.0000 q^{84} -6.00000i q^{87} +(-7.50000 + 12.9904i) q^{89} +(4.00000 - 6.92820i) q^{91} +(12.1244 - 7.00000i) q^{93} +(-6.92820 + 4.00000i) q^{97} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{4} + 2 q^{9} + 12 q^{11} - 8 q^{16} + 14 q^{19} - 16 q^{21} - 6 q^{29} - 28 q^{31} + 4 q^{36} + 16 q^{39} + 12 q^{41} - 12 q^{44} - 36 q^{49} + 24 q^{51} - 30 q^{59} - 10 q^{61} + 32 q^{64} + 6 q^{71} + 4 q^{76} + 10 q^{79} + 22 q^{81} + 64 q^{84} - 30 q^{89} + 16 q^{91} + 6 q^{99}+O(q^{100}) \) 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 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(3\) −1.73205 + 1.00000i −1.00000 + 0.577350i −0.908248 0.418432i \(-0.862580\pi\)
−0.0917517 + 0.995782i \(0.529247\pi\)
\(4\) −1.00000 + 1.73205i −0.500000 + 0.866025i
\(5\) 0 0
\(6\) 0 0
\(7\) 4.00000i 1.51186i 0.654654 + 0.755929i \(0.272814\pi\)
−0.654654 + 0.755929i \(0.727186\pi\)
\(8\) 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 \(0.350615\pi\)
\(12\) 4.00000i 1.15470i
\(13\) −1.73205 1.00000i −0.480384 0.277350i 0.240192 0.970725i \(-0.422790\pi\)
−0.720577 + 0.693375i \(0.756123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −2.00000 3.46410i −0.500000 0.866025i
\(17\) −5.19615 + 3.00000i −1.26025 + 0.727607i −0.973123 0.230285i \(-0.926034\pi\)
−0.287129 + 0.957892i \(0.592701\pi\)
\(18\) 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 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4.00000i 0.769800i
\(28\) −6.92820 4.00000i −1.30931 0.755929i
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0 0
\(33\) −5.19615 + 3.00000i −0.904534 + 0.522233i
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 + 1.73205i 0.166667 + 0.288675i
\(37\) 8.00000i 1.31519i −0.753371 0.657596i \(-0.771573\pi\)
0.753371 0.657596i \(-0.228427\pi\)
\(38\) 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
\(43\) −3.46410 + 2.00000i −0.528271 + 0.304997i −0.740312 0.672264i \(-0.765322\pi\)
0.212041 + 0.977261i \(0.431989\pi\)
\(44\) −3.00000 + 5.19615i −0.452267 + 0.783349i
\(45\) 0 0
\(46\) 0 0
\(47\) 5.19615 + 3.00000i 0.757937 + 0.437595i 0.828554 0.559908i \(-0.189164\pi\)
−0.0706177 + 0.997503i \(0.522497\pi\)
\(48\) 6.92820 + 4.00000i 1.00000 + 0.577350i
\(49\) −9.00000 −1.28571
\(50\) 0 0
\(51\) 6.00000 10.3923i 0.840168 1.45521i
\(52\) 3.46410 2.00000i 0.480384 0.277350i
\(53\) 5.19615 + 3.00000i 0.713746 + 0.412082i 0.812447 0.583036i \(-0.198135\pi\)
−0.0987002 + 0.995117i \(0.531468\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −3.46410 + 8.00000i −0.458831 + 1.05963i
\(58\) 0 0
\(59\) −7.50000 12.9904i −0.976417 1.69120i −0.675178 0.737655i \(-0.735933\pi\)
−0.301239 0.953549i \(-0.597400\pi\)
\(60\) 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
\(63\) 3.46410 + 2.00000i 0.436436 + 0.251976i
\(64\) 8.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 1.73205 + 1.00000i 0.211604 + 0.122169i 0.602056 0.798454i \(-0.294348\pi\)
−0.390453 + 0.920623i \(0.627682\pi\)
\(68\) 12.0000i 1.45521i
\(69\) 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
\(73\) 6.92820 4.00000i 0.810885 0.468165i −0.0363782 0.999338i \(-0.511582\pi\)
0.847263 + 0.531174i \(0.178249\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 1.00000 + 8.66025i 0.114708 + 0.993399i
\(77\) 12.0000i 1.36753i
\(78\) 0 0
\(79\) 2.50000 + 4.33013i 0.281272 + 0.487177i 0.971698 0.236225i \(-0.0759104\pi\)
−0.690426 + 0.723403i \(0.742577\pi\)
\(80\) 0 0
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) 0 0
\(83\) 12.0000i 1.31717i 0.752506 + 0.658586i \(0.228845\pi\)
−0.752506 + 0.658586i \(0.771155\pi\)
\(84\) 16.0000 1.74574
\(85\) 0 0
\(86\) 0 0
\(87\) 6.00000i 0.643268i
\(88\) 0 0
\(89\) −7.50000 + 12.9904i −0.794998 + 1.37698i 0.127842 + 0.991795i \(0.459195\pi\)
−0.922840 + 0.385183i \(0.874138\pi\)
\(90\) 0 0
\(91\) 4.00000 6.92820i 0.419314 0.726273i
\(92\) 0 0
\(93\) 12.1244 7.00000i 1.25724 0.725866i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −6.92820 + 4.00000i −0.703452 + 0.406138i −0.808632 0.588315i \(-0.799792\pi\)
0.105180 + 0.994453i \(0.466458\pi\)
\(98\) 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
\(103\) 16.0000i 1.57653i −0.615338 0.788263i \(-0.710980\pi\)
0.615338 0.788263i \(-0.289020\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 6.92820 + 4.00000i 0.666667 + 0.384900i
\(109\) 5.50000 + 9.52628i 0.526804 + 0.912452i 0.999512 + 0.0312328i \(0.00994332\pi\)
−0.472708 + 0.881219i \(0.656723\pi\)
\(110\) 0 0
\(111\) 8.00000 + 13.8564i 0.759326 + 1.31519i
\(112\) 13.8564 8.00000i 1.30931 0.755929i
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −3.00000 5.19615i −0.278543 0.482451i
\(117\) −1.73205 + 1.00000i −0.160128 + 0.0924500i
\(118\) 0 0
\(119\) −12.0000 20.7846i −1.10004 1.90532i
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) −10.3923 6.00000i −0.937043 0.541002i
\(124\) 7.00000 12.1244i 0.628619 1.08880i
\(125\) 0 0
\(126\) 0 0
\(127\) 1.73205 + 1.00000i 0.153695 + 0.0887357i 0.574875 0.818241i \(-0.305051\pi\)
−0.421180 + 0.906977i \(0.638384\pi\)
\(128\) 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 \(-0.342311\pi\)
\(132\) 12.0000i 1.04447i
\(133\) 10.3923 + 14.0000i 0.901127 + 1.21395i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −10.3923 6.00000i −0.887875 0.512615i −0.0146279 0.999893i \(-0.504656\pi\)
−0.873247 + 0.487278i \(0.837990\pi\)
\(138\) 0 0
\(139\) −8.00000 + 13.8564i −0.678551 + 1.17529i 0.296866 + 0.954919i \(0.404058\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(140\) 0 0
\(141\) −12.0000 −1.01058
\(142\) 0 0
\(143\) −5.19615 3.00000i −0.434524 0.250873i
\(144\) −4.00000 −0.333333
\(145\) 0 0
\(146\) 0 0
\(147\) 15.5885 9.00000i 1.28571 0.742307i
\(148\) 13.8564 + 8.00000i 1.13899 + 0.657596i
\(149\) 1.50000 + 2.59808i 0.122885 + 0.212843i 0.920904 0.389789i \(-0.127452\pi\)
−0.798019 + 0.602632i \(0.794119\pi\)
\(150\) 0 0
\(151\) 17.0000 1.38344 0.691720 0.722166i \(-0.256853\pi\)
0.691720 + 0.722166i \(0.256853\pi\)
\(152\) 0 0
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) 0 0
\(156\) −4.00000 + 6.92820i −0.320256 + 0.554700i
\(157\) −1.73205 + 1.00000i −0.138233 + 0.0798087i −0.567521 0.823359i \(-0.692098\pi\)
0.429289 + 0.903167i \(0.358764\pi\)
\(158\) 0 0
\(159\) −12.0000 −0.951662
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 10.0000i 0.783260i −0.920123 0.391630i \(-0.871911\pi\)
0.920123 0.391630i \(-0.128089\pi\)
\(164\) −12.0000 −0.937043
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(168\) 0 0
\(169\) −4.50000 7.79423i −0.346154 0.599556i
\(170\) 0 0
\(171\) −0.500000 4.33013i −0.0382360 0.331133i
\(172\) 8.00000i 0.609994i
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −6.00000 10.3923i −0.452267 0.783349i
\(177\) 25.9808 + 15.0000i 1.95283 + 1.12747i
\(178\) 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 −0.900794 0.434246i \(-0.857015\pi\)
0.826465 + 0.562988i \(0.190348\pi\)
\(182\) 0 0
\(183\) 10.0000i 0.739221i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −15.5885 + 9.00000i −1.13994 + 0.658145i
\(188\) −10.3923 + 6.00000i −0.757937 + 0.437595i
\(189\) 16.0000 1.16383
\(190\) 0 0
\(191\) −15.0000 −1.08536 −0.542681 0.839939i \(-0.682591\pi\)
−0.542681 + 0.839939i \(0.682591\pi\)
\(192\) −13.8564 + 8.00000i −1.00000 + 0.577350i
\(193\) −13.8564 + 8.00000i −0.997406 + 0.575853i −0.907480 0.420096i \(-0.861996\pi\)
−0.0899262 + 0.995948i \(0.528663\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 9.00000 15.5885i 0.642857 1.11346i
\(197\) 18.0000i 1.28245i 0.767354 + 0.641223i \(0.221573\pi\)
−0.767354 + 0.641223i \(0.778427\pi\)
\(198\) 0 0
\(199\) −9.50000 + 16.4545i −0.673437 + 1.16643i 0.303486 + 0.952836i \(0.401849\pi\)
−0.976923 + 0.213591i \(0.931484\pi\)
\(200\) 0 0
\(201\) −4.00000 −0.282138
\(202\) 0 0
\(203\) −10.3923 6.00000i −0.729397 0.421117i
\(204\) 12.0000 + 20.7846i 0.840168 + 1.45521i
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 8.00000i 0.554700i
\(209\) 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 \(0.755874\pi\)
\(212\) −10.3923 + 6.00000i −0.713746 + 0.412082i
\(213\) −5.19615 3.00000i −0.356034 0.205557i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 28.0000i 1.90076i
\(218\) 0 0
\(219\) −8.00000 + 13.8564i −0.540590 + 0.936329i
\(220\) 0 0
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) −3.46410 + 2.00000i −0.231973 + 0.133930i −0.611482 0.791258i \(-0.709426\pi\)
0.379509 + 0.925188i \(0.376093\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 24.0000i 1.59294i 0.604681 + 0.796468i \(0.293301\pi\)
−0.604681 + 0.796468i \(0.706699\pi\)
\(228\) −10.3923 14.0000i −0.688247 0.927173i
\(229\) 7.00000 0.462573 0.231287 0.972886i \(-0.425707\pi\)
0.231287 + 0.972886i \(0.425707\pi\)
\(230\) 0 0
\(231\) −12.0000 20.7846i −0.789542 1.36753i
\(232\) 0 0
\(233\) 5.19615 3.00000i 0.340411 0.196537i −0.320043 0.947403i \(-0.603697\pi\)
0.660454 + 0.750867i \(0.270364\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 30.0000 1.95283
\(237\) −8.66025 5.00000i −0.562544 0.324785i
\(238\) 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 −0.935242 0.354010i \(-0.884818\pi\)
0.774202 + 0.632938i \(0.218151\pi\)
\(242\) 0 0
\(243\) −8.66025 5.00000i −0.555556 0.320750i
\(244\) −5.00000 8.66025i −0.320092 0.554416i
\(245\) 0 0
\(246\) 0 0
\(247\) −8.66025 + 1.00000i −0.551039 + 0.0636285i
\(248\) 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 \(0.00969471\pi\)
\(252\) −6.92820 + 4.00000i −0.436436 + 0.251976i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −15.5885 9.00000i −0.972381 0.561405i −0.0724199 0.997374i \(-0.523072\pi\)
−0.899961 + 0.435970i \(0.856405\pi\)
\(258\) 0 0
\(259\) 32.0000 1.98838
\(260\) 0 0
\(261\) 1.50000 + 2.59808i 0.0928477 + 0.160817i
\(262\) 0 0
\(263\) −15.5885 + 9.00000i −0.961225 + 0.554964i −0.896550 0.442943i \(-0.853935\pi\)
−0.0646755 + 0.997906i \(0.520601\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 30.0000i 1.83597i
\(268\) −3.46410 + 2.00000i −0.211604 + 0.122169i
\(269\) −10.5000 18.1865i −0.640196 1.10885i −0.985389 0.170321i \(-0.945520\pi\)
0.345192 0.938532i \(-0.387814\pi\)
\(270\) 0 0
\(271\) −5.50000 9.52628i −0.334101 0.578680i 0.649211 0.760609i \(-0.275099\pi\)
−0.983312 + 0.181928i \(0.941766\pi\)
\(272\) 20.7846 + 12.0000i 1.26025 + 0.727607i
\(273\) 16.0000i 0.968364i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 8.00000i 0.480673i −0.970690 0.240337i \(-0.922742\pi\)
0.970690 0.240337i \(-0.0772579\pi\)
\(278\) 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
\(283\) 12.1244 7.00000i 0.720718 0.416107i −0.0942988 0.995544i \(-0.530061\pi\)
0.815017 + 0.579437i \(0.196728\pi\)
\(284\) −6.00000 −0.356034
\(285\) 0 0
\(286\) 0 0
\(287\) −20.7846 + 12.0000i −1.22688 + 0.708338i
\(288\) 0 0
\(289\) 9.50000 16.4545i 0.558824 0.967911i
\(290\) 0 0
\(291\) 8.00000 13.8564i 0.468968 0.812277i
\(292\) 16.0000i 0.936329i
\(293\) 24.0000i 1.40209i 0.713115 + 0.701047i \(0.247284\pi\)
−0.713115 + 0.701047i \(0.752716\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 12.0000i 0.696311i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −8.00000 13.8564i −0.461112 0.798670i
\(302\) 0 0
\(303\) 30.0000i 1.72345i
\(304\) −16.0000 6.92820i −0.917663 0.397360i
\(305\) 0 0
\(306\) 0 0
\(307\) 29.4449 17.0000i 1.68051 0.970241i 0.719183 0.694820i \(-0.244516\pi\)
0.961324 0.275421i \(-0.0888172\pi\)
\(308\) −20.7846 12.0000i −1.18431 0.683763i
\(309\) 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
\(313\) 8.66025 + 5.00000i 0.489506 + 0.282617i 0.724370 0.689412i \(-0.242131\pi\)
−0.234863 + 0.972028i \(0.575464\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) 20.7846 + 12.0000i 1.16738 + 0.673987i 0.953062 0.302777i \(-0.0979136\pi\)
0.214318 + 0.976764i \(0.431247\pi\)
\(318\) 0 0
\(319\) −4.50000 + 7.79423i −0.251952 + 0.436393i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −10.3923 + 24.0000i −0.578243 + 1.33540i
\(324\) −22.0000 −1.22222
\(325\) 0 0
\(326\) 0 0
\(327\) −19.0526 11.0000i −1.05361 0.608301i
\(328\) 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 \(0.535063\pi\)
\(332\) −20.7846 12.0000i −1.14070 0.658586i
\(333\) −6.92820 4.00000i −0.379663 0.219199i
\(334\) 0 0
\(335\) 0 0
\(336\) −16.0000 + 27.7128i −0.872872 + 1.51186i
\(337\) 13.8564 8.00000i 0.754807 0.435788i −0.0726214 0.997360i \(-0.523136\pi\)
0.827428 + 0.561572i \(0.189803\pi\)
\(338\) 0 0
\(339\) −6.00000 10.3923i −0.325875 0.564433i
\(340\) 0 0
\(341\) −21.0000 −1.13721
\(342\) 0 0
\(343\) 8.00000i 0.431959i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −10.3923 + 6.00000i −0.557888 + 0.322097i −0.752297 0.658824i \(-0.771054\pi\)
0.194409 + 0.980921i \(0.437721\pi\)
\(348\) 10.3923 + 6.00000i 0.557086 + 0.321634i
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) −4.00000 + 6.92820i −0.213504 + 0.369800i
\(352\) 0 0
\(353\) 12.0000i 0.638696i 0.947638 + 0.319348i \(0.103464\pi\)
−0.947638 + 0.319348i \(0.896536\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −15.0000 25.9808i −0.794998 1.37698i
\(357\) 41.5692 + 24.0000i 2.20008 + 1.27021i
\(358\) 0 0
\(359\) 12.0000 + 20.7846i 0.633336 + 1.09697i 0.986865 + 0.161546i \(0.0516481\pi\)
−0.353529 + 0.935423i \(0.615019\pi\)
\(360\) 0 0
\(361\) 5.50000 18.1865i 0.289474 0.957186i
\(362\) 0 0
\(363\) 3.46410 2.00000i 0.181818 0.104973i
\(364\) 8.00000 + 13.8564i 0.419314 + 0.726273i
\(365\) 0 0
\(366\) 0 0
\(367\) −3.46410 2.00000i −0.180825 0.104399i 0.406855 0.913493i \(-0.366625\pi\)
−0.587680 + 0.809093i \(0.699959\pi\)
\(368\) 0 0
\(369\) 6.00000 0.312348
\(370\) 0 0
\(371\) −12.0000 + 20.7846i −0.623009 + 1.07908i
\(372\) 28.0000i 1.45173i
\(373\) 4.00000i 0.207112i −0.994624 0.103556i \(-0.966978\pi\)
0.994624 0.103556i \(-0.0330221\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.19615 3.00000i 0.267615 0.154508i
\(378\) 0 0
\(379\) 37.0000 1.90056 0.950281 0.311393i \(-0.100796\pi\)
0.950281 + 0.311393i \(0.100796\pi\)
\(380\) 0 0
\(381\) −4.00000 −0.204926
\(382\) 0 0
\(383\) 25.9808 15.0000i 1.32755 0.766464i 0.342634 0.939469i \(-0.388681\pi\)
0.984921 + 0.173005i \(0.0553476\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4.00000i 0.203331i
\(388\) 16.0000i 0.812277i
\(389\) 7.50000 12.9904i 0.380265 0.658638i −0.610835 0.791758i \(-0.709166\pi\)
0.991100 + 0.133120i \(0.0424994\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 20.7846 + 12.0000i 1.04844 + 0.605320i
\(394\) 0 0
\(395\) 0 0
\(396\) 3.00000 + 5.19615i 0.150756 + 0.261116i
\(397\) −6.92820 + 4.00000i −0.347717 + 0.200754i −0.663679 0.748017i \(-0.731006\pi\)
0.315963 + 0.948772i \(0.397673\pi\)
\(398\) 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
\(403\) 12.1244 + 7.00000i 0.603957 + 0.348695i
\(404\) −15.0000 25.9808i −0.746278 1.29259i
\(405\) 0 0
\(406\) 0 0
\(407\) 24.0000i 1.18964i
\(408\) 0 0
\(409\) 11.5000 19.9186i 0.568638 0.984911i −0.428063 0.903749i \(-0.640804\pi\)
0.996701 0.0811615i \(-0.0258630\pi\)
\(410\) 0 0
\(411\) 24.0000 1.18383
\(412\) 27.7128 + 16.0000i 1.36531 + 0.788263i
\(413\) 51.9615 30.0000i 2.55686 1.47620i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 32.0000i 1.56705i
\(418\) 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 0.999109 0.0422075i \(-0.0134391\pi\)
−0.536107 + 0.844150i \(0.680106\pi\)
\(422\) 0 0
\(423\) 5.19615 3.00000i 0.252646 0.145865i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −17.3205 10.0000i −0.838198 0.483934i
\(428\) 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 \(0.0490126\pi\)
\(432\) −13.8564 + 8.00000i −0.666667 + 0.384900i
\(433\) −6.92820 4.00000i −0.332948 0.192228i 0.324201 0.945988i \(-0.394905\pi\)
−0.657149 + 0.753760i \(0.728238\pi\)
\(434\) 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 \(-0.267072\pi\)
−0.978412 + 0.206666i \(0.933739\pi\)
\(440\) 0 0
\(441\) −4.50000 + 7.79423i −0.214286 + 0.371154i
\(442\) 0 0
\(443\) 10.3923 + 6.00000i 0.493753 + 0.285069i 0.726130 0.687557i \(-0.241317\pi\)
−0.232377 + 0.972626i \(0.574650\pi\)
\(444\) −32.0000 −1.51865
\(445\) 0 0
\(446\) 0 0
\(447\) −5.19615 3.00000i −0.245770 0.141895i
\(448\) 32.0000i 1.51186i
\(449\) 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
\(452\) −10.3923 6.00000i −0.488813 0.282216i
\(453\) −29.4449 + 17.0000i −1.38344 + 0.798730i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 22.0000i 1.02912i 0.857455 + 0.514558i \(0.172044\pi\)
−0.857455 + 0.514558i \(0.827956\pi\)
\(458\) 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
\(463\) 16.0000i 0.743583i −0.928316 0.371792i \(-0.878744\pi\)
0.928316 0.371792i \(-0.121256\pi\)
\(464\) 12.0000 0.557086
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 4.00000i 0.184900i
\(469\) −4.00000 + 6.92820i −0.184703 + 0.319915i
\(470\) 0 0
\(471\) 2.00000 3.46410i 0.0921551 0.159617i
\(472\) 0 0
\(473\) −10.3923 + 6.00000i −0.477839 + 0.275880i
\(474\) 0 0
\(475\) 0 0
\(476\) 48.0000 2.20008
\(477\) 5.19615 3.00000i 0.237915 0.137361i
\(478\) 0 0
\(479\) 7.50000 12.9904i 0.342684 0.593546i −0.642246 0.766498i \(-0.721997\pi\)
0.984930 + 0.172953i \(0.0553307\pi\)
\(480\) 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
\(487\) 2.00000i 0.0906287i −0.998973 0.0453143i \(-0.985571\pi\)
0.998973 0.0453143i \(-0.0144289\pi\)
\(488\) 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 \(0.723424\pi\)
\(492\) 20.7846 12.0000i 0.937043 0.541002i
\(493\) 18.0000i 0.810679i
\(494\) 0 0
\(495\) 0 0
\(496\) 14.0000 + 24.2487i 0.628619 + 1.08880i
\(497\) −10.3923 + 6.00000i −0.466159 + 0.269137i
\(498\) 0 0
\(499\) 10.0000 + 17.3205i 0.447661 + 0.775372i 0.998233 0.0594153i \(-0.0189236\pi\)
−0.550572 + 0.834788i \(0.685590\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 36.3731 + 21.0000i 1.62179 + 0.936344i 0.986440 + 0.164124i \(0.0524796\pi\)
0.635355 + 0.772220i \(0.280854\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 15.5885 + 9.00000i 0.692308 + 0.399704i
\(508\) −3.46410 + 2.00000i −0.153695 + 0.0887357i
\(509\) −9.00000 + 15.5885i −0.398918 + 0.690946i −0.993593 0.113020i \(-0.963948\pi\)
0.594675 + 0.803966i \(0.297281\pi\)
\(510\) 0 0
\(511\) 16.0000 + 27.7128i 0.707798 + 1.22594i
\(512\) 0 0
\(513\) −10.3923 14.0000i −0.458831 0.618115i
\(514\) 0 0
\(515\) 0 0
\(516\) 8.00000 + 13.8564i 0.352180 + 0.609994i
\(517\) 15.5885 + 9.00000i 0.685580 + 0.395820i
\(518\) 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
\(523\) −22.5167 13.0000i −0.984585 0.568450i −0.0809336 0.996719i \(-0.525790\pi\)
−0.903651 + 0.428269i \(0.859124\pi\)
\(524\) 24.0000 1.04844
\(525\) 0 0
\(526\) 0 0
\(527\) 36.3731 21.0000i 1.58444 0.914774i
\(528\) 20.7846 + 12.0000i 0.904534 + 0.522233i
\(529\) −11.5000 19.9186i −0.500000 0.866025i
\(530\) 0 0
\(531\) −15.0000 −0.650945
\(532\) −34.6410 + 4.00000i −1.50188 + 0.173422i
\(533\) 12.0000i 0.519778i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −15.5885 + 9.00000i −0.672692 + 0.388379i
\(538\) 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
\(543\) 4.00000i 0.171656i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −3.46410 2.00000i −0.148114 0.0855138i 0.424111 0.905610i \(-0.360587\pi\)
−0.572226 + 0.820096i \(0.693920\pi\)
\(548\) 20.7846 12.0000i 0.887875 0.512615i
\(549\) 2.50000 + 4.33013i 0.106697 + 0.184805i
\(550\) 0 0
\(551\) 1.50000 + 12.9904i 0.0639021 + 0.553409i
\(552\) 0 0
\(553\) −17.3205 + 10.0000i −0.736543 + 0.425243i
\(554\) 0 0
\(555\) 0 0
\(556\) −16.0000 27.7128i −0.678551 1.17529i
\(557\) 10.3923 + 6.00000i 0.440336 + 0.254228i 0.703740 0.710457i \(-0.251512\pi\)
−0.263404 + 0.964686i \(0.584845\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) 18.0000 31.1769i 0.759961 1.31629i
\(562\) 0 0
\(563\) 6.00000i 0.252870i 0.991975 + 0.126435i \(0.0403535\pi\)
−0.991975 + 0.126435i \(0.959647\pi\)
\(564\) 12.0000 20.7846i 0.505291 0.875190i
\(565\) 0 0
\(566\) 0 0
\(567\) −38.1051 + 22.0000i −1.60026 + 0.923913i
\(568\) 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 \(0.546791\pi\)
\(572\) 10.3923 6.00000i 0.434524 0.250873i
\(573\) 25.9808 15.0000i 1.08536 0.626634i
\(574\) 0 0
\(575\) 0 0
\(576\) 4.00000 6.92820i 0.166667 0.288675i
\(577\) 16.0000i 0.666089i 0.942911 + 0.333044i \(0.108076\pi\)
−0.942911 + 0.333044i \(0.891924\pi\)
\(578\) 0 0
\(579\) 16.0000 27.7128i 0.664937 1.15171i
\(580\) 0 0
\(581\) −48.0000 −1.99138
\(582\) 0 0
\(583\) 15.5885 + 9.00000i 0.645608 + 0.372742i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 31.1769 18.0000i 1.28681 0.742940i 0.308725 0.951151i \(-0.400098\pi\)
0.978084 + 0.208212i \(0.0667643\pi\)
\(588\) 36.0000i 1.48461i
\(589\) −24.5000 + 18.1865i −1.00950 + 0.749363i
\(590\) 0 0
\(591\) −18.0000 31.1769i −0.740421 1.28245i
\(592\) −27.7128 + 16.0000i −1.13899 + 0.657596i
\(593\) −10.3923 6.00000i −0.426761 0.246390i 0.271205 0.962522i \(-0.412578\pi\)
−0.697966 + 0.716131i \(0.745911\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 38.0000i 1.55524i
\(598\) 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
\(603\) 1.73205 1.00000i 0.0705346 0.0407231i
\(604\) −17.0000 + 29.4449i −0.691720 + 1.19809i
\(605\) 0 0
\(606\) 0 0
\(607\) 2.00000i 0.0811775i −0.999176 0.0405887i \(-0.987077\pi\)
0.999176 0.0405887i \(-0.0129233\pi\)
\(608\) 0 0
\(609\) 24.0000 0.972529
\(610\) 0 0
\(611\) −6.00000 10.3923i −0.242734 0.420428i
\(612\) −10.3923 6.00000i −0.420084 0.242536i
\(613\) 1.73205 1.00000i 0.0699569 0.0403896i −0.464614 0.885514i \(-0.653807\pi\)
0.534570 + 0.845124i \(0.320473\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 31.1769 + 18.0000i 1.25514 + 0.724653i 0.972125 0.234464i \(-0.0753335\pi\)
0.283011 + 0.959117i \(0.408667\pi\)
\(618\) 0 0
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −51.9615 30.0000i −2.08179 1.20192i
\(624\) −8.00000 13.8564i −0.320256 0.554700i
\(625\) 0 0
\(626\) 0 0
\(627\) −10.3923 + 24.0000i −0.415029 + 0.958468i
\(628\) 4.00000i 0.159617i
\(629\) 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
\(633\) −12.1244 7.00000i −0.481900 0.278225i
\(634\) 0 0
\(635\) 0 0
\(636\) 12.0000 20.7846i 0.475831 0.824163i
\(637\) 15.5885 + 9.00000i 0.617637 + 0.356593i
\(638\) 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
\(643\) −29.4449 + 17.0000i −1.16119 + 0.670415i −0.951589 0.307372i \(-0.900550\pi\)
−0.209603 + 0.977787i \(0.567217\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 18.0000i 0.707653i −0.935311 0.353827i \(-0.884880\pi\)
0.935311 0.353827i \(-0.115120\pi\)
\(648\) 0 0
\(649\) −22.5000 38.9711i −0.883202 1.52975i
\(650\) 0 0
\(651\) 28.0000 + 48.4974i 1.09741 + 1.90076i
\(652\) 17.3205 + 10.0000i 0.678323 + 0.391630i
\(653\) 24.0000i 0.939193i 0.882881 + 0.469596i \(0.155601\pi\)
−0.882881 + 0.469596i \(0.844399\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 12.0000 20.7846i 0.468521 0.811503i
\(657\) 8.00000i 0.312110i
\(658\) 0 0
\(659\) −6.00000 + 10.3923i −0.233727 + 0.404827i −0.958902 0.283738i \(-0.908425\pi\)
0.725175 + 0.688565i \(0.241759\pi\)
\(660\) 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
\(663\) −20.7846 + 12.0000i −0.807207 + 0.466041i
\(664\) 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
\(673\) 4.00000i 0.154189i −0.997024 0.0770943i \(-0.975436\pi\)
0.997024 0.0770943i \(-0.0245643\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 18.0000 0.692308
\(677\) 48.0000i 1.84479i −0.386248 0.922395i \(-0.626229\pi\)
0.386248 0.922395i \(-0.373771\pi\)
\(678\) 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
\(683\) 18.0000i 0.688751i −0.938832 0.344375i \(-0.888091\pi\)
0.938832 0.344375i \(-0.111909\pi\)
\(684\) 8.00000 + 3.46410i 0.305888 + 0.132453i
\(685\) 0 0
\(686\) 0 0
\(687\) −12.1244 + 7.00000i −0.462573 + 0.267067i
\(688\) 13.8564 + 8.00000i 0.528271 + 0.304997i
\(689\) −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
\(693\) 10.3923 + 6.00000i 0.394771 + 0.227921i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −31.1769 18.0000i −1.18091 0.681799i
\(698\) 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
\(703\) −20.7846 28.0000i −0.783906 1.05604i
\(704\) 24.0000 0.904534
\(705\) 0 0
\(706\) 0 0
\(707\) −51.9615 30.0000i −1.95421 1.12827i
\(708\) −51.9615 + 30.0000i −1.95283 + 1.12747i
\(709\) −15.5000 + 26.8468i −0.582115 + 1.00825i 0.413114 + 0.910679i \(0.364441\pi\)
−0.995228 + 0.0975728i \(0.968892\pi\)
\(710\) 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
\(717\) −5.19615 + 3.00000i −0.194054 + 0.112037i
\(718\) 0 0
\(719\) 7.50000 + 12.9904i 0.279703 + 0.484459i 0.971311 0.237814i \(-0.0764307\pi\)
−0.691608 + 0.722273i \(0.743097\pi\)
\(720\) 0 0
\(721\) 64.0000 2.38348
\(722\) 0 0
\(723\) 10.0000i 0.371904i
\(724\) −2.00000 3.46410i −0.0743294 0.128742i
\(725\) 0 0
\(726\) 0 0
\(727\) −12.1244 + 7.00000i −0.449667 + 0.259616i −0.707690 0.706523i \(-0.750263\pi\)
0.258022 + 0.966139i \(0.416929\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) 17.3205 + 10.0000i 0.640184 + 0.369611i
\(733\) 32.0000i 1.18195i 0.806691 + 0.590973i \(0.201256\pi\)
−0.806691 + 0.590973i \(0.798744\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.19615 + 3.00000i 0.191403 + 0.110506i
\(738\) 0 0
\(739\) 17.5000 + 30.3109i 0.643748 + 1.11500i 0.984589 + 0.174883i \(0.0559548\pi\)
−0.340841 + 0.940121i \(0.610712\pi\)
\(740\) 0 0
\(741\) 14.0000 10.3923i 0.514303 0.381771i
\(742\) 0 0
\(743\) −20.7846 + 12.0000i −0.762513 + 0.440237i −0.830197 0.557470i \(-0.811772\pi\)
0.0676840 + 0.997707i \(0.478439\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 10.3923 + 6.00000i 0.380235 + 0.219529i
\(748\) 36.0000i 1.31629i
\(749\) 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 \(0.125902\pi\)
\(752\) 24.0000i 0.875190i
\(753\) 30.0000i 1.09326i
\(754\) 0 0
\(755\) 0 0
\(756\) −16.0000 + 27.7128i −0.581914 + 1.00791i
\(757\) 8.66025 5.00000i 0.314762 0.181728i −0.334293 0.942469i \(-0.608498\pi\)
0.649056 + 0.760741i \(0.275164\pi\)
\(758\) 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
\(763\) −38.1051 + 22.0000i −1.37950 + 0.796453i
\(764\) 15.0000 25.9808i 0.542681 0.939951i
\(765\) 0 0
\(766\) 0 0
\(767\) 30.0000i 1.08324i
\(768\) 32.0000i 1.15470i
\(769\) 14.5000 25.1147i 0.522883 0.905661i −0.476762 0.879032i \(-0.658190\pi\)
0.999645 0.0266282i \(-0.00847701\pi\)
\(770\) 0 0
\(771\) 36.0000 1.29651
\(772\) 32.0000i 1.15171i
\(773\) −25.9808 15.0000i −0.934463 0.539513i −0.0462427 0.998930i \(-0.514725\pi\)
−0.888220 + 0.459418i \(0.848058\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −55.4256 + 32.0000i −1.98838 + 1.14799i
\(778\) 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
\(783\) 10.3923 + 6.00000i 0.371391 + 0.214423i
\(784\) 18.0000 + 31.1769i 0.642857 + 1.11346i
\(785\) 0 0
\(786\) 0 0
\(787\) 34.0000i 1.21197i 0.795476 + 0.605985i \(0.207221\pi\)
−0.795476 + 0.605985i \(0.792779\pi\)
\(788\) −31.1769 18.0000i −1.11063 0.641223i
\(789\) 18.0000 31.1769i 0.640817 1.10993i
\(790\) 0 0
\(791\) −24.0000 −0.853342
\(792\) 0 0
\(793\) 8.66025 5.00000i 0.307535 0.177555i
\(794\) 0 0