Properties

Label 1470.2.i.q.361.1
Level $1470$
Weight $2$
Character 1470.361
Analytic conductor $11.738$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 30)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1470.361
Dual form 1470.2.i.q.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{12} -2.00000 q^{13} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.00000 - 3.46410i) q^{19} +1.00000 q^{20} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} -1.00000 q^{27} -6.00000 q^{29} +(-0.500000 - 0.866025i) q^{30} +(4.00000 - 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} +6.00000 q^{34} +1.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(2.00000 - 3.46410i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(0.500000 + 0.866025i) q^{40} +6.00000 q^{41} -4.00000 q^{43} +(-0.500000 + 0.866025i) q^{45} -1.00000 q^{48} -1.00000 q^{50} +(-3.00000 - 5.19615i) q^{51} +(1.00000 - 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +(-0.500000 - 0.866025i) q^{54} -4.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(0.500000 - 0.866025i) q^{60} +(-5.00000 - 8.66025i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{65} +(2.00000 - 3.46410i) q^{67} +(3.00000 + 5.19615i) q^{68} +(0.500000 + 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(1.00000 - 1.73205i) q^{74} +(0.500000 + 0.866025i) q^{75} +4.00000 q^{76} -2.00000 q^{78} +(-4.00000 - 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.00000 + 5.19615i) q^{82} -12.0000 q^{83} -6.00000 q^{85} +(-2.00000 - 3.46410i) q^{86} +(-3.00000 + 5.19615i) q^{87} +(9.00000 + 15.5885i) q^{89} -1.00000 q^{90} +(-4.00000 - 6.92820i) q^{93} +(-2.00000 + 3.46410i) q^{95} +(-0.500000 - 0.866025i) q^{96} -2.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + q^{3} - q^{4} - q^{5} + 2q^{6} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} + q^{3} - q^{4} - q^{5} + 2q^{6} - 2q^{8} - q^{9} + q^{10} + q^{12} - 4q^{13} - 2q^{15} - q^{16} + 6q^{17} + q^{18} - 4q^{19} + 2q^{20} - q^{24} - q^{25} - 2q^{26} - 2q^{27} - 12q^{29} - q^{30} + 8q^{31} + q^{32} + 12q^{34} + 2q^{36} - 2q^{37} + 4q^{38} - 2q^{39} + q^{40} + 12q^{41} - 8q^{43} - q^{45} - 2q^{48} - 2q^{50} - 6q^{51} + 2q^{52} + 6q^{53} - q^{54} - 8q^{57} - 6q^{58} + q^{60} - 10q^{61} + 16q^{62} + 2q^{64} + 2q^{65} + 4q^{67} + 6q^{68} + q^{72} + 2q^{73} + 2q^{74} + q^{75} + 8q^{76} - 4q^{78} - 8q^{79} - q^{80} - q^{81} + 6q^{82} - 24q^{83} - 12q^{85} - 4q^{86} - 6q^{87} + 18q^{89} - 2q^{90} - 8q^{93} - 4q^{95} - q^{96} - 4q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −2.00000 −0.554700 −0.277350 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i \(-0.573966\pi\)
0.957892 0.287129i \(-0.0927008\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) −2.00000 3.46410i −0.458831 0.794719i 0.540068 0.841621i \(-0.318398\pi\)
−0.998899 + 0.0469020i \(0.985065\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) −0.500000 + 0.866025i −0.102062 + 0.176777i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −1.00000 1.73205i −0.196116 0.339683i
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −0.500000 0.866025i −0.0912871 0.158114i
\(31\) 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i \(-0.578198\pi\)
0.961625 0.274367i \(-0.0884683\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −1.00000 1.73205i −0.164399 0.284747i 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 2.00000 3.46410i 0.324443 0.561951i
\(39\) −1.00000 + 1.73205i −0.160128 + 0.277350i
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) −0.500000 + 0.866025i −0.0745356 + 0.129099i
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) −1.00000 −0.144338
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) −3.00000 5.19615i −0.420084 0.727607i
\(52\) 1.00000 1.73205i 0.138675 0.240192i
\(53\) 3.00000 5.19615i 0.412082 0.713746i −0.583036 0.812447i \(-0.698135\pi\)
0.995117 + 0.0987002i \(0.0314685\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0 0
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) −3.00000 5.19615i −0.393919 0.682288i
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0.500000 0.866025i 0.0645497 0.111803i
\(61\) −5.00000 8.66025i −0.640184 1.10883i −0.985391 0.170305i \(-0.945525\pi\)
0.345207 0.938527i \(-0.387809\pi\)
\(62\) 8.00000 1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 1.00000 + 1.73205i 0.124035 + 0.214834i
\(66\) 0 0
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) 3.00000 + 5.19615i 0.363803 + 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) 1.00000 1.73205i 0.117041 0.202721i −0.801553 0.597924i \(-0.795992\pi\)
0.918594 + 0.395203i \(0.129326\pi\)
\(74\) 1.00000 1.73205i 0.116248 0.201347i
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 3.00000 + 5.19615i 0.331295 + 0.573819i
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) −3.00000 + 5.19615i −0.321634 + 0.557086i
\(88\) 0 0
\(89\) 9.00000 + 15.5885i 0.953998 + 1.65237i 0.736644 + 0.676280i \(0.236409\pi\)
0.217354 + 0.976093i \(0.430258\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) 0 0
\(93\) −4.00000 6.92820i −0.414781 0.718421i
\(94\) 0 0
\(95\) −2.00000 + 3.46410i −0.205196 + 0.355409i
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 9.00000 15.5885i 0.895533 1.55111i 0.0623905 0.998052i \(-0.480128\pi\)
0.833143 0.553058i \(-0.186539\pi\)
\(102\) 3.00000 5.19615i 0.297044 0.514496i
\(103\) −2.00000 3.46410i −0.197066 0.341328i 0.750510 0.660859i \(-0.229808\pi\)
−0.947576 + 0.319531i \(0.896475\pi\)
\(104\) 2.00000 0.196116
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 5.00000 8.66025i 0.478913 0.829502i −0.520794 0.853682i \(-0.674364\pi\)
0.999708 + 0.0241802i \(0.00769755\pi\)
\(110\) 0 0
\(111\) −2.00000 −0.189832
\(112\) 0 0
\(113\) −18.0000 −1.69330 −0.846649 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) −2.00000 3.46410i −0.187317 0.324443i
\(115\) 0 0
\(116\) 3.00000 5.19615i 0.278543 0.482451i
\(117\) 1.00000 + 1.73205i 0.0924500 + 0.160128i
\(118\) 0 0
\(119\) 0 0
\(120\) 1.00000 0.0912871
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) 5.00000 8.66025i 0.452679 0.784063i
\(123\) 3.00000 5.19615i 0.270501 0.468521i
\(124\) 4.00000 + 6.92820i 0.359211 + 0.622171i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −2.00000 + 3.46410i −0.176090 + 0.304997i
\(130\) −1.00000 + 1.73205i −0.0877058 + 0.151911i
\(131\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) −3.00000 + 5.19615i −0.257248 + 0.445566i
\(137\) −3.00000 + 5.19615i −0.256307 + 0.443937i −0.965250 0.261329i \(-0.915839\pi\)
0.708942 + 0.705266i \(0.249173\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 3.00000 + 5.19615i 0.249136 + 0.431517i
\(146\) 2.00000 0.165521
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i \(-0.938871\pi\)
0.656101 + 0.754673i \(0.272204\pi\)
\(152\) 2.00000 + 3.46410i 0.162221 + 0.280976i
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) −1.00000 1.73205i −0.0800641 0.138675i
\(157\) 1.00000 1.73205i 0.0798087 0.138233i −0.823359 0.567521i \(-0.807902\pi\)
0.903167 + 0.429289i \(0.141236\pi\)
\(158\) 4.00000 6.92820i 0.318223 0.551178i
\(159\) −3.00000 5.19615i −0.237915 0.412082i
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 2.00000 + 3.46410i 0.156652 + 0.271329i 0.933659 0.358162i \(-0.116597\pi\)
−0.777007 + 0.629492i \(0.783263\pi\)
\(164\) −3.00000 + 5.19615i −0.234261 + 0.405751i
\(165\) 0 0
\(166\) −6.00000 10.3923i −0.465690 0.806599i
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) −3.00000 5.19615i −0.230089 0.398527i
\(171\) −2.00000 + 3.46410i −0.152944 + 0.264906i
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) 9.00000 + 15.5885i 0.684257 + 1.18517i 0.973670 + 0.227964i \(0.0732068\pi\)
−0.289412 + 0.957205i \(0.593460\pi\)
\(174\) −6.00000 −0.454859
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −9.00000 + 15.5885i −0.674579 + 1.16840i
\(179\) −12.0000 + 20.7846i −0.896922 + 1.55351i −0.0655145 + 0.997852i \(0.520869\pi\)
−0.831408 + 0.555663i \(0.812464\pi\)
\(180\) −0.500000 0.866025i −0.0372678 0.0645497i
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 0 0
\(183\) −10.0000 −0.739221
\(184\) 0 0
\(185\) −1.00000 + 1.73205i −0.0735215 + 0.127343i
\(186\) 4.00000 6.92820i 0.293294 0.508001i
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) 12.0000 + 20.7846i 0.868290 + 1.50392i 0.863743 + 0.503932i \(0.168114\pi\)
0.00454614 + 0.999990i \(0.498553\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 11.0000 19.0526i 0.791797 1.37143i −0.133056 0.991109i \(-0.542479\pi\)
0.924853 0.380325i \(-0.124188\pi\)
\(194\) −1.00000 1.73205i −0.0717958 0.124354i
\(195\) 2.00000 0.143223
\(196\) 0 0
\(197\) −6.00000 −0.427482 −0.213741 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) 4.00000 6.92820i 0.283552 0.491127i −0.688705 0.725042i \(-0.741820\pi\)
0.972257 + 0.233915i \(0.0751537\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) −2.00000 3.46410i −0.141069 0.244339i
\(202\) 18.0000 1.26648
\(203\) 0 0
\(204\) 6.00000 0.420084
\(205\) −3.00000 5.19615i −0.209529 0.362915i
\(206\) 2.00000 3.46410i 0.139347 0.241355i
\(207\) 0 0
\(208\) 1.00000 + 1.73205i 0.0693375 + 0.120096i
\(209\) 0 0
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 3.00000 + 5.19615i 0.206041 + 0.356873i
\(213\) 0 0
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) 2.00000 + 3.46410i 0.136399 + 0.236250i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 10.0000 0.677285
\(219\) −1.00000 1.73205i −0.0675737 0.117041i
\(220\) 0 0
\(221\) −6.00000 + 10.3923i −0.403604 + 0.699062i
\(222\) −1.00000 1.73205i −0.0671156 0.116248i
\(223\) −20.0000 −1.33930 −0.669650 0.742677i \(-0.733556\pi\)
−0.669650 + 0.742677i \(0.733556\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) −9.00000 15.5885i −0.598671 1.03693i
\(227\) −6.00000 + 10.3923i −0.398234 + 0.689761i −0.993508 0.113761i \(-0.963710\pi\)
0.595274 + 0.803523i \(0.297043\pi\)
\(228\) 2.00000 3.46410i 0.132453 0.229416i
\(229\) −5.00000 8.66025i −0.330409 0.572286i 0.652183 0.758062i \(-0.273853\pi\)
−0.982592 + 0.185776i \(0.940520\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) 9.00000 + 15.5885i 0.589610 + 1.02123i 0.994283 + 0.106773i \(0.0340517\pi\)
−0.404674 + 0.914461i \(0.632615\pi\)
\(234\) −1.00000 + 1.73205i −0.0653720 + 0.113228i
\(235\) 0 0
\(236\) 0 0
\(237\) −8.00000 −0.519656
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0.500000 + 0.866025i 0.0322749 + 0.0559017i
\(241\) 1.00000 1.73205i 0.0644157 0.111571i −0.832019 0.554747i \(-0.812815\pi\)
0.896435 + 0.443176i \(0.146148\pi\)
\(242\) −5.50000 + 9.52628i −0.353553 + 0.612372i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 10.0000 0.640184
\(245\) 0 0
\(246\) 6.00000 0.382546
\(247\) 4.00000 + 6.92820i 0.254514 + 0.440831i
\(248\) −4.00000 + 6.92820i −0.254000 + 0.439941i
\(249\) −6.00000 + 10.3923i −0.380235 + 0.658586i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 24.0000 1.51487 0.757433 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 10.0000 + 17.3205i 0.627456 + 1.08679i
\(255\) −3.00000 + 5.19615i −0.187867 + 0.325396i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −9.00000 15.5885i −0.561405 0.972381i −0.997374 0.0724199i \(-0.976928\pi\)
0.435970 0.899961i \(-0.356405\pi\)
\(258\) −4.00000 −0.249029
\(259\) 0 0
\(260\) −2.00000 −0.124035
\(261\) 3.00000 + 5.19615i 0.185695 + 0.321634i
\(262\) 0 0
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) 0 0
\(267\) 18.0000 1.10158
\(268\) 2.00000 + 3.46410i 0.122169 + 0.211604i
\(269\) −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i \(-0.891886\pi\)
0.759958 + 0.649972i \(0.225219\pi\)
\(270\) −0.500000 + 0.866025i −0.0304290 + 0.0527046i
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) 0 0
\(276\) 0 0
\(277\) −1.00000 + 1.73205i −0.0600842 + 0.104069i −0.894503 0.447062i \(-0.852470\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(278\) 2.00000 + 3.46410i 0.119952 + 0.207763i
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) 18.0000 1.07379 0.536895 0.843649i \(-0.319597\pi\)
0.536895 + 0.843649i \(0.319597\pi\)
\(282\) 0 0
\(283\) −14.0000 + 24.2487i −0.832214 + 1.44144i 0.0640654 + 0.997946i \(0.479593\pi\)
−0.896279 + 0.443491i \(0.853740\pi\)
\(284\) 0 0
\(285\) 2.00000 + 3.46410i 0.118470 + 0.205196i
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) −3.00000 + 5.19615i −0.176166 + 0.305129i
\(291\) −1.00000 + 1.73205i −0.0586210 + 0.101535i
\(292\) 1.00000 + 1.73205i 0.0585206 + 0.101361i
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.00000 + 1.73205i 0.0581238 + 0.100673i
\(297\) 0 0
\(298\) −3.00000 + 5.19615i −0.173785 + 0.301005i
\(299\) 0 0
\(300\) −1.00000 −0.0577350
\(301\) 0 0
\(302\) −8.00000 −0.460348
\(303\) −9.00000 15.5885i −0.517036 0.895533i
\(304\) −2.00000 + 3.46410i −0.114708 + 0.198680i
\(305\) −5.00000 + 8.66025i −0.286299 + 0.495885i
\(306\) −3.00000 5.19615i −0.171499 0.297044i
\(307\) −20.0000 −1.14146 −0.570730 0.821138i \(-0.693340\pi\)
−0.570730 + 0.821138i \(0.693340\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) −4.00000 6.92820i −0.227185 0.393496i
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 1.00000 1.73205i 0.0566139 0.0980581i
\(313\) 1.00000 + 1.73205i 0.0565233 + 0.0979013i 0.892903 0.450250i \(-0.148665\pi\)
−0.836379 + 0.548151i \(0.815332\pi\)
\(314\) 2.00000 0.112867
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) −9.00000 15.5885i −0.505490 0.875535i −0.999980 0.00635137i \(-0.997978\pi\)
0.494489 0.869184i \(-0.335355\pi\)
\(318\) 3.00000 5.19615i 0.168232 0.291386i
\(319\) 0 0
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) −24.0000 −1.33540
\(324\) −0.500000 0.866025i −0.0277778 0.0481125i
\(325\) 1.00000 1.73205i 0.0554700 0.0960769i
\(326\) −2.00000 + 3.46410i −0.110770 + 0.191859i
\(327\) −5.00000 8.66025i −0.276501 0.478913i
\(328\) −6.00000 −0.331295
\(329\) 0 0
\(330\) 0 0
\(331\) 14.0000 + 24.2487i 0.769510 + 1.33283i 0.937829 + 0.347097i \(0.112833\pi\)
−0.168320 + 0.985732i \(0.553834\pi\)
\(332\) 6.00000 10.3923i 0.329293 0.570352i
\(333\) −1.00000 + 1.73205i −0.0547997 + 0.0949158i
\(334\) 0 0
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) 26.0000 1.41631 0.708155 0.706057i \(-0.249528\pi\)
0.708155 + 0.706057i \(0.249528\pi\)
\(338\) −4.50000 7.79423i −0.244768 0.423950i
\(339\) −9.00000 + 15.5885i −0.488813 + 0.846649i
\(340\) 3.00000 5.19615i 0.162698 0.281801i
\(341\) 0 0
\(342\) −4.00000 −0.216295
\(343\) 0 0
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) −9.00000 + 15.5885i −0.483843 + 0.838041i
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) −3.00000 5.19615i −0.160817 0.278543i
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) 2.00000 0.106752
\(352\) 0 0
\(353\) 3.00000 5.19615i 0.159674 0.276563i −0.775077 0.631867i \(-0.782289\pi\)
0.934751 + 0.355303i \(0.115622\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −18.0000 −0.953998
\(357\) 0 0
\(358\) −24.0000 −1.26844
\(359\) 12.0000 + 20.7846i 0.633336 + 1.09697i 0.986865 + 0.161546i \(0.0516481\pi\)
−0.353529 + 0.935423i \(0.615019\pi\)
\(360\) 0.500000 0.866025i 0.0263523 0.0456435i
\(361\) 1.50000 2.59808i 0.0789474 0.136741i
\(362\) −7.00000 12.1244i −0.367912 0.637242i
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) −2.00000 −0.104685
\(366\) −5.00000 8.66025i −0.261354 0.452679i
\(367\) −14.0000 + 24.2487i −0.730794 + 1.26577i 0.225750 + 0.974185i \(0.427517\pi\)
−0.956544 + 0.291587i \(0.905817\pi\)
\(368\) 0 0
\(369\) −3.00000 5.19615i −0.156174 0.270501i
\(370\) −2.00000 −0.103975
\(371\) 0 0
\(372\) 8.00000 0.414781
\(373\) −13.0000 22.5167i −0.673114 1.16587i −0.977016 0.213165i \(-0.931623\pi\)
0.303902 0.952703i \(-0.401711\pi\)
\(374\) 0 0
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) −2.00000 3.46410i −0.102598 0.177705i
\(381\) 10.0000 17.3205i 0.512316 0.887357i
\(382\) −12.0000 + 20.7846i −0.613973 + 1.06343i
\(383\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 22.0000 1.11977
\(387\) 2.00000 + 3.46410i 0.101666 + 0.176090i
\(388\) 1.00000 1.73205i 0.0507673 0.0879316i
\(389\) 3.00000 5.19615i 0.152106 0.263455i −0.779895 0.625910i \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 1.00000 + 1.73205i 0.0506370 + 0.0877058i
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) −3.00000 5.19615i −0.151138 0.261778i
\(395\) −4.00000 + 6.92820i −0.201262 + 0.348596i
\(396\) 0 0
\(397\) −11.0000 19.0526i −0.552074 0.956221i −0.998125 0.0612128i \(-0.980503\pi\)
0.446051 0.895008i \(-0.352830\pi\)
\(398\) 8.00000 0.401004
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 3.00000 + 5.19615i 0.149813 + 0.259483i 0.931158 0.364615i \(-0.118800\pi\)
−0.781345 + 0.624099i \(0.785466\pi\)
\(402\) 2.00000 3.46410i 0.0997509 0.172774i
\(403\) −8.00000 + 13.8564i −0.398508 + 0.690237i
\(404\) 9.00000 + 15.5885i 0.447767 + 0.775555i
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 0 0
\(408\) 3.00000 + 5.19615i 0.148522 + 0.257248i
\(409\) 13.0000 22.5167i 0.642809 1.11338i −0.341994 0.939702i \(-0.611102\pi\)
0.984803 0.173675i \(-0.0555643\pi\)
\(410\) 3.00000 5.19615i 0.148159 0.256620i
\(411\) 3.00000 + 5.19615i 0.147979 + 0.256307i
\(412\) 4.00000 0.197066
\(413\) 0 0
\(414\) 0 0
\(415\) 6.00000 + 10.3923i 0.294528 + 0.510138i
\(416\) −1.00000 + 1.73205i −0.0490290 + 0.0849208i
\(417\) 2.00000 3.46410i 0.0979404 0.169638i
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 10.0000 + 17.3205i 0.486792 + 0.843149i
\(423\) 0 0
\(424\) −3.00000 + 5.19615i −0.145693 + 0.252347i
\(425\) 3.00000 + 5.19615i 0.145521 + 0.252050i
\(426\) 0 0
\(427\) 0 0
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) −2.00000 + 3.46410i −0.0964486 + 0.167054i
\(431\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 6.00000 0.287678
\(436\) 5.00000 + 8.66025i 0.239457 + 0.414751i
\(437\) 0 0
\(438\) 1.00000 1.73205i 0.0477818 0.0827606i
\(439\) 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −12.0000 −0.570782
\(443\) −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i \(-0.258683\pi\)
−0.972626 + 0.232377i \(0.925350\pi\)
\(444\) 1.00000 1.73205i 0.0474579 0.0821995i
\(445\) 9.00000 15.5885i 0.426641 0.738964i
\(446\) −10.0000 17.3205i −0.473514 0.820150i
\(447\) 6.00000 0.283790
\(448\) 0 0
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0.500000 + 0.866025i 0.0235702 + 0.0408248i
\(451\) 0 0
\(452\) 9.00000 15.5885i 0.423324 0.733219i
\(453\) 4.00000 + 6.92820i 0.187936 + 0.325515i
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −13.0000 22.5167i −0.608114 1.05328i −0.991551 0.129718i \(-0.958593\pi\)
0.383437 0.923567i \(-0.374740\pi\)
\(458\) 5.00000 8.66025i 0.233635 0.404667i
\(459\) −3.00000 + 5.19615i −0.140028 + 0.242536i
\(460\) 0 0
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 0 0
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 3.00000 + 5.19615i 0.139272 + 0.241225i
\(465\) −4.00000 + 6.92820i −0.185496 + 0.321288i
\(466\) −9.00000 + 15.5885i −0.416917 + 0.722121i
\(467\) −18.0000 31.1769i −0.832941 1.44270i −0.895696 0.444667i \(-0.853322\pi\)
0.0627555 0.998029i \(-0.480011\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) 0 0
\(471\) −1.00000 1.73205i −0.0460776 0.0798087i
\(472\) 0 0
\(473\) 0 0
\(474\) −4.00000 6.92820i −0.183726 0.318223i
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 12.0000 + 20.7846i 0.548867 + 0.950666i
\(479\) −12.0000 + 20.7846i −0.548294 + 0.949673i 0.450098 + 0.892979i \(0.351389\pi\)
−0.998392 + 0.0566937i \(0.981944\pi\)
\(480\) −0.500000 + 0.866025i −0.0228218 + 0.0395285i
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) 2.00000 0.0910975
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 1.00000 + 1.73205i 0.0454077 + 0.0786484i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) 14.0000 24.2487i 0.634401 1.09881i −0.352241 0.935909i \(-0.614580\pi\)
0.986642 0.162905i \(-0.0520863\pi\)
\(488\) 5.00000 + 8.66025i 0.226339 + 0.392031i
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 3.00000 + 5.19615i 0.135250 + 0.234261i
\(493\) −18.0000 + 31.1769i −0.810679 + 1.40414i
\(494\) −4.00000 + 6.92820i −0.179969 + 0.311715i
\(495\) 0 0
\(496\) −8.00000 −0.359211
\(497\) 0 0
\(498\) −12.0000 −0.537733
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) 12.0000 + 20.7846i 0.535586 + 0.927663i
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) 0 0
\(507\) −4.50000 + 7.79423i −0.199852 + 0.346154i
\(508\) −10.0000 + 17.3205i −0.443678 + 0.768473i
\(509\) −3.00000 5.19615i −0.132973 0.230315i 0.791849 0.610718i \(-0.209119\pi\)
−0.924821 + 0.380402i \(0.875786\pi\)
\(510\) −6.00000 −0.265684
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 2.00000 + 3.46410i 0.0883022 + 0.152944i
\(514\) 9.00000 15.5885i 0.396973 0.687577i
\(515\) −2.00000 + 3.46410i −0.0881305 + 0.152647i
\(516\) −2.00000 3.46410i −0.0880451 0.152499i
\(517\) 0 0
\(518\) 0 0
\(519\) 18.0000 0.790112
\(520\) −1.00000 1.73205i −0.0438529 0.0759555i
\(521\) 9.00000 15.5885i 0.394297 0.682943i −0.598714 0.800963i \(-0.704321\pi\)
0.993011 + 0.118020i \(0.0376547\pi\)
\(522\) −3.00000 + 5.19615i −0.131306 + 0.227429i
\(523\) 10.0000 + 17.3205i 0.437269 + 0.757373i 0.997478 0.0709788i \(-0.0226123\pi\)
−0.560208 + 0.828352i \(0.689279\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −24.0000 41.5692i −1.04546 1.81078i
\(528\) 0 0
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) −3.00000 5.19615i −0.130312 0.225706i
\(531\) 0 0
\(532\) 0 0
\(533\) −12.0000 −0.519778
\(534\) 9.00000 + 15.5885i 0.389468 + 0.674579i
\(535\) 6.00000 10.3923i 0.259403 0.449299i
\(536\) −2.00000 + 3.46410i −0.0863868 + 0.149626i
\(537\) 12.0000 + 20.7846i 0.517838 + 0.896922i
\(538\) −6.00000 −0.258678
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) 5.00000 + 8.66025i 0.214967 + 0.372333i 0.953262 0.302144i \(-0.0977023\pi\)
−0.738296 + 0.674477i \(0.764369\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) −7.00000 + 12.1244i −0.300399 + 0.520306i
\(544\) −3.00000 5.19615i −0.128624 0.222783i
\(545\) −10.0000 −0.428353
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) −3.00000 5.19615i −0.128154 0.221969i
\(549\) −5.00000 + 8.66025i −0.213395 + 0.369611i
\(550\) 0 0
\(551\) 12.0000 + 20.7846i 0.511217 + 0.885454i
\(552\) 0 0
\(553\) 0 0
\(554\) −2.00000 −0.0849719
\(555\) 1.00000 + 1.73205i 0.0424476 + 0.0735215i
\(556\) −2.00000 + 3.46410i −0.0848189 + 0.146911i
\(557\) −9.00000 + 15.5885i −0.381342 + 0.660504i −0.991254 0.131965i \(-0.957871\pi\)
0.609912 + 0.792469i \(0.291205\pi\)
\(558\) −4.00000 6.92820i −0.169334 0.293294i
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 9.00000 + 15.5885i 0.379642 + 0.657559i
\(563\) −6.00000 + 10.3923i −0.252870 + 0.437983i −0.964315 0.264758i \(-0.914708\pi\)
0.711445 + 0.702742i \(0.248041\pi\)
\(564\) 0 0
\(565\) 9.00000 + 15.5885i 0.378633 + 0.655811i
\(566\) −28.0000 −1.17693
\(567\) 0 0
\(568\) 0 0
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) −2.00000 + 3.46410i −0.0837708 + 0.145095i
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) 0 0
\(573\) 24.0000 1.00261
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 1.00000 1.73205i 0.0416305 0.0721062i −0.844459 0.535620i \(-0.820078\pi\)
0.886090 + 0.463513i \(0.153411\pi\)
\(578\) 9.50000 16.4545i 0.395148 0.684416i
\(579\) −11.0000 19.0526i −0.457144 0.791797i
\(580\) −6.00000 −0.249136
\(581\) 0 0
\(582\) −2.00000 −0.0829027
\(583\) 0 0
\(584\) −1.00000 + 1.73205i −0.0413803 + 0.0716728i
\(585\) 1.00000 1.73205i 0.0413449 0.0716115i
\(586\) 3.00000 + 5.19615i 0.123929 + 0.214651i
\(587\) 12.0000 0.495293 0.247647 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 0 0
\(589\) −32.0000 −1.31854
\(590\) 0 0
\(591\) −3.00000 + 5.19615i −0.123404 + 0.213741i
\(592\) −1.00000 + 1.73205i −0.0410997 + 0.0711868i
\(593\) 15.0000 + 25.9808i 0.615976 + 1.06690i 0.990212 + 0.139569i \(0.0445716\pi\)
−0.374236 + 0.927333i \(0.622095\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −4.00000 6.92820i −0.163709 0.283552i
\(598\) 0 0
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) −0.500000 0.866025i −0.0204124 0.0353553i
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) 5.50000 9.52628i 0.223607 0.387298i
\(606\) 9.00000 15.5885i 0.365600 0.633238i
\(607\) −2.00000 3.46410i −0.0811775 0.140604i 0.822578 0.568652i \(-0.192535\pi\)
−0.903756 + 0.428048i \(0.859201\pi\)
\(608\) −4.00000 −0.162221
\(609\) 0 0
\(610\) −10.0000 −0.404888
\(611\) 0 0
\(612\) 3.00000 5.19615i 0.121268 0.210042i
\(613\) −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) −10.0000 17.3205i −0.403567 0.698999i
\(615\) −6.00000 −0.241943
\(616\) 0 0
\(617\) 30.0000 1.20775 0.603877 0.797077i \(-0.293622\pi\)
0.603877 + 0.797077i \(0.293622\pi\)
\(618\) −2.00000 3.46410i −0.0804518 0.139347i
\(619\) 22.0000 38.1051i 0.884255 1.53157i 0.0376891 0.999290i \(-0.488000\pi\)
0.846566 0.532284i \(-0.178666\pi\)
\(620\) 4.00000 6.92820i 0.160644 0.278243i
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 2.00000 0.0800641
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −1.00000 + 1.73205i −0.0399680 + 0.0692267i
\(627\) 0 0
\(628\) 1.00000 + 1.73205i 0.0399043 + 0.0691164i
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 4.00000 + 6.92820i 0.159111 + 0.275589i
\(633\) 10.0000 17.3205i 0.397464 0.688428i
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) −10.0000 17.3205i −0.396838 0.687343i
\(636\) 6.00000 0.237915
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 15.0000 25.9808i 0.592464 1.02618i −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) 6.00000 + 10.3923i 0.236801 + 0.410152i
\(643\) 4.00000 0.157745 0.0788723 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) 4.00000 0.157500
\(646\) −12.0000 20.7846i −0.472134 0.817760i
\(647\) 12.0000 20.7846i 0.471769 0.817127i −0.527710 0.849425i \(-0.676949\pi\)
0.999478 + 0.0322975i \(0.0102824\pi\)
\(648\) 0.500000 0.866025i 0.0196419 0.0340207i
\(649\) 0 0
\(650\) 2.00000 0.0784465
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) −9.00000 15.5885i −0.352197 0.610023i 0.634437 0.772975i \(-0.281232\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(654\) 5.00000 8.66025i 0.195515 0.338643i
\(655\) 0 0
\(656\) −3.00000 5.19615i −0.117130 0.202876i
\(657\) −2.00000 −0.0780274
\(658\) 0 0
\(659\) 48.0000 1.86981 0.934907 0.354892i \(-0.115482\pi\)
0.934907 + 0.354892i \(0.115482\pi\)
\(660\) 0 0
\(661\) 7.00000 12.1244i 0.272268 0.471583i −0.697174 0.716902i \(-0.745559\pi\)
0.969442 + 0.245319i \(0.0788928\pi\)
\(662\) −14.0000 + 24.2487i −0.544125 + 0.942453i
\(663\) 6.00000 + 10.3923i 0.233021 + 0.403604i
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) 0 0
\(668\) 0 0
\(669\) −10.0000 + 17.3205i −0.386622 + 0.669650i
\(670\) −2.00000 3.46410i −0.0772667 0.133830i
\(671\) 0 0
\(672\) 0 0
\(673\) 26.0000 1.00223 0.501113 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) 13.0000 + 22.5167i 0.500741 + 0.867309i
\(675\) 0.500000 0.866025i 0.0192450 0.0333333i
\(676\) 4.50000 7.79423i 0.173077 0.299778i
\(677\) −3.00000 5.19615i −0.115299 0.199704i 0.802600 0.596518i \(-0.203449\pi\)
−0.917899 + 0.396813i \(0.870116\pi\)
\(678\) −18.0000 −0.691286
\(679\) 0 0
\(680\) 6.00000 0.230089
\(681\) 6.00000 + 10.3923i 0.229920 + 0.398234i
\(682\) 0 0
\(683\) 6.00000 10.3923i 0.229584 0.397650i −0.728101 0.685470i \(-0.759597\pi\)
0.957685 + 0.287819i \(0.0929302\pi\)
\(684\) −2.00000 3.46410i −0.0764719 0.132453i
\(685\) 6.00000 0.229248
\(686\) 0 0
\(687\) −10.0000 −0.381524
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) 0 0
\(691\) 22.0000 + 38.1051i 0.836919 + 1.44959i 0.892458 + 0.451130i \(0.148979\pi\)
−0.0555386 + 0.998457i \(0.517688\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −2.00000 3.46410i −0.0758643 0.131401i
\(696\) 3.00000 5.19615i 0.113715 0.196960i
\(697\) 18.0000 31.1769i 0.681799 1.18091i
\(698\) 5.00000 + 8.66025i 0.189253 + 0.327795i
\(699\) 18.0000 0.680823
\(700\) 0 0
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 1.00000 + 1.73205i 0.0377426 + 0.0653720i
\(703\) −4.00000 + 6.92820i −0.150863 + 0.261302i
\(704\) 0 0
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) 0 0
\(709\) −19.0000 32.9090i −0.713560 1.23592i −0.963512 0.267664i \(-0.913748\pi\)
0.249952 0.968258i \(-0.419585\pi\)
\(710\) 0 0
\(711\) −4.00000 + 6.92820i −0.150012 + 0.259828i
\(712\) −9.00000 15.5885i −0.337289 0.584202i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −12.0000 20.7846i −0.448461 0.776757i
\(717\) 12.0000 20.7846i 0.448148 0.776215i
\(718\) −12.0000 + 20.7846i −0.447836 + 0.775675i
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 1.00000 0.0372678
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) −1.00000 1.73205i −0.0371904 0.0644157i
\(724\) 7.00000 12.1244i 0.260153 0.450598i
\(725\) 3.00000 5.19615i 0.111417 0.192980i
\(726\) 5.50000 + 9.52628i 0.204124 + 0.353553i
\(727\) 28.0000 1.03846 0.519231 0.854634i \(-0.326218\pi\)
0.519231 + 0.854634i \(0.326218\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −1.00000 1.73205i −0.0370117 0.0641061i
\(731\) −12.0000 + 20.7846i −0.443836 + 0.768747i
\(732\) 5.00000 8.66025i 0.184805 0.320092i
\(733\) −11.0000 19.0526i −0.406294 0.703722i 0.588177 0.808732i \(-0.299846\pi\)
−0.994471 + 0.105010i \(0.966513\pi\)
\(734\) −28.0000 −1.03350
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 3.00000 5.19615i 0.110432 0.191273i
\(739\) 26.0000 45.0333i 0.956425 1.65658i 0.225354 0.974277i \(-0.427646\pi\)
0.731072 0.682300i \(-0.239020\pi\)
\(740\) −1.00000 1.73205i −0.0367607 0.0636715i
\(741\) 8.00000 0.293887
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 4.00000 + 6.92820i 0.146647 + 0.254000i
\(745\) 3.00000 5.19615i 0.109911 0.190372i
\(746\) 13.0000 22.5167i 0.475964 0.824394i
\(747\) 6.00000 + 10.3923i 0.219529 + 0.380235i
\(748\) 0 0
\(749\) 0 0
\(750\) 1.00000 0.0365148
\(751\) 20.0000 + 34.6410i 0.729810 + 1.26407i 0.956963 + 0.290209i \(0.0937250\pi\)
−0.227153 + 0.973859i \(0.572942\pi\)
\(752\) 0 0
\(753\) 12.0000 20.7846i 0.437304 0.757433i
\(754\) 6.00000 + 10.3923i 0.218507 + 0.378465i
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −2.00000 3.46410i −0.0726433 0.125822i
\(759\) 0 0
\(760\) 2.00000 3.46410i 0.0725476 0.125656i
\(761\) 9.00000 + 15.5885i 0.326250 + 0.565081i 0.981764 0.190101i \(-0.0608816\pi\)
−0.655515 + 0.755182i \(0.727548\pi\)
\(762\) 20.0000 0.724524
\(763\) 0 0
\(764\) −24.0000 −0.868290
\(765\) 3.00000 + 5.19615i 0.108465 + 0.187867i
\(766\) 0 0
\(767\) 0 0
\(768\) 0.500000 + 0.866025i 0.0180422 + 0.0312500i
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) 11.0000 + 19.0526i 0.395899 + 0.685717i
\(773\) 21.0000 36.3731i 0.755318 1.30825i −0.189899 0.981804i \(-0.560816\pi\)
0.945216 0.326445i \(-0.105851\pi\)
\(774\) −2.00000 + 3.46410i −0.0718885 + 0.124515i
\(775\) 4.00000 + 6.92820i 0.143684 + 0.248868i
\(776\) 2.00000 0.0717958
\(777\) 0 0
\(778\) 6.00000 0.215110
\(779\) −12.0000 20.7846i −0.429945 0.744686i
\(780\) −1.00000 + 1.73205i −0.0358057 + 0.0620174i
\(781\) 0 0
\(782\) 0 0
\(783\) 6.00000 0.214423
\(784\) 0 0
\(785\) −2.00000 −0.0713831
\(786\) 0 0
\(787\) −2.00000 + 3.46410i −0.0712923 + 0.123482i −0.899468 0.436987i \(-0.856046\pi\)
0.828176 + 0.560469i \(0.189379\pi\)
\(788\) 3.00000 5.19615i 0.106871 0.185105i
\(789\) 0 0
\(790\) −8.00000 −0.284627
\(791\) 0 0
\(792\) 0 0
\(793\) 10.0000 + 17.3205i 0.355110 + 0.615069i
\(794\) 11.0000 19.0526i 0.390375 0.676150i
\(795\) −3.00000 + 5.19615i −0.106399 + 0.184289i
\(796\) 4.00000 + 6.92820i 0.141776 + 0.245564i
\(797\) 30.0000 1.06265 0.531327 0.847167i \(-0.321693\pi\)
0.531327 + 0.847167i \(0.321693\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.500000 + 0.866025i 0.0176777 + 0.0306186i
\(801\) 9.00000 15.5885i 0.317999 0.550791i
\(802\) −3.00000 + 5.19615i −0.105934 + 0.183483i
\(803\) 0 0
\(804\) 4.00000 0.141069
\(805\) 0