Properties

Label 810.2.e.b.271.1
Level $810$
Weight $2$
Character 810.271
Analytic conductor $6.468$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 810.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.46788256372\)
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 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 810.271
Dual form 810.2.e.b.541.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +1.00000 q^{10} +(-1.00000 + 1.73205i) q^{13} +(2.00000 - 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} -6.00000 q^{17} -4.00000 q^{19} +(-0.500000 - 0.866025i) q^{20} +(-0.500000 - 0.866025i) q^{25} +2.00000 q^{26} -4.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{34} -4.00000 q^{35} +2.00000 q^{37} +(2.00000 + 3.46410i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(2.00000 + 3.46410i) q^{43} +(-4.50000 + 7.79423i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.00000 - 1.73205i) q^{52} +6.00000 q^{53} +(2.00000 + 3.46410i) q^{56} +(-3.00000 + 5.19615i) q^{58} +(5.00000 + 8.66025i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +(2.00000 - 3.46410i) q^{67} +(3.00000 - 5.19615i) q^{68} +(2.00000 + 3.46410i) q^{70} +2.00000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-4.00000 - 6.92820i) q^{79} +1.00000 q^{80} +6.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +(3.00000 - 5.19615i) q^{85} +(2.00000 - 3.46410i) q^{86} -18.0000 q^{89} -8.00000 q^{91} +(2.00000 - 3.46410i) q^{95} +(-1.00000 - 1.73205i) q^{97} +9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} - q^{5} + 4q^{7} + 2q^{8} + O(q^{10}) \) \( 2q - q^{2} - q^{4} - q^{5} + 4q^{7} + 2q^{8} + 2q^{10} - 2q^{13} + 4q^{14} - q^{16} - 12q^{17} - 8q^{19} - q^{20} - q^{25} + 4q^{26} - 8q^{28} - 6q^{29} - 8q^{31} - q^{32} + 6q^{34} - 8q^{35} + 4q^{37} + 4q^{38} - q^{40} - 6q^{41} + 4q^{43} - 9q^{49} - q^{50} - 2q^{52} + 12q^{53} + 4q^{56} - 6q^{58} + 10q^{61} + 16q^{62} + 2q^{64} - 2q^{65} + 4q^{67} + 6q^{68} + 4q^{70} + 4q^{73} - 2q^{74} + 4q^{76} - 8q^{79} + 2q^{80} + 12q^{82} + 12q^{83} + 6q^{85} + 4q^{86} - 36q^{89} - 16q^{91} + 4q^{95} - 2q^{97} + 18q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 2.00000 + 3.46410i 0.755929 + 1.30931i 0.944911 + 0.327327i \(0.106148\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 1.00000 0.316228
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.73205i −0.277350 + 0.480384i −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 2.00000 3.46410i 0.534522 0.925820i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) −0.500000 0.866025i −0.111803 0.193649i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 2.00000 0.392232
\(27\) 0 0
\(28\) −4.00000 −0.755929
\(29\) −3.00000 5.19615i −0.557086 0.964901i −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 0 0
\(31\) −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i \(0.421802\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 3.00000 + 5.19615i 0.514496 + 0.891133i
\(35\) −4.00000 −0.676123
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 2.00000 + 3.46410i 0.324443 + 0.561951i
\(39\) 0 0
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) −3.00000 + 5.19615i −0.468521 + 0.811503i −0.999353 0.0359748i \(-0.988546\pi\)
0.530831 + 0.847477i \(0.321880\pi\)
\(42\) 0 0
\(43\) 2.00000 + 3.46410i 0.304997 + 0.528271i 0.977261 0.212041i \(-0.0680112\pi\)
−0.672264 + 0.740312i \(0.734678\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) −4.50000 + 7.79423i −0.642857 + 1.11346i
\(50\) −0.500000 + 0.866025i −0.0707107 + 0.122474i
\(51\) 0 0
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.00000 + 3.46410i 0.267261 + 0.462910i
\(57\) 0 0
\(58\) −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 0
\(61\) 5.00000 + 8.66025i 0.640184 + 1.10883i 0.985391 + 0.170305i \(0.0544754\pi\)
−0.345207 + 0.938527i \(0.612191\pi\)
\(62\) 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
\(70\) 2.00000 + 3.46410i 0.239046 + 0.414039i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −1.00000 1.73205i −0.116248 0.201347i
\(75\) 0 0
\(76\) 2.00000 3.46410i 0.229416 0.397360i
\(77\) 0 0
\(78\) 0 0
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) 1.00000 0.111803
\(81\) 0 0
\(82\) 6.00000 0.662589
\(83\) 6.00000 + 10.3923i 0.658586 + 1.14070i 0.980982 + 0.194099i \(0.0621783\pi\)
−0.322396 + 0.946605i \(0.604488\pi\)
\(84\) 0 0
\(85\) 3.00000 5.19615i 0.325396 0.563602i
\(86\) 2.00000 3.46410i 0.215666 0.373544i
\(87\) 0 0
\(88\) 0 0
\(89\) −18.0000 −1.90800 −0.953998 0.299813i \(-0.903076\pi\)
−0.953998 + 0.299813i \(0.903076\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.838628
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.00000 3.46410i 0.205196 0.355409i
\(96\) 0 0
\(97\) −1.00000 1.73205i −0.101535 0.175863i 0.810782 0.585348i \(-0.199042\pi\)
−0.912317 + 0.409484i \(0.865709\pi\)
\(98\) 9.00000 0.909137
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 9.00000 + 15.5885i 0.895533 + 1.55111i 0.833143 + 0.553058i \(0.186539\pi\)
0.0623905 + 0.998052i \(0.480128\pi\)
\(102\) 0 0
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) −1.00000 + 1.73205i −0.0980581 + 0.169842i
\(105\) 0 0
\(106\) −3.00000 5.19615i −0.291386 0.504695i
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.00000 3.46410i 0.188982 0.327327i
\(113\) −9.00000 + 15.5885i −0.846649 + 1.46644i 0.0375328 + 0.999295i \(0.488050\pi\)
−0.884182 + 0.467143i \(0.845283\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) 0 0
\(118\) 0 0
\(119\) −12.0000 20.7846i −1.10004 1.90532i
\(120\) 0 0
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) 5.00000 8.66025i 0.452679 0.784063i
\(123\) 0 0
\(124\) −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
\(129\) 0 0
\(130\) −1.00000 + 1.73205i −0.0877058 + 0.151911i
\(131\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(132\) 0 0
\(133\) −8.00000 13.8564i −0.693688 1.20150i
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) −6.00000 −0.514496
\(137\) 3.00000 + 5.19615i 0.256307 + 0.443937i 0.965250 0.261329i \(-0.0841608\pi\)
−0.708942 + 0.705266i \(0.750827\pi\)
\(138\) 0 0
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) 2.00000 3.46410i 0.169031 0.292770i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 6.00000 0.498273
\(146\) −1.00000 1.73205i −0.0827606 0.143346i
\(147\) 0 0
\(148\) −1.00000 + 1.73205i −0.0821995 + 0.142374i
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0 0
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) −4.00000 −0.324443
\(153\) 0 0
\(154\) 0 0
\(155\) −4.00000 6.92820i −0.321288 0.556487i
\(156\) 0 0
\(157\) −1.00000 + 1.73205i −0.0798087 + 0.138233i −0.903167 0.429289i \(-0.858764\pi\)
0.823359 + 0.567521i \(0.192098\pi\)
\(158\) −4.00000 + 6.92820i −0.318223 + 0.551178i
\(159\) 0 0
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) 0 0
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) −3.00000 5.19615i −0.234261 0.405751i
\(165\) 0 0
\(166\) 6.00000 10.3923i 0.465690 0.806599i
\(167\) 0 0 −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
\(170\) −6.00000 −0.460179
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) 9.00000 + 15.5885i 0.684257 + 1.18517i 0.973670 + 0.227964i \(0.0732068\pi\)
−0.289412 + 0.957205i \(0.593460\pi\)
\(174\) 0 0
\(175\) 2.00000 3.46410i 0.151186 0.261861i
\(176\) 0 0
\(177\) 0 0
\(178\) 9.00000 + 15.5885i 0.674579 + 1.16840i
\(179\) −24.0000 −1.79384 −0.896922 0.442189i \(-0.854202\pi\)
−0.896922 + 0.442189i \(0.854202\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 4.00000 + 6.92820i 0.296500 + 0.513553i
\(183\) 0 0
\(184\) 0 0
\(185\) −1.00000 + 1.73205i −0.0735215 + 0.127343i
\(186\) 0 0
\(187\) 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 \(-0.831886\pi\)
−0.00454614 0.999990i \(-0.501447\pi\)
\(192\) 0 0
\(193\) 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
\(195\) 0 0
\(196\) −4.50000 7.79423i −0.321429 0.556731i
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 0 0
\(202\) 9.00000 15.5885i 0.633238 1.09680i
\(203\) 12.0000 20.7846i 0.842235 1.45879i
\(204\) 0 0
\(205\) −3.00000 5.19615i −0.209529 0.362915i
\(206\) −4.00000 −0.278693
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) 0 0
\(210\) 0 0
\(211\) −10.0000 + 17.3205i −0.688428 + 1.19239i 0.283918 + 0.958849i \(0.408366\pi\)
−0.972346 + 0.233544i \(0.924968\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 0 0
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) −4.00000 −0.272798
\(216\) 0 0
\(217\) −32.0000 −2.17230
\(218\) 5.00000 + 8.66025i 0.338643 + 0.586546i
\(219\) 0 0
\(220\) 0 0
\(221\) 6.00000 10.3923i 0.403604 0.699062i
\(222\) 0 0
\(223\) −10.0000 17.3205i −0.669650 1.15987i −0.978002 0.208595i \(-0.933111\pi\)
0.308353 0.951272i \(-0.400222\pi\)
\(224\) −4.00000 −0.267261
\(225\) 0 0
\(226\) 18.0000 1.19734
\(227\) −6.00000 10.3923i −0.398234 0.689761i 0.595274 0.803523i \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) 0 0
\(229\) 5.00000 8.66025i 0.330409 0.572286i −0.652183 0.758062i \(-0.726147\pi\)
0.982592 + 0.185776i \(0.0594799\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.00000 5.19615i −0.196960 0.341144i
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) −12.0000 + 20.7846i −0.777844 + 1.34727i
\(239\) 12.0000 20.7846i 0.776215 1.34444i −0.157893 0.987456i \(-0.550470\pi\)
0.934109 0.356988i \(-0.116196\pi\)
\(240\) 0 0
\(241\) −1.00000 1.73205i −0.0644157 0.111571i 0.832019 0.554747i \(-0.187185\pi\)
−0.896435 + 0.443176i \(0.853852\pi\)
\(242\) −11.0000 −0.707107
\(243\) 0 0
\(244\) −10.0000 −0.640184
\(245\) −4.50000 7.79423i −0.287494 0.497955i
\(246\) 0 0
\(247\) 4.00000 6.92820i 0.254514 0.440831i
\(248\) −4.00000 + 6.92820i −0.254000 + 0.439941i
\(249\) 0 0
\(250\) −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
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −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
\(259\) 4.00000 + 6.92820i 0.248548 + 0.430498i
\(260\) 2.00000 0.124035
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 0 0
\(265\) −3.00000 + 5.19615i −0.184289 + 0.319197i
\(266\) −8.00000 + 13.8564i −0.490511 + 0.849591i
\(267\) 0 0
\(268\) 2.00000 + 3.46410i 0.122169 + 0.211604i
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) 3.00000 + 5.19615i 0.181902 + 0.315063i
\(273\) 0 0
\(274\) 3.00000 5.19615i 0.181237 0.313911i
\(275\) 0 0
\(276\) 0 0
\(277\) −1.00000 1.73205i −0.0600842 0.104069i 0.834419 0.551131i \(-0.185804\pi\)
−0.894503 + 0.447062i \(0.852470\pi\)
\(278\) −4.00000 −0.239904
\(279\) 0 0
\(280\) −4.00000 −0.239046
\(281\) 9.00000 + 15.5885i 0.536895 + 0.929929i 0.999069 + 0.0431402i \(0.0137362\pi\)
−0.462174 + 0.886789i \(0.652930\pi\)
\(282\) 0 0
\(283\) 14.0000 24.2487i 0.832214 1.44144i −0.0640654 0.997946i \(-0.520407\pi\)
0.896279 0.443491i \(-0.146260\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −24.0000 −1.41668
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) −3.00000 5.19615i −0.176166 0.305129i
\(291\) 0 0
\(292\) −1.00000 + 1.73205i −0.0585206 + 0.101361i
\(293\) −3.00000 + 5.19615i −0.175262 + 0.303562i −0.940252 0.340480i \(-0.889411\pi\)
0.764990 + 0.644042i \(0.222744\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 2.00000 0.116248
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) 0 0
\(300\) 0 0
\(301\) −8.00000 + 13.8564i −0.461112 + 0.798670i
\(302\) −4.00000 + 6.92820i −0.230174 + 0.398673i
\(303\) 0 0
\(304\) 2.00000 + 3.46410i 0.114708 + 0.198680i
\(305\) −10.0000 −0.572598
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −4.00000 + 6.92820i −0.227185 + 0.393496i
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) −1.00000 1.73205i −0.0565233 0.0979013i 0.836379 0.548151i \(-0.184668\pi\)
−0.892903 + 0.450250i \(0.851335\pi\)
\(314\) 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 \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) 0 0
\(323\) 24.0000 1.33540
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) 0 0
\(328\) −3.00000 + 5.19615i −0.165647 + 0.286910i
\(329\) 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 \(0.553834\pi\)
\(332\) −12.0000 −0.658586
\(333\) 0 0
\(334\) 0 0
\(335\) 2.00000 + 3.46410i 0.109272 + 0.189264i
\(336\) 0 0
\(337\) −13.0000 + 22.5167i −0.708155 + 1.22656i 0.257386 + 0.966309i \(0.417139\pi\)
−0.965541 + 0.260252i \(0.916194\pi\)
\(338\) 4.50000 7.79423i 0.244768 0.423950i
\(339\) 0 0
\(340\) 3.00000 + 5.19615i 0.162698 + 0.281801i
\(341\) 0 0
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 2.00000 + 3.46410i 0.107833 + 0.186772i
\(345\) 0 0
\(346\) 9.00000 15.5885i 0.483843 0.838041i
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 0 0
\(349\) 5.00000 + 8.66025i 0.267644 + 0.463573i 0.968253 0.249973i \(-0.0804216\pi\)
−0.700609 + 0.713545i \(0.747088\pi\)
\(350\) −4.00000 −0.213809
\(351\) 0 0
\(352\) 0 0
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 9.00000 15.5885i 0.476999 0.826187i
\(357\) 0 0
\(358\) 12.0000 + 20.7846i 0.634220 + 1.09850i
\(359\) 24.0000 1.26667 0.633336 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) −7.00000 12.1244i −0.367912 0.637242i
\(363\) 0 0
\(364\) 4.00000 6.92820i 0.209657 0.363137i
\(365\) −1.00000 + 1.73205i −0.0523424 + 0.0906597i
\(366\) 0 0
\(367\) 14.0000 + 24.2487i 0.730794 + 1.26577i 0.956544 + 0.291587i \(0.0941834\pi\)
−0.225750 + 0.974185i \(0.572483\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 2.00000 0.103975
\(371\) 12.0000 + 20.7846i 0.623009 + 1.07908i
\(372\) 0 0
\(373\) −13.0000 + 22.5167i −0.673114 + 1.16587i 0.303902 + 0.952703i \(0.401711\pi\)
−0.977016 + 0.213165i \(0.931623\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 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
\(381\) 0 0
\(382\) −12.0000 + 20.7846i −0.613973 + 1.06343i
\(383\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −22.0000 −1.11977
\(387\) 0 0
\(388\) 2.00000 0.101535
\(389\) −3.00000 5.19615i −0.152106 0.263455i 0.779895 0.625910i \(-0.215272\pi\)
−0.932002 + 0.362454i \(0.881939\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −4.50000 + 7.79423i −0.227284 + 0.393668i
\(393\) 0 0
\(394\) −3.00000 5.19615i −0.151138 0.261778i
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) −22.0000 −1.10415 −0.552074 0.833795i \(-0.686163\pi\)
−0.552074 + 0.833795i \(0.686163\pi\)
\(398\) −4.00000 6.92820i −0.200502 0.347279i
\(399\) 0 0
\(400\) −0.500000 + 0.866025i −0.0250000 + 0.0433013i
\(401\) −3.00000 + 5.19615i −0.149813 + 0.259483i −0.931158 0.364615i \(-0.881200\pi\)
0.781345 + 0.624099i \(0.214534\pi\)
\(402\) 0 0
\(403\) −8.00000 13.8564i −0.398508 0.690237i
\(404\) −18.0000 −0.895533
\(405\) 0 0
\(406\) −24.0000 −1.19110
\(407\) 0 0
\(408\) 0 0
\(409\) −13.0000 + 22.5167i −0.642809 + 1.11338i 0.341994 + 0.939702i \(0.388898\pi\)
−0.984803 + 0.173675i \(0.944436\pi\)
\(410\) −3.00000 + 5.19615i −0.148159 + 0.256620i
\(411\) 0 0
\(412\) 2.00000 + 3.46410i 0.0985329 + 0.170664i
\(413\) 0 0
\(414\) 0 0
\(415\) −12.0000 −0.589057
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(420\) 0 0
\(421\) 5.00000 + 8.66025i 0.243685 + 0.422075i 0.961761 0.273890i \(-0.0883103\pi\)
−0.718076 + 0.695965i \(0.754977\pi\)
\(422\) 20.0000 0.973585
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 3.00000 + 5.19615i 0.145521 + 0.252050i
\(426\) 0 0
\(427\) −20.0000 + 34.6410i −0.967868 + 1.67640i
\(428\) −6.00000 + 10.3923i −0.290021 + 0.502331i
\(429\) 0 0
\(430\) 2.00000 + 3.46410i 0.0964486 + 0.167054i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 26.0000 1.24948 0.624740 0.780833i \(-0.285205\pi\)
0.624740 + 0.780833i \(0.285205\pi\)
\(434\) 16.0000 + 27.7128i 0.768025 + 1.33026i
\(435\) 0 0
\(436\) 5.00000 8.66025i 0.239457 0.414751i
\(437\) 0 0
\(438\) 0 0
\(439\) −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −12.0000 −0.570782
\(443\) 6.00000 + 10.3923i 0.285069 + 0.493753i 0.972626 0.232377i \(-0.0746503\pi\)
−0.687557 + 0.726130i \(0.741317\pi\)
\(444\) 0 0
\(445\) 9.00000 15.5885i 0.426641 0.738964i
\(446\) −10.0000 + 17.3205i −0.473514 + 0.820150i
\(447\) 0 0
\(448\) 2.00000 + 3.46410i 0.0944911 + 0.163663i
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −9.00000 15.5885i −0.423324 0.733219i
\(453\) 0 0
\(454\) −6.00000 + 10.3923i −0.281594 + 0.487735i
\(455\) 4.00000 6.92820i 0.187523 0.324799i
\(456\) 0 0
\(457\) −13.0000 22.5167i −0.608114 1.05328i −0.991551 0.129718i \(-0.958593\pi\)
0.383437 0.923567i \(-0.374740\pi\)
\(458\) −10.0000 −0.467269
\(459\) 0 0
\(460\) 0 0
\(461\) −15.0000 25.9808i −0.698620 1.21004i −0.968945 0.247276i \(-0.920465\pi\)
0.270326 0.962769i \(-0.412869\pi\)
\(462\) 0 0
\(463\) 2.00000 3.46410i 0.0929479 0.160990i −0.815802 0.578331i \(-0.803704\pi\)
0.908750 + 0.417340i \(0.137038\pi\)
\(464\) −3.00000 + 5.19615i −0.139272 + 0.241225i
\(465\) 0 0
\(466\) −9.00000 15.5885i −0.416917 0.722121i
\(467\) 36.0000 1.66588 0.832941 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) 0 0
\(469\) 16.0000 0.738811
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 2.00000 + 3.46410i 0.0917663 + 0.158944i
\(476\) 24.0000 1.10004
\(477\) 0 0
\(478\) −24.0000 −1.09773
\(479\) −12.0000 20.7846i −0.548294 0.949673i −0.998392 0.0566937i \(-0.981944\pi\)
0.450098 0.892979i \(-0.351389\pi\)
\(480\) 0 0
\(481\) −2.00000 + 3.46410i −0.0911922 + 0.157949i
\(482\) −1.00000 + 1.73205i −0.0455488 + 0.0788928i
\(483\) 0 0
\(484\) 5.50000 + 9.52628i 0.250000 + 0.433013i
\(485\) 2.00000 0.0908153
\(486\) 0 0
\(487\) −28.0000 −1.26880 −0.634401 0.773004i \(-0.718753\pi\)
−0.634401 + 0.773004i \(0.718753\pi\)
\(488\) 5.00000 + 8.66025i 0.226339 + 0.392031i
\(489\) 0 0
\(490\) −4.50000 + 7.79423i −0.203289 + 0.352107i
\(491\) 12.0000 20.7846i 0.541552 0.937996i −0.457263 0.889332i \(-0.651170\pi\)
0.998815 0.0486647i \(-0.0154966\pi\)
\(492\) 0 0
\(493\) 18.0000 + 31.1769i 0.810679 + 1.40414i
\(494\) −8.00000 −0.359937
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) 0 0
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) −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
\(507\) 0 0
\(508\) −10.0000 + 17.3205i −0.443678 + 0.768473i
\(509\) −3.00000 + 5.19615i −0.132973 + 0.230315i −0.924821 0.380402i \(-0.875786\pi\)
0.791849 + 0.610718i \(0.209119\pi\)
\(510\) 0 0
\(511\) 4.00000 + 6.92820i 0.176950 + 0.306486i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 18.0000 0.793946
\(515\) 2.00000 + 3.46410i 0.0881305 + 0.152647i
\(516\) 0 0
\(517\) 0 0
\(518\) 4.00000 6.92820i 0.175750 0.304408i
\(519\) 0 0
\(520\) −1.00000 1.73205i −0.0438529 0.0759555i
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 0 0
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) 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
\(530\) 6.00000 0.260623
\(531\) 0 0
\(532\) 16.0000 0.693688
\(533\) −6.00000 10.3923i −0.259889 0.450141i
\(534\) 0 0
\(535\) −6.00000 + 10.3923i −0.259403 + 0.449299i
\(536\) 2.00000 3.46410i 0.0863868 0.149626i
\(537\) 0 0
\(538\) −3.00000 5.19615i −0.129339 0.224022i
\(539\) 0 0
\(540\) 0 0
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 8.00000 + 13.8564i 0.343629 + 0.595184i
\(543\) 0 0
\(544\) 3.00000 5.19615i 0.128624 0.222783i
\(545\) 5.00000 8.66025i 0.214176 0.370965i
\(546\) 0 0
\(547\) 14.0000 + 24.2487i 0.598597 + 1.03680i 0.993028 + 0.117875i \(0.0376081\pi\)
−0.394432 + 0.918925i \(0.629059\pi\)
\(548\) −6.00000 −0.256307
\(549\) 0 0
\(550\) 0 0
\(551\) 12.0000 + 20.7846i 0.511217 + 0.885454i
\(552\) 0 0
\(553\) 16.0000 27.7128i 0.680389 1.17847i
\(554\) −1.00000 + 1.73205i −0.0424859 + 0.0735878i
\(555\) 0 0
\(556\) 2.00000 + 3.46410i 0.0848189 + 0.146911i
\(557\) −18.0000 −0.762684 −0.381342 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) 0 0
\(559\) −8.00000 −0.338364
\(560\) 2.00000 + 3.46410i 0.0845154 + 0.146385i
\(561\) 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 0.990668 0.136295i \(-0.0435194\pi\)
−0.613369 + 0.789797i \(0.710186\pi\)
\(570\) 0 0
\(571\) −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
\(573\) 0 0
\(574\) 12.0000 + 20.7846i 0.500870 + 0.867533i
\(575\) 0 0
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) −9.50000 16.4545i −0.395148 0.684416i
\(579\) 0 0
\(580\) −3.00000 + 5.19615i −0.124568 + 0.215758i
\(581\) −24.0000 + 41.5692i −0.995688 + 1.72458i
\(582\) 0 0
\(583\) 0 0
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) 6.00000 0.247858
\(587\) −6.00000 10.3923i −0.247647 0.428936i 0.715226 0.698893i \(-0.246324\pi\)
−0.962872 + 0.269957i \(0.912990\pi\)
\(588\) 0 0
\(589\) 16.0000 27.7128i 0.659269 1.14189i
\(590\) 0 0
\(591\) 0 0
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) −30.0000 −1.23195 −0.615976 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) 0 0
\(595\) 24.0000 0.983904
\(596\) −3.00000 5.19615i −0.122885 0.212843i
\(597\) 0 0
\(598\) 0 0
\(599\) −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i \(-0.996449\pi\)
0.509631 + 0.860393i \(0.329782\pi\)
\(600\) 0 0
\(601\) 11.0000 + 19.0526i 0.448699 + 0.777170i 0.998302 0.0582563i \(-0.0185541\pi\)
−0.549602 + 0.835426i \(0.685221\pi\)
\(602\) 16.0000 0.652111
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) 5.50000 + 9.52628i 0.223607 + 0.387298i
\(606\) 0 0
\(607\) 2.00000 3.46410i 0.0811775 0.140604i −0.822578 0.568652i \(-0.807465\pi\)
0.903756 + 0.428048i \(0.140799\pi\)
\(608\) 2.00000 3.46410i 0.0811107 0.140488i
\(609\) 0 0
\(610\) 5.00000 + 8.66025i 0.202444 + 0.350643i
\(611\) 0 0
\(612\) 0 0
\(613\) 2.00000 0.0807792 0.0403896 0.999184i \(-0.487140\pi\)
0.0403896 + 0.999184i \(0.487140\pi\)
\(614\) −10.0000 17.3205i −0.403567 0.698999i
\(615\) 0 0
\(616\) 0 0
\(617\) 15.0000 25.9808i 0.603877 1.04595i −0.388351 0.921512i \(-0.626955\pi\)
0.992228 0.124434i \(-0.0397116\pi\)
\(618\) 0 0
\(619\) −22.0000 38.1051i −0.884255 1.53157i −0.846566 0.532284i \(-0.821334\pi\)
−0.0376891 0.999290i \(-0.512000\pi\)
\(620\) 8.00000 0.321288
\(621\) 0 0
\(622\) 0 0
\(623\) −36.0000 62.3538i −1.44231 2.49815i
\(624\) 0 0
\(625\) −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
\(633\) 0 0
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) −10.0000 + 17.3205i −0.396838 + 0.687343i
\(636\) 0 0
\(637\) −9.00000 15.5885i −0.356593 0.617637i
\(638\) 0 0
\(639\) 0 0
\(640\) 1.00000 0.0395285
\(641\) −15.0000 25.9808i −0.592464 1.02618i −0.993899 0.110291i \(-0.964822\pi\)
0.401435 0.915888i \(-0.368512\pi\)
\(642\) 0 0
\(643\) 2.00000 3.46410i 0.0788723 0.136611i −0.823891 0.566748i \(-0.808201\pi\)
0.902764 + 0.430137i \(0.141535\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −12.0000 20.7846i −0.472134 0.817760i
\(647\) −24.0000 −0.943537 −0.471769 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −1.00000 1.73205i −0.0392232 0.0679366i
\(651\) 0 0
\(652\) 2.00000 3.46410i 0.0783260 0.135665i
\(653\) 9.00000 15.5885i 0.352197 0.610023i −0.634437 0.772975i \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 6.00000 0.234261
\(657\) 0 0
\(658\) 0 0
\(659\) 24.0000 + 41.5692i 0.934907 + 1.61931i 0.774799 + 0.632207i \(0.217851\pi\)
0.160108 + 0.987099i \(0.448816\pi\)
\(660\) 0 0
\(661\) −7.00000 + 12.1244i −0.272268 + 0.471583i −0.969442 0.245319i \(-0.921107\pi\)
0.697174 + 0.716902i \(0.254441\pi\)
\(662\) 14.0000 24.2487i 0.544125 0.942453i
\(663\) 0 0
\(664\) 6.00000 + 10.3923i 0.232845 + 0.403300i
\(665\) 16.0000 0.620453
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 2.00000 3.46410i 0.0772667 0.133830i
\(671\) 0 0
\(672\) 0 0
\(673\) −13.0000 22.5167i −0.501113 0.867953i −0.999999 0.00128586i \(-0.999591\pi\)
0.498886 0.866668i \(-0.333743\pi\)
\(674\) 26.0000 1.00148
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) −3.00000 5.19615i −0.115299 0.199704i 0.802600 0.596518i \(-0.203449\pi\)
−0.917899 + 0.396813i \(0.870116\pi\)
\(678\) 0 0
\(679\) 4.00000 6.92820i 0.153506 0.265880i
\(680\) 3.00000 5.19615i 0.115045 0.199263i
\(681\) 0 0
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) −6.00000 −0.229248
\(686\) 4.00000 + 6.92820i 0.152721 + 0.264520i
\(687\) 0 0
\(688\) 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 \(-0.851021\pi\)
0.0555386 0.998457i \(-0.482312\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 2.00000 + 3.46410i 0.0758643 + 0.131401i
\(696\) 0 0
\(697\) 18.0000 31.1769i 0.681799 1.18091i
\(698\) 5.00000 8.66025i 0.189253 0.327795i
\(699\) 0 0
\(700\) 2.00000 + 3.46410i 0.0755929 + 0.130931i
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 0 0
\(703\) −8.00000 −0.301726
\(704\) 0 0
\(705\) 0 0
\(706\) 3.00000 5.19615i 0.112906 0.195560i
\(707\) −36.0000 + 62.3538i −1.35392 + 2.34506i
\(708\) 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
\(711\) 0 0
\(712\) −18.0000 −0.674579
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 20.7846i 0.448461 0.776757i
\(717\) 0 0
\(718\) −12.0000 20.7846i −0.447836 0.775675i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 16.0000 0.595871
\(722\) 1.50000 + 2.59808i 0.0558242 + 0.0966904i
\(723\) 0 0
\(724\) −7.00000 + 12.1244i −0.260153 + 0.450598i
\(725\) −3.00000 + 5.19615i −0.111417 + 0.192980i
\(726\) 0 0
\(727\) 14.0000 + 24.2487i 0.519231 + 0.899335i 0.999750 + 0.0223506i \(0.00711500\pi\)
−0.480519 + 0.876984i \(0.659552\pi\)
\(728\) −8.00000 −0.296500
\(729\) 0 0
\(730\) 2.00000 0.0740233
\(731\) −12.0000 20.7846i −0.443836 0.768747i
\(732\) 0 0
\(733\) 11.0000 19.0526i 0.406294 0.703722i −0.588177 0.808732i \(-0.700154\pi\)
0.994471 + 0.105010i \(0.0334875\pi\)
\(734\) 14.0000 24.2487i 0.516749 0.895036i
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −52.0000 −1.91285 −0.956425 0.291977i \(-0.905687\pi\)
−0.956425 + 0.291977i \(0.905687\pi\)
\(740\) −1.00000 1.73205i −0.0367607 0.0636715i
\(741\) 0 0
\(742\) 12.0000 20.7846i 0.440534 0.763027i
\(743\) −12.0000 + 20.7846i −0.440237 + 0.762513i −0.997707 0.0676840i \(-0.978439\pi\)
0.557470 + 0.830197i \(0.311772\pi\)
\(744\) 0 0
\(745\) −3.00000 5.19615i −0.109911 0.190372i
\(746\) 26.0000 0.951928
\(747\) 0 0
\(748\) 0 0
\(749\) 24.0000 + 41.5692i 0.876941 + 1.51891i
\(750\) 0 0
\(751\) 20.0000 34.6410i 0.729810 1.26407i −0.227153 0.973859i \(-0.572942\pi\)
0.956963 0.290209i \(-0.0937250\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −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 −0.655515 0.755182i \(-0.727548\pi\)
0.981764 + 0.190101i \(0.0608816\pi\)
\(762\) 0 0
\(763\) −20.0000 34.6410i −0.724049 1.25409i
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −1.00000 + 1.73205i −0.0360609 + 0.0624593i −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 11.0000 + 19.0526i 0.395899 + 0.685717i
\(773\) −42.0000 −1.51064 −0.755318 0.655359i \(-0.772517\pi\)
−0.755318 + 0.655359i \(0.772517\pi\)
\(774\) 0 0
\(775\) 8.00000 0.287368
\(776\) −1.00000 1.73205i −0.0358979 0.0621770i
\(777\) 0 0
\(778\) −3.00000 + 5.19615i −0.107555 + 0.186291i
\(779\) 12.0000 20.7846i 0.429945 0.744686i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 9.00000 0.321429
\(785\) −1.00000 1.73205i −0.0356915 0.0618195i
\(786\) 0 0
\(787\) 2.00000 3.46410i 0.0712923 0.123482i −0.828176 0.560469i \(-0.810621\pi\)
0.899468 + 0.436987i \(0.143954\pi\)
\(788\) −3.00000 + 5.19615i −0.106871 + 0.185105i
\(789\) 0 0
\(790\) −4.00000 6.92820i −0.142314 0.246494i
\(791\) −72.0000 −2.56003
\(792\) 0 0
\(793\) −20.0000 −0.710221
\(794\) 11.0000 + 19.0526i 0.390375 + 0.676150i
\(795\) 0 0
\(796\) −4.00000 + 6.92820i −0.141776