Properties

Label 810.2.e.l.541.1
Level $810$
Weight $2$
Character 810.541
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 541.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 810.541
Dual form 810.2.e.l.271.1

$q$-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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 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 −0.188982 0.981981i \(-0.560519\pi\)
0.944911 0.327327i \(-0.106148\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.00000 0.316228
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 0 0
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) −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 \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 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 −0.440652 0.897678i \(-0.645253\pi\)
0.997738 0.0672232i \(-0.0214140\pi\)
\(30\) 0 0
\(31\) −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) 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 \(-0.0114536\pi\)
−0.530831 + 0.847477i \(0.678120\pi\)
\(42\) 0 0
\(43\) 2.00000 3.46410i 0.304997 0.528271i −0.672264 0.740312i \(-0.734678\pi\)
0.977261 + 0.212041i \(0.0680112\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 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 \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) −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 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −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 −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) −1.00000 −0.111803
\(81\) 0 0
\(82\) 6.00000 0.662589
\(83\) −6.00000 + 10.3923i −0.658586 + 1.14070i 0.322396 + 0.946605i \(0.395512\pi\)
−0.980982 + 0.194099i \(0.937822\pi\)
\(84\) 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 \(-0.0969242\pi\)
0.953998 + 0.299813i \(0.0969242\pi\)
\(90\) 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 −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) −9.00000 −0.909137
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) −9.00000 + 15.5885i −0.895533 + 1.55111i −0.0623905 + 0.998052i \(0.519872\pi\)
−0.833143 + 0.553058i \(0.813461\pi\)
\(102\) 0 0
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) 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 \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) 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 0.884182 + 0.467143i \(0.154717\pi\)
−0.0375328 + 0.999295i \(0.511950\pi\)
\(114\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 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 \(-0.915839\pi\)
0.708942 + 0.705266i \(0.249173\pi\)
\(138\) 0 0
\(139\) 2.00000 + 3.46410i 0.169638 + 0.293821i 0.938293 0.345843i \(-0.112407\pi\)
−0.768655 + 0.639664i \(0.779074\pi\)
\(140\) −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 \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 0 0
\(151\) −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i \(-0.938871\pi\)
0.656101 + 0.754673i \(0.272204\pi\)
\(152\) 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 0.823359 0.567521i \(-0.192098\pi\)
−0.903167 + 0.429289i \(0.858764\pi\)
\(158\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 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 0.289412 + 0.957205i \(0.406540\pi\)
−0.973670 + 0.227964i \(0.926793\pi\)
\(174\) 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 \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) 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 0.00454614 0.999990i \(-0.498553\pi\)
0.863743 0.503932i \(-0.168114\pi\)
\(192\) 0 0
\(193\) 11.0000 + 19.0526i 0.791797 + 1.37143i 0.924853 + 0.380325i \(0.124188\pi\)
−0.133056 + 0.991109i \(0.542479\pi\)
\(194\) 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 \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 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 −0.972346 0.233544i \(-0.924968\pi\)
0.283918 0.958849i \(-0.408366\pi\)
\(212\) 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 0.308353 + 0.951272i \(0.400222\pi\)
−0.978002 + 0.208595i \(0.933111\pi\)
\(224\) 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 \(-0.702957\pi\)
0.993508 + 0.113761i \(0.0362899\pi\)
\(228\) 0 0
\(229\) 5.00000 + 8.66025i 0.330409 + 0.572286i 0.982592 0.185776i \(-0.0594799\pi\)
−0.652183 + 0.758062i \(0.726147\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −3.00000 + 5.19615i −0.196960 + 0.341144i
\(233\) −18.0000 −1.17922 −0.589610 0.807688i \(-0.700718\pi\)
−0.589610 + 0.807688i \(0.700718\pi\)
\(234\) 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 −0.934109 0.356988i \(-0.883804\pi\)
0.157893 0.987456i \(-0.449530\pi\)
\(240\) 0 0
\(241\) −1.00000 + 1.73205i −0.0644157 + 0.111571i −0.896435 0.443176i \(-0.853852\pi\)
0.832019 + 0.554747i \(0.187185\pi\)
\(242\) 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 \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) 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 0.997374 + 0.0724199i \(0.0230722\pi\)
−0.435970 + 0.899961i \(0.643595\pi\)
\(258\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 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 \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 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 −0.894503 0.447062i \(-0.852470\pi\)
0.834419 + 0.551131i \(0.185804\pi\)
\(278\) 4.00000 0.239904
\(279\) 0 0
\(280\) −4.00000 −0.239046
\(281\) −9.00000 + 15.5885i −0.536895 + 0.929929i 0.462174 + 0.886789i \(0.347070\pi\)
−0.999069 + 0.0431402i \(0.986264\pi\)
\(282\) 0 0
\(283\) 14.0000 + 24.2487i 0.832214 + 1.44144i 0.896279 + 0.443491i \(0.146260\pi\)
−0.0640654 + 0.997946i \(0.520407\pi\)
\(284\) 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 \(-0.110589\pi\)
−0.764990 + 0.644042i \(0.777256\pi\)
\(294\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(312\) 0 0
\(313\) −1.00000 + 1.73205i −0.0565233 + 0.0979013i −0.892903 0.450250i \(-0.851335\pi\)
0.836379 + 0.548151i \(0.184668\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 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 −0.168320 0.985732i \(-0.553834\pi\)
0.937829 0.347097i \(-0.112833\pi\)
\(332\) 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 −0.965541 0.260252i \(-0.916194\pi\)
0.257386 0.966309i \(-0.417139\pi\)
\(338\) −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 \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 0 0
\(349\) 5.00000 8.66025i 0.267644 0.463573i −0.700609 0.713545i \(-0.747088\pi\)
0.968253 + 0.249973i \(0.0804216\pi\)
\(350\) 4.00000 0.213809
\(351\) 0 0
\(352\) 0 0
\(353\) −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i \(-0.884378\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(354\) 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 \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 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 −0.225750 0.974185i \(-0.572483\pi\)
0.956544 0.291587i \(-0.0941834\pi\)
\(368\) 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 −0.977016 0.213165i \(-0.931623\pi\)
0.303902 0.952703i \(-0.401711\pi\)
\(374\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) 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 \(-0.784728\pi\)
0.932002 + 0.362454i \(0.118061\pi\)
\(390\) 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 \(-0.118800\pi\)
−0.781345 + 0.624099i \(0.785466\pi\)
\(402\) 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 −0.984803 0.173675i \(-0.944436\pi\)
0.341994 0.939702i \(-0.388898\pi\)
\(410\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(420\) 0 0
\(421\) 5.00000 8.66025i 0.243685 0.422075i −0.718076 0.695965i \(-0.754977\pi\)
0.961761 + 0.273890i \(0.0883103\pi\)
\(422\) −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 −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −12.0000 −0.570782
\(443\) −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i \(-0.925350\pi\)
0.687557 + 0.726130i \(0.258683\pi\)
\(444\) 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 \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 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 0.383437 + 0.923567i \(0.374740\pi\)
−0.991551 + 0.129718i \(0.958593\pi\)
\(458\) 10.0000 0.467269
\(459\) 0 0
\(460\) 0 0
\(461\) 15.0000 25.9808i 0.698620 1.21004i −0.270326 0.962769i \(-0.587131\pi\)
0.968945 0.247276i \(-0.0795353\pi\)
\(462\) 0 0
\(463\) 2.00000 + 3.46410i 0.0929479 + 0.160990i 0.908750 0.417340i \(-0.137038\pi\)
−0.815802 + 0.578331i \(0.803704\pi\)
\(464\) 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 \(-0.813345\pi\)
−0.832941 + 0.553362i \(0.813345\pi\)
\(468\) 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 −0.450098 0.892979i \(-0.648611\pi\)
0.998392 0.0566937i \(-0.0180558\pi\)
\(480\) 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 −0.998815 0.0486647i \(-0.984503\pi\)
0.457263 0.889332i \(-0.348830\pi\)
\(492\) 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 0.907314 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 \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 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 \(-0.124214\pi\)
−0.791849 + 0.610718i \(0.790881\pi\)
\(510\) 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 \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 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 −0.394432 0.918925i \(-0.629059\pi\)
0.993028 0.117875i \(-0.0376081\pi\)
\(548\) 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 \(-0.375462\pi\)
0.381342 + 0.924434i \(0.375462\pi\)
\(558\) 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 \(-0.0852922\pi\)
−0.711445 + 0.702742i \(0.751959\pi\)
\(564\) 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 \(-0.956481\pi\)
0.613369 + 0.789797i \(0.289814\pi\)
\(570\) 0 0
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) 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 \(-0.753676\pi\)
0.962872 + 0.269957i \(0.0870095\pi\)
\(588\) 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 \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 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 \(-0.00355143\pi\)
−0.509631 + 0.860393i \(0.670218\pi\)
\(600\) 0 0
\(601\) 11.0000 19.0526i 0.448699 0.777170i −0.549602 0.835426i \(-0.685221\pi\)
0.998302 + 0.0582563i \(0.0185541\pi\)
\(602\) −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 0.903756 0.428048i \(-0.140799\pi\)
−0.822578 + 0.568652i \(0.807465\pi\)
\(608\) −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 −0.992228 0.124434i \(-0.960288\pi\)
0.388351 0.921512i \(-0.373045\pi\)
\(618\) 0 0
\(619\) −22.0000 + 38.1051i −0.884255 + 1.53157i −0.0376891 + 0.999290i \(0.512000\pi\)
−0.846566 + 0.532284i \(0.821334\pi\)
\(620\) −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 −0.401435 0.915888i \(-0.631488\pi\)
0.993899 0.110291i \(-0.0351782\pi\)
\(642\) 0 0
\(643\) 2.00000 + 3.46410i 0.0788723 + 0.136611i 0.902764 0.430137i \(-0.141535\pi\)
−0.823891 + 0.566748i \(0.808201\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −12.0000 + 20.7846i −0.472134 + 0.817760i
\(647\) 24.0000 0.943537 0.471769 0.881722i \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(648\) 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 \(-0.281232\pi\)
−0.986634 + 0.162951i \(0.947899\pi\)
\(654\) 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 −0.160108 + 0.987099i \(0.551184\pi\)
−0.774799 + 0.632207i \(0.782149\pi\)
\(660\) 0 0
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) −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 0.498886 + 0.866668i \(0.333743\pi\)
−0.999999 + 0.00128586i \(0.999591\pi\)
\(674\) −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 \(-0.796551\pi\)
0.917899 + 0.396813i \(0.129884\pi\)
\(678\) 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 \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 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 0.0555386 + 0.998457i \(0.482312\pi\)
−0.892458 + 0.451130i \(0.851021\pi\)
\(692\) 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 \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 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 0.249952 + 0.968258i \(0.419585\pi\)
−0.963512 + 0.267664i \(0.913748\pi\)
\(710\) 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 −0.480519 0.876984i \(-0.659552\pi\)
0.999750 0.0223506i \(-0.00711500\pi\)
\(728\) 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 0.994471 0.105010i \(-0.0334875\pi\)
−0.588177 + 0.808732i \(0.700154\pi\)
\(734\) −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 \(-0.0215610\pi\)
−0.557470 + 0.830197i \(0.688228\pi\)
\(744\) 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 0.956963 + 0.290209i \(0.0937250\pi\)
−0.227153 + 0.973859i \(0.572942\pi\)
\(752\) 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 \(-0.272452\pi\)
−0.981764 + 0.190101i \(0.939118\pi\)
\(762\) 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 0.847432 0.530904i \(-0.178148\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 11.0000 19.0526i 0.395899 0.685717i
\(773\) 42.0000 1.51064 0.755318 0.655359i \(-0.227483\pi\)
0.755318 + 0.655359i \(0.227483\pi\)
\(774\) 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 0.899468 0.436987i \(-0.143954\pi\)
−0.828176 + 0.560469i \(0.810621\pi\)
\(788\) 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 0.245564i
\(797\) 15.0000 + 25.9808i 0.531327 + 0.920286i 0.999331 + 0.0365596i \(0.0116399\pi\)
−0.468004 + 0.883726i \(0.655027\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1.00000 −0.0353553
\(801\) 0 0
\(802\) 6.00000 0.211867
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 8.00000 + 13.8564i 0.281788 + 0.488071i
\(807\) 0 0
\(808\) 9.00000 15.5885i 0.316619 0.548400i
\(809\) −54.0000 −1.89854 −0.949269 0.314464i \(-0.898175\pi\)
−0.949269 + 0.314464i \(0.898175\pi\)
\(810\) 0 0