Properties

Label 490.2.e.c.471.1
Level $490$
Weight $2$
Character 490.471
Analytic conductor $3.913$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.91266969904\)
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 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 471.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 490.471
Dual form 490.2.e.c.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.00000 - 3.46410i) q^{11} +6.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(1.50000 + 2.59808i) q^{18} +1.00000 q^{20} +4.00000 q^{22} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} +6.00000 q^{29} +(4.00000 + 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} -2.00000 q^{34} -3.00000 q^{36} +(5.00000 - 8.66025i) q^{37} +(-0.500000 + 0.866025i) q^{40} -2.00000 q^{41} +4.00000 q^{43} +(-2.00000 + 3.46410i) q^{44} +(1.50000 + 2.59808i) q^{45} +(4.00000 - 6.92820i) q^{47} +1.00000 q^{50} +(-3.00000 - 5.19615i) q^{52} +(1.00000 + 1.73205i) q^{53} +4.00000 q^{55} +(-3.00000 + 5.19615i) q^{58} +(-4.00000 - 6.92820i) q^{59} +(-7.00000 + 12.1244i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(6.00000 + 10.3923i) q^{67} +(1.00000 - 1.73205i) q^{68} -16.0000 q^{71} +(1.50000 - 2.59808i) q^{72} +(1.00000 + 1.73205i) q^{73} +(5.00000 + 8.66025i) q^{74} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.00000 - 1.73205i) q^{82} -8.00000 q^{83} -2.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(-2.00000 - 3.46410i) q^{88} +(5.00000 - 8.66025i) q^{89} -3.00000 q^{90} +(4.00000 + 6.92820i) q^{94} -2.00000 q^{97} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{2} - q^{4} - q^{5} + 2q^{8} + 3q^{9} + O(q^{10}) \) \( 2q - q^{2} - q^{4} - q^{5} + 2q^{8} + 3q^{9} - q^{10} - 4q^{11} + 12q^{13} - q^{16} + 2q^{17} + 3q^{18} + 2q^{20} + 8q^{22} - q^{25} - 6q^{26} + 12q^{29} + 8q^{31} - q^{32} - 4q^{34} - 6q^{36} + 10q^{37} - q^{40} - 4q^{41} + 8q^{43} - 4q^{44} + 3q^{45} + 8q^{47} + 2q^{50} - 6q^{52} + 2q^{53} + 8q^{55} - 6q^{58} - 8q^{59} - 14q^{61} - 16q^{62} + 2q^{64} - 6q^{65} + 12q^{67} + 2q^{68} - 32q^{71} + 3q^{72} + 2q^{73} + 10q^{74} + 8q^{79} - q^{80} - 9q^{81} + 2q^{82} - 16q^{83} - 4q^{85} - 4q^{86} - 4q^{88} + 10q^{89} - 6q^{90} + 8q^{94} - 4q^{97} - 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) −0.500000 0.866025i −0.158114 0.273861i
\(11\) −2.00000 3.46410i −0.603023 1.04447i −0.992361 0.123371i \(-0.960630\pi\)
0.389338 0.921095i \(-0.372704\pi\)
\(12\) 0 0
\(13\) 6.00000 1.66410 0.832050 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 1.50000 + 2.59808i 0.353553 + 0.612372i
\(19\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 4.00000 0.852803
\(23\) 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
\(26\) −3.00000 + 5.19615i −0.588348 + 1.01905i
\(27\) 0 0
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 4.00000 + 6.92820i 0.718421 + 1.24434i 0.961625 + 0.274367i \(0.0884683\pi\)
−0.243204 + 0.969975i \(0.578198\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) 5.00000 8.66025i 0.821995 1.42374i −0.0821995 0.996616i \(-0.526194\pi\)
0.904194 0.427121i \(-0.140472\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −0.500000 + 0.866025i −0.0790569 + 0.136931i
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) −2.00000 + 3.46410i −0.301511 + 0.522233i
\(45\) 1.50000 + 2.59808i 0.223607 + 0.387298i
\(46\) 0 0
\(47\) 4.00000 6.92820i 0.583460 1.01058i −0.411606 0.911362i \(-0.635032\pi\)
0.995066 0.0992202i \(-0.0316348\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) −3.00000 5.19615i −0.416025 0.720577i
\(53\) 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i \(-0.122805\pi\)
−0.789136 + 0.614218i \(0.789471\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 0 0
\(58\) −3.00000 + 5.19615i −0.393919 + 0.682288i
\(59\) −4.00000 6.92820i −0.520756 0.901975i −0.999709 0.0241347i \(-0.992317\pi\)
0.478953 0.877841i \(-0.341016\pi\)
\(60\) 0 0
\(61\) −7.00000 + 12.1244i −0.896258 + 1.55236i −0.0640184 + 0.997949i \(0.520392\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) −8.00000 −1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −3.00000 + 5.19615i −0.372104 + 0.644503i
\(66\) 0 0
\(67\) 6.00000 + 10.3923i 0.733017 + 1.26962i 0.955588 + 0.294706i \(0.0952216\pi\)
−0.222571 + 0.974916i \(0.571445\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) 0 0
\(70\) 0 0
\(71\) −16.0000 −1.89885 −0.949425 0.313993i \(-0.898333\pi\)
−0.949425 + 0.313993i \(0.898333\pi\)
\(72\) 1.50000 2.59808i 0.176777 0.306186i
\(73\) 1.00000 + 1.73205i 0.117041 + 0.202721i 0.918594 0.395203i \(-0.129326\pi\)
−0.801553 + 0.597924i \(0.795992\pi\)
\(74\) 5.00000 + 8.66025i 0.581238 + 1.00673i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 4.00000 6.92820i 0.450035 0.779484i −0.548352 0.836247i \(-0.684745\pi\)
0.998388 + 0.0567635i \(0.0180781\pi\)
\(80\) −0.500000 0.866025i −0.0559017 0.0968246i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 1.00000 1.73205i 0.110432 0.191273i
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) −2.00000 + 3.46410i −0.215666 + 0.373544i
\(87\) 0 0
\(88\) −2.00000 3.46410i −0.213201 0.369274i
\(89\) 5.00000 8.66025i 0.529999 0.917985i −0.469389 0.882992i \(-0.655526\pi\)
0.999388 0.0349934i \(-0.0111410\pi\)
\(90\) −3.00000 −0.316228
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 4.00000 + 6.92820i 0.412568 + 0.714590i
\(95\) 0 0
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) −12.0000 −1.20605
\(100\) −0.500000 + 0.866025i −0.0500000 + 0.0866025i
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 0 0
\(103\) 8.00000 13.8564i 0.788263 1.36531i −0.138767 0.990325i \(-0.544314\pi\)
0.927030 0.374987i \(-0.122353\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) −2.00000 −0.194257
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 0 0
\(109\) −3.00000 5.19615i −0.287348 0.497701i 0.685828 0.727764i \(-0.259440\pi\)
−0.973176 + 0.230063i \(0.926107\pi\)
\(110\) −2.00000 + 3.46410i −0.190693 + 0.330289i
\(111\) 0 0
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −3.00000 5.19615i −0.278543 0.482451i
\(117\) 9.00000 15.5885i 0.832050 1.44115i
\(118\) 8.00000 0.736460
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) −7.00000 12.1244i −0.633750 1.09769i
\(123\) 0 0
\(124\) 4.00000 6.92820i 0.359211 0.622171i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −3.00000 5.19615i −0.263117 0.455733i
\(131\) −8.00000 + 13.8564i −0.698963 + 1.21064i 0.269863 + 0.962899i \(0.413022\pi\)
−0.968826 + 0.247741i \(0.920312\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −12.0000 −1.03664
\(135\) 0 0
\(136\) 1.00000 + 1.73205i 0.0857493 + 0.148522i
\(137\) 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
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 8.00000 13.8564i 0.671345 1.16280i
\(143\) −12.0000 20.7846i −1.00349 1.73810i
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) −3.00000 + 5.19615i −0.249136 + 0.431517i
\(146\) −2.00000 −0.165521
\(147\) 0 0
\(148\) −10.0000 −0.821995
\(149\) −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 \(0.938871\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) 0 0
\(157\) 5.00000 + 8.66025i 0.399043 + 0.691164i 0.993608 0.112884i \(-0.0360089\pi\)
−0.594565 + 0.804048i \(0.702676\pi\)
\(158\) 4.00000 + 6.92820i 0.318223 + 0.551178i
\(159\) 0 0
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) 9.00000 0.707107
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 1.00000 + 1.73205i 0.0780869 + 0.135250i
\(165\) 0 0
\(166\) 4.00000 6.92820i 0.310460 0.537733i
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 1.00000 1.73205i 0.0766965 0.132842i
\(171\) 0 0
\(172\) −2.00000 3.46410i −0.152499 0.264135i
\(173\) −11.0000 + 19.0526i −0.836315 + 1.44854i 0.0566411 + 0.998395i \(0.481961\pi\)
−0.892956 + 0.450145i \(0.851372\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 4.00000 0.301511
\(177\) 0 0
\(178\) 5.00000 + 8.66025i 0.374766 + 0.649113i
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 1.50000 2.59808i 0.111803 0.193649i
\(181\) 14.0000 1.04061 0.520306 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.00000 + 8.66025i 0.367607 + 0.636715i
\(186\) 0 0
\(187\) 4.00000 6.92820i 0.292509 0.506640i
\(188\) −8.00000 −0.583460
\(189\) 0 0
\(190\) 0 0
\(191\) −12.0000 + 20.7846i −0.868290 + 1.50392i −0.00454614 + 0.999990i \(0.501447\pi\)
−0.863743 + 0.503932i \(0.831886\pi\)
\(192\) 0 0
\(193\) −1.00000 1.73205i −0.0719816 0.124676i 0.827788 0.561041i \(-0.189599\pi\)
−0.899770 + 0.436365i \(0.856266\pi\)
\(194\) 1.00000 1.73205i 0.0717958 0.124354i
\(195\) 0 0
\(196\) 0 0
\(197\) 14.0000 0.997459 0.498729 0.866758i \(-0.333800\pi\)
0.498729 + 0.866758i \(0.333800\pi\)
\(198\) 6.00000 10.3923i 0.426401 0.738549i
\(199\) −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(-0.358603\pi\)
\(200\) −0.500000 0.866025i −0.0353553 0.0612372i
\(201\) 0 0
\(202\) 6.00000 0.422159
\(203\) 0 0
\(204\) 0 0
\(205\) 1.00000 1.73205i 0.0698430 0.120972i
\(206\) 8.00000 + 13.8564i 0.557386 + 0.965422i
\(207\) 0 0
\(208\) −3.00000 + 5.19615i −0.208013 + 0.360288i
\(209\) 0 0
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 1.00000 1.73205i 0.0686803 0.118958i
\(213\) 0 0
\(214\) −6.00000 10.3923i −0.410152 0.710403i
\(215\) −2.00000 + 3.46410i −0.136399 + 0.236250i
\(216\) 0 0
\(217\) 0 0
\(218\) 6.00000 0.406371
\(219\) 0 0
\(220\) −2.00000 3.46410i −0.134840 0.233550i
\(221\) 6.00000 + 10.3923i 0.403604 + 0.699062i
\(222\) 0 0
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) −1.00000 + 1.73205i −0.0665190 + 0.115214i
\(227\) 4.00000 + 6.92820i 0.265489 + 0.459841i 0.967692 0.252136i \(-0.0811332\pi\)
−0.702202 + 0.711977i \(0.747800\pi\)
\(228\) 0 0
\(229\) −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) 9.00000 + 15.5885i 0.588348 + 1.01905i
\(235\) 4.00000 + 6.92820i 0.260931 + 0.451946i
\(236\) −4.00000 + 6.92820i −0.260378 + 0.450988i
\(237\) 0 0
\(238\) 0 0
\(239\) 16.0000 1.03495 0.517477 0.855697i \(-0.326871\pi\)
0.517477 + 0.855697i \(0.326871\pi\)
\(240\) 0 0
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) −2.50000 4.33013i −0.160706 0.278351i
\(243\) 0 0
\(244\) 14.0000 0.896258
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 4.00000 + 6.92820i 0.254000 + 0.439941i
\(249\) 0 0
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 4.00000 6.92820i 0.250982 0.434714i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −11.0000 + 19.0526i −0.686161 + 1.18847i 0.286909 + 0.957958i \(0.407372\pi\)
−0.973070 + 0.230508i \(0.925961\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 6.00000 0.372104
\(261\) 9.00000 15.5885i 0.557086 0.964901i
\(262\) −8.00000 13.8564i −0.494242 0.856052i
\(263\) −4.00000 6.92820i −0.246651 0.427211i 0.715944 0.698158i \(-0.245997\pi\)
−0.962594 + 0.270947i \(0.912663\pi\)
\(264\) 0 0
\(265\) −2.00000 −0.122859
\(266\) 0 0
\(267\) 0 0
\(268\) 6.00000 10.3923i 0.366508 0.634811i
\(269\) −3.00000 5.19615i −0.182913 0.316815i 0.759958 0.649972i \(-0.225219\pi\)
−0.942871 + 0.333157i \(0.891886\pi\)
\(270\) 0 0
\(271\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(272\) −2.00000 −0.121268
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) −2.00000 + 3.46410i −0.120605 + 0.208893i
\(276\) 0 0
\(277\) 9.00000 + 15.5885i 0.540758 + 0.936620i 0.998861 + 0.0477206i \(0.0151957\pi\)
−0.458103 + 0.888899i \(0.651471\pi\)
\(278\) 8.00000 13.8564i 0.479808 0.831052i
\(279\) 24.0000 1.43684
\(280\) 0 0
\(281\) 26.0000 1.55103 0.775515 0.631329i \(-0.217490\pi\)
0.775515 + 0.631329i \(0.217490\pi\)
\(282\) 0 0
\(283\) 16.0000 + 27.7128i 0.951101 + 1.64736i 0.743048 + 0.669238i \(0.233379\pi\)
0.208053 + 0.978117i \(0.433287\pi\)
\(284\) 8.00000 + 13.8564i 0.474713 + 0.822226i
\(285\) 0 0
\(286\) 24.0000 1.41915
\(287\) 0 0
\(288\) −3.00000 −0.176777
\(289\) 6.50000 11.2583i 0.382353 0.662255i
\(290\) −3.00000 5.19615i −0.176166 0.305129i
\(291\) 0 0
\(292\) 1.00000 1.73205i 0.0585206 0.101361i
\(293\) −10.0000 −0.584206 −0.292103 0.956387i \(-0.594355\pi\)
−0.292103 + 0.956387i \(0.594355\pi\)
\(294\) 0 0
\(295\) 8.00000 0.465778
\(296\) 5.00000 8.66025i 0.290619 0.503367i
\(297\) 0 0
\(298\) −3.00000 5.19615i −0.173785 0.301005i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 8.00000 0.460348
\(303\) 0 0
\(304\) 0 0
\(305\) −7.00000 12.1244i −0.400819 0.694239i
\(306\) −3.00000 + 5.19615i −0.171499 + 0.297044i
\(307\) 8.00000 0.456584 0.228292 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4.00000 6.92820i 0.227185 0.393496i
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) 0 0
\(313\) −11.0000 + 19.0526i −0.621757 + 1.07691i 0.367402 + 0.930062i \(0.380247\pi\)
−0.989158 + 0.146852i \(0.953086\pi\)
\(314\) −10.0000 −0.564333
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −11.0000 + 19.0526i −0.617822 + 1.07010i 0.372061 + 0.928208i \(0.378651\pi\)
−0.989882 + 0.141890i \(0.954682\pi\)
\(318\) 0 0
\(319\) −12.0000 20.7846i −0.671871 1.16371i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) −3.00000 5.19615i −0.166410 0.288231i
\(326\) 2.00000 + 3.46410i 0.110770 + 0.191859i
\(327\) 0 0
\(328\) −2.00000 −0.110432
\(329\) 0 0
\(330\) 0 0
\(331\) −2.00000 + 3.46410i −0.109930 + 0.190404i −0.915742 0.401768i \(-0.868396\pi\)
0.805812 + 0.592172i \(0.201729\pi\)
\(332\) 4.00000 + 6.92820i 0.219529 + 0.380235i
\(333\) −15.0000 25.9808i −0.821995 1.42374i
\(334\) 0 0
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) −11.5000 + 19.9186i −0.625518 + 1.08343i
\(339\) 0 0
\(340\) 1.00000 + 1.73205i 0.0542326 + 0.0939336i
\(341\) 16.0000 27.7128i 0.866449 1.50073i
\(342\) 0 0
\(343\) 0 0
\(344\) 4.00000 0.215666
\(345\) 0 0
\(346\) −11.0000 19.0526i −0.591364 1.02427i
\(347\) −2.00000 3.46410i −0.107366 0.185963i 0.807337 0.590091i \(-0.200908\pi\)
−0.914702 + 0.404128i \(0.867575\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.00000 + 3.46410i −0.106600 + 0.184637i
\(353\) −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i \(-0.217711\pi\)
−0.934751 + 0.355303i \(0.884378\pi\)
\(354\) 0 0
\(355\) 8.00000 13.8564i 0.424596 0.735422i
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) −4.00000 + 6.92820i −0.211112 + 0.365657i −0.952063 0.305903i \(-0.901042\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(360\) 1.50000 + 2.59808i 0.0790569 + 0.136931i
\(361\) 9.50000 + 16.4545i 0.500000 + 0.866025i
\(362\) −7.00000 + 12.1244i −0.367912 + 0.637242i
\(363\) 0 0
\(364\) 0 0
\(365\) −2.00000 −0.104685
\(366\) 0 0
\(367\) 8.00000 + 13.8564i 0.417597 + 0.723299i 0.995697 0.0926670i \(-0.0295392\pi\)
−0.578101 + 0.815966i \(0.696206\pi\)
\(368\) 0 0
\(369\) −3.00000 + 5.19615i −0.156174 + 0.270501i
\(370\) −10.0000 −0.519875
\(371\) 0 0
\(372\) 0 0
\(373\) −7.00000 + 12.1244i −0.362446 + 0.627775i −0.988363 0.152115i \(-0.951392\pi\)
0.625917 + 0.779890i \(0.284725\pi\)
\(374\) 4.00000 + 6.92820i 0.206835 + 0.358249i
\(375\) 0 0
\(376\) 4.00000 6.92820i 0.206284 0.357295i
\(377\) 36.0000 1.85409
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −12.0000 20.7846i −0.613973 1.06343i
\(383\) 12.0000 20.7846i 0.613171 1.06204i −0.377531 0.925997i \(-0.623227\pi\)
0.990702 0.136047i \(-0.0434398\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.00000 0.101797
\(387\) 6.00000 10.3923i 0.304997 0.528271i
\(388\) 1.00000 + 1.73205i 0.0507673 + 0.0879316i
\(389\) −7.00000 12.1244i −0.354914 0.614729i 0.632189 0.774814i \(-0.282157\pi\)
−0.987103 + 0.160085i \(0.948823\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) −7.00000 + 12.1244i −0.352655 + 0.610816i
\(395\) 4.00000 + 6.92820i 0.201262 + 0.348596i
\(396\) 6.00000 + 10.3923i 0.301511 + 0.522233i
\(397\) 5.00000 8.66025i 0.250943 0.434646i −0.712843 0.701324i \(-0.752593\pi\)
0.963786 + 0.266678i \(0.0859261\pi\)
\(398\) 16.0000 0.802008
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 7.00000 12.1244i 0.349563 0.605461i −0.636609 0.771187i \(-0.719663\pi\)
0.986172 + 0.165726i \(0.0529966\pi\)
\(402\) 0 0
\(403\) 24.0000 + 41.5692i 1.19553 + 2.07071i
\(404\) −3.00000 + 5.19615i −0.149256 + 0.258518i
\(405\) 9.00000 0.447214
\(406\) 0 0
\(407\) −40.0000 −1.98273
\(408\) 0 0
\(409\) −15.0000 25.9808i −0.741702 1.28467i −0.951720 0.306968i \(-0.900685\pi\)
0.210017 0.977698i \(-0.432648\pi\)
\(410\) 1.00000 + 1.73205i 0.0493865 + 0.0855399i
\(411\) 0 0
\(412\) −16.0000 −0.788263
\(413\) 0 0
\(414\) 0 0
\(415\) 4.00000 6.92820i 0.196352 0.340092i
\(416\) −3.00000 5.19615i −0.147087 0.254762i
\(417\) 0 0
\(418\) 0 0
\(419\) −24.0000 −1.17248 −0.586238 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) −2.00000 + 3.46410i −0.0973585 + 0.168630i
\(423\) −12.0000 20.7846i −0.583460 1.01058i
\(424\) 1.00000 + 1.73205i 0.0485643 + 0.0841158i
\(425\) 1.00000 1.73205i 0.0485071 0.0840168i
\(426\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3.00000 + 5.19615i −0.143674 + 0.248851i
\(437\) 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 \(0.227810\pi\)
\(440\) 4.00000 0.190693
\(441\) 0 0
\(442\) −12.0000 −0.570782
\(443\) 10.0000 17.3205i 0.475114 0.822922i −0.524479 0.851423i \(-0.675740\pi\)
0.999594 + 0.0285009i \(0.00907336\pi\)
\(444\) 0 0
\(445\) 5.00000 + 8.66025i 0.237023 + 0.410535i
\(446\) 8.00000 13.8564i 0.378811 0.656120i
\(447\) 0 0
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 1.50000 2.59808i 0.0707107 0.122474i
\(451\) 4.00000 + 6.92820i 0.188353 + 0.326236i
\(452\) −1.00000 1.73205i −0.0470360 0.0814688i
\(453\) 0 0
\(454\) −8.00000 −0.375459
\(455\) 0 0
\(456\) 0 0
\(457\) −5.00000 + 8.66025i −0.233890 + 0.405110i −0.958950 0.283577i \(-0.908479\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) −7.00000 12.1244i −0.327089 0.566534i
\(459\) 0 0
\(460\) 0 0
\(461\) −10.0000 −0.465746 −0.232873 0.972507i \(-0.574813\pi\)
−0.232873 + 0.972507i \(0.574813\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) −3.00000 + 5.19615i −0.139272 + 0.241225i
\(465\) 0 0
\(466\) 3.00000 + 5.19615i 0.138972 + 0.240707i
\(467\) −20.0000 + 34.6410i −0.925490 + 1.60300i −0.134718 + 0.990884i \(0.543013\pi\)
−0.790772 + 0.612111i \(0.790321\pi\)
\(468\) −18.0000 −0.832050
\(469\) 0 0
\(470\) −8.00000 −0.369012
\(471\) 0 0
\(472\) −4.00000 6.92820i −0.184115 0.318896i
\(473\) −8.00000 13.8564i −0.367840 0.637118i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) −8.00000 + 13.8564i −0.365911 + 0.633777i
\(479\) 12.0000 + 20.7846i 0.548294 + 0.949673i 0.998392 + 0.0566937i \(0.0180558\pi\)
−0.450098 + 0.892979i \(0.648611\pi\)
\(480\) 0 0
\(481\) 30.0000 51.9615i 1.36788 2.36924i
\(482\) −10.0000 −0.455488
\(483\) 0 0
\(484\) 5.00000 0.227273
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 0 0
\(487\) −16.0000 27.7128i −0.725029 1.25579i −0.958962 0.283535i \(-0.908493\pi\)
0.233933 0.972253i \(-0.424840\pi\)
\(488\) −7.00000 + 12.1244i −0.316875 + 0.548844i
\(489\) 0 0
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) 6.00000 + 10.3923i 0.270226 + 0.468046i
\(494\) 0 0
\(495\) 6.00000 10.3923i 0.269680 0.467099i
\(496\) −8.00000 −0.359211
\(497\) 0 0
\(498\) 0 0
\(499\) 6.00000 10.3923i 0.268597 0.465223i −0.699903 0.714238i \(-0.746773\pi\)
0.968500 + 0.249015i \(0.0801067\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 0 0
\(502\) 0 0
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) 0 0
\(508\) 4.00000 + 6.92820i 0.177471 + 0.307389i
\(509\) 5.00000 8.66025i 0.221621 0.383859i −0.733679 0.679496i \(-0.762199\pi\)
0.955300 + 0.295637i \(0.0955319\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −11.0000 19.0526i −0.485189 0.840372i
\(515\) 8.00000 + 13.8564i 0.352522 + 0.610586i
\(516\) 0 0
\(517\) −32.0000 −1.40736
\(518\) 0 0
\(519\) 0 0
\(520\) −3.00000 + 5.19615i −0.131559 + 0.227866i
\(521\) 1.00000 + 1.73205i 0.0438108 + 0.0758825i 0.887099 0.461579i \(-0.152717\pi\)
−0.843288 + 0.537461i \(0.819383\pi\)
\(522\) 9.00000 + 15.5885i 0.393919 + 0.682288i
\(523\) 8.00000 13.8564i 0.349816 0.605898i −0.636401 0.771358i \(-0.719578\pi\)
0.986216 + 0.165460i \(0.0529109\pi\)
\(524\) 16.0000 0.698963
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) −8.00000 + 13.8564i −0.348485 + 0.603595i
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 1.00000 1.73205i 0.0434372 0.0752355i
\(531\) −24.0000 −1.04151
\(532\) 0 0
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) −6.00000 10.3923i −0.259403 0.449299i
\(536\) 6.00000 + 10.3923i 0.259161 + 0.448879i
\(537\) 0 0
\(538\) 6.00000 0.258678
\(539\) 0 0
\(540\) 0 0
\(541\) 9.00000 15.5885i 0.386940 0.670200i −0.605096 0.796152i \(-0.706865\pi\)
0.992036 + 0.125952i \(0.0401986\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 1.00000 1.73205i 0.0428746 0.0742611i
\(545\) 6.00000 0.257012
\(546\) 0 0
\(547\) 12.0000 0.513083 0.256541 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) 3.00000 5.19615i 0.128154 0.221969i
\(549\) 21.0000 + 36.3731i 0.896258 + 1.55236i
\(550\) −2.00000 3.46410i −0.0852803 0.147710i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −18.0000 −0.764747
\(555\) 0 0
\(556\) 8.00000 + 13.8564i 0.339276 + 0.587643i
\(557\) −11.0000 19.0526i −0.466085 0.807283i 0.533165 0.846011i \(-0.321003\pi\)
−0.999250 + 0.0387286i \(0.987669\pi\)
\(558\) −12.0000 + 20.7846i −0.508001 + 0.879883i
\(559\) 24.0000 1.01509
\(560\) 0 0
\(561\) 0 0
\(562\) −13.0000 + 22.5167i −0.548372 + 0.949808i
\(563\) −8.00000 13.8564i −0.337160 0.583978i 0.646737 0.762713i \(-0.276133\pi\)
−0.983897 + 0.178735i \(0.942800\pi\)
\(564\) 0 0
\(565\) −1.00000 + 1.73205i −0.0420703 + 0.0728679i
\(566\) −32.0000 −1.34506
\(567\) 0 0
\(568\) −16.0000 −0.671345
\(569\) 3.00000 5.19615i 0.125767 0.217834i −0.796266 0.604947i \(-0.793194\pi\)
0.922032 + 0.387113i \(0.126528\pi\)
\(570\) 0 0
\(571\) 6.00000 + 10.3923i 0.251092 + 0.434904i 0.963827 0.266529i \(-0.0858769\pi\)
−0.712735 + 0.701434i \(0.752544\pi\)
\(572\) −12.0000 + 20.7846i −0.501745 + 0.869048i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) 5.00000 + 8.66025i 0.208153 + 0.360531i 0.951133 0.308783i \(-0.0999216\pi\)
−0.742980 + 0.669314i \(0.766588\pi\)
\(578\) 6.50000 + 11.2583i 0.270364 + 0.468285i
\(579\) 0 0
\(580\) 6.00000 0.249136
\(581\) 0 0
\(582\) 0 0
\(583\) 4.00000 6.92820i 0.165663 0.286937i
\(584\) 1.00000 + 1.73205i 0.0413803 + 0.0716728i
\(585\) 9.00000 + 15.5885i 0.372104 + 0.644503i
\(586\) 5.00000 8.66025i 0.206548 0.357752i
\(587\) −8.00000 −0.330195 −0.165098 0.986277i \(-0.552794\pi\)
−0.165098 + 0.986277i \(0.552794\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −4.00000 + 6.92820i −0.164677 + 0.285230i
\(591\) 0 0
\(592\) 5.00000 + 8.66025i 0.205499 + 0.355934i
\(593\) −3.00000 + 5.19615i −0.123195 + 0.213380i −0.921026 0.389501i \(-0.872647\pi\)
0.797831 + 0.602881i \(0.205981\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6.00000 0.245770
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(600\) 0 0
\(601\) −42.0000 −1.71322 −0.856608 0.515968i \(-0.827432\pi\)
−0.856608 + 0.515968i \(0.827432\pi\)
\(602\) 0 0
\(603\) 36.0000 1.46603
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) −2.50000 4.33013i −0.101639 0.176045i
\(606\) 0 0
\(607\) −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i \(0.391655\pi\)
−0.983262 + 0.182199i \(0.941678\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 14.0000 0.566843
\(611\) 24.0000 41.5692i 0.970936 1.68171i
\(612\) −3.00000 5.19615i −0.121268 0.210042i
\(613\) −3.00000 5.19615i −0.121169 0.209871i 0.799060 0.601251i \(-0.205331\pi\)
−0.920229 + 0.391381i \(0.871998\pi\)
\(614\) −4.00000 + 6.92820i −0.161427 + 0.279600i
\(615\) 0 0
\(616\) 0 0
\(617\) −22.0000 −0.885687 −0.442843 0.896599i \(-0.646030\pi\)
−0.442843 + 0.896599i \(0.646030\pi\)
\(618\) 0 0
\(619\) 4.00000 + 6.92820i 0.160774 + 0.278468i 0.935146 0.354262i \(-0.115268\pi\)
−0.774373 + 0.632730i \(0.781934\pi\)
\(620\) 4.00000 + 6.92820i 0.160644 + 0.278243i
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −11.0000 19.0526i −0.439648 0.761493i
\(627\) 0 0
\(628\) 5.00000 8.66025i 0.199522 0.345582i
\(629\) 20.0000 0.797452
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 4.00000 6.92820i 0.159111 0.275589i
\(633\) 0 0
\(634\) −11.0000 19.0526i −0.436866 0.756674i
\(635\) 4.00000 6.92820i 0.158735 0.274937i
\(636\) 0 0
\(637\) 0 0
\(638\) 24.0000 0.950169
\(639\) −24.0000 + 41.5692i −0.949425 + 1.64445i
\(640\) −0.500000 0.866025i −0.0197642 0.0342327i
\(641\) −1.00000 1.73205i −0.0394976 0.0684119i 0.845601 0.533816i \(-0.179242\pi\)
−0.885098 + 0.465404i \(0.845909\pi\)
\(642\) 0 0
\(643\) 32.0000 1.26196 0.630978 0.775800i \(-0.282654\pi\)
0.630978 + 0.775800i \(0.282654\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.00000 + 13.8564i 0.314512 + 0.544752i 0.979334 0.202251i \(-0.0648256\pi\)
−0.664821 + 0.747002i \(0.731492\pi\)
\(648\) −4.50000 7.79423i −0.176777 0.306186i
\(649\) −16.0000 + 27.7128i −0.628055 + 1.08782i
\(650\) 6.00000 0.235339
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) −7.00000 + 12.1244i −0.273931 + 0.474463i −0.969865 0.243643i \(-0.921657\pi\)
0.695934 + 0.718106i \(0.254991\pi\)
\(654\) 0 0
\(655\) −8.00000 13.8564i −0.312586 0.541415i
\(656\) 1.00000 1.73205i 0.0390434 0.0676252i
\(657\) 6.00000 0.234082
\(658\) 0 0
\(659\) 28.0000 1.09073 0.545363 0.838200i \(-0.316392\pi\)
0.545363 + 0.838200i \(0.316392\pi\)
\(660\) 0 0
\(661\) −19.0000 32.9090i −0.739014 1.28001i −0.952940 0.303160i \(-0.901958\pi\)
0.213925 0.976850i \(-0.431375\pi\)
\(662\) −2.00000 3.46410i −0.0777322 0.134636i
\(663\) 0 0
\(664\) −8.00000 −0.310460
\(665\) 0 0
\(666\) 30.0000 1.16248
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 6.00000 10.3923i 0.231800 0.401490i
\(671\) 56.0000 2.16186
\(672\) 0 0
\(673\) −14.0000 −0.539660 −0.269830 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) 7.00000 12.1244i 0.269630 0.467013i
\(675\) 0 0
\(676\) −11.5000 19.9186i −0.442308 0.766099i
\(677\) 9.00000 15.5885i 0.345898 0.599113i −0.639618 0.768693i \(-0.720908\pi\)
0.985517 + 0.169580i \(0.0542410\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −2.00000 −0.0766965
\(681\) 0 0
\(682\) 16.0000 + 27.7128i 0.612672 + 1.06118i
\(683\) 2.00000 + 3.46410i 0.0765279 + 0.132550i 0.901750 0.432259i \(-0.142283\pi\)
−0.825222 + 0.564809i \(0.808950\pi\)
\(684\) 0 0
\(685\) −6.00000 −0.229248
\(686\) 0 0
\(687\) 0 0
\(688\) −2.00000 + 3.46410i −0.0762493 + 0.132068i
\(689\) 6.00000 + 10.3923i 0.228582 + 0.395915i
\(690\) 0 0
\(691\) −16.0000 + 27.7128i −0.608669 + 1.05425i 0.382791 + 0.923835i \(0.374963\pi\)
−0.991460 + 0.130410i \(0.958371\pi\)
\(692\) 22.0000 0.836315
\(693\) 0 0
\(694\) 4.00000 0.151838
\(695\) 8.00000 13.8564i 0.303457 0.525603i
\(696\) 0 0
\(697\) −2.00000 3.46410i −0.0757554 0.131212i
\(698\) 5.00000 8.66025i 0.189253 0.327795i
\(699\) 0 0
\(700\) 0 0
\(701\) 22.0000 0.830929 0.415464 0.909610i \(-0.363619\pi\)
0.415464 + 0.909610i \(0.363619\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −2.00000 3.46410i −0.0753778 0.130558i
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) 0 0
\(709\) 1.00000 1.73205i 0.0375558 0.0650485i −0.846637 0.532172i \(-0.821376\pi\)
0.884192 + 0.467123i \(0.154709\pi\)
\(710\) 8.00000 + 13.8564i 0.300235 + 0.520022i
\(711\) −12.0000 20.7846i −0.450035 0.779484i
\(712\) 5.00000 8.66025i 0.187383 0.324557i
\(713\) 0 0
\(714\) 0 0
\(715\) 24.0000 0.897549
\(716\) 6.00000 10.3923i 0.224231 0.388379i
\(717\) 0 0
\(718\) −4.00000 6.92820i −0.149279 0.258558i
\(719\) 12.0000 20.7846i 0.447524 0.775135i −0.550700 0.834703i \(-0.685639\pi\)
0.998224 + 0.0595683i \(0.0189724\pi\)
\(720\) −3.00000 −0.111803
\(721\) 0 0
\(722\) −19.0000 −0.707107
\(723\) 0 0
\(724\) −7.00000 12.1244i −0.260153 0.450598i
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 1.00000 1.73205i 0.0370117 0.0641061i
\(731\) 4.00000 + 6.92820i 0.147945 + 0.256249i
\(732\) 0 0
\(733\) −7.00000 + 12.1244i −0.258551 + 0.447823i −0.965854 0.259087i \(-0.916578\pi\)
0.707303 + 0.706910i \(0.249912\pi\)
\(734\) −16.0000 −0.590571
\(735\) 0 0
\(736\) 0 0
\(737\) 24.0000 41.5692i 0.884051 1.53122i
\(738\) −3.00000 5.19615i −0.110432 0.191273i
\(739\) −14.0000 24.2487i −0.514998 0.892003i −0.999849 0.0174060i \(-0.994459\pi\)
0.484850 0.874597i \(-0.338874\pi\)
\(740\) 5.00000 8.66025i 0.183804 0.318357i
\(741\) 0 0
\(742\) 0 0
\(743\) 48.0000 1.76095 0.880475 0.474093i \(-0.157224\pi\)
0.880475 + 0.474093i \(0.157224\pi\)
\(744\) 0 0
\(745\) −3.00000 5.19615i −0.109911 0.190372i
\(746\) −7.00000 12.1244i −0.256288 0.443904i
\(747\) −12.0000 + 20.7846i −0.439057 + 0.760469i
\(748\) −8.00000 −0.292509
\(749\) 0 0
\(750\) 0 0
\(751\) 8.00000 13.8564i 0.291924 0.505627i −0.682341 0.731034i \(-0.739038\pi\)
0.974265 + 0.225407i \(0.0723712\pi\)
\(752\) 4.00000 + 6.92820i 0.145865 + 0.252646i
\(753\) 0 0
\(754\) −18.0000 + 31.1769i −0.655521 + 1.13540i
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) 22.0000 0.799604 0.399802 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) 6.00000 10.3923i 0.217930 0.377466i
\(759\) 0 0
\(760\) 0 0
\(761\) 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
\(763\) 0 0
\(764\) 24.0000 0.868290
\(765\) −3.00000 + 5.19615i −0.108465 + 0.187867i
\(766\) 12.0000 + 20.7846i 0.433578 + 0.750978i
\(767\) −24.0000 41.5692i −0.866590 1.50098i
\(768\) 0 0
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.00000 + 1.73205i −0.0359908 + 0.0623379i
\(773\) 21.0000 + 36.3731i 0.755318 + 1.30825i 0.945216 + 0.326445i \(0.105851\pi\)
−0.189899 + 0.981804i \(0.560816\pi\)
\(774\) 6.00000 + 10.3923i 0.215666 + 0.373544i
\(775\) 4.00000 6.92820i 0.143684 0.248868i
\(776\) −2.00000 −0.0717958
\(777\) 0 0
\(778\) 14.0000 0.501924
\(779\) 0 0
\(780\) 0 0
\(781\) 32.0000 + 55.4256i 1.14505 + 1.98328i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −10.0000 −0.356915
\(786\) 0 0
\(787\) −4.00000 6.92820i −0.142585 0.246964i 0.785885 0.618373i \(-0.212208\pi\)
−0.928469 + 0.371409i \(0.878875\pi\)
\(788\) −7.00000 12.1244i −0.249365 0.431912i
\(789\) 0 0
\(790\) −8.00000 −0.284627
\(791\) 0 0
\(792\) −12.0000 −0.426401
\(793\) −42.0000 + 72.7461i −1.49146 + 2.58329i
\(794\) 5.00000 + 8.66025i 0.177443 + 0.307341i<