Properties

Label 1960.2.q.e.361.1
Level $1960$
Weight $2$
Character 1960.361
Analytic conductor $15.651$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1960.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.6506787962\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 280)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1960.361
Dual form 1960.2.q.e.961.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +(2.50000 - 4.33013i) q^{11} -1.00000 q^{13} +1.00000 q^{15} +(1.50000 - 2.59808i) q^{17} +(-3.00000 - 5.19615i) q^{19} +(3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.00000 q^{27} -9.00000 q^{29} +(2.50000 + 4.33013i) q^{33} +(-3.00000 - 5.19615i) q^{37} +(0.500000 - 0.866025i) q^{39} -8.00000 q^{41} +6.00000 q^{43} +(1.00000 - 1.73205i) q^{45} +(1.50000 + 2.59808i) q^{47} +(1.50000 + 2.59808i) q^{51} +(6.00000 - 10.3923i) q^{53} -5.00000 q^{55} +6.00000 q^{57} +(4.00000 - 6.92820i) q^{59} +(-2.00000 - 3.46410i) q^{61} +(0.500000 + 0.866025i) q^{65} +(2.00000 - 3.46410i) q^{67} -6.00000 q^{69} +8.00000 q^{71} +(5.00000 - 8.66025i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(1.50000 + 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{81} +12.0000 q^{83} -3.00000 q^{85} +(4.50000 - 7.79423i) q^{87} +(-8.00000 - 13.8564i) q^{89} +(-3.00000 + 5.19615i) q^{95} -7.00000 q^{97} +10.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} - q^{5} + 2q^{9} + O(q^{10}) \) \( 2q - q^{3} - q^{5} + 2q^{9} + 5q^{11} - 2q^{13} + 2q^{15} + 3q^{17} - 6q^{19} + 6q^{23} - q^{25} - 10q^{27} - 18q^{29} + 5q^{33} - 6q^{37} + q^{39} - 16q^{41} + 12q^{43} + 2q^{45} + 3q^{47} + 3q^{51} + 12q^{53} - 10q^{55} + 12q^{57} + 8q^{59} - 4q^{61} + q^{65} + 4q^{67} - 12q^{69} + 16q^{71} + 10q^{73} - q^{75} + 3q^{79} - q^{81} + 24q^{83} - 6q^{85} + 9q^{87} - 16q^{89} - 6q^{95} - 14q^{97} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\) \(981\) \(1081\) \(1177\) \(1471\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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 0
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i −0.973494 0.228714i \(-0.926548\pi\)
0.684819 + 0.728714i \(0.259881\pi\)
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) 2.50000 4.33013i 0.753778 1.30558i −0.192201 0.981356i \(-0.561563\pi\)
0.945979 0.324227i \(-0.105104\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) 1.50000 2.59808i 0.363803 0.630126i −0.624780 0.780801i \(-0.714811\pi\)
0.988583 + 0.150675i \(0.0481447\pi\)
\(18\) 0 0
\(19\) −3.00000 5.19615i −0.688247 1.19208i −0.972404 0.233301i \(-0.925047\pi\)
0.284157 0.958778i \(-0.408286\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 0 0
\(33\) 2.50000 + 4.33013i 0.435194 + 0.753778i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.00000 5.19615i −0.493197 0.854242i 0.506772 0.862080i \(-0.330838\pi\)
−0.999969 + 0.00783774i \(0.997505\pi\)
\(38\) 0 0
\(39\) 0.500000 0.866025i 0.0800641 0.138675i
\(40\) 0 0
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 6.00000 0.914991 0.457496 0.889212i \(-0.348747\pi\)
0.457496 + 0.889212i \(0.348747\pi\)
\(44\) 0 0
\(45\) 1.00000 1.73205i 0.149071 0.258199i
\(46\) 0 0
\(47\) 1.50000 + 2.59808i 0.218797 + 0.378968i 0.954441 0.298401i \(-0.0964533\pi\)
−0.735643 + 0.677369i \(0.763120\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) 1.50000 + 2.59808i 0.210042 + 0.363803i
\(52\) 0 0
\(53\) 6.00000 10.3923i 0.824163 1.42749i −0.0783936 0.996922i \(-0.524979\pi\)
0.902557 0.430570i \(-0.141688\pi\)
\(54\) 0 0
\(55\) −5.00000 −0.674200
\(56\) 0 0
\(57\) 6.00000 0.794719
\(58\) 0 0
\(59\) 4.00000 6.92820i 0.520756 0.901975i −0.478953 0.877841i \(-0.658984\pi\)
0.999709 0.0241347i \(-0.00768307\pi\)
\(60\) 0 0
\(61\) −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i \(-0.249096\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.500000 + 0.866025i 0.0620174 + 0.107417i
\(66\) 0 0
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) 0 0
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 0 0
\(73\) 5.00000 8.66025i 0.585206 1.01361i −0.409644 0.912245i \(-0.634347\pi\)
0.994850 0.101361i \(-0.0323196\pi\)
\(74\) 0 0
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.50000 + 2.59808i 0.168763 + 0.292306i 0.937985 0.346675i \(-0.112689\pi\)
−0.769222 + 0.638982i \(0.779356\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −3.00000 −0.325396
\(86\) 0 0
\(87\) 4.50000 7.79423i 0.482451 0.835629i
\(88\) 0 0
\(89\) −8.00000 13.8564i −0.847998 1.46878i −0.882992 0.469389i \(-0.844474\pi\)
0.0349934 0.999388i \(-0.488859\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.00000 + 5.19615i −0.307794 + 0.533114i
\(96\) 0 0
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) 0 0
\(99\) 10.0000 1.00504
\(100\) 0 0
\(101\) −7.00000 + 12.1244i −0.696526 + 1.20642i 0.273138 + 0.961975i \(0.411939\pi\)
−0.969664 + 0.244443i \(0.921395\pi\)
\(102\) 0 0
\(103\) −4.50000 7.79423i −0.443398 0.767988i 0.554541 0.832156i \(-0.312894\pi\)
−0.997939 + 0.0641683i \(0.979561\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.00000 1.73205i −0.0966736 0.167444i 0.813632 0.581380i \(-0.197487\pi\)
−0.910306 + 0.413936i \(0.864154\pi\)
\(108\) 0 0
\(109\) 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i \(-0.656723\pi\)
0.999512 0.0312328i \(-0.00994332\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 3.00000 5.19615i 0.279751 0.484544i
\(116\) 0 0
\(117\) −1.00000 1.73205i −0.0924500 0.160128i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 0 0
\(123\) 4.00000 6.92820i 0.360668 0.624695i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) −3.00000 + 5.19615i −0.264135 + 0.457496i
\(130\) 0 0
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 2.50000 + 4.33013i 0.215166 + 0.372678i
\(136\) 0 0
\(137\) 8.00000 13.8564i 0.683486 1.18383i −0.290424 0.956898i \(-0.593796\pi\)
0.973910 0.226935i \(-0.0728704\pi\)
\(138\) 0 0
\(139\) −18.0000 −1.52674 −0.763370 0.645961i \(-0.776457\pi\)
−0.763370 + 0.645961i \(0.776457\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) 0 0
\(143\) −2.50000 + 4.33013i −0.209061 + 0.362103i
\(144\) 0 0
\(145\) 4.50000 + 7.79423i 0.373705 + 0.647275i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 7.00000 + 12.1244i 0.573462 + 0.993266i 0.996207 + 0.0870170i \(0.0277334\pi\)
−0.422744 + 0.906249i \(0.638933\pi\)
\(150\) 0 0
\(151\) 9.50000 16.4545i 0.773099 1.33905i −0.162758 0.986666i \(-0.552039\pi\)
0.935857 0.352381i \(-0.114628\pi\)
\(152\) 0 0
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.00000 + 1.73205i −0.0798087 + 0.138233i −0.903167 0.429289i \(-0.858764\pi\)
0.823359 + 0.567521i \(0.192098\pi\)
\(158\) 0 0
\(159\) 6.00000 + 10.3923i 0.475831 + 0.824163i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −3.00000 5.19615i −0.234978 0.406994i 0.724288 0.689497i \(-0.242169\pi\)
−0.959266 + 0.282503i \(0.908835\pi\)
\(164\) 0 0
\(165\) 2.50000 4.33013i 0.194625 0.337100i
\(166\) 0 0
\(167\) 9.00000 0.696441 0.348220 0.937413i \(-0.386786\pi\)
0.348220 + 0.937413i \(0.386786\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 6.00000 10.3923i 0.458831 0.794719i
\(172\) 0 0
\(173\) 9.50000 + 16.4545i 0.722272 + 1.25101i 0.960087 + 0.279701i \(0.0902353\pi\)
−0.237816 + 0.971310i \(0.576431\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.00000 + 6.92820i 0.300658 + 0.520756i
\(178\) 0 0
\(179\) −2.00000 + 3.46410i −0.149487 + 0.258919i −0.931038 0.364922i \(-0.881096\pi\)
0.781551 + 0.623841i \(0.214429\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 0 0
\(183\) 4.00000 0.295689
\(184\) 0 0
\(185\) −3.00000 + 5.19615i −0.220564 + 0.382029i
\(186\) 0 0
\(187\) −7.50000 12.9904i −0.548454 0.949951i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −5.50000 9.52628i −0.397966 0.689297i 0.595509 0.803349i \(-0.296950\pi\)
−0.993475 + 0.114051i \(0.963617\pi\)
\(192\) 0 0
\(193\) −4.00000 + 6.92820i −0.287926 + 0.498703i −0.973315 0.229475i \(-0.926299\pi\)
0.685388 + 0.728178i \(0.259632\pi\)
\(194\) 0 0
\(195\) −1.00000 −0.0716115
\(196\) 0 0
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 0 0
\(201\) 2.00000 + 3.46410i 0.141069 + 0.244339i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 4.00000 + 6.92820i 0.279372 + 0.483887i
\(206\) 0 0
\(207\) −6.00000 + 10.3923i −0.417029 + 0.722315i
\(208\) 0 0
\(209\) −30.0000 −2.07514
\(210\) 0 0
\(211\) 13.0000 0.894957 0.447478 0.894295i \(-0.352322\pi\)
0.447478 + 0.894295i \(0.352322\pi\)
\(212\) 0 0
\(213\) −4.00000 + 6.92820i −0.274075 + 0.474713i
\(214\) 0 0
\(215\) −3.00000 5.19615i −0.204598 0.354375i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 5.00000 + 8.66025i 0.337869 + 0.585206i
\(220\) 0 0
\(221\) −1.50000 + 2.59808i −0.100901 + 0.174766i
\(222\) 0 0
\(223\) 25.0000 1.67412 0.837062 0.547108i \(-0.184271\pi\)
0.837062 + 0.547108i \(0.184271\pi\)
\(224\) 0 0
\(225\) −2.00000 −0.133333
\(226\) 0 0
\(227\) −6.50000 + 11.2583i −0.431420 + 0.747242i −0.996996 0.0774548i \(-0.975321\pi\)
0.565576 + 0.824696i \(0.308654\pi\)
\(228\) 0 0
\(229\) 8.00000 + 13.8564i 0.528655 + 0.915657i 0.999442 + 0.0334101i \(0.0106368\pi\)
−0.470787 + 0.882247i \(0.656030\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4.00000 6.92820i −0.262049 0.453882i 0.704737 0.709468i \(-0.251065\pi\)
−0.966786 + 0.255586i \(0.917731\pi\)
\(234\) 0 0
\(235\) 1.50000 2.59808i 0.0978492 0.169480i
\(236\) 0 0
\(237\) −3.00000 −0.194871
\(238\) 0 0
\(239\) −7.00000 −0.452792 −0.226396 0.974035i \(-0.572694\pi\)
−0.226396 + 0.974035i \(0.572694\pi\)
\(240\) 0 0
\(241\) 9.00000 15.5885i 0.579741 1.00414i −0.415768 0.909471i \(-0.636487\pi\)
0.995509 0.0946700i \(-0.0301796\pi\)
\(242\) 0 0
\(243\) −8.00000 13.8564i −0.513200 0.888889i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 3.00000 + 5.19615i 0.190885 + 0.330623i
\(248\) 0 0
\(249\) −6.00000 + 10.3923i −0.380235 + 0.658586i
\(250\) 0 0
\(251\) −14.0000 −0.883672 −0.441836 0.897096i \(-0.645673\pi\)
−0.441836 + 0.897096i \(0.645673\pi\)
\(252\) 0 0
\(253\) 30.0000 1.88608
\(254\) 0 0
\(255\) 1.50000 2.59808i 0.0939336 0.162698i
\(256\) 0 0
\(257\) 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −9.00000 15.5885i −0.557086 0.964901i
\(262\) 0 0
\(263\) −9.00000 + 15.5885i −0.554964 + 0.961225i 0.442943 + 0.896550i \(0.353935\pi\)
−0.997906 + 0.0646755i \(0.979399\pi\)
\(264\) 0 0
\(265\) −12.0000 −0.737154
\(266\) 0 0
\(267\) 16.0000 0.979184
\(268\) 0 0
\(269\) 5.00000 8.66025i 0.304855 0.528025i −0.672374 0.740212i \(-0.734725\pi\)
0.977229 + 0.212187i \(0.0680585\pi\)
\(270\) 0 0
\(271\) 2.00000 + 3.46410i 0.121491 + 0.210429i 0.920356 0.391082i \(-0.127899\pi\)
−0.798865 + 0.601511i \(0.794566\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.50000 + 4.33013i 0.150756 + 0.261116i
\(276\) 0 0
\(277\) −7.00000 + 12.1244i −0.420589 + 0.728482i −0.995997 0.0893846i \(-0.971510\pi\)
0.575408 + 0.817867i \(0.304843\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −13.0000 −0.775515 −0.387757 0.921761i \(-0.626750\pi\)
−0.387757 + 0.921761i \(0.626750\pi\)
\(282\) 0 0
\(283\) 14.5000 25.1147i 0.861936 1.49292i −0.00812260 0.999967i \(-0.502586\pi\)
0.870058 0.492949i \(-0.164081\pi\)
\(284\) 0 0
\(285\) −3.00000 5.19615i −0.177705 0.307794i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 4.00000 + 6.92820i 0.235294 + 0.407541i
\(290\) 0 0
\(291\) 3.50000 6.06218i 0.205174 0.355371i
\(292\) 0 0
\(293\) 1.00000 0.0584206 0.0292103 0.999573i \(-0.490701\pi\)
0.0292103 + 0.999573i \(0.490701\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) 0 0
\(297\) −12.5000 + 21.6506i −0.725324 + 1.25630i
\(298\) 0 0
\(299\) −3.00000 5.19615i −0.173494 0.300501i
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −7.00000 12.1244i −0.402139 0.696526i
\(304\) 0 0
\(305\) −2.00000 + 3.46410i −0.114520 + 0.198354i
\(306\) 0 0
\(307\) 27.0000 1.54097 0.770486 0.637457i \(-0.220014\pi\)
0.770486 + 0.637457i \(0.220014\pi\)
\(308\) 0 0
\(309\) 9.00000 0.511992
\(310\) 0 0
\(311\) −7.00000 + 12.1244i −0.396934 + 0.687509i −0.993346 0.115169i \(-0.963259\pi\)
0.596412 + 0.802678i \(0.296592\pi\)
\(312\) 0 0
\(313\) 14.5000 + 25.1147i 0.819588 + 1.41957i 0.905986 + 0.423308i \(0.139131\pi\)
−0.0863973 + 0.996261i \(0.527535\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −15.0000 25.9808i −0.842484 1.45922i −0.887788 0.460252i \(-0.847759\pi\)
0.0453045 0.998973i \(-0.485574\pi\)
\(318\) 0 0
\(319\) −22.5000 + 38.9711i −1.25976 + 2.18197i
\(320\) 0 0
\(321\) 2.00000 0.111629
\(322\) 0 0
\(323\) −18.0000 −1.00155
\(324\) 0 0
\(325\) 0.500000 0.866025i 0.0277350 0.0480384i
\(326\) 0 0
\(327\) 5.50000 + 9.52628i 0.304151 + 0.526804i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 10.0000 + 17.3205i 0.549650 + 0.952021i 0.998298 + 0.0583130i \(0.0185721\pi\)
−0.448649 + 0.893708i \(0.648095\pi\)
\(332\) 0 0
\(333\) 6.00000 10.3923i 0.328798 0.569495i
\(334\) 0 0
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) −26.0000 −1.41631 −0.708155 0.706057i \(-0.750472\pi\)
−0.708155 + 0.706057i \(0.750472\pi\)
\(338\) 0 0
\(339\) 3.00000 5.19615i 0.162938 0.282216i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 3.00000 + 5.19615i 0.161515 + 0.279751i
\(346\) 0 0
\(347\) 5.00000 8.66025i 0.268414 0.464907i −0.700038 0.714105i \(-0.746834\pi\)
0.968452 + 0.249198i \(0.0801671\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) 5.00000 0.266880
\(352\) 0 0
\(353\) −16.5000 + 28.5788i −0.878206 + 1.52110i −0.0248989 + 0.999690i \(0.507926\pi\)
−0.853307 + 0.521408i \(0.825407\pi\)
\(354\) 0 0
\(355\) −4.00000 6.92820i −0.212298 0.367711i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(360\) 0 0
\(361\) −8.50000 + 14.7224i −0.447368 + 0.774865i
\(362\) 0 0
\(363\) 14.0000 0.734809
\(364\) 0 0
\(365\) −10.0000 −0.523424
\(366\) 0 0
\(367\) −14.5000 + 25.1147i −0.756894 + 1.31098i 0.187533 + 0.982258i \(0.439951\pi\)
−0.944427 + 0.328720i \(0.893383\pi\)
\(368\) 0 0
\(369\) −8.00000 13.8564i −0.416463 0.721336i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(374\) 0 0
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) 9.00000 0.463524
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 0 0
\(381\) −4.00000 + 6.92820i −0.204926 + 0.354943i
\(382\) 0 0
\(383\) 6.00000 + 10.3923i 0.306586 + 0.531022i 0.977613 0.210411i \(-0.0674801\pi\)
−0.671027 + 0.741433i \(0.734147\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 6.00000 + 10.3923i 0.304997 + 0.528271i
\(388\) 0 0
\(389\) −12.5000 + 21.6506i −0.633775 + 1.09773i 0.352998 + 0.935624i \(0.385162\pi\)
−0.986773 + 0.162107i \(0.948171\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 0 0
\(393\) 6.00000 0.302660
\(394\) 0 0
\(395\) 1.50000 2.59808i 0.0754732 0.130723i
\(396\) 0 0
\(397\) −14.5000 25.1147i −0.727734 1.26047i −0.957839 0.287307i \(-0.907240\pi\)
0.230105 0.973166i \(-0.426093\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4.50000 7.79423i −0.224719 0.389225i 0.731516 0.681824i \(-0.238813\pi\)
−0.956235 + 0.292599i \(0.905480\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −30.0000 −1.48704
\(408\) 0 0
\(409\) 7.00000 12.1244i 0.346128 0.599511i −0.639430 0.768849i \(-0.720830\pi\)
0.985558 + 0.169338i \(0.0541630\pi\)
\(410\) 0 0
\(411\) 8.00000 + 13.8564i 0.394611 + 0.683486i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −6.00000 10.3923i −0.294528 0.510138i
\(416\) 0 0
\(417\) 9.00000 15.5885i 0.440732 0.763370i
\(418\) 0 0
\(419\) −36.0000 −1.75872 −0.879358 0.476162i \(-0.842028\pi\)
−0.879358 + 0.476162i \(0.842028\pi\)
\(420\) 0 0
\(421\) −19.0000 −0.926003 −0.463002 0.886357i \(-0.653228\pi\)
−0.463002 + 0.886357i \(0.653228\pi\)
\(422\) 0 0
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) 1.50000 + 2.59808i 0.0727607 + 0.126025i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −2.50000 4.33013i −0.120701 0.209061i
\(430\) 0 0
\(431\) −11.5000 + 19.9186i −0.553936 + 0.959444i 0.444050 + 0.896002i \(0.353541\pi\)
−0.997985 + 0.0634424i \(0.979792\pi\)
\(432\) 0 0
\(433\) 30.0000 1.44171 0.720854 0.693087i \(-0.243750\pi\)
0.720854 + 0.693087i \(0.243750\pi\)
\(434\) 0 0
\(435\) −9.00000 −0.431517
\(436\) 0 0
\(437\) 18.0000 31.1769i 0.861057 1.49139i
\(438\) 0 0
\(439\) −17.0000 29.4449i −0.811366 1.40533i −0.911908 0.410394i \(-0.865391\pi\)
0.100543 0.994933i \(-0.467942\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −15.0000 25.9808i −0.712672 1.23438i −0.963851 0.266443i \(-0.914152\pi\)
0.251179 0.967941i \(-0.419182\pi\)
\(444\) 0 0
\(445\) −8.00000 + 13.8564i −0.379236 + 0.656857i
\(446\) 0 0
\(447\) −14.0000 −0.662177
\(448\) 0 0
\(449\) −33.0000 −1.55737 −0.778683 0.627417i \(-0.784112\pi\)
−0.778683 + 0.627417i \(0.784112\pi\)
\(450\) 0 0
\(451\) −20.0000 + 34.6410i −0.941763 + 1.63118i
\(452\) 0 0
\(453\) 9.50000 + 16.4545i 0.446349 + 0.773099i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 14.0000 + 24.2487i 0.654892 + 1.13431i 0.981921 + 0.189292i \(0.0606194\pi\)
−0.327028 + 0.945015i \(0.606047\pi\)
\(458\) 0 0
\(459\) −7.50000 + 12.9904i −0.350070 + 0.606339i
\(460\) 0 0
\(461\) 24.0000 1.11779 0.558896 0.829238i \(-0.311225\pi\)
0.558896 + 0.829238i \(0.311225\pi\)
\(462\) 0 0
\(463\) 20.0000 0.929479 0.464739 0.885448i \(-0.346148\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 16.5000 + 28.5788i 0.763529 + 1.32247i 0.941021 + 0.338349i \(0.109868\pi\)
−0.177492 + 0.984122i \(0.556798\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −1.00000 1.73205i −0.0460776 0.0798087i
\(472\) 0 0
\(473\) 15.0000 25.9808i 0.689701 1.19460i
\(474\) 0 0
\(475\) 6.00000 0.275299
\(476\) 0 0
\(477\) 24.0000 1.09888
\(478\) 0 0
\(479\) −3.00000 + 5.19615i −0.137073 + 0.237418i −0.926388 0.376571i \(-0.877103\pi\)
0.789314 + 0.613990i \(0.210436\pi\)
\(480\) 0 0
\(481\) 3.00000 + 5.19615i 0.136788 + 0.236924i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 3.50000 + 6.06218i 0.158927 + 0.275269i
\(486\) 0 0
\(487\) −13.0000 + 22.5167i −0.589086 + 1.02033i 0.405266 + 0.914199i \(0.367179\pi\)
−0.994352 + 0.106129i \(0.966154\pi\)
\(488\) 0 0
\(489\) 6.00000 0.271329
\(490\) 0 0
\(491\) 33.0000 1.48927 0.744635 0.667472i \(-0.232624\pi\)
0.744635 + 0.667472i \(0.232624\pi\)
\(492\) 0 0
\(493\) −13.5000 + 23.3827i −0.608009 + 1.05310i
\(494\) 0 0
\(495\) −5.00000 8.66025i −0.224733 0.389249i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i \(0.0223697\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(500\) 0 0
\(501\) −4.50000 + 7.79423i −0.201045 + 0.348220i
\(502\) 0 0
\(503\) 31.0000 1.38222 0.691111 0.722749i \(-0.257122\pi\)
0.691111 + 0.722749i \(0.257122\pi\)
\(504\) 0 0
\(505\) 14.0000 0.622992
\(506\) 0 0
\(507\) 6.00000 10.3923i 0.266469 0.461538i
\(508\) 0 0
\(509\) 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i \(-0.0360525\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 15.0000 + 25.9808i 0.662266 + 1.14708i
\(514\) 0 0
\(515\) −4.50000 + 7.79423i −0.198294 + 0.343455i
\(516\) 0 0
\(517\) 15.0000 0.659699
\(518\) 0 0
\(519\) −19.0000 −0.834007
\(520\) 0 0
\(521\) −3.00000 + 5.19615i −0.131432 + 0.227648i −0.924229 0.381839i \(-0.875291\pi\)
0.792797 + 0.609486i \(0.208624\pi\)
\(522\) 0 0
\(523\) 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i \(-0.138794\pi\)
−0.818980 + 0.573822i \(0.805460\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 16.0000 0.694341
\(532\) 0 0
\(533\) 8.00000 0.346518
\(534\) 0 0
\(535\) −1.00000 + 1.73205i −0.0432338 + 0.0748831i
\(536\) 0 0
\(537\) −2.00000 3.46410i −0.0863064 0.149487i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 4.50000 + 7.79423i 0.193470 + 0.335100i 0.946398 0.323003i \(-0.104692\pi\)
−0.752928 + 0.658103i \(0.771359\pi\)
\(542\) 0 0
\(543\) −10.0000 + 17.3205i −0.429141 + 0.743294i
\(544\) 0 0
\(545\) −11.0000 −0.471188
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 0 0
\(549\) 4.00000 6.92820i 0.170716 0.295689i
\(550\) 0 0
\(551\) 27.0000 + 46.7654i 1.15024 + 1.99227i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −3.00000 5.19615i −0.127343 0.220564i
\(556\) 0 0
\(557\) −12.0000 + 20.7846i −0.508456 + 0.880672i 0.491496 + 0.870880i \(0.336450\pi\)
−0.999952 + 0.00979220i \(0.996883\pi\)
\(558\) 0 0
\(559\) −6.00000 −0.253773
\(560\) 0 0
\(561\) 15.0000 0.633300
\(562\) 0 0
\(563\) 2.00000 3.46410i 0.0842900 0.145994i −0.820798 0.571218i \(-0.806471\pi\)
0.905088 + 0.425223i \(0.139804\pi\)
\(564\) 0 0
\(565\) 3.00000 + 5.19615i 0.126211 + 0.218604i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −17.0000 29.4449i −0.712677 1.23439i −0.963849 0.266450i \(-0.914149\pi\)
0.251172 0.967943i \(-0.419184\pi\)
\(570\) 0 0
\(571\) 18.0000 31.1769i 0.753277 1.30471i −0.192950 0.981209i \(-0.561806\pi\)
0.946227 0.323505i \(-0.104861\pi\)
\(572\) 0 0
\(573\) 11.0000 0.459532
\(574\) 0 0
\(575\) −6.00000 −0.250217
\(576\) 0 0
\(577\) 8.50000 14.7224i 0.353860 0.612903i −0.633062 0.774101i \(-0.718202\pi\)
0.986922 + 0.161198i \(0.0515357\pi\)
\(578\) 0 0
\(579\) −4.00000 6.92820i −0.166234 0.287926i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −30.0000 51.9615i −1.24247 2.15203i
\(584\) 0 0
\(585\) −1.00000 + 1.73205i −0.0413449 + 0.0716115i
\(586\) 0 0
\(587\) −8.00000 −0.330195 −0.165098 0.986277i \(-0.552794\pi\)
−0.165098 + 0.986277i \(0.552794\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 6.00000 10.3923i 0.246807 0.427482i
\(592\) 0 0
\(593\) −3.50000 6.06218i −0.143728 0.248944i 0.785170 0.619281i \(-0.212576\pi\)
−0.928898 + 0.370337i \(0.879242\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 16.5000 28.5788i 0.674172 1.16770i −0.302539 0.953137i \(-0.597834\pi\)
0.976710 0.214563i \(-0.0688326\pi\)
\(600\) 0 0
\(601\) 34.0000 1.38689 0.693444 0.720510i \(-0.256092\pi\)
0.693444 + 0.720510i \(0.256092\pi\)
\(602\) 0 0
\(603\) 8.00000 0.325785
\(604\) 0 0
\(605\) −7.00000 + 12.1244i −0.284590 + 0.492925i
\(606\) 0 0
\(607\) 8.50000 + 14.7224i 0.345004 + 0.597565i 0.985355 0.170518i \(-0.0545441\pi\)
−0.640350 + 0.768083i \(0.721211\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.50000 2.59808i −0.0606835 0.105107i
\(612\) 0 0
\(613\) 11.0000 19.0526i 0.444286 0.769526i −0.553716 0.832705i \(-0.686791\pi\)
0.998002 + 0.0631797i \(0.0201241\pi\)
\(614\) 0 0
\(615\) −8.00000 −0.322591
\(616\) 0 0
\(617\) 10.0000 0.402585 0.201292 0.979531i \(-0.435486\pi\)
0.201292 + 0.979531i \(0.435486\pi\)
\(618\) 0 0
\(619\) 1.00000 1.73205i 0.0401934 0.0696170i −0.845229 0.534404i \(-0.820536\pi\)
0.885422 + 0.464787i \(0.153869\pi\)
\(620\) 0 0
\(621\) −15.0000 25.9808i −0.601929 1.04257i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 15.0000 25.9808i 0.599042 1.03757i
\(628\) 0 0
\(629\) −18.0000 −0.717707
\(630\) 0 0
\(631\) −9.00000 −0.358284 −0.179142 0.983823i \(-0.557332\pi\)
−0.179142 + 0.983823i \(0.557332\pi\)
\(632\) 0 0
\(633\) −6.50000 + 11.2583i −0.258352 + 0.447478i
\(634\) 0 0
\(635\) −4.00000 6.92820i −0.158735 0.274937i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 8.00000 + 13.8564i 0.316475 + 0.548151i
\(640\) 0 0
\(641\) −17.0000 + 29.4449i −0.671460 + 1.16300i 0.306031 + 0.952022i \(0.400999\pi\)
−0.977490 + 0.210981i \(0.932334\pi\)
\(642\) 0 0
\(643\) −47.0000 −1.85350 −0.926750 0.375680i \(-0.877409\pi\)
−0.926750 + 0.375680i \(0.877409\pi\)
\(644\) 0 0
\(645\) 6.00000 0.236250
\(646\) 0 0
\(647\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(648\) 0 0
\(649\) −20.0000 34.6410i −0.785069 1.35978i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −15.0000 25.9808i −0.586995 1.01671i −0.994623 0.103558i \(-0.966977\pi\)
0.407628 0.913148i \(-0.366356\pi\)
\(654\) 0 0
\(655\) −3.00000 + 5.19615i −0.117220 + 0.203030i
\(656\) 0 0
\(657\) 20.0000 0.780274
\(658\) 0 0
\(659\) −25.0000 −0.973862 −0.486931 0.873441i \(-0.661884\pi\)
−0.486931 + 0.873441i \(0.661884\pi\)
\(660\) 0 0
\(661\) 4.00000 6.92820i 0.155582 0.269476i −0.777689 0.628649i \(-0.783608\pi\)
0.933271 + 0.359174i \(0.116941\pi\)
\(662\) 0 0
\(663\) −1.50000 2.59808i −0.0582552 0.100901i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −27.0000 46.7654i −1.04544 1.81076i
\(668\) 0 0
\(669\) −12.5000 + 21.6506i −0.483278 + 0.837062i
\(670\) 0 0
\(671\) −20.0000 −0.772091
\(672\) 0 0
\(673\) 32.0000 1.23351 0.616755 0.787155i \(-0.288447\pi\)
0.616755 + 0.787155i \(0.288447\pi\)
\(674\) 0 0
\(675\) 2.50000 4.33013i 0.0962250 0.166667i
\(676\) 0 0
\(677\) 16.5000 + 28.5788i 0.634147 + 1.09837i 0.986695 + 0.162581i \(0.0519817\pi\)
−0.352549 + 0.935793i \(0.614685\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −6.50000 11.2583i −0.249081 0.431420i
\(682\) 0 0
\(683\) 10.0000 17.3205i 0.382639 0.662751i −0.608799 0.793324i \(-0.708349\pi\)
0.991439 + 0.130573i \(0.0416818\pi\)
\(684\) 0 0
\(685\) −16.0000 −0.611329
\(686\) 0 0
\(687\) −16.0000 −0.610438
\(688\) 0 0
\(689\) −6.00000 + 10.3923i −0.228582 + 0.395915i
\(690\) 0 0
\(691\) 10.0000 + 17.3205i 0.380418 + 0.658903i 0.991122 0.132956i \(-0.0424468\pi\)
−0.610704 + 0.791859i \(0.709113\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9.00000 + 15.5885i 0.341389 + 0.591304i
\(696\) 0 0
\(697\) −12.0000 + 20.7846i −0.454532 + 0.787273i
\(698\) 0 0
\(699\) 8.00000 0.302588
\(700\) 0 0
\(701\) −21.0000 −0.793159 −0.396580 0.918000i \(-0.629803\pi\)
−0.396580 + 0.918000i \(0.629803\pi\)
\(702\) 0 0
\(703\) −18.0000 + 31.1769i −0.678883 + 1.17586i
\(704\) 0 0
\(705\) 1.50000 + 2.59808i 0.0564933 + 0.0978492i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 20.5000 + 35.5070i 0.769894 + 1.33349i 0.937620 + 0.347661i \(0.113024\pi\)
−0.167727 + 0.985834i \(0.553643\pi\)
\(710\) 0 0
\(711\) −3.00000 + 5.19615i −0.112509 + 0.194871i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 5.00000 0.186989
\(716\) 0 0
\(717\) 3.50000 6.06218i 0.130710 0.226396i
\(718\) 0 0
\(719\) 25.0000 + 43.3013i 0.932343 + 1.61486i 0.779305 + 0.626644i \(0.215572\pi\)
0.153037 + 0.988220i \(0.451094\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 9.00000 + 15.5885i 0.334714 + 0.579741i
\(724\) 0 0
\(725\) 4.50000 7.79423i 0.167126 0.289470i
\(726\) 0 0
\(727\) 16.0000 0.593407 0.296704 0.954970i \(-0.404113\pi\)
0.296704 + 0.954970i \(0.404113\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 9.00000 15.5885i 0.332877 0.576560i
\(732\) 0 0
\(733\) 2.50000 + 4.33013i 0.0923396 + 0.159937i 0.908495 0.417895i \(-0.137232\pi\)
−0.816156 + 0.577832i \(0.803899\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −10.0000 17.3205i −0.368355 0.638009i
\(738\) 0 0
\(739\) 18.5000 32.0429i 0.680534 1.17872i −0.294285 0.955718i \(-0.595081\pi\)
0.974818 0.223001i \(-0.0715853\pi\)
\(740\) 0 0
\(741\) −6.00000 −0.220416
\(742\) 0 0
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 0 0
\(745\) 7.00000 12.1244i 0.256460 0.444202i
\(746\) 0 0
\(747\) 12.0000 + 20.7846i 0.439057 + 0.760469i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 17.5000 + 30.3109i 0.638584 + 1.10606i 0.985744 + 0.168254i \(0.0538129\pi\)
−0.347160 + 0.937806i \(0.612854\pi\)
\(752\) 0 0
\(753\) 7.00000 12.1244i 0.255094 0.441836i
\(754\) 0 0
\(755\) −19.0000 −0.691481
\(756\) 0 0
\(757\) 8.00000 0.290765 0.145382 0.989376i \(-0.453559\pi\)
0.145382 + 0.989376i \(0.453559\pi\)
\(758\) 0 0
\(759\) −15.0000 + 25.9808i −0.544466 + 0.943042i
\(760\) 0 0
\(761\) −23.0000 39.8372i −0.833749 1.44410i −0.895045 0.445977i \(-0.852856\pi\)
0.0612953 0.998120i \(-0.480477\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −3.00000 5.19615i −0.108465 0.187867i
\(766\) 0 0
\(767\) −4.00000 + 6.92820i −0.144432 + 0.250163i
\(768\) 0 0
\(769\) 10.0000 0.360609 0.180305 0.983611i \(-0.442292\pi\)
0.180305 + 0.983611i \(0.442292\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) 0 0
\(773\) 0.500000 0.866025i 0.0179838 0.0311488i −0.856893 0.515494i \(-0.827609\pi\)
0.874877 + 0.484345i \(0.160942\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 24.0000 + 41.5692i 0.859889 + 1.48937i
\(780\) 0 0
\(781\) 20.0000 34.6410i 0.715656 1.23955i
\(782\) 0 0
\(783\) 45.0000 1.60817
\(784\) 0 0
\(785\) 2.00000 0.0713831
\(786\) 0 0
\(787\) 5.50000 9.52628i 0.196054 0.339575i −0.751192 0.660084i \(-0.770521\pi\)
0.947245 + 0.320509i \(0.103854\pi\)
\(788\) 0 0
\(789\) −9.00000 15.5885i −0.320408 0.554964i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 2.00000 + 3.46410i 0.0710221 + 0.123014i
\(794\) 0 0
\(795\) 6.00000 10.3923i 0.212798 0.368577i
\(796\) 0 0
\(797\) −35.0000 −1.23976 −0.619882 0.784695i \(-0.712819\pi\)
−0.619882 + 0.784695i \(0.712819\pi\)
\(798\) 0 0
\(799\) 9.00000 0.318397
\(800\) 0