Properties

Label 252.2.bf.e.19.2
Level $252$
Weight $2$
Character 252.19
Analytic conductor $2.012$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 28)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 252.19
Dual form 252.2.bf.e.199.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\) \(q+(1.36603 - 0.366025i) q^{2} +(1.73205 - 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-1.73205 - 2.00000i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.36603 + 0.633975i) q^{10} +(-0.866025 + 0.500000i) q^{11} +3.46410i q^{13} +(-3.09808 - 2.09808i) q^{14} +(2.00000 - 3.46410i) q^{16} +(1.50000 - 0.866025i) q^{17} +(-2.59808 + 4.50000i) q^{19} +3.46410 q^{20} +(-1.00000 + 1.00000i) q^{22} +(-0.866025 - 0.500000i) q^{23} +(-1.00000 - 1.73205i) q^{25} +(1.26795 + 4.73205i) q^{26} +(-5.00000 - 1.73205i) q^{28} -4.00000 q^{29} +(-0.866025 - 1.50000i) q^{31} +(1.46410 - 5.46410i) q^{32} +(1.73205 - 1.73205i) q^{34} +(-0.866025 - 4.50000i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(-1.90192 + 7.09808i) q^{38} +(4.73205 - 1.26795i) q^{40} +3.46410i q^{41} -2.00000i q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.36603 - 0.366025i) q^{46} +(-4.33013 + 7.50000i) q^{47} +(-1.00000 + 6.92820i) q^{49} +(-2.00000 - 2.00000i) q^{50} +(3.46410 + 6.00000i) q^{52} +(-0.500000 - 0.866025i) q^{53} -1.73205 q^{55} +(-7.46410 - 0.535898i) q^{56} +(-5.46410 + 1.46410i) q^{58} +(2.59808 + 4.50000i) q^{59} +(-4.50000 - 2.59808i) q^{61} +(-1.73205 - 1.73205i) q^{62} -8.00000i q^{64} +(-3.00000 + 5.19615i) q^{65} +(2.59808 - 1.50000i) q^{67} +(1.73205 - 3.00000i) q^{68} +(-2.83013 - 5.83013i) q^{70} -14.0000i q^{71} +(7.50000 - 4.33013i) q^{73} +(-1.09808 + 4.09808i) q^{74} +10.3923i q^{76} +(2.50000 + 0.866025i) q^{77} +(7.79423 + 4.50000i) q^{79} +(6.00000 - 3.46410i) q^{80} +(1.26795 + 4.73205i) q^{82} +13.8564 q^{83} +3.00000 q^{85} +(-0.732051 - 2.73205i) q^{86} +(-0.732051 + 2.73205i) q^{88} +(-13.5000 - 7.79423i) q^{89} +(6.92820 - 6.00000i) q^{91} -2.00000 q^{92} +(-3.16987 + 11.8301i) q^{94} +(-7.79423 + 4.50000i) q^{95} -17.3205i q^{97} +(1.16987 + 9.83013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} + 6q^{5} + 8q^{8} + O(q^{10}) \) \( 4q + 2q^{2} + 6q^{5} + 8q^{8} + 6q^{10} - 2q^{14} + 8q^{16} + 6q^{17} - 4q^{22} - 4q^{25} + 12q^{26} - 20q^{28} - 16q^{29} - 8q^{32} - 6q^{37} - 18q^{38} + 12q^{40} - 4q^{44} - 2q^{46} - 4q^{49} - 8q^{50} - 2q^{53} - 16q^{56} - 8q^{58} - 18q^{61} - 12q^{65} + 6q^{70} + 30q^{73} + 6q^{74} + 10q^{77} + 24q^{80} + 12q^{82} + 12q^{85} + 4q^{86} + 4q^{88} - 54q^{89} - 8q^{92} - 30q^{94} + 22q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 0.366025i 0.965926 0.258819i
\(3\) 0 0
\(4\) 1.73205 1.00000i 0.866025 0.500000i
\(5\) 1.50000 + 0.866025i 0.670820 + 0.387298i 0.796387 0.604787i \(-0.206742\pi\)
−0.125567 + 0.992085i \(0.540075\pi\)
\(6\) 0 0
\(7\) −1.73205 2.00000i −0.654654 0.755929i
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) 0 0
\(10\) 2.36603 + 0.633975i 0.748203 + 0.200480i
\(11\) −0.866025 + 0.500000i −0.261116 + 0.150756i −0.624844 0.780750i \(-0.714837\pi\)
0.363727 + 0.931505i \(0.381504\pi\)
\(12\) 0 0
\(13\) 3.46410i 0.960769i 0.877058 + 0.480384i \(0.159503\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(14\) −3.09808 2.09808i −0.827996 0.560734i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 1.50000 0.866025i 0.363803 0.210042i −0.306944 0.951727i \(-0.599307\pi\)
0.670748 + 0.741685i \(0.265973\pi\)
\(18\) 0 0
\(19\) −2.59808 + 4.50000i −0.596040 + 1.03237i 0.397360 + 0.917663i \(0.369927\pi\)
−0.993399 + 0.114708i \(0.963407\pi\)
\(20\) 3.46410 0.774597
\(21\) 0 0
\(22\) −1.00000 + 1.00000i −0.213201 + 0.213201i
\(23\) −0.866025 0.500000i −0.180579 0.104257i 0.406986 0.913434i \(-0.366580\pi\)
−0.587565 + 0.809177i \(0.699913\pi\)
\(24\) 0 0
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) 1.26795 + 4.73205i 0.248665 + 0.928032i
\(27\) 0 0
\(28\) −5.00000 1.73205i −0.944911 0.327327i
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) −0.866025 1.50000i −0.155543 0.269408i 0.777714 0.628619i \(-0.216379\pi\)
−0.933257 + 0.359211i \(0.883046\pi\)
\(32\) 1.46410 5.46410i 0.258819 0.965926i
\(33\) 0 0
\(34\) 1.73205 1.73205i 0.297044 0.297044i
\(35\) −0.866025 4.50000i −0.146385 0.760639i
\(36\) 0 0
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) −1.90192 + 7.09808i −0.308533 + 1.15146i
\(39\) 0 0
\(40\) 4.73205 1.26795i 0.748203 0.200480i
\(41\) 3.46410i 0.541002i 0.962720 + 0.270501i \(0.0871893\pi\)
−0.962720 + 0.270501i \(0.912811\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) −1.00000 + 1.73205i −0.150756 + 0.261116i
\(45\) 0 0
\(46\) −1.36603 0.366025i −0.201409 0.0539675i
\(47\) −4.33013 + 7.50000i −0.631614 + 1.09399i 0.355608 + 0.934635i \(0.384274\pi\)
−0.987222 + 0.159352i \(0.949059\pi\)
\(48\) 0 0
\(49\) −1.00000 + 6.92820i −0.142857 + 0.989743i
\(50\) −2.00000 2.00000i −0.282843 0.282843i
\(51\) 0 0
\(52\) 3.46410 + 6.00000i 0.480384 + 0.832050i
\(53\) −0.500000 0.866025i −0.0686803 0.118958i 0.829640 0.558298i \(-0.188546\pi\)
−0.898321 + 0.439340i \(0.855212\pi\)
\(54\) 0 0
\(55\) −1.73205 −0.233550
\(56\) −7.46410 0.535898i −0.997433 0.0716124i
\(57\) 0 0
\(58\) −5.46410 + 1.46410i −0.717472 + 0.192246i
\(59\) 2.59808 + 4.50000i 0.338241 + 0.585850i 0.984102 0.177605i \(-0.0568349\pi\)
−0.645861 + 0.763455i \(0.723502\pi\)
\(60\) 0 0
\(61\) −4.50000 2.59808i −0.576166 0.332650i 0.183442 0.983030i \(-0.441276\pi\)
−0.759608 + 0.650381i \(0.774609\pi\)
\(62\) −1.73205 1.73205i −0.219971 0.219971i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) −3.00000 + 5.19615i −0.372104 + 0.644503i
\(66\) 0 0
\(67\) 2.59808 1.50000i 0.317406 0.183254i −0.332830 0.942987i \(-0.608004\pi\)
0.650236 + 0.759733i \(0.274670\pi\)
\(68\) 1.73205 3.00000i 0.210042 0.363803i
\(69\) 0 0
\(70\) −2.83013 5.83013i −0.338265 0.696833i
\(71\) 14.0000i 1.66149i −0.556650 0.830747i \(-0.687914\pi\)
0.556650 0.830747i \(-0.312086\pi\)
\(72\) 0 0
\(73\) 7.50000 4.33013i 0.877809 0.506803i 0.00787336 0.999969i \(-0.497494\pi\)
0.869935 + 0.493166i \(0.164160\pi\)
\(74\) −1.09808 + 4.09808i −0.127649 + 0.476392i
\(75\) 0 0
\(76\) 10.3923i 1.19208i
\(77\) 2.50000 + 0.866025i 0.284901 + 0.0986928i
\(78\) 0 0
\(79\) 7.79423 + 4.50000i 0.876919 + 0.506290i 0.869641 0.493684i \(-0.164350\pi\)
0.00727784 + 0.999974i \(0.497683\pi\)
\(80\) 6.00000 3.46410i 0.670820 0.387298i
\(81\) 0 0
\(82\) 1.26795 + 4.73205i 0.140022 + 0.522568i
\(83\) 13.8564 1.52094 0.760469 0.649374i \(-0.224969\pi\)
0.760469 + 0.649374i \(0.224969\pi\)
\(84\) 0 0
\(85\) 3.00000 0.325396
\(86\) −0.732051 2.73205i −0.0789391 0.294605i
\(87\) 0 0
\(88\) −0.732051 + 2.73205i −0.0780369 + 0.291238i
\(89\) −13.5000 7.79423i −1.43100 0.826187i −0.433800 0.901009i \(-0.642828\pi\)
−0.997197 + 0.0748225i \(0.976161\pi\)
\(90\) 0 0
\(91\) 6.92820 6.00000i 0.726273 0.628971i
\(92\) −2.00000 −0.208514
\(93\) 0 0
\(94\) −3.16987 + 11.8301i −0.326947 + 1.22018i
\(95\) −7.79423 + 4.50000i −0.799671 + 0.461690i
\(96\) 0 0
\(97\) 17.3205i 1.75863i −0.476240 0.879316i \(-0.658000\pi\)
0.476240 0.879316i \(-0.342000\pi\)
\(98\) 1.16987 + 9.83013i 0.118175 + 0.992993i
\(99\) 0 0
\(100\) −3.46410 2.00000i −0.346410 0.200000i
\(101\) 7.50000 4.33013i 0.746278 0.430864i −0.0780696 0.996948i \(-0.524876\pi\)
0.824347 + 0.566084i \(0.191542\pi\)
\(102\) 0 0
\(103\) −4.33013 + 7.50000i −0.426660 + 0.738997i −0.996574 0.0827075i \(-0.973643\pi\)
0.569914 + 0.821705i \(0.306977\pi\)
\(104\) 6.92820 + 6.92820i 0.679366 + 0.679366i
\(105\) 0 0
\(106\) −1.00000 1.00000i −0.0971286 0.0971286i
\(107\) 11.2583 + 6.50000i 1.08838 + 0.628379i 0.933146 0.359498i \(-0.117052\pi\)
0.155238 + 0.987877i \(0.450386\pi\)
\(108\) 0 0
\(109\) −4.50000 7.79423i −0.431022 0.746552i 0.565940 0.824447i \(-0.308513\pi\)
−0.996962 + 0.0778949i \(0.975180\pi\)
\(110\) −2.36603 + 0.633975i −0.225592 + 0.0604471i
\(111\) 0 0
\(112\) −10.3923 + 2.00000i −0.981981 + 0.188982i
\(113\) 16.0000 1.50515 0.752577 0.658505i \(-0.228811\pi\)
0.752577 + 0.658505i \(0.228811\pi\)
\(114\) 0 0
\(115\) −0.866025 1.50000i −0.0807573 0.139876i
\(116\) −6.92820 + 4.00000i −0.643268 + 0.371391i
\(117\) 0 0
\(118\) 5.19615 + 5.19615i 0.478345 + 0.478345i
\(119\) −4.33013 1.50000i −0.396942 0.137505i
\(120\) 0 0
\(121\) −5.00000 + 8.66025i −0.454545 + 0.787296i
\(122\) −7.09808 1.90192i −0.642630 0.172192i
\(123\) 0 0
\(124\) −3.00000 1.73205i −0.269408 0.155543i
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 6.00000i 0.532414i −0.963916 0.266207i \(-0.914230\pi\)
0.963916 0.266207i \(-0.0857705\pi\)
\(128\) −2.92820 10.9282i −0.258819 0.965926i
\(129\) 0 0
\(130\) −2.19615 + 8.19615i −0.192615 + 0.718850i
\(131\) −2.59808 + 4.50000i −0.226995 + 0.393167i −0.956916 0.290365i \(-0.906223\pi\)
0.729921 + 0.683531i \(0.239557\pi\)
\(132\) 0 0
\(133\) 13.5000 2.59808i 1.17060 0.225282i
\(134\) 3.00000 3.00000i 0.259161 0.259161i
\(135\) 0 0
\(136\) 1.26795 4.73205i 0.108726 0.405770i
\(137\) 0.500000 + 0.866025i 0.0427179 + 0.0739895i 0.886594 0.462549i \(-0.153065\pi\)
−0.843876 + 0.536538i \(0.819732\pi\)
\(138\) 0 0
\(139\) 6.92820 0.587643 0.293821 0.955860i \(-0.405073\pi\)
0.293821 + 0.955860i \(0.405073\pi\)
\(140\) −6.00000 6.92820i −0.507093 0.585540i
\(141\) 0 0
\(142\) −5.12436 19.1244i −0.430026 1.60488i
\(143\) −1.73205 3.00000i −0.144841 0.250873i
\(144\) 0 0
\(145\) −6.00000 3.46410i −0.498273 0.287678i
\(146\) 8.66025 8.66025i 0.716728 0.716728i
\(147\) 0 0
\(148\) 6.00000i 0.493197i
\(149\) 0.500000 0.866025i 0.0409616 0.0709476i −0.844818 0.535054i \(-0.820291\pi\)
0.885779 + 0.464107i \(0.153625\pi\)
\(150\) 0 0
\(151\) −6.06218 + 3.50000i −0.493333 + 0.284826i −0.725956 0.687741i \(-0.758602\pi\)
0.232623 + 0.972567i \(0.425269\pi\)
\(152\) 3.80385 + 14.1962i 0.308533 + 1.15146i
\(153\) 0 0
\(154\) 3.73205 + 0.267949i 0.300737 + 0.0215920i
\(155\) 3.00000i 0.240966i
\(156\) 0 0
\(157\) 1.50000 0.866025i 0.119713 0.0691164i −0.438948 0.898513i \(-0.644649\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 12.2942 + 3.29423i 0.978076 + 0.262075i
\(159\) 0 0
\(160\) 6.92820 6.92820i 0.547723 0.547723i
\(161\) 0.500000 + 2.59808i 0.0394055 + 0.204757i
\(162\) 0 0
\(163\) 18.1865 + 10.5000i 1.42448 + 0.822423i 0.996678 0.0814491i \(-0.0259548\pi\)
0.427802 + 0.903873i \(0.359288\pi\)
\(164\) 3.46410 + 6.00000i 0.270501 + 0.468521i
\(165\) 0 0
\(166\) 18.9282 5.07180i 1.46911 0.393648i
\(167\) −17.3205 −1.34030 −0.670151 0.742225i \(-0.733770\pi\)
−0.670151 + 0.742225i \(0.733770\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 4.09808 1.09808i 0.314308 0.0842186i
\(171\) 0 0
\(172\) −2.00000 3.46410i −0.152499 0.264135i
\(173\) 10.5000 + 6.06218i 0.798300 + 0.460899i 0.842876 0.538107i \(-0.180860\pi\)
−0.0445762 + 0.999006i \(0.514194\pi\)
\(174\) 0 0
\(175\) −1.73205 + 5.00000i −0.130931 + 0.377964i
\(176\) 4.00000i 0.301511i
\(177\) 0 0
\(178\) −21.2942 5.70577i −1.59607 0.427666i
\(179\) 16.4545 9.50000i 1.22987 0.710063i 0.262864 0.964833i \(-0.415333\pi\)
0.967002 + 0.254770i \(0.0819996\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i 0.966282 + 0.257485i \(0.0828937\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 7.26795 10.7321i 0.538736 0.795513i
\(183\) 0 0
\(184\) −2.73205 + 0.732051i −0.201409 + 0.0539675i
\(185\) −4.50000 + 2.59808i −0.330847 + 0.191014i
\(186\) 0 0
\(187\) −0.866025 + 1.50000i −0.0633300 + 0.109691i
\(188\) 17.3205i 1.26323i
\(189\) 0 0
\(190\) −9.00000 + 9.00000i −0.652929 + 0.652929i
\(191\) 0.866025 + 0.500000i 0.0626634 + 0.0361787i 0.531004 0.847369i \(-0.321815\pi\)
−0.468341 + 0.883548i \(0.655148\pi\)
\(192\) 0 0
\(193\) 7.50000 + 12.9904i 0.539862 + 0.935068i 0.998911 + 0.0466572i \(0.0148568\pi\)
−0.459049 + 0.888411i \(0.651810\pi\)
\(194\) −6.33975 23.6603i −0.455167 1.69871i
\(195\) 0 0
\(196\) 5.19615 + 13.0000i 0.371154 + 0.928571i
\(197\) −16.0000 −1.13995 −0.569976 0.821661i \(-0.693048\pi\)
−0.569976 + 0.821661i \(0.693048\pi\)
\(198\) 0 0
\(199\) −11.2583 19.5000i −0.798082 1.38232i −0.920864 0.389885i \(-0.872515\pi\)
0.122782 0.992434i \(1.53918\pi\)
\(200\) −5.46410 1.46410i −0.386370 0.103528i
\(201\) 0 0
\(202\) 8.66025 8.66025i 0.609333 0.609333i
\(203\) 6.92820 + 8.00000i 0.486265 + 0.561490i
\(204\) 0 0
\(205\) −3.00000 + 5.19615i −0.209529 + 0.362915i
\(206\) −3.16987 + 11.8301i −0.220856 + 0.824244i
\(207\) 0 0
\(208\) 12.0000 + 6.92820i 0.832050 + 0.480384i
\(209\) 5.19615i 0.359425i
\(210\) 0 0
\(211\) 10.0000i 0.688428i −0.938891 0.344214i \(-0.888145\pi\)
0.938891 0.344214i \(-0.111855\pi\)
\(212\) −1.73205 1.00000i −0.118958 0.0686803i
\(213\) 0 0
\(214\) 17.7583 + 4.75833i 1.21393 + 0.325273i
\(215\) 1.73205 3.00000i 0.118125 0.204598i
\(216\) 0 0
\(217\) −1.50000 + 4.33013i −0.101827 + 0.293948i
\(218\) −9.00000 9.00000i −0.609557 0.609557i
\(219\) 0 0
\(220\) −3.00000 + 1.73205i −0.202260 + 0.116775i
\(221\) 3.00000 + 5.19615i 0.201802 + 0.349531i
\(222\) 0 0
\(223\) −6.92820 −0.463947 −0.231973 0.972722i \(-0.574518\pi\)
−0.231973 + 0.972722i \(0.574518\pi\)
\(224\) −13.4641 + 6.53590i −0.899608 + 0.436698i
\(225\) 0 0
\(226\) 21.8564 5.85641i 1.45387 0.389562i
\(227\) −9.52628 16.5000i −0.632281 1.09514i −0.987084 0.160202i \(-0.948785\pi\)
0.354803 0.934941i \(1.61545\pi\)
\(228\) 0 0
\(229\) −13.5000 7.79423i −0.892105 0.515057i −0.0174746 0.999847i \(-0.505563\pi\)
−0.874630 + 0.484790i \(0.838896\pi\)
\(230\) −1.73205 1.73205i −0.114208 0.114208i
\(231\) 0 0
\(232\) −8.00000 + 8.00000i −0.525226 + 0.525226i
\(233\) −3.50000 + 6.06218i −0.229293 + 0.397146i −0.957599 0.288106i \(-0.906975\pi\)
0.728306 + 0.685252i \(0.240308\pi\)
\(234\) 0 0
\(235\) −12.9904 + 7.50000i −0.847399 + 0.489246i
\(236\) 9.00000 + 5.19615i 0.585850 + 0.338241i
\(237\) 0 0
\(238\) −6.46410 0.464102i −0.419005 0.0300832i
\(239\) 20.0000i 1.29369i 0.762620 + 0.646846i \(0.223912\pi\)
−0.762620 + 0.646846i \(0.776088\pi\)
\(240\) 0 0
\(241\) −4.50000 + 2.59808i −0.289870 + 0.167357i −0.637883 0.770133i \(-0.720190\pi\)
0.348013 + 0.937490i \(0.386857\pi\)
\(242\) −3.66025 + 13.6603i −0.235290 + 0.878114i
\(243\) 0 0
\(244\) −10.3923 −0.665299
\(245\) −7.50000 + 9.52628i −0.479157 + 0.608612i
\(246\) 0 0
\(247\) −15.5885 9.00000i −0.991870 0.572656i
\(248\) −4.73205 1.26795i −0.300486 0.0805149i
\(249\) 0 0
\(250\) −4.43782 16.5622i −0.280673 1.04748i
\(251\) −3.46410 −0.218652 −0.109326 0.994006i \(-0.534869\pi\)
−0.109326 + 0.994006i \(0.534869\pi\)
\(252\) 0 0
\(253\) 1.00000 0.0628695
\(254\) −2.19615 8.19615i −0.137799 0.514272i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −4.50000 2.59808i −0.280702 0.162064i 0.353039 0.935609i \(-0.385148\pi\)
−0.633741 + 0.773545i \(0.718482\pi\)
\(258\) 0 0
\(259\) 7.79423 1.50000i 0.484310 0.0932055i
\(260\) 12.0000i 0.744208i
\(261\) 0 0
\(262\) −1.90192 + 7.09808i −0.117501 + 0.438521i
\(263\) −19.9186 + 11.5000i −1.22823 + 0.709120i −0.966660 0.256063i \(-0.917574\pi\)
−0.261573 + 0.965184i \(0.584241\pi\)
\(264\) 0 0
\(265\) 1.73205i 0.106399i
\(266\) 17.4904 8.49038i 1.07240 0.520579i
\(267\) 0 0
\(268\) 3.00000 5.19615i 0.183254 0.317406i
\(269\) −19.5000 + 11.2583i −1.18894 + 0.686433i −0.958065 0.286552i \(-0.907491\pi\)
−0.230871 + 0.972984i \(0.574158\pi\)
\(270\) 0 0
\(271\) −7.79423 + 13.5000i −0.473466 + 0.820067i −0.999539 0.0303728i \(-0.990331\pi\)
0.526073 + 0.850439i \(0.323664\pi\)
\(272\) 6.92820i 0.420084i
\(273\) 0 0
\(274\) 1.00000 + 1.00000i 0.0604122 + 0.0604122i
\(275\) 1.73205 + 1.00000i 0.104447 + 0.0603023i
\(276\) 0 0
\(277\) 6.50000 + 11.2583i 0.390547 + 0.676448i 0.992522 0.122068i \(-0.0389525\pi\)
−0.601975 + 0.798515i \(0.705619\pi\)
\(278\) 9.46410 2.53590i 0.567619 0.152093i
\(279\) 0 0
\(280\) −10.7321 7.26795i −0.641363 0.434343i
\(281\) 4.00000 0.238620 0.119310 0.992857i \(-0.461932\pi\)
0.119310 + 0.992857i \(0.461932\pi\)
\(282\) 0 0
\(283\) 6.06218 + 10.5000i 0.360359 + 0.624160i 0.988020 0.154327i \(-0.0493208\pi\)
−0.627661 + 0.778487i \(0.715988\pi\)
\(284\) −14.0000 24.2487i −0.830747 1.43890i
\(285\) 0 0
\(286\) −3.46410 3.46410i −0.204837 0.204837i
\(287\) 6.92820 6.00000i 0.408959 0.354169i
\(288\) 0 0
\(289\) −7.00000 + 12.1244i −0.411765 + 0.713197i
\(290\) −9.46410 2.53590i −0.555751 0.148913i
\(291\) 0 0
\(292\) 8.66025 15.0000i 0.506803 0.877809i
\(293\) 20.7846i 1.21425i 0.794606 + 0.607125i \(0.207677\pi\)
−0.794606 + 0.607125i \(0.792323\pi\)
\(294\) 0 0
\(295\) 9.00000i 0.524000i
\(296\) 2.19615 + 8.19615i 0.127649 + 0.476392i
\(297\) 0 0
\(298\) 0.366025 1.36603i 0.0212033 0.0791317i
\(299\) 1.73205 3.00000i 0.100167 0.173494i
\(300\) 0 0
\(301\) −4.00000 + 3.46410i −0.230556 + 0.199667i
\(302\) −7.00000 + 7.00000i −0.402805 + 0.402805i
\(303\) 0 0
\(304\) 10.3923 + 18.0000i 0.596040 + 1.03237i
\(305\) −4.50000 7.79423i −0.257669 0.446296i
\(306\) 0 0
\(307\) −20.7846 −1.18624 −0.593120 0.805114i \(-0.702104\pi\)
−0.593120 + 0.805114i \(0.702104\pi\)
\(308\) 5.19615 1.00000i 0.296078 0.0569803i
\(309\) 0 0
\(310\) −1.09808 4.09808i −0.0623665 0.232755i
\(311\) −4.33013 7.50000i −0.245539 0.425286i 0.716744 0.697336i \(-0.245632\pi\)
−0.962283 + 0.272050i \(0.912298\pi\)
\(312\) 0 0
\(313\) 1.50000 + 0.866025i 0.0847850 + 0.0489506i 0.541793 0.840512i \(-0.317746\pi\)
−0.457008 + 0.889463i \(0.651079\pi\)
\(314\) 1.73205 1.73205i 0.0977453 0.0977453i
\(315\) 0 0
\(316\) 18.0000 1.01258
\(317\) 5.50000 9.52628i 0.308911 0.535049i −0.669214 0.743070i \(-0.733369\pi\)
0.978124 + 0.208021i \(0.0667022\pi\)
\(318\) 0 0
\(319\) 3.46410 2.00000i 0.193952 0.111979i
\(320\) 6.92820 12.0000i 0.387298 0.670820i
\(321\) 0 0
\(322\) 1.63397 + 3.36603i 0.0910578 + 0.187581i
\(323\) 9.00000i 0.500773i
\(324\) 0 0
\(325\) 6.00000 3.46410i 0.332820 0.192154i
\(326\) 28.6865 + 7.68653i 1.58880 + 0.425718i
\(327\) 0 0
\(328\) 6.92820 + 6.92820i 0.382546 + 0.382546i
\(329\) 22.5000 4.33013i 1.24047 0.238728i
\(330\) 0 0
\(331\) −6.06218 3.50000i −0.333207 0.192377i 0.324057 0.946038i \(-0.394953\pi\)
−0.657264 + 0.753660i \(0.728286\pi\)
\(332\) 24.0000 13.8564i 1.31717 0.760469i
\(333\) 0 0
\(334\) −23.6603 + 6.33975i −1.29463 + 0.346895i
\(335\) 5.19615 0.283896
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 1.36603 0.366025i 0.0743020 0.0199092i
\(339\) 0 0
\(340\) 5.19615 3.00000i 0.281801 0.162698i
\(341\) 1.50000 + 0.866025i 0.0812296 + 0.0468979i
\(342\) 0 0
\(343\) 15.5885 10.0000i 0.841698 0.539949i
\(344\) −4.00000 4.00000i −0.215666 0.215666i
\(345\) 0 0
\(346\) 16.5622 + 4.43782i 0.890388 + 0.238579i
\(347\) 11.2583 6.50000i 0.604379 0.348938i −0.166383 0.986061i \(-0.553209\pi\)
0.770762 + 0.637123i \(0.219876\pi\)
\(348\) 0 0
\(349\) 10.3923i 0.556287i 0.960539 + 0.278144i \(0.0897191\pi\)
−0.960539 + 0.278144i \(0.910281\pi\)
\(350\) −0.535898 + 7.46410i −0.0286450 + 0.398973i
\(351\) 0 0
\(352\) 1.46410 + 5.46410i 0.0780369 + 0.291238i
\(353\) 25.5000 14.7224i 1.35723 0.783596i 0.367979 0.929834i \(-0.380050\pi\)
0.989249 + 0.146238i \(0.0467166\pi\)
\(354\) 0 0
\(355\) 12.1244 21.0000i 0.643494 1.11456i
\(356\) −31.1769 −1.65237
\(357\) 0 0
\(358\) 19.0000 19.0000i 1.00418 1.00418i
\(359\) −19.9186 11.5000i −1.05126 0.606947i −0.128260 0.991741i \(-0.540939\pi\)
−0.923003 + 0.384794i \(0.874273\pi\)
\(360\) 0 0
\(361\) −4.00000 6.92820i −0.210526 0.364642i
\(362\) 2.53590 + 9.46410i 0.133284 + 0.497422i
\(363\) 0 0
\(364\) 6.00000 17.3205i 0.314485 0.907841i
\(365\) 15.0000 0.785136
\(366\) 0 0
\(367\) 0.866025 + 1.50000i 0.0452062 + 0.0782994i 0.887743 0.460339i \(-0.152272\pi\)
−0.842537 + 0.538639i \(0.818939\pi\)
\(368\) −3.46410 + 2.00000i −0.180579 + 0.104257i
\(369\) 0 0
\(370\) −5.19615 + 5.19615i −0.270135 + 0.270135i
\(371\) −0.866025 + 2.50000i −0.0449618 + 0.129794i
\(372\) 0 0
\(373\) 14.5000 25.1147i 0.750782 1.30039i −0.196663 0.980471i \(-0.563010\pi\)
0.947444 0.319921i \(-0.103656\pi\)
\(374\) −0.633975 + 2.36603i −0.0327820 + 0.122344i
\(375\) 0 0
\(376\) 6.33975 + 23.6603i 0.326947 + 1.22018i
\(377\) 13.8564i 0.713641i
\(378\) 0 0
\(379\) 8.00000i 0.410932i 0.978664 + 0.205466i \(0.0658711\pi\)
−0.978664 + 0.205466i \(0.934129\pi\)
\(380\) −9.00000 + 15.5885i −0.461690 + 0.799671i
\(381\) 0 0
\(382\) 1.36603 + 0.366025i 0.0698919 + 0.0187275i
\(383\) 2.59808 4.50000i 0.132755 0.229939i −0.791982 0.610544i \(-0.790951\pi\)
0.924738 + 0.380605i \(0.124284\pi\)
\(384\) 0 0
\(385\) 3.00000 + 3.46410i 0.152894 + 0.176547i
\(386\) 15.0000 + 15.0000i 0.763480 + 0.763480i
\(387\) 0 0
\(388\) −17.3205 30.0000i −0.879316 1.52302i
\(389\) −9.50000 16.4545i −0.481669 0.834275i 0.518110 0.855314i \(-0.326636\pi\)
−0.999779 + 0.0210389i \(0.993303\pi\)
\(390\) 0 0
\(391\) −1.73205 −0.0875936
\(392\) 11.8564 + 15.8564i 0.598839 + 0.800869i
\(393\) 0 0
\(394\) −21.8564 + 5.85641i −1.10111 + 0.295041i
\(395\) 7.79423 + 13.5000i 0.392170 + 0.679259i
\(396\) 0 0
\(397\) 16.5000 + 9.52628i 0.828111 + 0.478110i 0.853206 0.521575i \(-0.174655\pi\)
−0.0250943 + 0.999685i \(0.507989\pi\)
\(398\) −22.5167 22.5167i −1.12866 1.12866i
\(399\) 0 0
\(400\) −8.00000 −0.400000
\(401\) −11.5000 + 19.9186i −0.574283 + 0.994687i 0.421837 + 0.906672i \(0.361386\pi\)
−0.996119 + 0.0880147i \(0.971948\pi\)
\(402\) 0 0
\(403\) 5.19615 3.00000i 0.258839 0.149441i
\(404\) 8.66025 15.0000i 0.430864 0.746278i
\(405\) 0 0
\(406\) 12.3923 + 8.39230i 0.615020 + 0.416503i
\(407\) 3.00000i 0.148704i
\(408\) 0 0
\(409\) 22.5000 12.9904i 1.11255 0.642333i 0.173064 0.984911i \(-0.444633\pi\)
0.939490 + 0.342578i \(0.111300\pi\)
\(410\) −2.19615 + 8.19615i −0.108460 + 0.404779i
\(411\) 0 0
\(412\) 17.3205i 0.853320i
\(413\) 4.50000 12.9904i 0.221431 0.639215i
\(414\) 0 0
\(415\) 20.7846 + 12.0000i 1.02028 + 0.589057i
\(416\) 18.9282 + 5.07180i 0.928032 + 0.248665i
\(417\) 0 0
\(418\) −1.90192 7.09808i −0.0930261 0.347178i
\(419\) −20.7846 −1.01539 −0.507697 0.861536i \(-0.669503\pi\)
−0.507697 + 0.861536i \(0.669503\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −3.66025 13.6603i −0.178178 0.664971i
\(423\) 0 0
\(424\) −2.73205 0.732051i −0.132680 0.0355515i
\(425\) −3.00000 1.73205i −0.145521 0.0840168i
\(426\) 0 0
\(427\) 2.59808 + 13.5000i 0.125730 + 0.653311i
\(428\) 26.0000 1.25676
\(429\) 0 0
\(430\) 1.26795 4.73205i 0.0611459 0.228200i
\(431\) 19.9186 11.5000i 0.959444 0.553936i 0.0634424 0.997985i \(-0.479792\pi\)
0.896002 + 0.444050i \(0.146459\pi\)
\(432\) 0 0
\(433\) 10.3923i 0.499422i −0.968320 0.249711i \(-0.919664\pi\)
0.968320 0.249711i \(-0.0803357\pi\)
\(434\) −0.464102 + 6.46410i −0.0222776 + 0.310287i
\(435\) 0 0
\(436\) −15.5885 9.00000i −0.746552 0.431022i
\(437\) 4.50000 2.59808i 0.215264 0.124283i
\(438\) 0 0
\(439\) 11.2583 19.5000i 0.537331 0.930684i −0.461716 0.887028i \(-0.652766\pi\)
0.999047 0.0436563i \(-0.0139007\pi\)
\(440\) −3.46410 + 3.46410i −0.165145 + 0.165145i
\(441\) 0 0
\(442\) 6.00000 + 6.00000i 0.285391 + 0.285391i
\(443\) 14.7224 + 8.50000i 0.699484 + 0.403847i 0.807155 0.590339i \(-0.201006\pi\)
−0.107671 + 0.994187i \(0.534339\pi\)
\(444\) 0 0
\(445\) −13.5000 23.3827i −0.639961 1.10845i
\(446\) −9.46410 + 2.53590i −0.448138 + 0.120078i
\(447\) 0 0
\(448\) −16.0000 + 13.8564i −0.755929 + 0.654654i
\(449\) −8.00000 −0.377543 −0.188772 0.982021i \(-0.560451\pi\)
−0.188772 + 0.982021i \(0.560451\pi\)
\(450\) 0 0
\(451\) −1.73205 3.00000i −0.0815591 0.141264i
\(452\) 27.7128 16.0000i 1.30350 0.752577i
\(453\) 0 0
\(454\) −19.0526 19.0526i −0.894181 0.894181i
\(455\) 15.5885 3.00000i 0.730798 0.140642i
\(456\) 0 0
\(457\) −7.50000 + 12.9904i −0.350835 + 0.607664i −0.986396 0.164386i \(-0.947436\pi\)
0.635561 + 0.772051i \(0.280769\pi\)
\(458\) −21.2942 5.70577i −0.995014 0.266613i
\(459\) 0 0
\(460\) −3.00000 1.73205i −0.139876 0.0807573i
\(461\) 17.3205i 0.806696i 0.915047 + 0.403348i \(0.132154\pi\)
−0.915047 + 0.403348i \(0.867846\pi\)
\(462\) 0 0
\(463\) 30.0000i 1.39422i 0.716965 + 0.697109i \(0.245531\pi\)
−0.716965 + 0.697109i \(0.754469\pi\)
\(464\) −8.00000 + 13.8564i −0.371391 + 0.643268i
\(465\) 0 0
\(466\) −2.56218 + 9.56218i −0.118691 + 0.442959i
\(467\) 4.33013 7.50000i 0.200374 0.347059i −0.748275 0.663389i \(-0.769117\pi\)
0.948649 + 0.316330i \(0.102451\pi\)
\(468\) 0 0
\(469\) −7.50000 2.59808i −0.346318 0.119968i
\(470\) −15.0000 + 15.0000i −0.691898 + 0.691898i
\(471\) 0 0
\(472\) 14.1962 + 3.80385i 0.653431 + 0.175086i
\(473\) 1.00000 + 1.73205i 0.0459800 + 0.0796398i
\(474\) 0 0
\(475\) 10.3923 0.476832
\(476\) −9.00000 + 1.73205i −0.412514 + 0.0793884i
\(477\) 0 0
\(478\) 7.32051 + 27.3205i 0.334832 + 1.24961i
\(479\) 6.06218 + 10.5000i 0.276988 + 0.479757i 0.970635 0.240558i \(-0.0773304\pi\)
−0.693647 + 0.720315i \(0.743997\pi\)
\(480\) 0 0
\(481\) −9.00000 5.19615i −0.410365 0.236924i
\(482\) −5.19615 + 5.19615i −0.236678 + 0.236678i
\(483\) 0 0
\(484\) 20.0000i 0.909091i
\(485\) 15.0000 25.9808i 0.681115 1.17973i
\(486\) 0 0
\(487\) 26.8468 15.5000i 1.21654 0.702372i 0.252367 0.967632i \(-0.418791\pi\)
0.964177 + 0.265260i \(0.0854576\pi\)
\(488\) −14.1962 + 3.80385i −0.642630 + 0.172192i
\(489\) 0 0
\(490\) −6.75833 + 15.7583i −0.305310 + 0.711889i
\(491\) 32.0000i 1.44414i 0.691820 + 0.722070i \(0.256809\pi\)
−0.691820 + 0.722070i \(0.743191\pi\)
\(492\) 0 0
\(493\) −6.00000 + 3.46410i −0.270226 + 0.156015i
\(494\) −24.5885 6.58846i −1.10629 0.296429i
\(495\) 0 0
\(496\) −6.92820 −0.311086
\(497\) −28.0000 + 24.2487i −1.25597 + 1.08770i
\(498\) 0 0
\(499\) −30.3109 17.5000i −1.35690 0.783408i −0.367697 0.929946i \(-0.619854\pi\)
−0.989205 + 0.146538i \(0.953187\pi\)
\(500\) −12.1244 21.0000i −0.542218 0.939149i
\(501\) 0 0
\(502\) −4.73205 + 1.26795i −0.211202 + 0.0565913i
\(503\) −6.92820 −0.308913 −0.154457 0.988000i \(-0.549363\pi\)
−0.154457 + 0.988000i \(0.549363\pi\)
\(504\) 0 0
\(505\) 15.0000 0.667491
\(506\) 1.36603 0.366025i 0.0607272 0.0162718i
\(507\) 0 0
\(508\) −6.00000 10.3923i −0.266207 0.461084i
\(509\) −10.5000 6.06218i −0.465404 0.268701i 0.248910 0.968527i \(-0.419928\pi\)
−0.714314 + 0.699825i \(0.753261\pi\)
\(510\) 0 0
\(511\) −21.6506 7.50000i −0.957768 0.331780i
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) 0 0
\(514\) −7.09808 1.90192i −0.313083 0.0838903i
\(515\) −12.9904 + 7.50000i −0.572425 + 0.330489i
\(516\) 0 0
\(517\) 8.66025i 0.380878i
\(518\) 10.0981 4.90192i 0.443684 0.215378i
\(519\) 0 0
\(520\) 4.39230 + 16.3923i 0.192615 + 0.718850i
\(521\) −1.50000 + 0.866025i −0.0657162 + 0.0379413i −0.532498 0.846431i \(-0.678747\pi\)
0.466782 + 0.884372i \(0.345413\pi\)
\(522\) 0 0
\(523\) −12.9904 + 22.5000i −0.568030 + 0.983856i 0.428731 + 0.903432i \(0.358961\pi\)
−0.996761 + 0.0804241i \(0.974373\pi\)
\(524\) 10.3923i 0.453990i
\(525\) 0 0
\(526\) −23.0000 + 23.0000i −1.00285 + 1.00285i
\(527\) −2.59808 1.50000i −0.113174 0.0653410i
\(528\) 0 0
\(529\) −11.0000 19.0526i −0.478261 0.828372i
\(530\) −0.633975 2.36603i −0.0275381 0.102774i
\(531\) 0 0
\(532\) 20.7846 18.0000i 0.901127 0.780399i
\(533\) −12.0000 −0.519778
\(534\) 0 0
\(535\) 11.2583 + 19.5000i 0.486740 + 0.843059i
\(536\) 2.19615 8.19615i 0.0948593 0.354020i
\(537\) 0 0
\(538\) −22.5167 + 22.5167i −0.970762 + 0.970762i
\(539\) −2.59808 6.50000i −0.111907 0.279975i
\(540\) 0 0
\(541\) 9.50000 16.4545i 0.408437 0.707433i −0.586278 0.810110i \(-0.699407\pi\)
0.994715 + 0.102677i \(0.0327407\pi\)
\(542\) −5.70577 + 21.2942i −0.245084 + 0.914665i
\(543\) 0 0
\(544\) −2.53590 9.46410i −0.108726 0.405770i
\(545\) 15.5885i 0.667736i
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 1.73205 + 1.00000i 0.0739895 + 0.0427179i
\(549\) 0 0
\(550\) 2.73205 + 0.732051i 0.116495 + 0.0312148i
\(551\) 10.3923 18.0000i 0.442727 0.766826i
\(552\) 0 0
\(553\) −4.50000 23.3827i −0.191359 0.994333i
\(554\) 13.0000 + 13.0000i 0.552317 + 0.552317i
\(555\) 0 0
\(556\) 12.0000 6.92820i 0.508913 0.293821i
\(557\) 18.5000 + 32.0429i 0.783870 + 1.35770i 0.929672 + 0.368389i \(0.120091\pi\)
−0.145802 + 0.989314i \(0.546576\pi\)
\(558\) 0 0
\(559\) 6.92820 0.293032
\(560\) −17.3205 6.00000i −0.731925 0.253546i
\(561\) 0 0
\(562\) 5.46410 1.46410i 0.230489 0.0617594i
\(563\) −11.2583 19.5000i −0.474482 0.821827i 0.525091 0.851046i \(-0.324031\pi\)
−0.999573 + 0.0292191i \(0.990698\pi\)
\(564\) 0 0
\(565\) 24.0000 + 13.8564i 1.00969 + 0.582943i
\(566\) 12.1244 + 12.1244i 0.509625 + 0.509625i
\(567\) 0 0
\(568\) −28.0000 28.0000i −1.17485 1.17485i
\(569\) −6.50000 + 11.2583i −0.272494 + 0.471974i −0.969500 0.245092i \(-0.921182\pi\)
0.697006 + 0.717066i \(0.254515\pi\)
\(570\) 0 0
\(571\) 18.1865 10.5000i 0.761083 0.439411i −0.0686016 0.997644i \(-0.521854\pi\)
0.829684 + 0.558233i \(0.188520\pi\)
\(572\) −6.00000 3.46410i −0.250873 0.144841i
\(573\) 0 0
\(574\) 7.26795 10.7321i 0.303358 0.447947i
\(575\) 2.00000i 0.0834058i
\(576\) 0 0
\(577\) −28.5000 + 16.4545i −1.18647 + 0.685009i −0.957503 0.288425i \(-0.906868\pi\)
−0.228968 + 0.973434i \(0.573535\pi\)
\(578\) −5.12436 + 19.1244i −0.213145 + 0.795468i
\(579\) 0 0
\(580\) −13.8564 −0.575356
\(581\) −24.0000 27.7128i −0.995688 1.14972i
\(582\) 0 0
\(583\) 0.866025 + 0.500000i 0.0358671 + 0.0207079i
\(584\) 6.33975 23.6603i 0.262341 0.979068i
\(585\) 0 0
\(586\) 7.60770 + 28.3923i 0.314271 + 1.17288i
\(587\) 6.92820 0.285958 0.142979 0.989726i \(-0.454332\pi\)
0.142979 + 0.989726i \(0.454332\pi\)
\(588\) 0 0
\(589\) 9.00000 0.370839
\(590\) 3.29423 + 12.2942i 0.135621 + 0.506145i
\(591\) 0 0
\(592\) 6.00000 + 10.3923i 0.246598 + 0.427121i
\(593\) 13.5000 + 7.79423i 0.554379 + 0.320071i 0.750886 0.660432i \(-0.229627\pi\)
−0.196508 + 0.980502i \(0.562960\pi\)
\(594\) 0 0
\(595\) −5.19615 6.00000i −0.213021 0.245976i
\(596\) 2.00000i 0.0819232i
\(597\) 0 0
\(598\) 1.26795 4.73205i 0.0518503 0.193508i
\(599\) 14.7224 8.50000i 0.601542 0.347301i −0.168106 0.985769i \(-0.553765\pi\)
0.769648 + 0.638468i \(0.220432\pi\)
\(600\) 0 0
\(601\) 38.1051i 1.55434i 0.629291 + 0.777170i \(0.283346\pi\)
−0.629291 + 0.777170i \(0.716654\pi\)
\(602\) −4.19615 + 6.19615i −0.171022 + 0.252536i
\(603\) 0 0
\(604\) −7.00000 + 12.1244i −0.284826 + 0.493333i
\(605\) −15.0000 + 8.66025i −0.609837 + 0.352089i
\(606\) 0 0
\(607\) 7.79423 13.5000i 0.316358 0.547948i −0.663367 0.748294i \(-0.730873\pi\)
0.979725 + 0.200346i \(0.0642066\pi\)
\(608\) 20.7846 + 20.7846i 0.842927 + 0.842927i
\(609\) 0 0
\(610\) −9.00000 9.00000i −0.364399 0.364399i
\(611\) −25.9808 15.0000i −1.05107 0.606835i
\(612\) 0 0
\(613\) 15.5000 + 26.8468i 0.626039 + 1.08433i 0.988339 + 0.152270i \(0.0486583\pi\)
−0.362300 + 0.932062i \(0.618008\pi\)
\(614\) −28.3923 + 7.60770i −1.14582 + 0.307022i
\(615\) 0 0
\(616\) 6.73205 3.26795i 0.271242 0.131669i
\(617\) −20.0000 −0.805170 −0.402585 0.915383i \(-0.631888\pi\)
−0.402585 + 0.915383i \(0.631888\pi\)
\(618\) 0 0
\(619\) 7.79423 + 13.5000i 0.313276 + 0.542611i 0.979070 0.203526i \(-0.0652400\pi\)
−0.665793 + 0.746136i \(0.731907\pi\)
\(620\) −3.00000 5.19615i −0.120483 0.208683i
\(621\) 0 0
\(622\) −8.66025 8.66025i −0.347245 0.347245i
\(623\) 7.79423 + 40.5000i 0.312269 + 1.62260i
\(624\) 0 0
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) 2.36603 + 0.633975i 0.0945654 + 0.0253387i
\(627\) 0 0
\(628\) 1.73205 3.00000i 0.0691164 0.119713i
\(629\) 5.19615i 0.207184i
\(630\) 0 0
\(631\) 30.0000i 1.19428i −0.802137 0.597141i \(-0.796303\pi\)
0.802137 0.597141i \(-0.203697\pi\)
\(632\) 24.5885 6.58846i 0.978076 0.262075i
\(633\) 0 0
\(634\) 4.02628 15.0263i 0.159904 0.596770i
\(635\) 5.19615 9.00000i 0.206203 0.357154i
\(636\) 0 0
\(637\) −24.0000 3.46410i −0.950915 0.137253i
\(638\) 4.00000 4.00000i 0.158362 0.158362i
\(639\) 0 0
\(640\) 5.07180 18.9282i 0.200480 0.748203i
\(641\) −6.50000 11.2583i −0.256735 0.444677i 0.708631 0.705580i \(-0.249313\pi\)
−0.965365 + 0.260902i \(0.915980\pi\)
\(642\) 0 0
\(643\) 13.8564 0.546443 0.273222 0.961951i \(-0.411911\pi\)
0.273222 + 0.961951i \(0.411911\pi\)
\(644\) 3.46410 + 4.00000i 0.136505 + 0.157622i
\(645\) 0 0
\(646\) 3.29423 + 12.2942i 0.129610 + 0.483710i
\(647\) 16.4545 + 28.5000i 0.646892 + 1.12045i 0.983861 + 0.178935i \(0.0572651\pi\)
−0.336968 + 0.941516i \(0.609402\pi\)
\(648\) 0 0
\(649\) −4.50000 2.59808i −0.176640 0.101983i
\(650\) 6.92820 6.92820i 0.271746 0.271746i
\(651\) 0 0
\(652\) 42.0000 1.64485
\(653\) 15.5000 26.8468i 0.606562 1.05060i −0.385241 0.922816i \(-0.625882\pi\)
0.991803 0.127780i \(-0.0407851\pi\)
\(654\) 0 0
\(655\) −7.79423 + 4.50000i −0.304546 + 0.175830i
\(656\) 12.0000 + 6.92820i 0.468521 + 0.270501i
\(657\) 0 0
\(658\) 29.1506 14.1506i 1.13641 0.551649i
\(659\) 38.0000i 1.48027i −0.672458 0.740135i \(-0.734762\pi\)
0.672458 0.740135i \(-0.265238\pi\)
\(660\) 0 0
\(661\) −34.5000 + 19.9186i −1.34189 + 0.774743i −0.987085 0.160196i \(-0.948788\pi\)
−0.354809 + 0.934939i \(0.615454\pi\)
\(662\) −9.56218 2.56218i −0.371645 0.0995819i
\(663\) 0 0
\(664\) 27.7128 27.7128i 1.07547 1.07547i
\(665\) 22.5000 + 7.79423i 0.872513 + 0.302247i
\(666\) 0 0
\(667\) 3.46410 + 2.00000i 0.134131 + 0.0774403i
\(668\) −30.0000 + 17.3205i −1.16073 + 0.670151i
\(669\) 0 0
\(670\) 7.09808 1.90192i 0.274223 0.0734777i
\(671\) 5.19615 0.200595
\(672\) 0 0
\(673\) 24.0000 0.925132 0.462566 0.886585i \(-0.346929\pi\)
0.462566 + 0.886585i \(0.346929\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 1.73205 1.00000i 0.0666173 0.0384615i
\(677\) 37.5000 + 21.6506i 1.44124 + 0.832102i 0.997933 0.0642672i \(-0.0204710\pi\)
0.443309 + 0.896369i \(0.353804\pi\)
\(678\) 0 0
\(679\) −34.6410 + 30.0000i −1.32940 + 1.15129i
\(680\) 6.00000 6.00000i 0.230089 0.230089i
\(681\) 0 0
\(682\) 2.36603 + 0.633975i 0.0905998 + 0.0242761i
\(683\) −21.6506 + 12.5000i −0.828439 + 0.478299i −0.853318 0.521391i \(-0.825413\pi\)
0.0248792 + 0.999690i \(0.492080\pi\)
\(684\) 0 0
\(685\) 1.73205i 0.0661783i
\(686\) 17.6340 19.3660i 0.673268 0.739398i
\(687\) 0 0
\(688\) −6.92820 4.00000i −0.264135 0.152499i
\(689\) 3.00000 1.73205i 0.114291 0.0659859i
\(690\) 0 0
\(691\) 6.06218 10.5000i 0.230616 0.399439i −0.727373 0.686242i \(-0.759259\pi\)
0.957990 + 0.286803i \(0.0925925\pi\)
\(692\) 24.2487 0.921798
\(693\) 0 0
\(694\) 13.0000 13.0000i 0.493473 0.493473i
\(695\) 10.3923 + 6.00000i 0.394203 + 0.227593i
\(696\) 0 0
\(697\) 3.00000 + 5.19615i 0.113633 + 0.196818i
\(698\) 3.80385 + 14.1962i 0.143978 + 0.537332i
\(699\) 0 0
\(700\) 2.00000 + 10.3923i 0.0755929 + 0.392792i
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) 0 0
\(703\) −7.79423 13.5000i −0.293965 0.509162i
\(704\) 4.00000 + 6.92820i 0.150756 + 0.261116i
\(705\) 0 0
\(706\) 29.4449 29.4449i 1.10817 1.10817i
\(707\) −21.6506 7.50000i −0.814256 0.282067i
\(708\) 0 0
\(709\) 4.50000 7.79423i 0.169001 0.292718i −0.769068 0.639167i \(-0.779279\pi\)
0.938069 + 0.346449i \(0.112613\pi\)
\(710\) 8.87564 33.1244i 0.333097 1.24313i
\(711\) 0 0
\(712\) −42.5885 + 11.4115i −1.59607 + 0.427666i
\(713\) 1.73205i 0.0648658i
\(714\) 0 0
\(715\) 6.00000i 0.224387i
\(716\) 19.0000 32.9090i 0.710063 1.22987i
\(717\) 0 0
\(718\) −31.4186 8.41858i −1.17253 0.314179i
\(719\) −12.9904 + 22.5000i −0.484459 + 0.839108i −0.999841 0.0178527i \(-0.994317\pi\)
0.515381 + 0.856961i \(0.327650\pi\)
\(720\) 0 0
\(721\) 22.5000 4.33013i 0.837944 0.161262i
\(722\) −8.00000 8.00000i −0.297729 0.297729i
\(723\) 0 0
\(724\) 6.92820 + 12.0000i 0.257485 + 0.445976i
\(725\) 4.00000 + 6.92820i 0.148556 + 0.257307i
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 1.85641 25.8564i 0.0688030 0.958302i
\(729\) 0 0
\(730\) 20.4904 5.49038i 0.758383 0.203208i
\(731\) −1.73205 3.00000i −0.0640622 0.110959i
\(732\) 0 0
\(733\) 37.5000 + 21.6506i 1.38509 + 0.799684i 0.992757 0.120137i \(-0.0383334\pi\)
0.392337 + 0.919822i \(0.371667\pi\)
\(734\) 1.73205 + 1.73205i 0.0639312 + 0.0639312i
\(735\) 0 0
\(736\) −4.00000 + 4.00000i −0.147442 + 0.147442i
\(737\) −1.50000 + 2.59808i −0.0552532 + 0.0957014i
\(738\) 0 0
\(739\) −44.1673 + 25.5000i −1.62472 + 0.938033i −0.639087 + 0.769135i \(0.720687\pi\)
−0.985634 + 0.168898i \(0.945979\pi\)
\(740\) −5.19615 + 9.00000i −0.191014 + 0.330847i
\(741\) 0 0
\(742\) −0.267949 + 3.73205i −0.00983672 + 0.137008i
\(743\) 34.0000i 1.24734i −0.781688 0.623670i \(-0.785641\pi\)
0.781688 0.623670i \(-0.214359\pi\)
\(744\) 0 0
\(745\) 1.50000 0.866025i 0.0549557 0.0317287i
\(746\) 10.6147 39.6147i 0.388633 1.45040i
\(747\) 0 0
\(748\) 3.46410i 0.126660i
\(749\) −6.50000 33.7750i −0.237505 1.23411i
\(750\) 0 0
\(751\) −21.6506 12.5000i −0.790043 0.456131i 0.0499348 0.998752i \(-0.484099\pi\)
−0.839978 + 0.542621i \(0.817432\pi\)
\(752\) 17.3205 + 30.0000i 0.631614 + 1.09399i
\(753\) 0 0
\(754\) −5.07180 18.9282i −0.184704 0.689325i
\(755\) −12.1244 −0.441250
\(756\) 0 0
\(757\) −48.0000 −1.74459 −0.872295 0.488980i \(-0.837369\pi\)
−0.872295 + 0.488980i \(0.837369\pi\)
\(758\) 2.92820 + 10.9282i 0.106357 + 0.396930i
\(759\) 0 0
\(760\) −6.58846 + 24.5885i −0.238988 + 0.891917i
\(761\) −16.5000 9.52628i −0.598125 0.345327i 0.170179 0.985413i \(-0.445565\pi\)
−0.768303 + 0.640086i \(0.778899\pi\)
\(762\) 0 0
\(763\) −7.79423 + 22.5000i −0.282170 + 0.814555i
\(764\) 2.00000 0.0723575
\(765\) 0 0
\(766\) 1.90192 7.09808i 0.0687193 0.256464i
\(767\) −15.5885 + 9.00000i −0.562867 + 0.324971i
\(768\) 0 0
\(769\) 3.46410i 0.124919i −0.998048 0.0624593i \(-0.980106\pi\)
0.998048 0.0624593i \(-0.0198944\pi\)
\(770\) 5.36603 + 3.63397i 0.193378 + 0.130959i
\(771\) 0 0
\(772\) 25.9808 + 15.0000i 0.935068 + 0.539862i
\(773\) −22.5000 + 12.9904i −0.809269 + 0.467232i −0.846702 0.532068i \(-0.821415\pi\)
0.0374331 + 0.999299i \(0.488082\pi\)
\(774\) 0 0
\(775\) −1.73205 + 3.00000i −0.0622171 + 0.107763i
\(776\) −34.6410 34.6410i −1.24354 1.24354i
\(777\) 0 0
\(778\) −19.0000 19.0000i −0.681183 0.681183i
\(779\) −15.5885 9.00000i −0.558514 0.322458i
\(780\) 0 0
\(781\) 7.00000 + 12.1244i 0.250480 + 0.433844i
\(782\) −2.36603 + 0.633975i −0.0846089 + 0.0226709i
\(783\) 0 0
\(784\) 22.0000 + 17.3205i 0.785714 + 0.618590i
\(785\) 3.00000 0.107075
\(786\) 0 0
\(787\) −2.59808 4.50000i −0.0926114 0.160408i 0.815998