Properties

Label 252.2.bf.e.19.1
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 19.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 252.19
Dual form 252.2.bf.e.199.1

$q$-expansion

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 1.36603i −0.258819 0.965926i
\(3\) 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
\(10\) 0.633975 2.36603i 0.200480 0.748203i
\(11\) 0.866025 0.500000i 0.261116 0.150756i −0.363727 0.931505i \(-0.618496\pi\)
0.624844 + 0.780750i \(0.285163\pi\)
\(12\) 0 0
\(13\) 3.46410i 0.960769i 0.877058 + 0.480384i \(0.159503\pi\)
−0.877058 + 0.480384i \(0.840497\pi\)
\(14\) 2.09808 3.09808i 0.560734 0.827996i
\(15\) 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 \(-0.630073\pi\)
0.993399 0.114708i \(-0.0365932\pi\)
\(20\) −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 0.587565 0.809177i \(-0.300087\pi\)
−0.406986 + 0.913434i \(0.633420\pi\)
\(24\) 0 0
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) 4.73205 1.26795i 0.928032 0.248665i
\(27\) 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 0.933257 0.359211i \(-0.116954\pi\)
−0.777714 + 0.628619i \(0.783621\pi\)
\(32\) −5.46410 1.46410i −0.965926 0.258819i
\(33\) 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 \(0.245980\pi\)
\(38\) −7.09808 1.90192i −1.15146 0.308533i
\(39\) 0 0
\(40\) 1.26795 + 4.73205i 0.200480 + 0.748203i
\(41\) 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 \(0.0487319\pi\)
−0.988304 + 0.152499i \(0.951268\pi\)
\(44\) −1.00000 + 1.73205i −0.150756 + 0.261116i
\(45\) 0 0
\(46\) 0.366025 1.36603i 0.0539675 0.201409i
\(47\) 4.33013 7.50000i 0.631614 1.09399i −0.355608 0.934635i \(-0.615726\pi\)
0.987222 0.159352i \(-0.0509405\pi\)
\(48\) 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
\(56\) −0.535898 + 7.46410i −0.0716124 + 0.997433i
\(57\) 0 0
\(58\) 1.46410 + 5.46410i 0.192246 + 0.717472i
\(59\) −2.59808 4.50000i −0.338241 0.585850i 0.645861 0.763455i \(-0.276498\pi\)
−0.984102 + 0.177605i \(0.943165\pi\)
\(60\) 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 −0.650236 0.759733i \(-0.725330\pi\)
0.332830 + 0.942987i \(0.391996\pi\)
\(68\) −1.73205 + 3.00000i −0.210042 + 0.363803i
\(69\) 0 0
\(70\) 5.83013 2.83013i 0.696833 0.338265i
\(71\) 14.0000i 1.66149i 0.556650 + 0.830747i \(0.312086\pi\)
−0.556650 + 0.830747i \(0.687914\pi\)
\(72\) 0 0
\(73\) 7.50000 4.33013i 0.877809 0.506803i 0.00787336 0.999969i \(-0.497494\pi\)
0.869935 + 0.493166i \(0.164160\pi\)
\(74\) 4.09808 + 1.09808i 0.476392 + 0.127649i
\(75\) 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 −0.00727784 0.999974i \(-0.502317\pi\)
−0.869641 + 0.493684i \(0.835650\pi\)
\(80\) 6.00000 3.46410i 0.670820 0.387298i
\(81\) 0 0
\(82\) 4.73205 1.26795i 0.522568 0.140022i
\(83\) −13.8564 −1.52094 −0.760469 0.649374i \(-0.775031\pi\)
−0.760469 + 0.649374i \(0.775031\pi\)
\(84\) 0 0
\(85\) 3.00000 0.325396
\(86\) 2.73205 0.732051i 0.294605 0.0789391i
\(87\) 0 0
\(88\) 2.73205 + 0.732051i 0.291238 + 0.0780369i
\(89\) −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
\(94\) −11.8301 3.16987i −1.22018 0.326947i
\(95\) 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 \(-0.342000\pi\)
\(98\) 9.83013 1.16987i 0.992993 0.118175i
\(99\) 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 −0.569914 0.821705i \(-0.693023\pi\)
0.996574 + 0.0827075i \(0.0263567\pi\)
\(104\) −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 −0.155238 0.987877i \(-0.549614\pi\)
−0.933146 + 0.359498i \(0.882948\pi\)
\(108\) 0 0
\(109\) −4.50000 7.79423i −0.431022 0.746552i 0.565940 0.824447i \(-0.308513\pi\)
−0.996962 + 0.0778949i \(0.975180\pi\)
\(110\) −0.633975 2.36603i −0.0604471 0.225592i
\(111\) 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
\(122\) −1.90192 + 7.09808i −0.172192 + 0.642630i
\(123\) 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 \(0.0857705\pi\)
−0.963916 + 0.266207i \(0.914230\pi\)
\(128\) 10.9282 2.92820i 0.965926 0.258819i
\(129\) 0 0
\(130\) 8.19615 + 2.19615i 0.718850 + 0.192615i
\(131\) 2.59808 4.50000i 0.226995 0.393167i −0.729921 0.683531i \(-0.760443\pi\)
0.956916 + 0.290365i \(0.0937766\pi\)
\(132\) 0 0
\(133\) 13.5000 2.59808i 1.17060 0.225282i
\(134\) 3.00000 + 3.00000i 0.259161 + 0.259161i
\(135\) 0 0
\(136\) 4.73205 + 1.26795i 0.405770 + 0.108726i
\(137\) 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 \(-0.594927\pi\)
−0.293821 + 0.955860i \(0.594927\pi\)
\(140\) −6.00000 6.92820i −0.507093 0.585540i
\(141\) 0 0
\(142\) 19.1244 5.12436i 1.60488 0.430026i
\(143\) 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 −0.232623 0.972567i \(-0.574731\pi\)
0.725956 + 0.687741i \(0.241398\pi\)
\(152\) 14.1962 3.80385i 1.15146 0.308533i
\(153\) 0 0
\(154\) 0.267949 3.73205i 0.0215920 0.300737i
\(155\) 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 \(0.311315\pi\)
\(158\) −3.29423 + 12.2942i −0.262075 + 0.978076i
\(159\) 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 −0.427802 0.903873i \(-0.640712\pi\)
−0.996678 + 0.0814491i \(0.974045\pi\)
\(164\) −3.46410 6.00000i −0.270501 0.468521i
\(165\) 0 0
\(166\) 5.07180 + 18.9282i 0.393648 + 1.46911i
\(167\) 17.3205 1.34030 0.670151 0.742225i \(-0.266230\pi\)
0.670151 + 0.742225i \(0.266230\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −1.09808 4.09808i −0.0842186 0.314308i
\(171\) 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
\(178\) −5.70577 + 21.2942i −0.427666 + 1.59607i
\(179\) −16.4545 + 9.50000i −1.22987 + 0.710063i −0.967002 0.254770i \(-0.918000\pi\)
−0.262864 + 0.964833i \(0.584667\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i 0.966282 + 0.257485i \(0.0828937\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 10.7321 + 7.26795i 0.795513 + 0.538736i
\(183\) 0 0
\(184\) 0.732051 + 2.73205i 0.0539675 + 0.201409i
\(185\) −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 0.468341 0.883548i \(-0.344852\pi\)
−0.531004 + 0.847369i \(0.678185\pi\)
\(192\) 0 0
\(193\) 7.50000 + 12.9904i 0.539862 + 0.935068i 0.998911 + 0.0466572i \(0.0148568\pi\)
−0.459049 + 0.888411i \(0.651810\pi\)
\(194\) −23.6603 + 6.33975i −1.69871 + 0.455167i
\(195\) 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 \(0.127485\pi\)
−0.122782 + 0.992434i \(0.539182\pi\)
\(200\) 1.46410 5.46410i 0.103528 0.386370i
\(201\) 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
\(206\) −11.8301 3.16987i −0.824244 0.220856i
\(207\) 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 \(0.111855\pi\)
−0.938891 + 0.344214i \(0.888145\pi\)
\(212\) 1.73205 + 1.00000i 0.118958 + 0.0686803i
\(213\) 0 0
\(214\) −4.75833 + 17.7583i −0.325273 + 1.21393i
\(215\) −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 \(-0.425482\pi\)
0.231973 + 0.972722i \(0.425482\pi\)
\(224\) −6.53590 13.4641i −0.436698 0.899608i
\(225\) 0 0
\(226\) −5.85641 21.8564i −0.389562 1.45387i
\(227\) 9.52628 + 16.5000i 0.632281 + 1.09514i 0.987084 + 0.160202i \(0.0512147\pi\)
−0.354803 + 0.934941i \(0.615452\pi\)
\(228\) 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
\(238\) 0.464102 6.46410i 0.0300832 0.419005i
\(239\) 20.0000i 1.29369i −0.762620 0.646846i \(-0.776088\pi\)
0.762620 0.646846i \(-0.223912\pi\)
\(240\) 0 0
\(241\) −4.50000 + 2.59808i −0.289870 + 0.167357i −0.637883 0.770133i \(-0.720190\pi\)
0.348013 + 0.937490i \(0.386857\pi\)
\(242\) 13.6603 + 3.66025i 0.878114 + 0.235290i
\(243\) 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
\(248\) −1.26795 + 4.73205i −0.0805149 + 0.300486i
\(249\) 0 0
\(250\) −16.5622 + 4.43782i −1.04748 + 0.280673i
\(251\) 3.46410 0.218652 0.109326 0.994006i \(-0.465131\pi\)
0.109326 + 0.994006i \(0.465131\pi\)
\(252\) 0 0
\(253\) 1.00000 0.0628695
\(254\) 8.19615 2.19615i 0.514272 0.137799i
\(255\) 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
\(262\) −7.09808 1.90192i −0.438521 0.117501i
\(263\) 19.9186 11.5000i 1.22823 0.709120i 0.261573 0.965184i \(-0.415759\pi\)
0.966660 + 0.256063i \(0.0824256\pi\)
\(264\) 0 0
\(265\) 1.73205i 0.106399i
\(266\) −8.49038 17.4904i −0.520579 1.07240i
\(267\) 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 −0.526073 0.850439i \(-0.676336\pi\)
0.999539 + 0.0303728i \(0.00966946\pi\)
\(272\) 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 \(0.705619\pi\)
\(278\) 2.53590 + 9.46410i 0.152093 + 0.567619i
\(279\) 0 0
\(280\) −7.26795 + 10.7321i −0.434343 + 0.641363i
\(281\) 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 0.627661 0.778487i \(-0.284012\pi\)
−0.988020 + 0.154327i \(0.950679\pi\)
\(284\) −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
\(290\) −2.53590 + 9.46410i −0.148913 + 0.555751i
\(291\) 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
\(296\) −8.19615 + 2.19615i −0.476392 + 0.127649i
\(297\) 0 0
\(298\) −1.36603 0.366025i −0.0791317 0.0212033i
\(299\) −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 \(-0.297896\pi\)
0.593120 + 0.805114i \(0.297896\pi\)
\(308\) −5.19615 + 1.00000i −0.296078 + 0.0569803i
\(309\) 0 0
\(310\) 4.09808 1.09808i 0.232755 0.0623665i
\(311\) 4.33013 + 7.50000i 0.245539 + 0.425286i 0.962283 0.272050i \(-0.0877017\pi\)
−0.716744 + 0.697336i \(0.754368\pi\)
\(312\) 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
\(322\) 3.36603 1.63397i 0.187581 0.0910578i
\(323\) 9.00000i 0.500773i
\(324\) 0 0
\(325\) 6.00000 3.46410i 0.332820 0.192154i
\(326\) −7.68653 + 28.6865i −0.425718 + 1.58880i
\(327\) 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 0.657264 0.753660i \(-0.271714\pi\)
−0.324057 + 0.946038i \(0.605047\pi\)
\(332\) 24.0000 13.8564i 1.31717 0.760469i
\(333\) 0 0
\(334\) −6.33975 23.6603i −0.346895 1.29463i
\(335\) −5.19615 −0.283896
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) −0.366025 1.36603i −0.0199092 0.0743020i
\(339\) 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
\(346\) 4.43782 16.5622i 0.238579 0.890388i
\(347\) −11.2583 + 6.50000i −0.604379 + 0.348938i −0.770762 0.637123i \(-0.780124\pi\)
0.166383 + 0.986061i \(0.446791\pi\)
\(348\) 0 0
\(349\) 10.3923i 0.556287i 0.960539 + 0.278144i \(0.0897191\pi\)
−0.960539 + 0.278144i \(0.910281\pi\)
\(350\) −7.46410 0.535898i −0.398973 0.0286450i
\(351\) 0 0
\(352\) −5.46410 + 1.46410i −0.291238 + 0.0780369i
\(353\) 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 0.923003 0.384794i \(-0.125727\pi\)
0.128260 + 0.991741i \(0.459061\pi\)
\(360\) 0 0
\(361\) −4.00000 6.92820i −0.210526 0.364642i
\(362\) 9.46410 2.53590i 0.497422 0.133284i
\(363\) 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 0.842537 0.538639i \(-0.181061\pi\)
−0.887743 + 0.460339i \(0.847728\pi\)
\(368\) 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 \(-0.103656\pi\)
\(374\) −2.36603 0.633975i −0.122344 0.0327820i
\(375\) 0 0
\(376\) 23.6603 6.33975i 1.22018 0.326947i
\(377\) 13.8564i 0.713641i
\(378\) 0 0
\(379\) 8.00000i 0.410932i −0.978664 0.205466i \(-0.934129\pi\)
0.978664 0.205466i \(-0.0658711\pi\)
\(380\) −9.00000 + 15.5885i −0.461690 + 0.799671i
\(381\) 0 0
\(382\) −0.366025 + 1.36603i −0.0187275 + 0.0698919i
\(383\) −2.59808 + 4.50000i −0.132755 + 0.229939i −0.924738 0.380605i \(-0.875716\pi\)
0.791982 + 0.610544i \(0.209049\pi\)
\(384\) 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
\(392\) −15.8564 + 11.8564i −0.800869 + 0.598839i
\(393\) 0 0
\(394\) 5.85641 + 21.8564i 0.295041 + 1.10111i
\(395\) −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
\(406\) −8.39230 + 12.3923i −0.416503 + 0.615020i
\(407\) 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 \(0.111300\pi\)
\(410\) 8.19615 + 2.19615i 0.404779 + 0.108460i
\(411\) 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
\(416\) 5.07180 18.9282i 0.248665 0.928032i
\(417\) 0 0
\(418\) −7.09808 + 1.90192i −0.347178 + 0.0930261i
\(419\) 20.7846 1.01539 0.507697 0.861536i \(-0.330497\pi\)
0.507697 + 0.861536i \(0.330497\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 13.6603 3.66025i 0.664971 0.178178i
\(423\) 0 0
\(424\) 0.732051 2.73205i 0.0355515 0.132680i
\(425\) −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
\(430\) 4.73205 + 1.26795i 0.228200 + 0.0611459i
\(431\) −19.9186 + 11.5000i −0.959444 + 0.553936i −0.896002 0.444050i \(-0.853541\pi\)
−0.0634424 + 0.997985i \(0.520208\pi\)
\(432\) 0 0
\(433\) 10.3923i 0.499422i −0.968320 0.249711i \(-0.919664\pi\)
0.968320 0.249711i \(-0.0803357\pi\)
\(434\) 6.46410 + 0.464102i 0.310287 + 0.0222776i
\(435\) 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 \(0.347234\pi\)
−0.999047 + 0.0436563i \(0.986099\pi\)
\(440\) 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 0.107671 0.994187i \(-0.465661\pi\)
−0.807155 + 0.590339i \(0.798994\pi\)
\(444\) 0 0
\(445\) −13.5000 23.3827i −0.639961 1.10845i
\(446\) −2.53590 9.46410i −0.120078 0.448138i
\(447\) 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 \(0.280769\pi\)
\(458\) −5.70577 + 21.2942i −0.266613 + 0.995014i
\(459\) 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 \(-0.754469\pi\)
0.716965 0.697109i \(-0.245531\pi\)
\(464\) −8.00000 + 13.8564i −0.371391 + 0.643268i
\(465\) 0 0
\(466\) 9.56218 + 2.56218i 0.442959 + 0.118691i
\(467\) −4.33013 + 7.50000i −0.200374 + 0.347059i −0.948649 0.316330i \(-0.897549\pi\)
0.748275 + 0.663389i \(0.230883\pi\)
\(468\) 0 0
\(469\) −7.50000 2.59808i −0.346318 0.119968i
\(470\) −15.0000 15.0000i −0.691898 0.691898i
\(471\) 0 0
\(472\) 3.80385 14.1962i 0.175086 0.653431i
\(473\) 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
\(478\) −27.3205 + 7.32051i −1.24961 + 0.334832i
\(479\) −6.06218 10.5000i −0.276988 0.479757i 0.693647 0.720315i \(-0.256003\pi\)
−0.970635 + 0.240558i \(0.922670\pi\)
\(480\) 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 −0.964177 0.265260i \(-0.914542\pi\)
−0.252367 + 0.967632i \(0.581209\pi\)
\(488\) −3.80385 14.1962i −0.172192 0.642630i
\(489\) 0 0
\(490\) 15.7583 + 6.75833i 0.711889 + 0.305310i
\(491\) 32.0000i 1.44414i −0.691820 0.722070i \(-0.743191\pi\)
0.691820 0.722070i \(-0.256809\pi\)
\(492\) 0 0
\(493\) −6.00000 + 3.46410i −0.270226 + 0.156015i
\(494\) 6.58846 24.5885i 0.296429 1.10629i
\(495\) 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 0.989205 0.146538i \(-0.0468131\pi\)
0.367697 + 0.929946i \(0.380146\pi\)
\(500\) 12.1244 + 21.0000i 0.542218 + 0.939149i
\(501\) 0 0
\(502\) −1.26795 4.73205i −0.0565913 0.211202i
\(503\) 6.92820 0.308913 0.154457 0.988000i \(-0.450637\pi\)
0.154457 + 0.988000i \(0.450637\pi\)
\(504\) 0 0
\(505\) 15.0000 0.667491
\(506\) −0.366025 1.36603i −0.0162718 0.0607272i
\(507\) 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
\(514\) −1.90192 + 7.09808i −0.0838903 + 0.313083i
\(515\) 12.9904 7.50000i 0.572425 0.330489i
\(516\) 0 0
\(517\) 8.66025i 0.380878i
\(518\) 4.90192 + 10.0981i 0.215378 + 0.443684i
\(519\) 0 0
\(520\) −16.3923 + 4.39230i −0.718850 + 0.192615i
\(521\) −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 \(-0.641039\pi\)
0.996761 0.0804241i \(-0.0256275\pi\)
\(524\) 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
\(530\) −2.36603 + 0.633975i −0.102774 + 0.0275381i
\(531\) 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
\(536\) −8.19615 2.19615i −0.354020 0.0948593i
\(537\) 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 \(0.0327407\pi\)
\(542\) −21.2942 5.70577i −0.914665 0.245084i
\(543\) 0 0
\(544\) −9.46410 + 2.53590i −0.405770 + 0.108726i
\(545\) 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
\(550\) −0.732051 + 2.73205i −0.0312148 + 0.116495i
\(551\) −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
\(562\) −1.46410 5.46410i −0.0617594 0.230489i
\(563\) 11.2583 + 19.5000i 0.474482 + 0.821827i 0.999573 0.0292191i \(-0.00930205\pi\)
−0.525091 + 0.851046i \(0.675969\pi\)
\(564\) 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 −0.829684 0.558233i \(-0.811480\pi\)
0.0686016 + 0.997644i \(0.478146\pi\)
\(572\) −6.00000 3.46410i −0.250873 0.144841i
\(573\) 0 0
\(574\) 10.7321 + 7.26795i 0.447947 + 0.303358i
\(575\) 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 \(0.573535\pi\)
\(578\) 19.1244 + 5.12436i 0.795468 + 0.213145i
\(579\) 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
\(584\) 23.6603 + 6.33975i 0.979068 + 0.262341i
\(585\) 0 0
\(586\) 28.3923 7.60770i 1.17288 0.314271i
\(587\) −6.92820 −0.285958 −0.142979 0.989726i \(-0.545668\pi\)
−0.142979 + 0.989726i \(0.545668\pi\)
\(588\) 0 0
\(589\) 9.00000 0.370839
\(590\) −12.2942 + 3.29423i −0.506145 + 0.135621i
\(591\) 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
\(598\) 4.73205 + 1.26795i 0.193508 + 0.0518503i
\(599\) −14.7224 + 8.50000i −0.601542 + 0.347301i −0.769648 0.638468i \(-0.779568\pi\)
0.168106 + 0.985769i \(0.446235\pi\)
\(600\) 0 0
\(601\) 38.1051i 1.55434i 0.629291 + 0.777170i \(0.283346\pi\)
−0.629291 + 0.777170i \(0.716654\pi\)
\(602\) 6.19615 + 4.19615i 0.252536 + 0.171022i
\(603\) 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 −0.979725 0.200346i \(-0.935793\pi\)
0.663367 + 0.748294i \(0.269127\pi\)
\(608\) −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 \(0.618008\pi\)
\(614\) −7.60770 28.3923i −0.307022 1.14582i
\(615\) 0 0
\(616\) 3.26795 + 6.73205i 0.131669 + 0.271242i
\(617\) −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 0.665793 0.746136i \(-0.268093\pi\)
−0.979070 + 0.203526i \(0.934760\pi\)
\(620\) −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
\(626\) 0.633975 2.36603i 0.0253387 0.0945654i
\(627\) 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 \(0.203697\pi\)
−0.802137 + 0.597141i \(0.796303\pi\)
\(632\) −6.58846 24.5885i −0.262075 0.978076i
\(633\) 0 0
\(634\) −15.0263 4.02628i −0.596770 0.159904i
\(635\) −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
\(640\) 18.9282 + 5.07180i 0.748203 + 0.200480i
\(641\) −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 \(-0.588089\pi\)
−0.273222 + 0.961951i \(0.588089\pi\)
\(644\) −3.46410 4.00000i −0.136505 0.157622i
\(645\) 0 0
\(646\) −12.2942 + 3.29423i −0.483710 + 0.129610i
\(647\) −16.4545 28.5000i −0.646892 1.12045i −0.983861 0.178935i \(-0.942735\pi\)
0.336968 0.941516i \(1.60940\pi\)
\(648\) 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
\(658\) −14.1506 29.1506i −0.551649 1.13641i
\(659\) 38.0000i 1.48027i 0.672458 + 0.740135i \(0.265238\pi\)
−0.672458 + 0.740135i \(0.734762\pi\)
\(660\) 0 0
\(661\) −34.5000 + 19.9186i −1.34189 + 0.774743i −0.987085 0.160196i \(-0.948788\pi\)
−0.354809 + 0.934939i \(0.615454\pi\)
\(662\) 2.56218 9.56218i 0.0995819 0.371645i
\(663\) 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
\(670\) 1.90192 + 7.09808i 0.0734777 + 0.274223i
\(671\) −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
\(682\) 0.633975 2.36603i 0.0242761 0.0905998i
\(683\) 21.6506 12.5000i 0.828439 0.478299i −0.0248792 0.999690i \(-0.507920\pi\)
0.853318 + 0.521391i \(0.174587\pi\)
\(684\) 0 0
\(685\) 1.73205i 0.0661783i
\(686\) 19.3660 + 17.6340i 0.739398 + 0.673268i
\(687\) 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 −0.957990 0.286803i \(-0.907407\pi\)
0.727373 + 0.686242i \(0.240741\pi\)
\(692\) −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
\(698\) 14.1962 3.80385i 0.537332 0.143978i
\(699\) 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 \(0.112613\pi\)
\(710\) 33.1244 + 8.87564i 1.24313 + 0.333097i
\(711\) 0 0
\(712\) −11.4115 42.5885i −0.427666 1.59607i
\(713\) 1.73205i 0.0648658i
\(714\) 0 0
\(715\) 6.00000i 0.224387i
\(716\) 19.0000 32.9090i 0.710063 1.22987i
\(717\) 0 0
\(718\) 8.41858 31.4186i 0.314179 1.17253i
\(719\) 12.9904 22.5000i 0.484459 0.839108i −0.515381 0.856961i \(-0.672350\pi\)
0.999841 + 0.0178527i \(0.00568298\pi\)
\(720\) 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 \(0.5\pi\)
\(728\) −25.8564 1.85641i −0.958302 0.0688030i
\(729\) 0 0
\(730\) −5.49038 20.4904i −0.203208 0.758383i
\(731\) 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 \(-0.279313\pi\)
0.985634 0.168898i \(-0.0540208\pi\)
\(740\) 5.19615 9.00000i 0.191014 0.330847i
\(741\) 0 0
\(742\) −3.73205 0.267949i −0.137008 0.00983672i
\(743\) 34.0000i 1.24734i 0.781688 + 0.623670i \(0.214359\pi\)
−0.781688 + 0.623670i \(0.785641\pi\)
\(744\) 0 0
\(745\) 1.50000 0.866025i 0.0549557 0.0317287i
\(746\) −39.6147 10.6147i −1.45040 0.388633i
\(747\) 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 0.839978 0.542621i \(-0.182568\pi\)
−0.0499348 + 0.998752i \(0.515901\pi\)
\(752\) −17.3205 30.0000i −0.631614 1.09399i
\(753\) 0 0
\(754\) −18.9282 + 5.07180i −0.689325 + 0.184704i
\(755\) 12.1244 0.441250
\(756\) 0 0
\(757\) −48.0000 −1.74459 −0.872295 0.488980i \(-0.837369\pi\)
−0.872295 + 0.488980i \(0.837369\pi\)
\(758\) −10.9282 + 2.92820i −0.396930 + 0.106357i
\(759\) 0 0
\(760\) 24.5885 + 6.58846i 0.891917 + 0.238988i
\(761\) −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
\(766\) 7.09808 + 1.90192i 0.256464 + 0.0687193i
\(767\) 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 \(-0.0198944\pi\)
\(770\) 3.63397 5.36603i 0.130959 0.193378i
\(771\) 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
\(782\) −0.633975 2.36603i −0.0226709 0.0846089i
\(783\) 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 0.908609 0.417647i \(-0.137