Properties

Label 1050.2.o.i.949.2
Level $1050$
Weight $2$
Character 1050.949
Analytic conductor $8.384$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.o (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 949.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1050.949
Dual form 1050.2.o.i.499.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(1.73205 - 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000 q^{6} +(1.73205 - 2.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{11} +(0.866025 - 0.500000i) q^{12} +1.00000i q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.866025 + 0.500000i) q^{18} +(-1.50000 - 2.59808i) q^{19} +(2.50000 - 0.866025i) q^{21} -1.00000i q^{22} +(6.06218 - 3.50000i) q^{23} +(0.500000 - 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{26} +1.00000i q^{27} +(-0.866025 - 2.50000i) q^{28} +8.00000 q^{29} +(1.00000 - 1.73205i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.866025 - 0.500000i) q^{33} +1.00000 q^{36} +(-9.52628 + 5.50000i) q^{37} +(-2.59808 - 1.50000i) q^{38} +(-0.500000 + 0.866025i) q^{39} -11.0000 q^{41} +(1.73205 - 2.00000i) q^{42} +8.00000i q^{43} +(-0.500000 - 0.866025i) q^{44} +(3.50000 - 6.06218i) q^{46} +(4.33013 - 2.50000i) q^{47} -1.00000i q^{48} +(-1.00000 - 6.92820i) q^{49} +(0.866025 + 0.500000i) q^{52} +(9.52628 + 5.50000i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.00000 - 1.73205i) q^{56} -3.00000i q^{57} +(6.92820 - 4.00000i) q^{58} +(2.00000 - 3.46410i) q^{59} -2.00000i q^{62} +(2.59808 + 0.500000i) q^{63} -1.00000 q^{64} +(0.500000 - 0.866025i) q^{66} +7.00000 q^{69} -6.00000 q^{71} +(0.866025 - 0.500000i) q^{72} +(5.19615 + 3.00000i) q^{73} +(-5.50000 + 9.52628i) q^{74} -3.00000 q^{76} +(-0.866025 - 2.50000i) q^{77} +1.00000i q^{78} +(-4.00000 - 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-9.52628 + 5.50000i) q^{82} +8.00000i q^{83} +(0.500000 - 2.59808i) q^{84} +(4.00000 + 6.92820i) q^{86} +(6.92820 + 4.00000i) q^{87} +(-0.866025 - 0.500000i) q^{88} +(-5.00000 - 8.66025i) q^{89} +(2.00000 + 1.73205i) q^{91} -7.00000i q^{92} +(1.73205 - 1.00000i) q^{93} +(2.50000 - 4.33013i) q^{94} +(-0.500000 - 0.866025i) q^{96} +16.0000i q^{97} +(-4.33013 - 5.50000i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + 4q^{6} + 2q^{9} + O(q^{10}) \) \( 4q + 2q^{4} + 4q^{6} + 2q^{9} + 2q^{11} + 2q^{14} - 2q^{16} - 6q^{19} + 10q^{21} + 2q^{24} + 2q^{26} + 32q^{29} + 4q^{31} + 4q^{36} - 2q^{39} - 44q^{41} - 2q^{44} + 14q^{46} - 4q^{49} + 2q^{54} - 8q^{56} + 8q^{59} - 4q^{64} + 2q^{66} + 28q^{69} - 24q^{71} - 22q^{74} - 12q^{76} - 16q^{79} - 2q^{81} + 2q^{84} + 16q^{86} - 20q^{89} + 8q^{91} + 10q^{94} - 2q^{96} + 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 1.00000 0.408248
\(7\) 1.73205 2.00000i 0.654654 0.755929i
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 0.500000 0.866025i 0.150756 0.261116i −0.780750 0.624844i \(-0.785163\pi\)
0.931505 + 0.363727i \(0.118496\pi\)
\(12\) 0.866025 0.500000i 0.250000 0.144338i
\(13\) 1.00000i 0.277350i 0.990338 + 0.138675i \(0.0442844\pi\)
−0.990338 + 0.138675i \(0.955716\pi\)
\(14\) 0.500000 2.59808i 0.133631 0.694365i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 0.866025 + 0.500000i 0.204124 + 0.117851i
\(19\) −1.50000 2.59808i −0.344124 0.596040i 0.641071 0.767482i \(-0.278491\pi\)
−0.985194 + 0.171442i \(0.945157\pi\)
\(20\) 0 0
\(21\) 2.50000 0.866025i 0.545545 0.188982i
\(22\) 1.00000i 0.213201i
\(23\) 6.06218 3.50000i 1.26405 0.729800i 0.290196 0.956967i \(-0.406280\pi\)
0.973856 + 0.227167i \(0.0729463\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) 0 0
\(26\) 0.500000 + 0.866025i 0.0980581 + 0.169842i
\(27\) 1.00000i 0.192450i
\(28\) −0.866025 2.50000i −0.163663 0.472456i
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) 1.00000 1.73205i 0.179605 0.311086i −0.762140 0.647412i \(-0.775851\pi\)
0.941745 + 0.336327i \(0.109185\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0.866025 0.500000i 0.150756 0.0870388i
\(34\) 0 0
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −9.52628 + 5.50000i −1.56611 + 0.904194i −0.569495 + 0.821995i \(0.692861\pi\)
−0.996616 + 0.0821995i \(0.973806\pi\)
\(38\) −2.59808 1.50000i −0.421464 0.243332i
\(39\) −0.500000 + 0.866025i −0.0800641 + 0.138675i
\(40\) 0 0
\(41\) −11.0000 −1.71791 −0.858956 0.512050i \(-0.828886\pi\)
−0.858956 + 0.512050i \(0.828886\pi\)
\(42\) 1.73205 2.00000i 0.267261 0.308607i
\(43\) 8.00000i 1.21999i 0.792406 + 0.609994i \(0.208828\pi\)
−0.792406 + 0.609994i \(0.791172\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) 0 0
\(46\) 3.50000 6.06218i 0.516047 0.893819i
\(47\) 4.33013 2.50000i 0.631614 0.364662i −0.149763 0.988722i \(-0.547851\pi\)
0.781377 + 0.624059i \(0.214518\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −1.00000 6.92820i −0.142857 0.989743i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.866025 + 0.500000i 0.120096 + 0.0693375i
\(53\) 9.52628 + 5.50000i 1.30854 + 0.755483i 0.981852 0.189651i \(-0.0607356\pi\)
0.326683 + 0.945134i \(0.394069\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0 0
\(56\) −2.00000 1.73205i −0.267261 0.231455i
\(57\) 3.00000i 0.397360i
\(58\) 6.92820 4.00000i 0.909718 0.525226i
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 0 0
\(61\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(62\) 2.00000i 0.254000i
\(63\) 2.59808 + 0.500000i 0.327327 + 0.0629941i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0.500000 0.866025i 0.0615457 0.106600i
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 0 0
\(69\) 7.00000 0.842701
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 5.19615 + 3.00000i 0.608164 + 0.351123i 0.772246 0.635323i \(-0.219133\pi\)
−0.164083 + 0.986447i \(0.552466\pi\)
\(74\) −5.50000 + 9.52628i −0.639362 + 1.10741i
\(75\) 0 0
\(76\) −3.00000 −0.344124
\(77\) −0.866025 2.50000i −0.0986928 0.284901i
\(78\) 1.00000i 0.113228i
\(79\) −4.00000 6.92820i −0.450035 0.779484i 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −9.52628 + 5.50000i −1.05200 + 0.607373i
\(83\) 8.00000i 0.878114i 0.898459 + 0.439057i \(0.144687\pi\)
−0.898459 + 0.439057i \(0.855313\pi\)
\(84\) 0.500000 2.59808i 0.0545545 0.283473i
\(85\) 0 0
\(86\) 4.00000 + 6.92820i 0.431331 + 0.747087i
\(87\) 6.92820 + 4.00000i 0.742781 + 0.428845i
\(88\) −0.866025 0.500000i −0.0923186 0.0533002i
\(89\) −5.00000 8.66025i −0.529999 0.917985i −0.999388 0.0349934i \(-0.988859\pi\)
0.469389 0.882992i \(-0.344474\pi\)
\(90\) 0 0
\(91\) 2.00000 + 1.73205i 0.209657 + 0.181568i
\(92\) 7.00000i 0.729800i
\(93\) 1.73205 1.00000i 0.179605 0.103695i
\(94\) 2.50000 4.33013i 0.257855 0.446619i
\(95\) 0 0
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) 16.0000i 1.62455i 0.583272 + 0.812277i \(0.301772\pi\)
−0.583272 + 0.812277i \(0.698228\pi\)
\(98\) −4.33013 5.50000i −0.437409 0.555584i
\(99\) 1.00000 0.100504
\(100\) 0 0
\(101\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 0 0
\(103\) −13.8564 + 8.00000i −1.36531 + 0.788263i −0.990325 0.138767i \(-0.955686\pi\)
−0.374987 + 0.927030i \(0.622353\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) 11.0000 1.06841
\(107\) 8.66025 5.00000i 0.837218 0.483368i −0.0190994 0.999818i \(-0.506080\pi\)
0.856318 + 0.516449i \(0.172747\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) 3.00000 5.19615i 0.287348 0.497701i −0.685828 0.727764i \(-0.740560\pi\)
0.973176 + 0.230063i \(0.0738931\pi\)
\(110\) 0 0
\(111\) −11.0000 −1.04407
\(112\) −2.59808 0.500000i −0.245495 0.0472456i
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) −1.50000 2.59808i −0.140488 0.243332i
\(115\) 0 0
\(116\) 4.00000 6.92820i 0.371391 0.643268i
\(117\) −0.866025 + 0.500000i −0.0800641 + 0.0462250i
\(118\) 4.00000i 0.368230i
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 + 8.66025i 0.454545 + 0.787296i
\(122\) 0 0
\(123\) −9.52628 5.50000i −0.858956 0.495918i
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) 0 0
\(126\) 2.50000 0.866025i 0.222718 0.0771517i
\(127\) 17.0000i 1.50851i 0.656584 + 0.754253i \(0.272001\pi\)
−0.656584 + 0.754253i \(0.727999\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −4.00000 + 6.92820i −0.352180 + 0.609994i
\(130\) 0 0
\(131\) 2.50000 + 4.33013i 0.218426 + 0.378325i 0.954327 0.298764i \(-0.0965744\pi\)
−0.735901 + 0.677089i \(0.763241\pi\)
\(132\) 1.00000i 0.0870388i
\(133\) −7.79423 1.50000i −0.675845 0.130066i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −15.5885 9.00000i −1.33181 0.768922i −0.346235 0.938148i \(-0.612540\pi\)
−0.985577 + 0.169226i \(0.945873\pi\)
\(138\) 6.06218 3.50000i 0.516047 0.297940i
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 5.00000 0.421076
\(142\) −5.19615 + 3.00000i −0.436051 + 0.251754i
\(143\) 0.866025 + 0.500000i 0.0724207 + 0.0418121i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) 0 0
\(146\) 6.00000 0.496564
\(147\) 2.59808 6.50000i 0.214286 0.536111i
\(148\) 11.0000i 0.904194i
\(149\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) 0 0
\(151\) −3.00000 + 5.19615i −0.244137 + 0.422857i −0.961888 0.273442i \(-0.911838\pi\)
0.717752 + 0.696299i \(0.245171\pi\)
\(152\) −2.59808 + 1.50000i −0.210732 + 0.121666i
\(153\) 0 0
\(154\) −2.00000 1.73205i −0.161165 0.139573i
\(155\) 0 0
\(156\) 0.500000 + 0.866025i 0.0400320 + 0.0693375i
\(157\) −6.06218 3.50000i −0.483814 0.279330i 0.238190 0.971219i \(-0.423446\pi\)
−0.722005 + 0.691888i \(0.756779\pi\)
\(158\) −6.92820 4.00000i −0.551178 0.318223i
\(159\) 5.50000 + 9.52628i 0.436178 + 0.755483i
\(160\) 0 0
\(161\) 3.50000 18.1865i 0.275839 1.43330i
\(162\) 1.00000i 0.0785674i
\(163\) 13.8564 8.00000i 1.08532 0.626608i 0.152992 0.988227i \(-0.451109\pi\)
0.932326 + 0.361619i \(0.117776\pi\)
\(164\) −5.50000 + 9.52628i −0.429478 + 0.743877i
\(165\) 0 0
\(166\) 4.00000 + 6.92820i 0.310460 + 0.537733i
\(167\) 3.00000i 0.232147i 0.993241 + 0.116073i \(0.0370308\pi\)
−0.993241 + 0.116073i \(0.962969\pi\)
\(168\) −0.866025 2.50000i −0.0668153 0.192879i
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 1.50000 2.59808i 0.114708 0.198680i
\(172\) 6.92820 + 4.00000i 0.528271 + 0.304997i
\(173\) −12.9904 + 7.50000i −0.987640 + 0.570214i −0.904568 0.426329i \(-0.859807\pi\)
−0.0830722 + 0.996544i \(0.526473\pi\)
\(174\) 8.00000 0.606478
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 3.46410 2.00000i 0.260378 0.150329i
\(178\) −8.66025 5.00000i −0.649113 0.374766i
\(179\) −9.50000 + 16.4545i −0.710063 + 1.22987i 0.254770 + 0.967002i \(0.418000\pi\)
−0.964833 + 0.262864i \(0.915333\pi\)
\(180\) 0 0
\(181\) −24.0000 −1.78391 −0.891953 0.452128i \(-0.850665\pi\)
−0.891953 + 0.452128i \(0.850665\pi\)
\(182\) 2.59808 + 0.500000i 0.192582 + 0.0370625i
\(183\) 0 0
\(184\) −3.50000 6.06218i −0.258023 0.446910i
\(185\) 0 0
\(186\) 1.00000 1.73205i 0.0733236 0.127000i
\(187\) 0 0
\(188\) 5.00000i 0.364662i
\(189\) 2.00000 + 1.73205i 0.145479 + 0.125988i
\(190\) 0 0
\(191\) 3.00000 + 5.19615i 0.217072 + 0.375980i 0.953912 0.300088i \(-0.0970159\pi\)
−0.736839 + 0.676068i \(0.763683\pi\)
\(192\) −0.866025 0.500000i −0.0625000 0.0360844i
\(193\) −19.0526 11.0000i −1.37143 0.791797i −0.380325 0.924853i \(-0.624188\pi\)
−0.991109 + 0.133056i \(0.957521\pi\)
\(194\) 8.00000 + 13.8564i 0.574367 + 0.994832i
\(195\) 0 0
\(196\) −6.50000 2.59808i −0.464286 0.185577i
\(197\) 1.00000i 0.0712470i 0.999365 + 0.0356235i \(0.0113417\pi\)
−0.999365 + 0.0356235i \(0.988658\pi\)
\(198\) 0.866025 0.500000i 0.0615457 0.0355335i
\(199\) −12.0000 + 20.7846i −0.850657 + 1.47338i 0.0299585 + 0.999551i \(0.490462\pi\)
−0.880616 + 0.473831i \(0.842871\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 13.8564 16.0000i 0.972529 1.12298i
\(204\) 0 0
\(205\) 0 0
\(206\) −8.00000 + 13.8564i −0.557386 + 0.965422i
\(207\) 6.06218 + 3.50000i 0.421350 + 0.243267i
\(208\) 0.866025 0.500000i 0.0600481 0.0346688i
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) 9.52628 5.50000i 0.654268 0.377742i
\(213\) −5.19615 3.00000i −0.356034 0.205557i
\(214\) 5.00000 8.66025i 0.341793 0.592003i
\(215\) 0 0
\(216\) 1.00000 0.0680414
\(217\) −1.73205 5.00000i −0.117579 0.339422i
\(218\) 6.00000i 0.406371i
\(219\) 3.00000 + 5.19615i 0.202721 + 0.351123i
\(220\) 0 0
\(221\) 0 0
\(222\) −9.52628 + 5.50000i −0.639362 + 0.369136i
\(223\) 12.0000i 0.803579i 0.915732 + 0.401790i \(0.131612\pi\)
−0.915732 + 0.401790i \(0.868388\pi\)
\(224\) −2.50000 + 0.866025i −0.167038 + 0.0578638i
\(225\) 0 0
\(226\) 3.00000 + 5.19615i 0.199557 + 0.345643i
\(227\) 6.92820 + 4.00000i 0.459841 + 0.265489i 0.711977 0.702202i \(-0.247800\pi\)
−0.252136 + 0.967692i \(0.581133\pi\)
\(228\) −2.59808 1.50000i −0.172062 0.0993399i
\(229\) 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i \(-0.0135930\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(230\) 0 0
\(231\) 0.500000 2.59808i 0.0328976 0.170941i
\(232\) 8.00000i 0.525226i
\(233\) 15.5885 9.00000i 1.02123 0.589610i 0.106773 0.994283i \(-0.465948\pi\)
0.914461 + 0.404674i \(0.132615\pi\)
\(234\) −0.500000 + 0.866025i −0.0326860 + 0.0566139i
\(235\) 0 0
\(236\) −2.00000 3.46410i −0.130189 0.225494i
\(237\) 8.00000i 0.519656i
\(238\) 0 0
\(239\) 18.0000 1.16432 0.582162 0.813073i \(-0.302207\pi\)
0.582162 + 0.813073i \(0.302207\pi\)
\(240\) 0 0
\(241\) −3.50000 + 6.06218i −0.225455 + 0.390499i −0.956456 0.291877i \(-0.905720\pi\)
0.731001 + 0.682376i \(0.239053\pi\)
\(242\) 8.66025 + 5.00000i 0.556702 + 0.321412i
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 0 0
\(245\) 0 0
\(246\) −11.0000 −0.701334
\(247\) 2.59808 1.50000i 0.165312 0.0954427i
\(248\) −1.73205 1.00000i −0.109985 0.0635001i
\(249\) −4.00000 + 6.92820i −0.253490 + 0.439057i
\(250\) 0 0
\(251\) 13.0000 0.820553 0.410276 0.911961i \(-0.365432\pi\)
0.410276 + 0.911961i \(0.365432\pi\)
\(252\) 1.73205 2.00000i 0.109109 0.125988i
\(253\) 7.00000i 0.440086i
\(254\) 8.50000 + 14.7224i 0.533337 + 0.923768i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 17.3205 10.0000i 1.08042 0.623783i 0.149413 0.988775i \(-0.452262\pi\)
0.931011 + 0.364992i \(0.118928\pi\)
\(258\) 8.00000i 0.498058i
\(259\) −5.50000 + 28.5788i −0.341753 + 1.77580i
\(260\) 0 0
\(261\) 4.00000 + 6.92820i 0.247594 + 0.428845i
\(262\) 4.33013 + 2.50000i 0.267516 + 0.154451i
\(263\) −20.7846 12.0000i −1.28163 0.739952i −0.304487 0.952517i \(-0.598485\pi\)
−0.977147 + 0.212565i \(0.931818\pi\)
\(264\) −0.500000 0.866025i −0.0307729 0.0533002i
\(265\) 0 0
\(266\) −7.50000 + 2.59808i −0.459855 + 0.159298i
\(267\) 10.0000i 0.611990i
\(268\) 0 0
\(269\) 10.0000 17.3205i 0.609711 1.05605i −0.381577 0.924337i \(-0.624619\pi\)
0.991288 0.131713i \(-0.0420477\pi\)
\(270\) 0 0
\(271\) −16.0000 27.7128i −0.971931 1.68343i −0.689713 0.724083i \(-0.742263\pi\)
−0.282218 0.959350i \(-0.591070\pi\)
\(272\) 0 0
\(273\) 0.866025 + 2.50000i 0.0524142 + 0.151307i
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) 3.50000 6.06218i 0.210675 0.364900i
\(277\) −19.0526 11.0000i −1.14476 0.660926i −0.197153 0.980373i \(-0.563170\pi\)
−0.947604 + 0.319447i \(0.896503\pi\)
\(278\) −17.3205 + 10.0000i −1.03882 + 0.599760i
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) −1.00000 −0.0596550 −0.0298275 0.999555i \(-0.509496\pi\)
−0.0298275 + 0.999555i \(0.509496\pi\)
\(282\) 4.33013 2.50000i 0.257855 0.148873i
\(283\) 12.1244 + 7.00000i 0.720718 + 0.416107i 0.815017 0.579437i \(-0.196728\pi\)
−0.0942988 + 0.995544i \(0.530061\pi\)
\(284\) −3.00000 + 5.19615i −0.178017 + 0.308335i
\(285\) 0 0
\(286\) 1.00000 0.0591312
\(287\) −19.0526 + 22.0000i −1.12464 + 1.29862i
\(288\) 1.00000i 0.0589256i
\(289\) −8.50000 14.7224i −0.500000 0.866025i
\(290\) 0 0
\(291\) −8.00000 + 13.8564i −0.468968 + 0.812277i
\(292\) 5.19615 3.00000i 0.304082 0.175562i
\(293\) 27.0000i 1.57736i 0.614806 + 0.788678i \(0.289234\pi\)
−0.614806 + 0.788678i \(0.710766\pi\)
\(294\) −1.00000 6.92820i −0.0583212 0.404061i
\(295\) 0 0
\(296\) 5.50000 + 9.52628i 0.319681 + 0.553704i
\(297\) 0.866025 + 0.500000i 0.0502519 + 0.0290129i
\(298\) 0 0
\(299\) 3.50000 + 6.06218i 0.202410 + 0.350585i
\(300\) 0 0
\(301\) 16.0000 + 13.8564i 0.922225 + 0.798670i
\(302\) 6.00000i 0.345261i
\(303\) 0 0
\(304\) −1.50000 + 2.59808i −0.0860309 + 0.149010i
\(305\) 0 0
\(306\) 0 0
\(307\) 20.0000i 1.14146i −0.821138 0.570730i \(-0.806660\pi\)
0.821138 0.570730i \(-0.193340\pi\)
\(308\) −2.59808 0.500000i −0.148039 0.0284901i
\(309\) −16.0000 −0.910208
\(310\) 0 0
\(311\) −6.00000 + 10.3923i −0.340229 + 0.589294i −0.984475 0.175525i \(-0.943838\pi\)
0.644246 + 0.764818i \(0.277171\pi\)
\(312\) 0.866025 + 0.500000i 0.0490290 + 0.0283069i
\(313\) −10.3923 + 6.00000i −0.587408 + 0.339140i −0.764072 0.645131i \(-0.776803\pi\)
0.176664 + 0.984271i \(0.443469\pi\)
\(314\) −7.00000 −0.395033
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 15.5885 9.00000i 0.875535 0.505490i 0.00635137 0.999980i \(-0.497978\pi\)
0.869184 + 0.494489i \(0.164645\pi\)
\(318\) 9.52628 + 5.50000i 0.534207 + 0.308425i
\(319\) 4.00000 6.92820i 0.223957 0.387905i
\(320\) 0 0
\(321\) 10.0000 0.558146
\(322\) −6.06218 17.5000i −0.337832 0.975237i
\(323\) 0 0
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 0 0
\(326\) 8.00000 13.8564i 0.443079 0.767435i
\(327\) 5.19615 3.00000i 0.287348 0.165900i
\(328\) 11.0000i 0.607373i
\(329\) 2.50000 12.9904i 0.137829 0.716183i
\(330\) 0 0
\(331\) 6.50000 + 11.2583i 0.357272 + 0.618814i 0.987504 0.157593i \(-0.0503735\pi\)
−0.630232 + 0.776407i \(0.717040\pi\)
\(332\) 6.92820 + 4.00000i 0.380235 + 0.219529i
\(333\) −9.52628 5.50000i −0.522037 0.301398i
\(334\) 1.50000 + 2.59808i 0.0820763 + 0.142160i
\(335\) 0 0
\(336\) −2.00000 1.73205i −0.109109 0.0944911i
\(337\) 12.0000i 0.653682i 0.945079 + 0.326841i \(0.105984\pi\)
−0.945079 + 0.326841i \(0.894016\pi\)
\(338\) 10.3923 6.00000i 0.565267 0.326357i
\(339\) −3.00000 + 5.19615i −0.162938 + 0.282216i
\(340\) 0 0
\(341\) −1.00000 1.73205i −0.0541530 0.0937958i
\(342\) 3.00000i 0.162221i
\(343\) −15.5885 10.0000i −0.841698 0.539949i
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) −7.50000 + 12.9904i −0.403202 + 0.698367i
\(347\) 12.1244 + 7.00000i 0.650870 + 0.375780i 0.788789 0.614664i \(-0.210708\pi\)
−0.137920 + 0.990443i \(0.544042\pi\)
\(348\) 6.92820 4.00000i 0.371391 0.214423i
\(349\) −12.0000 −0.642345 −0.321173 0.947021i \(-0.604077\pi\)
−0.321173 + 0.947021i \(0.604077\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) −0.866025 + 0.500000i −0.0461593 + 0.0266501i
\(353\) −20.7846 12.0000i −1.10625 0.638696i −0.168397 0.985719i \(-0.553859\pi\)
−0.937856 + 0.347024i \(0.887192\pi\)
\(354\) 2.00000 3.46410i 0.106299 0.184115i
\(355\) 0 0
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 19.0000i 1.00418i
\(359\) 2.00000 + 3.46410i 0.105556 + 0.182828i 0.913965 0.405793i \(-0.133004\pi\)
−0.808409 + 0.588621i \(0.799671\pi\)
\(360\) 0 0
\(361\) 5.00000 8.66025i 0.263158 0.455803i
\(362\) −20.7846 + 12.0000i −1.09241 + 0.630706i
\(363\) 10.0000i 0.524864i
\(364\) 2.50000 0.866025i 0.131036 0.0453921i
\(365\) 0 0
\(366\) 0 0
\(367\) 21.6506 + 12.5000i 1.13015 + 0.652495i 0.943974 0.330021i \(-0.107056\pi\)
0.186180 + 0.982516i \(0.440389\pi\)
\(368\) −6.06218 3.50000i −0.316013 0.182450i
\(369\) −5.50000 9.52628i −0.286319 0.495918i
\(370\) 0 0
\(371\) 27.5000 9.52628i 1.42773 0.494580i
\(372\) 2.00000i 0.103695i
\(373\) 5.19615 3.00000i 0.269047 0.155334i −0.359408 0.933181i \(-0.617021\pi\)
0.628454 + 0.777847i \(0.283688\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −2.50000 4.33013i −0.128928 0.223309i
\(377\) 8.00000i 0.412021i
\(378\) 2.59808 + 0.500000i 0.133631 + 0.0257172i
\(379\) 19.0000 0.975964 0.487982 0.872854i \(-0.337733\pi\)
0.487982 + 0.872854i \(0.337733\pi\)
\(380\) 0 0
\(381\) −8.50000 + 14.7224i −0.435468 + 0.754253i
\(382\) 5.19615 + 3.00000i 0.265858 + 0.153493i
\(383\) 30.3109 17.5000i 1.54881 0.894208i 0.550581 0.834781i \(-0.314406\pi\)
0.998233 0.0594268i \(-0.0189273\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −22.0000 −1.11977
\(387\) −6.92820 + 4.00000i −0.352180 + 0.203331i
\(388\) 13.8564 + 8.00000i 0.703452 + 0.406138i
\(389\) 5.00000 8.66025i 0.253510 0.439092i −0.710980 0.703213i \(-0.751748\pi\)
0.964490 + 0.264120i \(0.0850816\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −6.92820 + 1.00000i −0.349927 + 0.0505076i
\(393\) 5.00000i 0.252217i
\(394\) 0.500000 + 0.866025i 0.0251896 + 0.0436297i
\(395\) 0 0
\(396\) 0.500000 0.866025i 0.0251259 0.0435194i
\(397\) −12.1244 + 7.00000i −0.608504 + 0.351320i −0.772380 0.635161i \(-0.780934\pi\)
0.163876 + 0.986481i \(0.447600\pi\)
\(398\) 24.0000i 1.20301i
\(399\) −6.00000 5.19615i −0.300376 0.260133i
\(400\) 0 0
\(401\) 2.50000 + 4.33013i 0.124844 + 0.216236i 0.921672 0.387970i \(-0.126824\pi\)
−0.796828 + 0.604206i \(0.793490\pi\)
\(402\) 0 0
\(403\) 1.73205 + 1.00000i 0.0862796 + 0.0498135i
\(404\) 0 0
\(405\) 0 0
\(406\) 4.00000 20.7846i 0.198517 1.03152i
\(407\) 11.0000i 0.545250i
\(408\) 0 0
\(409\) 1.00000 1.73205i 0.0494468 0.0856444i −0.840243 0.542211i \(-0.817588\pi\)
0.889689 + 0.456566i \(0.150921\pi\)
\(410\) 0 0
\(411\) −9.00000 15.5885i −0.443937 0.768922i
\(412\) 16.0000i 0.788263i
\(413\) −3.46410 10.0000i −0.170457 0.492068i
\(414\) 7.00000 0.344031
\(415\) 0 0
\(416\) 0.500000 0.866025i 0.0245145 0.0424604i
\(417\) −17.3205 10.0000i −0.848189 0.489702i
\(418\) −2.59808 + 1.50000i −0.127076 + 0.0733674i
\(419\) 5.00000 0.244266 0.122133 0.992514i \(-0.461027\pi\)
0.122133 + 0.992514i \(0.461027\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 4.33013 2.50000i 0.210787 0.121698i
\(423\) 4.33013 + 2.50000i 0.210538 + 0.121554i
\(424\) 5.50000 9.52628i 0.267104 0.462637i
\(425\) 0 0
\(426\) −6.00000 −0.290701
\(427\) 0 0
\(428\) 10.0000i 0.483368i
\(429\) 0.500000 + 0.866025i 0.0241402 + 0.0418121i
\(430\) 0 0
\(431\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) 0.866025 0.500000i 0.0416667 0.0240563i
\(433\) 32.0000i 1.53782i −0.639356 0.768911i \(-0.720799\pi\)
0.639356 0.768911i \(-0.279201\pi\)
\(434\) −4.00000 3.46410i −0.192006 0.166282i
\(435\) 0 0
\(436\) −3.00000 5.19615i −0.143674 0.248851i
\(437\) −18.1865 10.5000i −0.869980 0.502283i
\(438\) 5.19615 + 3.00000i 0.248282 + 0.143346i
\(439\) 16.0000 + 27.7128i 0.763638 + 1.32266i 0.940963 + 0.338508i \(0.109922\pi\)
−0.177325 + 0.984152i \(0.556744\pi\)
\(440\) 0 0
\(441\) 5.50000 4.33013i 0.261905 0.206197i
\(442\) 0 0
\(443\) 13.8564 8.00000i 0.658338 0.380091i −0.133306 0.991075i \(-0.542559\pi\)
0.791643 + 0.610984i \(0.209226\pi\)
\(444\) −5.50000 + 9.52628i −0.261018 + 0.452097i
\(445\) 0 0
\(446\) 6.00000 + 10.3923i 0.284108 + 0.492090i
\(447\) 0 0
\(448\) −1.73205 + 2.00000i −0.0818317 + 0.0944911i
\(449\) −11.0000 −0.519122 −0.259561 0.965727i \(-0.583578\pi\)
−0.259561 + 0.965727i \(0.583578\pi\)
\(450\) 0 0
\(451\) −5.50000 + 9.52628i −0.258985 + 0.448575i
\(452\) 5.19615 + 3.00000i 0.244406 + 0.141108i
\(453\) −5.19615 + 3.00000i −0.244137 + 0.140952i
\(454\) 8.00000 0.375459
\(455\) 0 0
\(456\) −3.00000 −0.140488
\(457\) 15.5885 9.00000i 0.729197 0.421002i −0.0889312 0.996038i \(-0.528345\pi\)
0.818128 + 0.575036i \(0.195012\pi\)
\(458\) 12.1244 + 7.00000i 0.566534 + 0.327089i
\(459\) 0 0
\(460\) 0 0
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) −0.866025 2.50000i −0.0402911 0.116311i
\(463\) 13.0000i 0.604161i −0.953282 0.302081i \(-0.902319\pi\)
0.953282 0.302081i \(-0.0976812\pi\)
\(464\) −4.00000 6.92820i −0.185695 0.321634i
\(465\) 0 0
\(466\) 9.00000 15.5885i 0.416917 0.722121i
\(467\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(468\) 1.00000i 0.0462250i
\(469\) 0 0
\(470\) 0 0
\(471\) −3.50000 6.06218i −0.161271 0.279330i
\(472\) −3.46410 2.00000i −0.159448 0.0920575i
\(473\) 6.92820 + 4.00000i 0.318559 + 0.183920i
\(474\) −4.00000 6.92820i −0.183726 0.318223i
\(475\) 0 0
\(476\) 0 0
\(477\) 11.0000i 0.503655i
\(478\) 15.5885 9.00000i 0.712999 0.411650i
\(479\) 11.0000 19.0526i 0.502603 0.870534i −0.497393 0.867526i \(-0.665709\pi\)
0.999995 0.00300810i \(-0.000957509\pi\)
\(480\) 0 0
\(481\) −5.50000 9.52628i −0.250778 0.434361i
\(482\) 7.00000i 0.318841i
\(483\) 12.1244 14.0000i 0.551677 0.637022i
\(484\) 10.0000 0.454545
\(485\) 0 0
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) −13.8564 8.00000i −0.627894 0.362515i 0.152042 0.988374i \(-0.451415\pi\)
−0.779936 + 0.625859i \(0.784748\pi\)
\(488\) 0 0
\(489\) 16.0000 0.723545
\(490\) 0 0
\(491\) 20.0000 0.902587 0.451294 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) −9.52628 + 5.50000i −0.429478 + 0.247959i
\(493\) 0 0
\(494\) 1.50000 2.59808i 0.0674882 0.116893i
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) −10.3923 + 12.0000i −0.466159 + 0.538274i
\(498\) 8.00000i 0.358489i
\(499\) −16.0000 27.7128i −0.716258 1.24060i −0.962472 0.271380i \(-0.912520\pi\)
0.246214 0.969216i \(-0.420813\pi\)
\(500\) 0 0
\(501\) −1.50000 + 2.59808i −0.0670151 + 0.116073i
\(502\) 11.2583 6.50000i 0.502484 0.290109i
\(503\) 36.0000i 1.60516i 0.596544 + 0.802580i \(0.296540\pi\)
−0.596544 + 0.802580i \(0.703460\pi\)
\(504\) 0.500000 2.59808i 0.0222718 0.115728i
\(505\) 0 0
\(506\) −3.50000 6.06218i −0.155594 0.269497i
\(507\) 10.3923 + 6.00000i 0.461538 + 0.266469i
\(508\) 14.7224 + 8.50000i 0.653202 + 0.377127i
\(509\) −17.0000 29.4449i −0.753512 1.30512i −0.946111 0.323843i \(-0.895025\pi\)
0.192599 0.981278i \(-0.438308\pi\)
\(510\) 0 0
\(511\) 15.0000 5.19615i 0.663561 0.229864i
\(512\) 1.00000i 0.0441942i
\(513\) 2.59808 1.50000i 0.114708 0.0662266i
\(514\) 10.0000 17.3205i 0.441081 0.763975i
\(515\) 0 0
\(516\) 4.00000 + 6.92820i 0.176090 + 0.304997i
\(517\) 5.00000i 0.219900i
\(518\) 9.52628 + 27.5000i 0.418561 + 1.20828i
\(519\) −15.0000 −0.658427
\(520\) 0 0
\(521\) 16.5000 28.5788i 0.722878 1.25206i −0.236963 0.971519i \(-0.576152\pi\)
0.959841 0.280543i \(-0.0905145\pi\)
\(522\) 6.92820 + 4.00000i 0.303239 + 0.175075i
\(523\) 1.73205 1.00000i 0.0757373 0.0437269i −0.461653 0.887061i \(-0.652744\pi\)
0.537390 + 0.843334i \(0.319410\pi\)
\(524\) 5.00000 0.218426
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 0 0
\(528\) −0.866025 0.500000i −0.0376889 0.0217597i
\(529\) 13.0000 22.5167i 0.565217 0.978985i
\(530\) 0 0
\(531\) 4.00000 0.173585
\(532\) −5.19615 + 6.00000i −0.225282 + 0.260133i
\(533\) 11.0000i 0.476463i
\(534\) −5.00000 8.66025i −0.216371 0.374766i
\(535\) 0 0
\(536\) 0 0
\(537\) −16.4545 + 9.50000i −0.710063 + 0.409955i
\(538\) 20.0000i 0.862261i
\(539\) −6.50000 2.59808i −0.279975 0.111907i
\(540\) 0 0
\(541\) 5.00000 + 8.66025i 0.214967 + 0.372333i 0.953262 0.302144i \(-0.0977023\pi\)
−0.738296 + 0.674477i \(0.764369\pi\)
\(542\) −27.7128 16.0000i −1.19037 0.687259i
\(543\) −20.7846 12.0000i −0.891953 0.514969i
\(544\) 0 0
\(545\) 0 0
\(546\) 2.00000 + 1.73205i 0.0855921 + 0.0741249i
\(547\) 16.0000i 0.684111i −0.939680 0.342055i \(-0.888877\pi\)
0.939680 0.342055i \(-0.111123\pi\)
\(548\) −15.5885 + 9.00000i −0.665906 + 0.384461i
\(549\) 0 0
\(550\) 0 0
\(551\) −12.0000 20.7846i −0.511217 0.885454i
\(552\) 7.00000i 0.297940i
\(553\) −20.7846 4.00000i −0.883852 0.170097i
\(554\) −22.0000 −0.934690
\(555\) 0 0
\(556\) −10.0000 + 17.3205i −0.424094 + 0.734553i
\(557\) −28.5788 16.5000i −1.21092 0.699127i −0.247964 0.968769i \(-0.579761\pi\)
−0.962961 + 0.269642i \(0.913095\pi\)
\(558\) 1.73205 1.00000i 0.0733236 0.0423334i
\(559\) −8.00000 −0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) −0.866025 + 0.500000i −0.0365311 + 0.0210912i
\(563\) 32.9090 + 19.0000i 1.38695 + 0.800755i 0.992970 0.118366i \(-0.0377655\pi\)
0.393977 + 0.919120i \(0.371099\pi\)
\(564\) 2.50000 4.33013i 0.105269 0.182331i
\(565\) 0 0
\(566\) 14.0000 0.588464
\(567\) 0.866025 + 2.50000i 0.0363696 + 0.104990i
\(568\) 6.00000i 0.251754i
\(569\) −4.50000 7.79423i −0.188650 0.326751i 0.756151 0.654398i \(-0.227078\pi\)
−0.944800 + 0.327647i \(0.893744\pi\)
\(570\) 0 0
\(571\) 16.0000 27.7128i 0.669579 1.15975i −0.308443 0.951243i \(-0.599808\pi\)
0.978022 0.208502i \(-0.0668588\pi\)
\(572\) 0.866025 0.500000i 0.0362103 0.0209061i
\(573\) 6.00000i 0.250654i
\(574\) −5.50000 + 28.5788i −0.229566 + 1.19286i
\(575\) 0 0
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −12.1244 7.00000i −0.504744 0.291414i 0.225927 0.974144i \(-0.427459\pi\)
−0.730670 + 0.682730i \(0.760792\pi\)
\(578\) −14.7224 8.50000i −0.612372 0.353553i
\(579\) −11.0000 19.0526i −0.457144 0.791797i
\(580\) 0 0
\(581\) 16.0000 + 13.8564i 0.663792 + 0.574861i
\(582\) 16.0000i 0.663221i
\(583\) 9.52628 5.50000i 0.394538 0.227787i
\(584\) 3.00000 5.19615i 0.124141 0.215018i
\(585\) 0 0
\(586\) 13.5000 + 23.3827i 0.557680 + 0.965930i
\(587\) 18.0000i 0.742940i 0.928445 + 0.371470i \(0.121146\pi\)
−0.928445 + 0.371470i \(0.878854\pi\)
\(588\) −4.33013 5.50000i −0.178571 0.226816i
\(589\) −6.00000 −0.247226
\(590\) 0 0
\(591\) −0.500000 + 0.866025i −0.0205673 + 0.0356235i
\(592\) 9.52628 + 5.50000i 0.391528 + 0.226049i
\(593\) 13.8564 8.00000i 0.569014 0.328521i −0.187741 0.982219i \(-0.560117\pi\)
0.756756 + 0.653698i \(0.226783\pi\)
\(594\) 1.00000 0.0410305
\(595\) 0 0
\(596\) 0 0
\(597\) −20.7846 + 12.0000i −0.850657 + 0.491127i
\(598\) 6.06218 + 3.50000i 0.247901 + 0.143126i
\(599\) 1.00000 1.73205i 0.0408589 0.0707697i −0.844873 0.534967i \(-0.820324\pi\)
0.885732 + 0.464198i \(0.153657\pi\)
\(600\) 0 0
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 20.7846 + 4.00000i 0.847117 + 0.163028i
\(603\) 0 0
\(604\) 3.00000 + 5.19615i 0.122068 + 0.211428i
\(605\) 0 0
\(606\) 0 0
\(607\) 32.0429 18.5000i 1.30058 0.750892i 0.320079 0.947391i \(-0.396291\pi\)
0.980504 + 0.196499i \(0.0629573\pi\)
\(608\) 3.00000i 0.121666i
\(609\) 20.0000 6.92820i 0.810441 0.280745i
\(610\) 0 0
\(611\) 2.50000 + 4.33013i 0.101139 + 0.175178i
\(612\) 0 0
\(613\) 35.5070 + 20.5000i 1.43412 + 0.827987i 0.997431 0.0716275i \(-0.0228193\pi\)
0.436684 + 0.899615i \(0.356153\pi\)
\(614\) −10.0000 17.3205i −0.403567 0.698999i
\(615\) 0 0
\(616\) −2.50000 + 0.866025i −0.100728 + 0.0348932i
\(617\) 28.0000i 1.12724i −0.826035 0.563619i \(-0.809409\pi\)
0.826035 0.563619i \(-0.190591\pi\)
\(618\) −13.8564 + 8.00000i −0.557386 + 0.321807i
\(619\) 14.5000 25.1147i 0.582804 1.00945i −0.412341 0.911030i \(-0.635289\pi\)
0.995145 0.0984169i \(-0.0313779\pi\)
\(620\) 0 0
\(621\) 3.50000 + 6.06218i 0.140450 + 0.243267i
\(622\) 12.0000i 0.481156i
\(623\) −25.9808 5.00000i −1.04090 0.200321i
\(624\) 1.00000 0.0400320
\(625\) 0 0
\(626\) −6.00000 + 10.3923i −0.239808 + 0.415360i
\(627\) −2.59808 1.50000i −0.103757 0.0599042i
\(628\) −6.06218 + 3.50000i −0.241907 + 0.139665i
\(629\) 0 0
\(630\) 0 0
\(631\) −26.0000 −1.03504 −0.517522 0.855670i \(-0.673145\pi\)
−0.517522 + 0.855670i \(0.673145\pi\)
\(632\) −6.92820 + 4.00000i −0.275589 + 0.159111i
\(633\) 4.33013 + 2.50000i 0.172107 + 0.0993661i
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) 0 0
\(636\) 11.0000 0.436178
\(637\) 6.92820 1.00000i 0.274505 0.0396214i
\(638\) 8.00000i 0.316723i
\(639\) −3.00000 5.19615i −0.118678 0.205557i
\(640\) 0 0
\(641\) 1.50000 2.59808i 0.0592464 0.102618i −0.834881 0.550431i \(-0.814464\pi\)
0.894127 + 0.447813i \(0.147797\pi\)
\(642\) 8.66025 5.00000i 0.341793 0.197334i
\(643\) 10.0000i 0.394362i −0.980367 0.197181i \(-0.936821\pi\)
0.980367 0.197181i \(-0.0631786\pi\)
\(644\) −14.0000 12.1244i −0.551677 0.477767i
\(645\) 0 0
\(646\) 0 0
\(647\) −14.7224 8.50000i −0.578799 0.334169i 0.181857 0.983325i \(-0.441789\pi\)
−0.760656 + 0.649155i \(0.775122\pi\)
\(648\) 0.866025 + 0.500000i 0.0340207 + 0.0196419i
\(649\) −2.00000 3.46410i −0.0785069 0.135978i
\(650\) 0 0
\(651\) 1.00000 5.19615i 0.0391931 0.203653i
\(652\) 16.0000i 0.626608i
\(653\) 6.06218 3.50000i 0.237231 0.136966i −0.376672 0.926347i \(-0.622932\pi\)
0.613904 + 0.789381i \(0.289598\pi\)
\(654\) 3.00000 5.19615i 0.117309 0.203186i
\(655\) 0 0
\(656\) 5.50000 + 9.52628i 0.214739 + 0.371939i
\(657\) 6.00000i 0.234082i
\(658\) −4.33013 12.5000i −0.168806 0.487301i
\(659\) −36.0000 −1.40236 −0.701180 0.712984i \(-0.747343\pi\)
−0.701180 + 0.712984i \(0.747343\pi\)
\(660\) 0 0
\(661\) 12.0000 20.7846i 0.466746 0.808428i −0.532533 0.846410i \(-0.678760\pi\)
0.999278 + 0.0379819i \(0.0120929\pi\)
\(662\) 11.2583 + 6.50000i 0.437567 + 0.252630i
\(663\) 0 0
\(664\) 8.00000 0.310460
\(665\) 0 0
\(666\) −11.0000 −0.426241
\(667\) 48.4974 28.0000i 1.87783 1.08416i
\(668\) 2.59808 + 1.50000i 0.100523 + 0.0580367i
\(669\) −6.00000 + 10.3923i −0.231973 + 0.401790i
\(670\) 0 0
\(671\) 0 0
\(672\) −2.59808 0.500000i −0.100223 0.0192879i
\(673\) 28.0000i 1.07932i 0.841883 + 0.539660i \(0.181447\pi\)
−0.841883 + 0.539660i \(0.818553\pi\)
\(674\) 6.00000 + 10.3923i 0.231111 + 0.400297i
\(675\) 0 0
\(676\) 6.00000 10.3923i 0.230769 0.399704i
\(677\) 11.2583 6.50000i 0.432693 0.249815i −0.267800 0.963474i \(-0.586297\pi\)
0.700493 + 0.713659i \(0.252963\pi\)
\(678\) 6.00000i 0.230429i
\(679\) 32.0000 + 27.7128i 1.22805 + 1.06352i
\(680\) 0 0
\(681\) 4.00000 + 6.92820i 0.153280 + 0.265489i
\(682\) −1.73205 1.00000i −0.0663237 0.0382920i
\(683\) −3.46410 2.00000i −0.132550 0.0765279i 0.432259 0.901750i \(-0.357717\pi\)
−0.564809 + 0.825222i \(0.691050\pi\)
\(684\) −1.50000 2.59808i −0.0573539 0.0993399i
\(685\) 0 0
\(686\) −18.5000 0.866025i −0.706333 0.0330650i
\(687\) 14.0000i 0.534133i
\(688\) 6.92820 4.00000i 0.264135 0.152499i
\(689\) −5.50000 + 9.52628i −0.209533 + 0.362922i
\(690\) 0 0
\(691\) 6.00000 + 10.3923i 0.228251 + 0.395342i 0.957290 0.289130i \(-0.0933661\pi\)
−0.729039 + 0.684472i \(0.760033\pi\)
\(692\) 15.0000i 0.570214i
\(693\) 1.73205 2.00000i 0.0657952 0.0759737i
\(694\) 14.0000 0.531433
\(695\) 0 0
\(696\) 4.00000 6.92820i 0.151620 0.262613i
\(697\) 0 0
\(698\) −10.3923 + 6.00000i −0.393355 + 0.227103i
\(699\) 18.0000 0.680823
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) −0.866025 + 0.500000i −0.0326860 + 0.0188713i
\(703\) 28.5788 + 16.5000i 1.07787 + 0.622309i
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) −24.0000 −0.903252
\(707\) 0 0
\(708\) 4.00000i 0.150329i
\(709\) 22.0000 + 38.1051i 0.826227 + 1.43107i 0.900978 + 0.433865i \(0.142851\pi\)
−0.0747503 + 0.997202i \(0.523816\pi\)
\(710\) 0 0
\(711\) 4.00000 6.92820i 0.150012 0.259828i
\(712\) −8.66025 + 5.00000i −0.324557 + 0.187383i
\(713\) 14.0000i 0.524304i
\(714\) 0 0
\(715\) 0 0
\(716\) 9.50000 + 16.4545i 0.355032 + 0.614933i
\(717\) 15.5885 + 9.00000i 0.582162 + 0.336111i
\(718\) 3.46410 + 2.00000i 0.129279 + 0.0746393i
\(719\) 1.00000 + 1.73205i 0.0372937 + 0.0645946i 0.884070 0.467355i \(-0.154793\pi\)
−0.846776 + 0.531949i \(0.821460\pi\)
\(720\) 0 0
\(721\) −8.00000 + 41.5692i −0.297936 + 1.54812i
\(722\) 10.0000i 0.372161i
\(723\) −6.06218 + 3.50000i −0.225455 + 0.130166i
\(724\) −12.0000 + 20.7846i −0.445976 + 0.772454i
\(725\) 0 0
\(726\) 5.00000 + 8.66025i 0.185567 + 0.321412i
\(727\) 11.0000i 0.407967i −0.978974 0.203984i \(-0.934611\pi\)
0.978974 0.203984i \(-0.0653890\pi\)
\(728\) 1.73205 2.00000i 0.0641941 0.0741249i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 9.52628 5.50000i 0.351861 0.203147i −0.313644 0.949541i \(-0.601550\pi\)
0.665505 + 0.746394i \(0.268216\pi\)
\(734\) 25.0000 0.922767
\(735\) 0 0
\(736\) −7.00000 −0.258023
\(737\) 0 0
\(738\) −9.52628 5.50000i −0.350667 0.202458i
\(739\) −9.50000 + 16.4545i −0.349463 + 0.605288i −0.986154 0.165831i \(-0.946969\pi\)
0.636691 + 0.771119i \(0.280303\pi\)
\(740\) 0 0
\(741\) 3.00000 0.110208
\(742\) 19.0526 22.0000i 0.699441 0.807645i
\(743\) 49.0000i 1.79764i 0.438322 + 0.898818i \(0.355573\pi\)
−0.438322 + 0.898818i \(0.644427\pi\)
\(744\) −1.00000 1.73205i −0.0366618 0.0635001i
\(745\) 0 0
\(746\) 3.00000 5.19615i 0.109838 0.190245i
\(747\) −6.92820 + 4.00000i −0.253490 + 0.146352i
\(748\) 0 0
\(749\) 5.00000 25.9808i 0.182696 0.949316i
\(750\) 0 0
\(751\) −13.0000 22.5167i −0.474377 0.821645i 0.525193 0.850983i \(-0.323993\pi\)
−0.999570 + 0.0293387i \(0.990660\pi\)
\(752\) −4.33013 2.50000i −0.157903 0.0911656i
\(753\) 11.2583 + 6.50000i 0.410276 + 0.236873i
\(754\) 4.00000 + 6.92820i 0.145671 + 0.252310i
\(755\) 0 0
\(756\) 2.50000 0.866025i 0.0909241 0.0314970i
\(757\) 2.00000i 0.0726912i −0.999339 0.0363456i \(-0.988428\pi\)
0.999339 0.0363456i \(-0.0115717\pi\)
\(758\) 16.4545 9.50000i 0.597654 0.345056i
\(759\) 3.50000 6.06218i 0.127042 0.220043i
\(760\) 0 0
\(761\) −13.5000 23.3827i −0.489375 0.847622i 0.510551 0.859848i \(-0.329442\pi\)
−0.999925 + 0.0122260i \(0.996108\pi\)
\(762\) 17.0000i 0.615845i
\(763\) −5.19615 15.0000i −0.188113 0.543036i
\(764\) 6.00000 0.217072
\(765\) 0 0
\(766\) 17.5000 30.3109i 0.632301 1.09518i
\(767\) 3.46410 + 2.00000i 0.125081 + 0.0722158i
\(768\) −0.866025 + 0.500000i −0.0312500 + 0.0180422i
\(769\) 5.00000 0.180305 0.0901523 0.995928i \(-0.471265\pi\)
0.0901523 + 0.995928i \(0.471265\pi\)
\(770\) 0 0
\(771\) 20.0000 0.720282
\(772\) −19.0526 + 11.0000i −0.685717 + 0.395899i
\(773\) −28.5788 16.5000i −1.02791 0.593464i −0.111524 0.993762i \(-0.535573\pi\)
−0.916385 + 0.400298i \(0.868907\pi\)
\(774\) −4.00000 + 6.92820i −0.143777 + 0.249029i
\(775\) 0 0
\(776\) 16.0000 0.574367
\(777\) −19.0526 + 22.0000i −0.683507 + 0.789246i
\(778\) 10.0000i 0.358517i
\(779\) 16.5000 + 28.5788i 0.591174 + 1.02394i
\(780\) 0 0
\(781\) −3.00000 + 5.19615i −0.107348 + 0.185933i
\(782\) 0 0
\(783\) 8.00000i 0.285897i
\(784\) −5.50000 + 4.33013i −0.196429 + 0.154647i
\(785\) 0 0
\(786\) 2.50000 + 4.33013i 0.0891720 + 0.154451i
\(787\) 19.0526 + 11.0000i 0.679150 + 0.392108i 0.799535 0.600620i \(-0.205079\pi\)
−0.120384 + 0.992727i \(0.538413\pi\)
\(788\) 0.866025 + 0.500000i 0.0308509 + 0.0178118i
\(789\) −12.0000 20.7846i −0.427211 0.739952i
\(790\) 0 0
\(791\) 12.0000 + 10.3923i 0.426671 + 0.369508i
\(792\) 1.00000i 0.0355335i
\(793\) 0 0
\(794\) −7.00000 + 12.1244i −0.248421 + 0.430277i
\(795\) 0 0