Properties

Label 576.2.bb.a.49.1
Level $576$
Weight $2$
Character 576.49
Analytic conductor $4.599$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(4\)
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 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 49.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 576.49
Dual form 576.2.bb.a.529.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.73205 q^{3} +(-1.86603 + 0.500000i) q^{5} +(-3.86603 + 2.23205i) q^{7} +3.00000 q^{9} +O(q^{10})\) \(q-1.73205 q^{3} +(-1.86603 + 0.500000i) q^{5} +(-3.86603 + 2.23205i) q^{7} +3.00000 q^{9} +(0.500000 - 1.86603i) q^{11} +(-0.598076 - 2.23205i) q^{13} +(3.23205 - 0.866025i) q^{15} +4.00000 q^{17} +(3.00000 - 3.00000i) q^{19} +(6.69615 - 3.86603i) q^{21} +(5.59808 + 3.23205i) q^{23} +(-1.09808 + 0.633975i) q^{25} -5.19615 q^{27} +(-0.866025 - 0.232051i) q^{29} +(4.59808 - 7.96410i) q^{31} +(-0.866025 + 3.23205i) q^{33} +(6.09808 - 6.09808i) q^{35} +(-4.26795 - 4.26795i) q^{37} +(1.03590 + 3.86603i) q^{39} +(0.696152 + 0.401924i) q^{41} +(1.69615 - 6.33013i) q^{43} +(-5.59808 + 1.50000i) q^{45} +(0.598076 + 1.03590i) q^{47} +(6.46410 - 11.1962i) q^{49} -6.92820 q^{51} +(5.73205 + 5.73205i) q^{53} +3.73205i q^{55} +(-5.19615 + 5.19615i) q^{57} +(1.50000 - 0.401924i) q^{59} +(-2.13397 - 0.571797i) q^{61} +(-11.5981 + 6.69615i) q^{63} +(2.23205 + 3.86603i) q^{65} +(2.23205 + 8.33013i) q^{67} +(-9.69615 - 5.59808i) q^{69} -2.92820i q^{71} -7.46410i q^{73} +(1.90192 - 1.09808i) q^{75} +(2.23205 + 8.33013i) q^{77} +(0.866025 + 1.50000i) q^{79} +9.00000 q^{81} +(14.1603 + 3.79423i) q^{83} +(-7.46410 + 2.00000i) q^{85} +(1.50000 + 0.401924i) q^{87} -15.8564i q^{89} +(7.29423 + 7.29423i) q^{91} +(-7.96410 + 13.7942i) q^{93} +(-4.09808 + 7.09808i) q^{95} +(-0.500000 - 0.866025i) q^{97} +(1.50000 - 5.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{5} - 12q^{7} + 12q^{9} + O(q^{10}) \) \( 4q - 4q^{5} - 12q^{7} + 12q^{9} + 2q^{11} + 8q^{13} + 6q^{15} + 16q^{17} + 12q^{19} + 6q^{21} + 12q^{23} + 6q^{25} + 8q^{31} + 14q^{35} - 24q^{37} + 18q^{39} - 18q^{41} - 14q^{43} - 12q^{45} - 8q^{47} + 12q^{49} + 16q^{53} + 6q^{59} - 12q^{61} - 36q^{63} + 2q^{65} + 2q^{67} - 18q^{69} + 18q^{75} + 2q^{77} + 36q^{81} + 22q^{83} - 16q^{85} + 6q^{87} - 2q^{91} - 18q^{93} - 6q^{95} - 2q^{97} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.73205 −1.00000
\(4\) 0 0
\(5\) −1.86603 + 0.500000i −0.834512 + 0.223607i −0.650681 0.759351i \(-0.725517\pi\)
−0.183831 + 0.982958i \(0.558850\pi\)
\(6\) 0 0
\(7\) −3.86603 + 2.23205i −1.46122 + 0.843636i −0.999068 0.0431647i \(-0.986256\pi\)
−0.462152 + 0.886801i \(0.652923\pi\)
\(8\) 0 0
\(9\) 3.00000 1.00000
\(10\) 0 0
\(11\) 0.500000 1.86603i 0.150756 0.562628i −0.848676 0.528913i \(-0.822600\pi\)
0.999432 0.0337145i \(-0.0107337\pi\)
\(12\) 0 0
\(13\) −0.598076 2.23205i −0.165876 0.619060i −0.997927 0.0643593i \(-0.979500\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) 0 0
\(15\) 3.23205 0.866025i 0.834512 0.223607i
\(16\) 0 0
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 0 0
\(19\) 3.00000 3.00000i 0.688247 0.688247i −0.273597 0.961844i \(-0.588214\pi\)
0.961844 + 0.273597i \(0.0882135\pi\)
\(20\) 0 0
\(21\) 6.69615 3.86603i 1.46122 0.843636i
\(22\) 0 0
\(23\) 5.59808 + 3.23205i 1.16728 + 0.673929i 0.953038 0.302851i \(-0.0979386\pi\)
0.214242 + 0.976781i \(0.431272\pi\)
\(24\) 0 0
\(25\) −1.09808 + 0.633975i −0.219615 + 0.126795i
\(26\) 0 0
\(27\) −5.19615 −1.00000
\(28\) 0 0
\(29\) −0.866025 0.232051i −0.160817 0.0430908i 0.177512 0.984119i \(-0.443195\pi\)
−0.338329 + 0.941028i \(0.609862\pi\)
\(30\) 0 0
\(31\) 4.59808 7.96410i 0.825839 1.43039i −0.0754376 0.997151i \(-0.524035\pi\)
0.901277 0.433244i \(-0.142631\pi\)
\(32\) 0 0
\(33\) −0.866025 + 3.23205i −0.150756 + 0.562628i
\(34\) 0 0
\(35\) 6.09808 6.09808i 1.03076 1.03076i
\(36\) 0 0
\(37\) −4.26795 4.26795i −0.701647 0.701647i 0.263117 0.964764i \(-0.415249\pi\)
−0.964764 + 0.263117i \(0.915249\pi\)
\(38\) 0 0
\(39\) 1.03590 + 3.86603i 0.165876 + 0.619060i
\(40\) 0 0
\(41\) 0.696152 + 0.401924i 0.108721 + 0.0627700i 0.553374 0.832933i \(-0.313340\pi\)
−0.444654 + 0.895703i \(0.646673\pi\)
\(42\) 0 0
\(43\) 1.69615 6.33013i 0.258661 0.965335i −0.707356 0.706857i \(-0.750112\pi\)
0.966017 0.258478i \(-0.0832210\pi\)
\(44\) 0 0
\(45\) −5.59808 + 1.50000i −0.834512 + 0.223607i
\(46\) 0 0
\(47\) 0.598076 + 1.03590i 0.0872384 + 0.151101i 0.906343 0.422543i \(-0.138862\pi\)
−0.819104 + 0.573644i \(0.805529\pi\)
\(48\) 0 0
\(49\) 6.46410 11.1962i 0.923443 1.59945i
\(50\) 0 0
\(51\) −6.92820 −0.970143
\(52\) 0 0
\(53\) 5.73205 + 5.73205i 0.787358 + 0.787358i 0.981060 0.193703i \(-0.0620497\pi\)
−0.193703 + 0.981060i \(0.562050\pi\)
\(54\) 0 0
\(55\) 3.73205i 0.503230i
\(56\) 0 0
\(57\) −5.19615 + 5.19615i −0.688247 + 0.688247i
\(58\) 0 0
\(59\) 1.50000 0.401924i 0.195283 0.0523260i −0.159852 0.987141i \(-0.551102\pi\)
0.355135 + 0.934815i \(0.384435\pi\)
\(60\) 0 0
\(61\) −2.13397 0.571797i −0.273227 0.0732111i 0.119604 0.992822i \(-0.461838\pi\)
−0.392831 + 0.919611i \(0.628504\pi\)
\(62\) 0 0
\(63\) −11.5981 + 6.69615i −1.46122 + 0.843636i
\(64\) 0 0
\(65\) 2.23205 + 3.86603i 0.276852 + 0.479521i
\(66\) 0 0
\(67\) 2.23205 + 8.33013i 0.272688 + 1.01769i 0.957375 + 0.288849i \(0.0932726\pi\)
−0.684686 + 0.728838i \(0.740061\pi\)
\(68\) 0 0
\(69\) −9.69615 5.59808i −1.16728 0.673929i
\(70\) 0 0
\(71\) 2.92820i 0.347514i −0.984789 0.173757i \(-0.944409\pi\)
0.984789 0.173757i \(-0.0555907\pi\)
\(72\) 0 0
\(73\) 7.46410i 0.873607i −0.899557 0.436804i \(-0.856111\pi\)
0.899557 0.436804i \(-0.143889\pi\)
\(74\) 0 0
\(75\) 1.90192 1.09808i 0.219615 0.126795i
\(76\) 0 0
\(77\) 2.23205 + 8.33013i 0.254366 + 0.949306i
\(78\) 0 0
\(79\) 0.866025 + 1.50000i 0.0974355 + 0.168763i 0.910622 0.413239i \(-0.135603\pi\)
−0.813187 + 0.582003i \(0.802269\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 14.1603 + 3.79423i 1.55429 + 0.416471i 0.930850 0.365401i \(-0.119068\pi\)
0.623440 + 0.781872i \(0.285735\pi\)
\(84\) 0 0
\(85\) −7.46410 + 2.00000i −0.809595 + 0.216930i
\(86\) 0 0
\(87\) 1.50000 + 0.401924i 0.160817 + 0.0430908i
\(88\) 0 0
\(89\) 15.8564i 1.68078i −0.541985 0.840388i \(-0.682327\pi\)
0.541985 0.840388i \(-0.317673\pi\)
\(90\) 0 0
\(91\) 7.29423 + 7.29423i 0.764643 + 0.764643i
\(92\) 0 0
\(93\) −7.96410 + 13.7942i −0.825839 + 1.43039i
\(94\) 0 0
\(95\) −4.09808 + 7.09808i −0.420454 + 0.728247i
\(96\) 0 0
\(97\) −0.500000 0.866025i −0.0507673 0.0879316i 0.839525 0.543321i \(-0.182833\pi\)
−0.890292 + 0.455389i \(0.849500\pi\)
\(98\) 0 0
\(99\) 1.50000 5.59808i 0.150756 0.562628i
\(100\) 0 0
\(101\) −0.133975 + 0.500000i −0.0133310 + 0.0497519i −0.972271 0.233857i \(-0.924865\pi\)
0.958940 + 0.283609i \(0.0915318\pi\)
\(102\) 0 0
\(103\) −13.7942 7.96410i −1.35919 0.784726i −0.369672 0.929162i \(-0.620530\pi\)
−0.989514 + 0.144436i \(0.953863\pi\)
\(104\) 0 0
\(105\) −10.5622 + 10.5622i −1.03076 + 1.03076i
\(106\) 0 0
\(107\) −9.39230 9.39230i −0.907988 0.907988i 0.0881214 0.996110i \(-0.471914\pi\)
−0.996110 + 0.0881214i \(0.971914\pi\)
\(108\) 0 0
\(109\) −1.73205 + 1.73205i −0.165900 + 0.165900i −0.785175 0.619274i \(-0.787427\pi\)
0.619274 + 0.785175i \(0.287427\pi\)
\(110\) 0 0
\(111\) 7.39230 + 7.39230i 0.701647 + 0.701647i
\(112\) 0 0
\(113\) −6.23205 + 10.7942i −0.586262 + 1.01544i 0.408455 + 0.912779i \(0.366068\pi\)
−0.994717 + 0.102657i \(0.967266\pi\)
\(114\) 0 0
\(115\) −12.0622 3.23205i −1.12480 0.301390i
\(116\) 0 0
\(117\) −1.79423 6.69615i −0.165876 0.619060i
\(118\) 0 0
\(119\) −15.4641 + 8.92820i −1.41759 + 0.818447i
\(120\) 0 0
\(121\) 6.29423 + 3.63397i 0.572203 + 0.330361i
\(122\) 0 0
\(123\) −1.20577 0.696152i −0.108721 0.0627700i
\(124\) 0 0
\(125\) 8.56218 8.56218i 0.765824 0.765824i
\(126\) 0 0
\(127\) −0.392305 −0.0348114 −0.0174057 0.999849i \(-0.505541\pi\)
−0.0174057 + 0.999849i \(0.505541\pi\)
\(128\) 0 0
\(129\) −2.93782 + 10.9641i −0.258661 + 0.965335i
\(130\) 0 0
\(131\) −1.30385 4.86603i −0.113918 0.425147i 0.885286 0.465047i \(-0.153963\pi\)
−0.999204 + 0.0399004i \(0.987296\pi\)
\(132\) 0 0
\(133\) −4.90192 + 18.2942i −0.425051 + 1.58631i
\(134\) 0 0
\(135\) 9.69615 2.59808i 0.834512 0.223607i
\(136\) 0 0
\(137\) −0.571797 + 0.330127i −0.0488519 + 0.0282047i −0.524227 0.851579i \(-0.675646\pi\)
0.475375 + 0.879783i \(0.342312\pi\)
\(138\) 0 0
\(139\) −16.1603 + 4.33013i −1.37069 + 0.367277i −0.867732 0.497032i \(-0.834423\pi\)
−0.502962 + 0.864308i \(0.667757\pi\)
\(140\) 0 0
\(141\) −1.03590 1.79423i −0.0872384 0.151101i
\(142\) 0 0
\(143\) −4.46410 −0.373307
\(144\) 0 0
\(145\) 1.73205 0.143839
\(146\) 0 0
\(147\) −11.1962 + 19.3923i −0.923443 + 1.59945i
\(148\) 0 0
\(149\) 16.0622 4.30385i 1.31586 0.352585i 0.468438 0.883497i \(-0.344817\pi\)
0.847427 + 0.530912i \(0.178150\pi\)
\(150\) 0 0
\(151\) 6.06218 3.50000i 0.493333 0.284826i −0.232623 0.972567i \(-0.574731\pi\)
0.725956 + 0.687741i \(0.241398\pi\)
\(152\) 0 0
\(153\) 12.0000 0.970143
\(154\) 0 0
\(155\) −4.59808 + 17.1603i −0.369326 + 1.37834i
\(156\) 0 0
\(157\) −0.866025 3.23205i −0.0691164 0.257946i 0.922719 0.385474i \(-0.125962\pi\)
−0.991835 + 0.127529i \(0.959296\pi\)
\(158\) 0 0
\(159\) −9.92820 9.92820i −0.787358 0.787358i
\(160\) 0 0
\(161\) −28.8564 −2.27420
\(162\) 0 0
\(163\) 1.92820 1.92820i 0.151029 0.151029i −0.627549 0.778577i \(-0.715942\pi\)
0.778577 + 0.627549i \(0.215942\pi\)
\(164\) 0 0
\(165\) 6.46410i 0.503230i
\(166\) 0 0
\(167\) 14.2583 + 8.23205i 1.10334 + 0.637015i 0.937097 0.349069i \(-0.113502\pi\)
0.166246 + 0.986084i \(0.446835\pi\)
\(168\) 0 0
\(169\) 6.63397 3.83013i 0.510306 0.294625i
\(170\) 0 0
\(171\) 9.00000 9.00000i 0.688247 0.688247i
\(172\) 0 0
\(173\) 7.59808 + 2.03590i 0.577671 + 0.154786i 0.535812 0.844337i \(-0.320005\pi\)
0.0418586 + 0.999124i \(0.486672\pi\)
\(174\) 0 0
\(175\) 2.83013 4.90192i 0.213937 0.370551i
\(176\) 0 0
\(177\) −2.59808 + 0.696152i −0.195283 + 0.0523260i
\(178\) 0 0
\(179\) 5.92820 5.92820i 0.443095 0.443095i −0.449956 0.893051i \(-0.648560\pi\)
0.893051 + 0.449956i \(0.148560\pi\)
\(180\) 0 0
\(181\) −7.73205 7.73205i −0.574719 0.574719i 0.358725 0.933443i \(-0.383212\pi\)
−0.933443 + 0.358725i \(0.883212\pi\)
\(182\) 0 0
\(183\) 3.69615 + 0.990381i 0.273227 + 0.0732111i
\(184\) 0 0
\(185\) 10.0981 + 5.83013i 0.742425 + 0.428639i
\(186\) 0 0
\(187\) 2.00000 7.46410i 0.146254 0.545829i
\(188\) 0 0
\(189\) 20.0885 11.5981i 1.46122 0.843636i
\(190\) 0 0
\(191\) −1.40192 2.42820i −0.101440 0.175699i 0.810838 0.585270i \(-0.199012\pi\)
−0.912278 + 0.409572i \(0.865678\pi\)
\(192\) 0 0
\(193\) 2.23205 3.86603i 0.160667 0.278283i −0.774441 0.632646i \(-0.781969\pi\)
0.935108 + 0.354363i \(0.115302\pi\)
\(194\) 0 0
\(195\) −3.86603 6.69615i −0.276852 0.479521i
\(196\) 0 0
\(197\) 3.53590 + 3.53590i 0.251922 + 0.251922i 0.821758 0.569836i \(-0.192993\pi\)
−0.569836 + 0.821758i \(0.692993\pi\)
\(198\) 0 0
\(199\) 21.8564i 1.54936i −0.632354 0.774680i \(-0.717911\pi\)
0.632354 0.774680i \(-0.282089\pi\)
\(200\) 0 0
\(201\) −3.86603 14.4282i −0.272688 1.01769i
\(202\) 0 0
\(203\) 3.86603 1.03590i 0.271342 0.0727058i
\(204\) 0 0
\(205\) −1.50000 0.401924i −0.104765 0.0280716i
\(206\) 0 0
\(207\) 16.7942 + 9.69615i 1.16728 + 0.673929i
\(208\) 0 0
\(209\) −4.09808 7.09808i −0.283470 0.490984i
\(210\) 0 0
\(211\) 4.96410 + 18.5263i 0.341743 + 1.27540i 0.896371 + 0.443304i \(0.146194\pi\)
−0.554629 + 0.832098i \(0.687140\pi\)
\(212\) 0 0
\(213\) 5.07180i 0.347514i
\(214\) 0 0
\(215\) 12.6603i 0.863422i
\(216\) 0 0
\(217\) 41.0526i 2.78683i
\(218\) 0 0
\(219\) 12.9282i 0.873607i
\(220\) 0 0
\(221\) −2.39230 8.92820i −0.160924 0.600576i
\(222\) 0 0
\(223\) −7.79423 13.5000i −0.521940 0.904027i −0.999674 0.0255224i \(-0.991875\pi\)
0.477734 0.878504i \(-0.341458\pi\)
\(224\) 0 0
\(225\) −3.29423 + 1.90192i −0.219615 + 0.126795i
\(226\) 0 0
\(227\) −19.6244 5.25833i −1.30251 0.349008i −0.460114 0.887860i \(-0.652191\pi\)
−0.842400 + 0.538852i \(0.818858\pi\)
\(228\) 0 0
\(229\) 16.5263 4.42820i 1.09209 0.292624i 0.332549 0.943086i \(-0.392091\pi\)
0.759539 + 0.650462i \(0.225425\pi\)
\(230\) 0 0
\(231\) −3.86603 14.4282i −0.254366 0.949306i
\(232\) 0 0
\(233\) 9.07180i 0.594313i −0.954829 0.297157i \(-0.903962\pi\)
0.954829 0.297157i \(-0.0960383\pi\)
\(234\) 0 0
\(235\) −1.63397 1.63397i −0.106589 0.106589i
\(236\) 0 0
\(237\) −1.50000 2.59808i −0.0974355 0.168763i
\(238\) 0 0
\(239\) 0.401924 0.696152i 0.0259983 0.0450304i −0.852734 0.522346i \(-0.825057\pi\)
0.878732 + 0.477316i \(0.158390\pi\)
\(240\) 0 0
\(241\) −2.76795 4.79423i −0.178299 0.308823i 0.762999 0.646400i \(-0.223726\pi\)
−0.941298 + 0.337576i \(0.890393\pi\)
\(242\) 0 0
\(243\) −15.5885 −1.00000
\(244\) 0 0
\(245\) −6.46410 + 24.1244i −0.412976 + 1.54125i
\(246\) 0 0
\(247\) −8.49038 4.90192i −0.540230 0.311902i
\(248\) 0 0
\(249\) −24.5263 6.57180i −1.55429 0.416471i
\(250\) 0 0
\(251\) 13.3923 + 13.3923i 0.845315 + 0.845315i 0.989544 0.144229i \(-0.0460703\pi\)
−0.144229 + 0.989544i \(0.546070\pi\)
\(252\) 0 0
\(253\) 8.83013 8.83013i 0.555145 0.555145i
\(254\) 0 0
\(255\) 12.9282 3.46410i 0.809595 0.216930i
\(256\) 0 0
\(257\) 12.1603 21.0622i 0.758536 1.31382i −0.185061 0.982727i \(-0.559248\pi\)
0.943597 0.331096i \(-0.107418\pi\)
\(258\) 0 0
\(259\) 26.0263 + 6.97372i 1.61719 + 0.433326i
\(260\) 0 0
\(261\) −2.59808 0.696152i −0.160817 0.0430908i
\(262\) 0 0
\(263\) 8.59808 4.96410i 0.530180 0.306100i −0.210910 0.977506i \(-0.567643\pi\)
0.741090 + 0.671406i \(0.234309\pi\)
\(264\) 0 0
\(265\) −13.5622 7.83013i −0.833118 0.481001i
\(266\) 0 0
\(267\) 27.4641i 1.68078i
\(268\) 0 0
\(269\) 4.26795 4.26795i 0.260221 0.260221i −0.564923 0.825144i \(-0.691094\pi\)
0.825144 + 0.564923i \(0.191094\pi\)
\(270\) 0 0
\(271\) 1.07180 0.0651070 0.0325535 0.999470i \(-0.489636\pi\)
0.0325535 + 0.999470i \(0.489636\pi\)
\(272\) 0 0
\(273\) −12.6340 12.6340i −0.764643 0.764643i
\(274\) 0 0
\(275\) 0.633975 + 2.36603i 0.0382301 + 0.142677i
\(276\) 0 0
\(277\) −1.79423 + 6.69615i −0.107805 + 0.402333i −0.998648 0.0519775i \(-0.983448\pi\)
0.890844 + 0.454310i \(0.150114\pi\)
\(278\) 0 0
\(279\) 13.7942 23.8923i 0.825839 1.43039i
\(280\) 0 0
\(281\) −10.0359 + 5.79423i −0.598692 + 0.345655i −0.768527 0.639818i \(-0.779010\pi\)
0.169835 + 0.985472i \(0.445676\pi\)
\(282\) 0 0
\(283\) 13.1603 3.52628i 0.782296 0.209616i 0.154499 0.987993i \(-0.450624\pi\)
0.627797 + 0.778377i \(0.283957\pi\)
\(284\) 0 0
\(285\) 7.09808 12.2942i 0.420454 0.728247i
\(286\) 0 0
\(287\) −3.58846 −0.211820
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 0.866025 + 1.50000i 0.0507673 + 0.0879316i
\(292\) 0 0
\(293\) 2.13397 0.571797i 0.124668 0.0334047i −0.195945 0.980615i \(-0.562778\pi\)
0.320614 + 0.947210i \(0.396111\pi\)
\(294\) 0 0
\(295\) −2.59808 + 1.50000i −0.151266 + 0.0873334i
\(296\) 0 0
\(297\) −2.59808 + 9.69615i −0.150756 + 0.562628i
\(298\) 0 0
\(299\) 3.86603 14.4282i 0.223578 0.834405i
\(300\) 0 0
\(301\) 7.57180 + 28.2583i 0.436431 + 1.62878i
\(302\) 0 0
\(303\) 0.232051 0.866025i 0.0133310 0.0497519i
\(304\) 0 0
\(305\) 4.26795 0.244382
\(306\) 0 0
\(307\) −7.92820 + 7.92820i −0.452486 + 0.452486i −0.896179 0.443693i \(-0.853668\pi\)
0.443693 + 0.896179i \(0.353668\pi\)
\(308\) 0 0
\(309\) 23.8923 + 13.7942i 1.35919 + 0.784726i
\(310\) 0 0
\(311\) −9.18653 5.30385i −0.520921 0.300754i 0.216391 0.976307i \(-0.430572\pi\)
−0.737311 + 0.675553i \(0.763905\pi\)
\(312\) 0 0
\(313\) 25.1603 14.5263i 1.42214 0.821074i 0.425660 0.904883i \(-0.360042\pi\)
0.996482 + 0.0838094i \(0.0267087\pi\)
\(314\) 0 0
\(315\) 18.2942 18.2942i 1.03076 1.03076i
\(316\) 0 0
\(317\) −33.4545 8.96410i −1.87899 0.503474i −0.999627 0.0273246i \(-0.991301\pi\)
−0.879364 0.476150i \(-0.842032\pi\)
\(318\) 0 0
\(319\) −0.866025 + 1.50000i −0.0484881 + 0.0839839i
\(320\) 0 0
\(321\) 16.2679 + 16.2679i 0.907988 + 0.907988i
\(322\) 0 0
\(323\) 12.0000 12.0000i 0.667698 0.667698i
\(324\) 0 0
\(325\) 2.07180 + 2.07180i 0.114923 + 0.114923i
\(326\) 0 0
\(327\) 3.00000 3.00000i 0.165900 0.165900i
\(328\) 0 0
\(329\) −4.62436 2.66987i −0.254949 0.147195i
\(330\) 0 0
\(331\) −1.35641 + 5.06218i −0.0745548 + 0.278242i −0.993132 0.116999i \(-0.962672\pi\)
0.918577 + 0.395242i \(0.129339\pi\)
\(332\) 0 0
\(333\) −12.8038 12.8038i −0.701647 0.701647i
\(334\) 0 0
\(335\) −8.33013 14.4282i −0.455123 0.788297i
\(336\) 0 0
\(337\) −9.69615 + 16.7942i −0.528183 + 0.914840i 0.471277 + 0.881985i \(0.343793\pi\)
−0.999460 + 0.0328547i \(0.989540\pi\)
\(338\) 0 0
\(339\) 10.7942 18.6962i 0.586262 1.01544i
\(340\) 0 0
\(341\) −12.5622 12.5622i −0.680280 0.680280i
\(342\) 0 0
\(343\) 26.4641i 1.42893i
\(344\) 0 0
\(345\) 20.8923 + 5.59808i 1.12480 + 0.301390i
\(346\) 0 0
\(347\) 1.76795 0.473721i 0.0949085 0.0254307i −0.211052 0.977475i \(-0.567689\pi\)
0.305961 + 0.952044i \(0.401022\pi\)
\(348\) 0 0
\(349\) −3.86603 1.03590i −0.206944 0.0554504i 0.153858 0.988093i \(-0.450830\pi\)
−0.360802 + 0.932643i \(0.617497\pi\)
\(350\) 0 0
\(351\) 3.10770 + 11.5981i 0.165876 + 0.619060i
\(352\) 0 0
\(353\) −11.7679 20.3827i −0.626345 1.08486i −0.988279 0.152657i \(-0.951217\pi\)
0.361934 0.932204i \(-0.382116\pi\)
\(354\) 0 0
\(355\) 1.46410 + 5.46410i 0.0777064 + 0.290004i
\(356\) 0 0
\(357\) 26.7846 15.4641i 1.41759 0.818447i
\(358\) 0 0
\(359\) 28.9282i 1.52677i −0.645942 0.763386i \(-0.723535\pi\)
0.645942 0.763386i \(-0.276465\pi\)
\(360\) 0 0
\(361\) 1.00000i 0.0526316i
\(362\) 0 0
\(363\) −10.9019 6.29423i −0.572203 0.330361i
\(364\) 0 0
\(365\) 3.73205 + 13.9282i 0.195344 + 0.729035i
\(366\) 0 0
\(367\) 17.4545 + 30.2321i 0.911117 + 1.57810i 0.812490 + 0.582976i \(0.198112\pi\)
0.0986270 + 0.995124i \(0.468555\pi\)
\(368\) 0 0
\(369\) 2.08846 + 1.20577i 0.108721 + 0.0627700i
\(370\) 0 0
\(371\) −34.9545 9.36603i −1.81475 0.486260i
\(372\) 0 0
\(373\) −1.59808 + 0.428203i −0.0827452 + 0.0221715i −0.299954 0.953954i \(-0.596971\pi\)
0.217209 + 0.976125i \(0.430305\pi\)
\(374\) 0 0
\(375\) −14.8301 + 14.8301i −0.765824 + 0.765824i
\(376\) 0 0
\(377\) 2.07180i 0.106703i
\(378\) 0 0
\(379\) 15.5885 + 15.5885i 0.800725 + 0.800725i 0.983209 0.182484i \(-0.0584137\pi\)
−0.182484 + 0.983209i \(0.558414\pi\)
\(380\) 0 0
\(381\) 0.679492 0.0348114
\(382\) 0 0
\(383\) −3.66987 + 6.35641i −0.187522 + 0.324797i −0.944423 0.328732i \(-0.893379\pi\)
0.756902 + 0.653529i \(0.226712\pi\)
\(384\) 0 0
\(385\) −8.33013 14.4282i −0.424543 0.735329i
\(386\) 0 0
\(387\) 5.08846 18.9904i 0.258661 0.965335i
\(388\) 0 0
\(389\) 2.40192 8.96410i 0.121782 0.454498i −0.877922 0.478803i \(-0.841071\pi\)
0.999705 + 0.0243053i \(0.00773738\pi\)
\(390\) 0 0
\(391\) 22.3923 + 12.9282i 1.13243 + 0.653807i
\(392\) 0 0
\(393\) 2.25833 + 8.42820i 0.113918 + 0.425147i
\(394\) 0 0
\(395\) −2.36603 2.36603i −0.119048 0.119048i
\(396\) 0 0
\(397\) 17.0526 17.0526i 0.855843 0.855843i −0.135002 0.990845i \(-0.543104\pi\)
0.990845 + 0.135002i \(0.0431041\pi\)
\(398\) 0 0
\(399\) 8.49038 31.6865i 0.425051 1.58631i
\(400\) 0 0
\(401\) −16.1603 + 27.9904i −0.807005 + 1.39777i 0.107925 + 0.994159i \(0.465579\pi\)
−0.914929 + 0.403614i \(0.867754\pi\)
\(402\) 0 0
\(403\) −20.5263 5.50000i −1.02249 0.273975i
\(404\) 0 0
\(405\) −16.7942 + 4.50000i −0.834512 + 0.223607i
\(406\) 0 0
\(407\) −10.0981 + 5.83013i −0.500543 + 0.288989i
\(408\) 0 0
\(409\) −19.6244 11.3301i −0.970362 0.560239i −0.0710154 0.997475i \(-0.522624\pi\)
−0.899347 + 0.437236i \(0.855957\pi\)
\(410\) 0 0
\(411\) 0.990381 0.571797i 0.0488519 0.0282047i
\(412\) 0 0
\(413\) −4.90192 + 4.90192i −0.241208 + 0.241208i
\(414\) 0 0
\(415\) −28.3205 −1.39020
\(416\) 0 0
\(417\) 27.9904 7.50000i 1.37069 0.367277i
\(418\) 0 0
\(419\) 4.96410 + 18.5263i 0.242512 + 0.905068i 0.974618 + 0.223876i \(0.0718712\pi\)
−0.732105 + 0.681191i \(0.761462\pi\)
\(420\) 0 0
\(421\) −4.79423 + 17.8923i −0.233656 + 0.872018i 0.745094 + 0.666960i \(0.232405\pi\)
−0.978750 + 0.205058i \(0.934262\pi\)
\(422\) 0 0
\(423\) 1.79423 + 3.10770i 0.0872384 + 0.151101i
\(424\) 0 0
\(425\) −4.39230 + 2.53590i −0.213058 + 0.123009i
\(426\) 0 0
\(427\) 9.52628 2.55256i 0.461009 0.123527i
\(428\) 0 0
\(429\) 7.73205 0.373307
\(430\) 0 0
\(431\) 3.32051 0.159943 0.0799716 0.996797i \(-0.474517\pi\)
0.0799716 + 0.996797i \(0.474517\pi\)
\(432\) 0 0
\(433\) 3.60770 0.173375 0.0866874 0.996236i \(-0.472372\pi\)
0.0866874 + 0.996236i \(0.472372\pi\)
\(434\) 0 0
\(435\) −3.00000 −0.143839
\(436\) 0 0
\(437\) 26.4904 7.09808i 1.26721 0.339547i
\(438\) 0 0
\(439\) −5.93782 + 3.42820i −0.283397 + 0.163619i −0.634960 0.772545i \(-0.718984\pi\)
0.351563 + 0.936164i \(0.385650\pi\)
\(440\) 0 0
\(441\) 19.3923 33.5885i 0.923443 1.59945i
\(442\) 0 0
\(443\) 1.16025 4.33013i 0.0551253 0.205731i −0.932870 0.360213i \(-0.882704\pi\)
0.987996 + 0.154482i \(0.0493708\pi\)
\(444\) 0 0
\(445\) 7.92820 + 29.5885i 0.375833 + 1.40263i
\(446\) 0 0
\(447\) −27.8205 + 7.45448i −1.31586 + 0.352585i
\(448\) 0 0
\(449\) 35.3205 1.66688 0.833439 0.552612i \(-0.186369\pi\)
0.833439 + 0.552612i \(0.186369\pi\)
\(450\) 0 0
\(451\) 1.09808 1.09808i 0.0517064 0.0517064i
\(452\) 0 0
\(453\) −10.5000 + 6.06218i −0.493333 + 0.284826i
\(454\) 0 0
\(455\) −17.2583 9.96410i −0.809083 0.467124i
\(456\) 0 0
\(457\) 25.9641 14.9904i 1.21455 0.701220i 0.250802 0.968038i \(-0.419306\pi\)
0.963747 + 0.266818i \(0.0859722\pi\)
\(458\) 0 0
\(459\) −20.7846 −0.970143
\(460\) 0 0
\(461\) 4.59808 + 1.23205i 0.214154 + 0.0573823i 0.364301 0.931281i \(-0.381308\pi\)
−0.150147 + 0.988664i \(0.547975\pi\)
\(462\) 0 0
\(463\) 5.33013 9.23205i 0.247712 0.429050i −0.715179 0.698942i \(-0.753655\pi\)
0.962891 + 0.269892i \(0.0869880\pi\)
\(464\) 0 0
\(465\) 7.96410 29.7224i 0.369326 1.37834i
\(466\) 0 0
\(467\) −21.7846 + 21.7846i −1.00807 + 1.00807i −0.00810436 + 0.999967i \(0.502580\pi\)
−0.999967 + 0.00810436i \(0.997420\pi\)
\(468\) 0 0
\(469\) −27.2224 27.2224i −1.25702 1.25702i
\(470\) 0 0
\(471\) 1.50000 + 5.59808i 0.0691164 + 0.257946i
\(472\) 0 0
\(473\) −10.9641 6.33013i −0.504130 0.291060i
\(474\) 0 0
\(475\) −1.39230 + 5.19615i −0.0638833 + 0.238416i
\(476\) 0 0
\(477\) 17.1962 + 17.1962i 0.787358 + 0.787358i
\(478\) 0 0
\(479\) −9.33013 16.1603i −0.426304 0.738381i 0.570237 0.821480i \(-0.306851\pi\)
−0.996541 + 0.0830995i \(0.973518\pi\)
\(480\) 0 0
\(481\) −6.97372 + 12.0788i −0.317974 + 0.550748i
\(482\) 0 0
\(483\) 49.9808 2.27420
\(484\) 0 0
\(485\) 1.36603 + 1.36603i 0.0620280 + 0.0620280i
\(486\) 0 0
\(487\) 6.78461i 0.307440i −0.988114 0.153720i \(-0.950875\pi\)
0.988114 0.153720i \(-0.0491254\pi\)
\(488\) 0 0
\(489\) −3.33975 + 3.33975i −0.151029 + 0.151029i
\(490\) 0 0
\(491\) −0.500000 + 0.133975i −0.0225647 + 0.00604619i −0.270084 0.962837i \(-0.587051\pi\)
0.247519 + 0.968883i \(0.420385\pi\)
\(492\) 0 0
\(493\) −3.46410 0.928203i −0.156015 0.0418042i
\(494\) 0 0
\(495\) 11.1962i 0.503230i
\(496\) 0 0
\(497\) 6.53590 + 11.3205i 0.293175 + 0.507794i
\(498\) 0 0
\(499\) 2.50000 + 9.33013i 0.111915 + 0.417674i 0.999038 0.0438606i \(-0.0139657\pi\)
−0.887122 + 0.461534i \(0.847299\pi\)
\(500\) 0 0
\(501\) −24.6962 14.2583i −1.10334 0.637015i
\(502\) 0 0
\(503\) 13.8564i 0.617827i 0.951090 + 0.308913i \(0.0999653\pi\)
−0.951090 + 0.308913i \(0.900035\pi\)
\(504\) 0 0
\(505\) 1.00000i 0.0444994i
\(506\) 0 0
\(507\) −11.4904 + 6.63397i −0.510306 + 0.294625i
\(508\) 0 0
\(509\) 1.25833 + 4.69615i 0.0557745 + 0.208153i 0.988190 0.153236i \(-0.0489693\pi\)
−0.932415 + 0.361389i \(0.882303\pi\)
\(510\) 0 0
\(511\) 16.6603 + 28.8564i 0.737006 + 1.27653i
\(512\) 0 0
\(513\) −15.5885 + 15.5885i −0.688247 + 0.688247i
\(514\) 0 0
\(515\) 29.7224 + 7.96410i 1.30973 + 0.350940i
\(516\) 0 0
\(517\) 2.23205 0.598076i 0.0981655 0.0263034i
\(518\) 0 0
\(519\) −13.1603 3.52628i −0.577671 0.154786i
\(520\) 0 0
\(521\) 41.8564i 1.83376i 0.399160 + 0.916881i \(0.369302\pi\)
−0.399160 + 0.916881i \(0.630698\pi\)
\(522\) 0 0
\(523\) −22.1244 22.1244i −0.967431 0.967431i 0.0320556 0.999486i \(-0.489795\pi\)
−0.999486 + 0.0320556i \(0.989795\pi\)
\(524\) 0 0
\(525\) −4.90192 + 8.49038i −0.213937 + 0.370551i
\(526\) 0 0
\(527\) 18.3923 31.8564i 0.801181 1.38769i
\(528\) 0 0
\(529\) 9.39230 + 16.2679i 0.408361 + 0.707302i
\(530\) 0 0
\(531\) 4.50000 1.20577i 0.195283 0.0523260i
\(532\) 0 0
\(533\) 0.480762 1.79423i 0.0208241 0.0777167i
\(534\) 0 0
\(535\) 22.2224 + 12.8301i 0.960760 + 0.554695i
\(536\) 0 0
\(537\) −10.2679 + 10.2679i −0.443095 + 0.443095i
\(538\) 0 0
\(539\) −17.6603 17.6603i −0.760681 0.760681i
\(540\) 0 0
\(541\) −15.0000 + 15.0000i −0.644900 + 0.644900i −0.951756 0.306856i \(-0.900723\pi\)
0.306856 + 0.951756i \(0.400723\pi\)
\(542\) 0 0
\(543\) 13.3923 + 13.3923i 0.574719 + 0.574719i
\(544\) 0 0
\(545\) 2.36603 4.09808i 0.101349 0.175542i
\(546\) 0 0
\(547\) −21.4282 5.74167i −0.916204 0.245496i −0.230242 0.973133i \(-0.573952\pi\)
−0.685962 + 0.727637i \(0.740618\pi\)
\(548\) 0 0
\(549\) −6.40192 1.71539i −0.273227 0.0732111i
\(550\) 0 0
\(551\) −3.29423 + 1.90192i −0.140339 + 0.0810247i
\(552\) 0 0
\(553\) −6.69615 3.86603i −0.284749 0.164400i
\(554\) 0 0
\(555\) −17.4904 10.0981i −0.742425 0.428639i
\(556\) 0 0
\(557\) −23.9808 + 23.9808i −1.01610 + 1.01610i −0.0162292 + 0.999868i \(0.505166\pi\)
−0.999868 + 0.0162292i \(0.994834\pi\)
\(558\) 0 0
\(559\) −15.1436 −0.640506
\(560\) 0 0
\(561\) −3.46410 + 12.9282i −0.146254 + 0.545829i
\(562\) 0 0
\(563\) 1.64359 + 6.13397i 0.0692692 + 0.258516i 0.991873 0.127233i \(-0.0406096\pi\)
−0.922604 + 0.385749i \(0.873943\pi\)
\(564\) 0 0
\(565\) 6.23205 23.2583i 0.262184 0.978485i
\(566\) 0 0
\(567\) −34.7942 + 20.0885i −1.46122 + 0.843636i
\(568\) 0 0
\(569\) −27.4808 + 15.8660i −1.15205 + 0.665138i −0.949387 0.314109i \(-0.898294\pi\)
−0.202667 + 0.979248i \(0.564961\pi\)
\(570\) 0 0
\(571\) −39.5526 + 10.5981i −1.65522 + 0.443516i −0.961068 0.276310i \(-0.910888\pi\)
−0.694155 + 0.719826i \(0.744222\pi\)
\(572\) 0 0
\(573\) 2.42820 + 4.20577i 0.101440 + 0.175699i
\(574\) 0 0
\(575\) −8.19615 −0.341803
\(576\) 0 0
\(577\) −25.1769 −1.04813 −0.524064 0.851679i \(-0.675585\pi\)
−0.524064 + 0.851679i \(0.675585\pi\)
\(578\) 0 0
\(579\) −3.86603 + 6.69615i −0.160667 + 0.278283i
\(580\) 0 0
\(581\) −63.2128 + 16.9378i −2.62251 + 0.702699i
\(582\) 0 0
\(583\) 13.5622 7.83013i 0.561688 0.324291i
\(584\) 0 0
\(585\) 6.69615 + 11.5981i 0.276852 + 0.479521i
\(586\) 0 0
\(587\) −3.96410 + 14.7942i −0.163616 + 0.610623i 0.834597 + 0.550861i \(0.185701\pi\)
−0.998213 + 0.0597617i \(0.980966\pi\)
\(588\) 0 0
\(589\) −10.0981 37.6865i −0.416084 1.55285i
\(590\) 0 0
\(591\) −6.12436 6.12436i −0.251922 0.251922i
\(592\) 0 0
\(593\) −5.46410 −0.224384 −0.112192 0.993687i \(-0.535787\pi\)
−0.112192 + 0.993687i \(0.535787\pi\)
\(594\) 0 0
\(595\) 24.3923 24.3923i 0.999987 0.999987i
\(596\) 0 0
\(597\) 37.8564i 1.54936i
\(598\) 0 0
\(599\) 30.3109 + 17.5000i 1.23847 + 0.715031i 0.968781 0.247917i \(-0.0797461\pi\)
0.269688 + 0.962948i \(0.413079\pi\)
\(600\) 0 0
\(601\) −26.7679 + 15.4545i −1.09189 + 0.630401i −0.934078 0.357068i \(-0.883776\pi\)
−0.157809 + 0.987470i \(0.550443\pi\)
\(602\) 0 0
\(603\) 6.69615 + 24.9904i 0.272688 + 1.01769i
\(604\) 0 0
\(605\) −13.5622 3.63397i −0.551381 0.147742i
\(606\) 0 0
\(607\) −0.598076 + 1.03590i −0.0242752 + 0.0420458i −0.877908 0.478830i \(-0.841061\pi\)
0.853633 + 0.520876i \(0.174394\pi\)
\(608\) 0 0
\(609\) −6.69615 + 1.79423i −0.271342 + 0.0727058i
\(610\) 0 0
\(611\) 1.95448 1.95448i 0.0790699 0.0790699i
\(612\) 0 0
\(613\) 23.5885 + 23.5885i 0.952729 + 0.952729i 0.998932 0.0462032i \(-0.0147122\pi\)
−0.0462032 + 0.998932i \(0.514712\pi\)
\(614\) 0 0
\(615\) 2.59808 + 0.696152i 0.104765 + 0.0280716i
\(616\) 0 0
\(617\) 23.0885 + 13.3301i 0.929506 + 0.536651i 0.886655 0.462431i \(-0.153023\pi\)
0.0428509 + 0.999081i \(0.486356\pi\)
\(618\) 0 0
\(619\) 1.91154 7.13397i 0.0768314 0.286739i −0.916811 0.399322i \(-0.869246\pi\)
0.993642 + 0.112583i \(0.0359124\pi\)
\(620\) 0 0
\(621\) −29.0885 16.7942i −1.16728 0.673929i
\(622\) 0 0
\(623\) 35.3923 + 61.3013i 1.41796 + 2.45598i
\(624\) 0 0
\(625\) −8.52628 + 14.7679i −0.341051 + 0.590718i
\(626\) 0 0
\(627\) 7.09808 + 12.2942i 0.283470 + 0.490984i
\(628\) 0 0
\(629\) −17.0718 17.0718i −0.680697 0.680697i
\(630\) 0 0
\(631\) 16.2487i 0.646851i 0.946254 + 0.323425i \(0.104835\pi\)
−0.946254 + 0.323425i \(0.895165\pi\)
\(632\) 0 0
\(633\) −8.59808 32.0885i −0.341743 1.27540i
\(634\) 0 0
\(635\) 0.732051 0.196152i 0.0290506 0.00778407i
\(636\) 0 0
\(637\) −28.8564 7.73205i −1.14333 0.306355i
\(638\) 0 0
\(639\) 8.78461i 0.347514i
\(640\) 0 0
\(641\) 9.23205 + 15.9904i 0.364644 + 0.631582i 0.988719 0.149782i \(-0.0478573\pi\)
−0.624075 + 0.781365i \(0.714524\pi\)
\(642\) 0 0
\(643\) −7.96410 29.7224i −0.314074 1.17214i −0.924849 0.380334i \(-0.875809\pi\)
0.610776 0.791804i \(-0.290858\pi\)
\(644\) 0 0
\(645\) 21.9282i 0.863422i
\(646\) 0 0
\(647\) 25.6077i 1.00674i 0.864070 + 0.503371i \(0.167907\pi\)
−0.864070 + 0.503371i \(0.832093\pi\)
\(648\) 0 0
\(649\) 3.00000i 0.117760i
\(650\) 0 0
\(651\) 71.1051i 2.78683i
\(652\) 0 0
\(653\) −12.6699 47.2846i −0.495810 1.85039i −0.525443 0.850829i \(-0.676100\pi\)
0.0296324 0.999561i \(-0.490566\pi\)
\(654\) 0 0
\(655\) 4.86603 + 8.42820i 0.190131 + 0.329317i
\(656\) 0 0
\(657\) 22.3923i 0.873607i
\(658\) 0 0
\(659\) −1.23205 0.330127i −0.0479939 0.0128599i 0.234742 0.972058i \(-0.424575\pi\)
−0.282736 + 0.959198i \(0.591242\pi\)
\(660\) 0 0
\(661\) 19.7942 5.30385i 0.769906 0.206296i 0.147576 0.989051i \(-0.452853\pi\)
0.622330 + 0.782755i \(0.286186\pi\)
\(662\) 0 0
\(663\) 4.14359 + 15.4641i 0.160924 + 0.600576i
\(664\) 0 0
\(665\) 36.5885i 1.41884i
\(666\) 0 0
\(667\) −4.09808 4.09808i −0.158678 0.158678i
\(668\) 0 0
\(669\) 13.5000 + 23.3827i 0.521940 + 0.904027i
\(670\) 0 0
\(671\) −2.13397 + 3.69615i −0.0823812 + 0.142688i
\(672\) 0 0
\(673\) 21.1603 + 36.6506i 0.815668 + 1.41278i 0.908847 + 0.417129i \(0.136964\pi\)
−0.0931795 + 0.995649i \(0.529703\pi\)
\(674\) 0 0
\(675\) 5.70577 3.29423i 0.219615 0.126795i
\(676\) 0 0
\(677\) 2.34936 8.76795i 0.0902934 0.336980i −0.905970 0.423341i \(-0.860857\pi\)
0.996264 + 0.0863612i \(0.0275239\pi\)
\(678\) 0 0
\(679\) 3.86603 + 2.23205i 0.148364 + 0.0856582i
\(680\) 0 0
\(681\) 33.9904 + 9.10770i 1.30251 + 0.349008i
\(682\) 0 0
\(683\) −15.3923 15.3923i −0.588970 0.588970i 0.348382 0.937353i \(-0.386731\pi\)
−0.937353 + 0.348382i \(0.886731\pi\)
\(684\) 0 0
\(685\) 0.901924 0.901924i 0.0344607 0.0344607i
\(686\) 0 0
\(687\) −28.6244 + 7.66987i −1.09209 + 0.292624i
\(688\) 0 0
\(689\) 9.36603 16.2224i 0.356817 0.618025i
\(690\) 0 0
\(691\) 1.96410 + 0.526279i 0.0747179 + 0.0200206i 0.295984 0.955193i \(-0.404352\pi\)
−0.221266 + 0.975213i \(0.571019\pi\)
\(692\) 0 0
\(693\) 6.69615 + 24.9904i 0.254366 + 0.949306i
\(694\) 0 0
\(695\) 27.9904 16.1603i 1.06174 0.612993i
\(696\) 0 0
\(697\) 2.78461 + 1.60770i 0.105475 + 0.0608958i
\(698\) 0 0
\(699\) 15.7128i 0.594313i
\(700\) 0 0
\(701\) 17.0526 17.0526i 0.644066 0.644066i −0.307486 0.951553i \(-0.599488\pi\)
0.951553 + 0.307486i \(0.0994878\pi\)
\(702\) 0 0
\(703\) −25.6077 −0.965813
\(704\) 0 0
\(705\) 2.83013 + 2.83013i 0.106589 + 0.106589i
\(706\) 0 0
\(707\) −0.598076 2.23205i −0.0224930 0.0839449i
\(708\) 0 0
\(709\) 10.1147 37.7487i 0.379867 1.41768i −0.466235 0.884661i \(-0.654390\pi\)
0.846102 0.533022i \(-0.178944\pi\)
\(710\) 0 0
\(711\) 2.59808 + 4.50000i 0.0974355 + 0.168763i
\(712\) 0 0
\(713\) 51.4808 29.7224i 1.92797 1.11311i
\(714\) 0 0
\(715\) 8.33013 2.23205i 0.311529 0.0834740i
\(716\) 0 0
\(717\) −0.696152 + 1.20577i −0.0259983 + 0.0450304i
\(718\) 0 0
\(719\) 11.3205 0.422184 0.211092 0.977466i \(-0.432298\pi\)
0.211092 + 0.977466i \(0.432298\pi\)
\(720\) 0 0
\(721\) 71.1051 2.64809
\(722\) 0 0
\(723\) 4.79423 + 8.30385i 0.178299 + 0.308823i
\(724\) 0 0
\(725\) 1.09808 0.294229i 0.0407815 0.0109274i
\(726\) 0 0
\(727\) −3.06218 + 1.76795i −0.113570 + 0.0655696i −0.555709 0.831377i \(-0.687553\pi\)
0.442139 + 0.896947i \(0.354220\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 0 0
\(731\) 6.78461 25.3205i 0.250938 0.936513i
\(732\) 0 0
\(733\) 8.47372 + 31.6244i 0.312984 + 1.16807i 0.925852 + 0.377887i \(0.123349\pi\)
−0.612868 + 0.790185i \(0.709984\pi\)
\(734\) 0 0
\(735\) 11.1962 41.7846i 0.412976 1.54125i
\(736\) 0 0
\(737\) 16.6603 0.613688
\(738\) 0 0
\(739\) 26.2679 26.2679i 0.966282 0.966282i −0.0331677 0.999450i \(-0.510560\pi\)
0.999450 + 0.0331677i \(0.0105595\pi\)
\(740\) 0 0
\(741\) 14.7058 + 8.49038i 0.540230 + 0.311902i
\(742\) 0 0
\(743\) −25.1147 14.5000i −0.921370 0.531953i −0.0372984 0.999304i \(-0.511875\pi\)
−0.884072 + 0.467351i \(0.845209\pi\)
\(744\) 0 0
\(745\) −27.8205 + 16.0622i −1.01926 + 0.588473i
\(746\) 0 0
\(747\) 42.4808 + 11.3827i 1.55429 + 0.416471i
\(748\) 0 0
\(749\) 57.2750 + 15.3468i 2.09278 + 0.560759i
\(750\) 0 0
\(751\) 24.7224 42.8205i 0.902134 1.56254i 0.0774160 0.996999i \(-0.475333\pi\)
0.824718 0.565544i \(-0.191334\pi\)
\(752\) 0 0
\(753\) −23.1962 23.1962i −0.845315 0.845315i
\(754\) 0 0
\(755\) −9.56218 + 9.56218i −0.348003 + 0.348003i
\(756\) 0 0
\(757\) 1.53590 + 1.53590i 0.0558232 + 0.0558232i 0.734467 0.678644i \(-0.237432\pi\)
−0.678644 + 0.734467i \(0.737432\pi\)
\(758\) 0 0
\(759\) −15.2942 + 15.2942i −0.555145 + 0.555145i
\(760\) 0 0
\(761\) −16.2846 9.40192i −0.590317 0.340819i 0.174906 0.984585i \(-0.444038\pi\)
−0.765223 + 0.643766i \(0.777371\pi\)
\(762\) 0 0
\(763\) 2.83013 10.5622i 0.102457 0.382377i
\(764\) 0 0
\(765\) −22.3923 + 6.00000i −0.809595 + 0.216930i
\(766\) 0 0
\(767\) −1.79423 3.10770i −0.0647858 0.112212i
\(768\) 0 0
\(769\) −3.50000 + 6.06218i −0.126213 + 0.218608i −0.922207 0.386698i \(-0.873616\pi\)
0.795993 + 0.605305i \(0.206949\pi\)
\(770\) 0 0
\(771\) −21.0622 + 36.4808i −0.758536 + 1.31382i
\(772\) 0 0
\(773\) −23.5885 23.5885i −0.848418 0.848418i 0.141518 0.989936i \(-0.454802\pi\)
−0.989936 + 0.141518i \(0.954802\pi\)
\(774\) 0 0
\(775\) 11.6603i 0.418849i
\(776\) 0 0
\(777\) −45.0788 12.0788i −1.61719 0.433326i
\(778\) 0 0
\(779\) 3.29423 0.882686i 0.118028 0.0316255i
\(780\) 0 0
\(781\) −5.46410 1.46410i −0.195521 0.0523897i
\(782\) 0 0
\(783\) 4.50000 + 1.20577i 0.160817 + 0.0430908i
\(784\) 0 0
\(785\) 3.23205 + 5.59808i 0.115357 + 0.199804i
\(786\) 0 0
\(787\) −0.820508 3.06218i −0.0292480 0.109155i 0.949759 0.312983i \(-0.101328\pi\)
−0.979007 + 0.203828i \(0.934662\pi\)
\(788\) 0 0
\(789\) −14.8923 + 8.59808i −0.530180 + 0.306100i
\(790\) 0 0
\(791\) 55.6410i 1.97837i
\(792\) 0 0
\(793\)