Properties

Label 576.2.bb.a.529.1
Level $576$
Weight $2$
Character 576.529
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 529.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 576.529
Dual form 576.2.bb.a.49.1

$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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 −0.183831 0.982958i \(-0.558850\pi\)
−0.650681 + 0.759351i \(0.725517\pi\)
\(6\) 0 0
\(7\) −3.86603 2.23205i −1.46122 0.843636i −0.462152 0.886801i \(-0.652923\pi\)
−0.999068 + 0.0431647i \(0.986256\pi\)
\(8\) 0 0
\(9\) 3.00000 1.00000
\(10\) 0 0
\(11\) 0.500000 + 1.86603i 0.150756 + 0.562628i 0.999432 + 0.0337145i \(0.0107337\pi\)
−0.848676 + 0.528913i \(0.822600\pi\)
\(12\) 0 0
\(13\) −0.598076 + 2.23205i −0.165876 + 0.619060i 0.832050 + 0.554700i \(0.187167\pi\)
−0.997927 + 0.0643593i \(0.979500\pi\)
\(14\) 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 0.961844 0.273597i \(-0.0882135\pi\)
−0.273597 + 0.961844i \(0.588214\pi\)
\(20\) 0 0
\(21\) 6.69615 + 3.86603i 1.46122 + 0.843636i
\(22\) 0 0
\(23\) 5.59808 3.23205i 1.16728 0.673929i 0.214242 0.976781i \(-0.431272\pi\)
0.953038 + 0.302851i \(0.0979386\pi\)
\(24\) 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 −0.338329 0.941028i \(-0.609862\pi\)
0.177512 + 0.984119i \(0.443195\pi\)
\(30\) 0 0
\(31\) 4.59808 + 7.96410i 0.825839 + 1.43039i 0.901277 + 0.433244i \(0.142631\pi\)
−0.0754376 + 0.997151i \(0.524035\pi\)
\(32\) 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 −0.964764 0.263117i \(-0.915249\pi\)
0.263117 + 0.964764i \(0.415249\pi\)
\(38\) 0 0
\(39\) 1.03590 3.86603i 0.165876 0.619060i
\(40\) 0 0
\(41\) 0.696152 0.401924i 0.108721 0.0627700i −0.444654 0.895703i \(-0.646673\pi\)
0.553374 + 0.832933i \(0.313340\pi\)
\(42\) 0 0
\(43\) 1.69615 + 6.33013i 0.258661 + 0.965335i 0.966017 + 0.258478i \(0.0832210\pi\)
−0.707356 + 0.706857i \(0.750112\pi\)
\(44\) 0 0
\(45\) −5.59808 1.50000i −0.834512 0.223607i
\(46\) 0 0
\(47\) 0.598076 1.03590i 0.0872384 0.151101i −0.819104 0.573644i \(-0.805529\pi\)
0.906343 + 0.422543i \(0.138862\pi\)
\(48\) 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 −0.193703 0.981060i \(-0.562050\pi\)
0.981060 + 0.193703i \(0.0620497\pi\)
\(54\) 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 0.355135 0.934815i \(-0.384435\pi\)
−0.159852 + 0.987141i \(0.551102\pi\)
\(60\) 0 0
\(61\) −2.13397 + 0.571797i −0.273227 + 0.0732111i −0.392831 0.919611i \(-0.628504\pi\)
0.119604 + 0.992822i \(0.461838\pi\)
\(62\) 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 −0.684686 0.728838i \(-0.740061\pi\)
0.957375 0.288849i \(-0.0932726\pi\)
\(68\) 0 0
\(69\) −9.69615 + 5.59808i −1.16728 + 0.673929i
\(70\) 0 0
\(71\) 2.92820i 0.347514i 0.984789 + 0.173757i \(0.0555907\pi\)
−0.984789 + 0.173757i \(0.944409\pi\)
\(72\) 0 0
\(73\) 7.46410i 0.873607i 0.899557 + 0.436804i \(0.143889\pi\)
−0.899557 + 0.436804i \(0.856111\pi\)
\(74\) 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 −0.813187 0.582003i \(-0.802269\pi\)
0.910622 + 0.413239i \(0.135603\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 14.1603 3.79423i 1.55429 0.416471i 0.623440 0.781872i \(-0.285735\pi\)
0.930850 + 0.365401i \(0.119068\pi\)
\(84\) 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 \(0.317673\pi\)
−0.541985 + 0.840388i \(0.682327\pi\)
\(90\) 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 −0.890292 0.455389i \(-0.849500\pi\)
0.839525 + 0.543321i \(0.182833\pi\)
\(98\) 0 0
\(99\) 1.50000 + 5.59808i 0.150756 + 0.562628i
\(100\) 0 0
\(101\) −0.133975 0.500000i −0.0133310 0.0497519i 0.958940 0.283609i \(-0.0915318\pi\)
−0.972271 + 0.233857i \(0.924865\pi\)
\(102\) 0 0
\(103\) −13.7942 + 7.96410i −1.35919 + 0.784726i −0.989514 0.144436i \(-0.953863\pi\)
−0.369672 + 0.929162i \(0.620530\pi\)
\(104\) 0 0
\(105\) −10.5622 10.5622i −1.03076 1.03076i
\(106\) 0 0
\(107\) −9.39230 + 9.39230i −0.907988 + 0.907988i −0.996110 0.0881214i \(-0.971914\pi\)
0.0881214 + 0.996110i \(0.471914\pi\)
\(108\) 0 0
\(109\) −1.73205 1.73205i −0.165900 0.165900i 0.619274 0.785175i \(-0.287427\pi\)
−0.785175 + 0.619274i \(0.787427\pi\)
\(110\) 0 0
\(111\) 7.39230 7.39230i 0.701647 0.701647i
\(112\) 0 0
\(113\) −6.23205 10.7942i −0.586262 1.01544i −0.994717 0.102657i \(-0.967266\pi\)
0.408455 0.912779i \(-0.366068\pi\)
\(114\) 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 −0.999204 0.0399004i \(-0.987296\pi\)
0.885286 + 0.465047i \(0.153963\pi\)
\(132\) 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 0.475375 0.879783i \(-0.342312\pi\)
−0.524227 + 0.851579i \(0.675646\pi\)
\(138\) 0 0
\(139\) −16.1603 4.33013i −1.37069 0.367277i −0.502962 0.864308i \(-0.667757\pi\)
−0.867732 + 0.497032i \(0.834423\pi\)
\(140\) 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 0.847427 0.530912i \(-0.178150\pi\)
0.468438 + 0.883497i \(0.344817\pi\)
\(150\) 0 0
\(151\) 6.06218 + 3.50000i 0.493333 + 0.284826i 0.725956 0.687741i \(-0.241398\pi\)
−0.232623 + 0.972567i \(0.574731\pi\)
\(152\) 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 −0.991835 0.127529i \(-0.959296\pi\)
0.922719 + 0.385474i \(0.125962\pi\)
\(158\) 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 0.778577 0.627549i \(-0.215942\pi\)
−0.627549 + 0.778577i \(0.715942\pi\)
\(164\) 0 0
\(165\) 6.46410i 0.503230i
\(166\) 0 0
\(167\) 14.2583 8.23205i 1.10334 0.637015i 0.166246 0.986084i \(-0.446835\pi\)
0.937097 + 0.349069i \(0.113502\pi\)
\(168\) 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 0.0418586 0.999124i \(-0.486672\pi\)
0.535812 + 0.844337i \(0.320005\pi\)
\(174\) 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 0.893051 0.449956i \(-0.148560\pi\)
−0.449956 + 0.893051i \(0.648560\pi\)
\(180\) 0 0
\(181\) −7.73205 + 7.73205i −0.574719 + 0.574719i −0.933443 0.358725i \(-0.883212\pi\)
0.358725 + 0.933443i \(0.383212\pi\)
\(182\) 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 −0.912278 0.409572i \(-0.865678\pi\)
0.810838 + 0.585270i \(0.199012\pi\)
\(192\) 0 0
\(193\) 2.23205 + 3.86603i 0.160667 + 0.278283i 0.935108 0.354363i \(-0.115302\pi\)
−0.774441 + 0.632646i \(0.781969\pi\)
\(194\) 0 0
\(195\) −3.86603 + 6.69615i −0.276852 + 0.479521i
\(196\) 0 0
\(197\) 3.53590 3.53590i 0.251922 0.251922i −0.569836 0.821758i \(-0.692993\pi\)
0.821758 + 0.569836i \(0.192993\pi\)
\(198\) 0 0
\(199\) 21.8564i 1.54936i 0.632354 + 0.774680i \(0.282089\pi\)
−0.632354 + 0.774680i \(0.717911\pi\)
\(200\) 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 −0.554629 0.832098i \(-0.687140\pi\)
0.896371 0.443304i \(-0.146194\pi\)
\(212\) 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 0.477734 + 0.878504i \(0.341458\pi\)
−0.999674 + 0.0255224i \(0.991875\pi\)
\(224\) 0 0
\(225\) −3.29423 1.90192i −0.219615 0.126795i
\(226\) 0 0
\(227\) −19.6244 + 5.25833i −1.30251 + 0.349008i −0.842400 0.538852i \(-0.818858\pi\)
−0.460114 + 0.887860i \(0.652191\pi\)
\(228\) 0 0
\(229\) 16.5263 + 4.42820i 1.09209 + 0.292624i 0.759539 0.650462i \(-0.225425\pi\)
0.332549 + 0.943086i \(0.392091\pi\)
\(230\) 0 0
\(231\) −3.86603 + 14.4282i −0.254366 + 0.949306i
\(232\) 0 0
\(233\) 9.07180i 0.594313i 0.954829 + 0.297157i \(0.0960383\pi\)
−0.954829 + 0.297157i \(0.903962\pi\)
\(234\) 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 0.878732 0.477316i \(-0.158390\pi\)
−0.852734 + 0.522346i \(0.825057\pi\)
\(240\) 0 0
\(241\) −2.76795 + 4.79423i −0.178299 + 0.308823i −0.941298 0.337576i \(-0.890393\pi\)
0.762999 + 0.646400i \(0.223726\pi\)
\(242\) 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 −0.144229 0.989544i \(-0.546070\pi\)
0.989544 + 0.144229i \(0.0460703\pi\)
\(252\) 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 0.943597 + 0.331096i \(0.107418\pi\)
−0.185061 + 0.982727i \(0.559248\pi\)
\(258\) 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 0.741090 0.671406i \(-0.234309\pi\)
−0.210910 + 0.977506i \(0.567643\pi\)
\(264\) 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 0.825144 0.564923i \(-0.191094\pi\)
−0.564923 + 0.825144i \(0.691094\pi\)
\(270\) 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 0.890844 0.454310i \(-0.150114\pi\)
−0.998648 + 0.0519775i \(0.983448\pi\)
\(278\) 0 0
\(279\) 13.7942 + 23.8923i 0.825839 + 1.43039i
\(280\) 0 0
\(281\) −10.0359 5.79423i −0.598692 0.345655i 0.169835 0.985472i \(-0.445676\pi\)
−0.768527 + 0.639818i \(0.779010\pi\)
\(282\) 0 0
\(283\) 13.1603 + 3.52628i 0.782296 + 0.209616i 0.627797 0.778377i \(-0.283957\pi\)
0.154499 + 0.987993i \(0.450624\pi\)
\(284\) 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 0.320614 0.947210i \(-0.396111\pi\)
−0.195945 + 0.980615i \(0.562778\pi\)
\(294\) 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 0.443693 0.896179i \(-0.353668\pi\)
−0.896179 + 0.443693i \(0.853668\pi\)
\(308\) 0 0
\(309\) 23.8923 13.7942i 1.35919 0.784726i
\(310\) 0 0
\(311\) −9.18653 + 5.30385i −0.520921 + 0.300754i −0.737311 0.675553i \(-0.763905\pi\)
0.216391 + 0.976307i \(0.430572\pi\)
\(312\) 0 0
\(313\) 25.1603 + 14.5263i 1.42214 + 0.821074i 0.996482 0.0838094i \(-0.0267087\pi\)
0.425660 + 0.904883i \(0.360042\pi\)
\(314\) 0 0
\(315\) 18.2942 + 18.2942i 1.03076 + 1.03076i
\(316\) 0 0
\(317\) −33.4545 + 8.96410i −1.87899 + 0.503474i −0.879364 + 0.476150i \(0.842032\pi\)
−0.999627 + 0.0273246i \(0.991301\pi\)
\(318\) 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 0.918577 0.395242i \(-0.129339\pi\)
−0.993132 + 0.116999i \(0.962672\pi\)
\(332\) 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 −0.999460 0.0328547i \(-0.989540\pi\)
0.471277 0.881985i \(-0.343793\pi\)
\(338\) 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 0.305961 0.952044i \(-0.401022\pi\)
−0.211052 + 0.977475i \(0.567689\pi\)
\(348\) 0 0
\(349\) −3.86603 + 1.03590i −0.206944 + 0.0554504i −0.360802 0.932643i \(-0.617497\pi\)
0.153858 + 0.988093i \(0.450830\pi\)
\(350\) 0 0
\(351\) 3.10770 11.5981i 0.165876 0.619060i
\(352\) 0 0
\(353\) −11.7679 + 20.3827i −0.626345 + 1.08486i 0.361934 + 0.932204i \(0.382116\pi\)
−0.988279 + 0.152657i \(0.951217\pi\)
\(354\) 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 \(0.276465\pi\)
−0.645942 + 0.763386i \(0.723535\pi\)
\(360\) 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 0.0986270 0.995124i \(-0.468555\pi\)
0.812490 0.582976i \(-0.198112\pi\)
\(368\) 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 0.217209 0.976125i \(-0.430305\pi\)
−0.299954 + 0.953954i \(0.596971\pi\)
\(374\) 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 −0.182484 0.983209i \(-0.558414\pi\)
0.983209 + 0.182484i \(0.0584137\pi\)
\(380\) 0 0
\(381\) 0.679492 0.0348114
\(382\) 0 0
\(383\) −3.66987 6.35641i −0.187522 0.324797i 0.756902 0.653529i \(-0.226712\pi\)
−0.944423 + 0.328732i \(0.893379\pi\)
\(384\) 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 0.999705 0.0243053i \(-0.00773738\pi\)
−0.877922 + 0.478803i \(0.841071\pi\)
\(390\) 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 0.990845 0.135002i \(-0.0431041\pi\)
−0.135002 + 0.990845i \(0.543104\pi\)
\(398\) 0 0
\(399\) 8.49038 + 31.6865i 0.425051 + 1.58631i
\(400\) 0 0
\(401\) −16.1603 27.9904i −0.807005 1.39777i −0.914929 0.403614i \(-0.867754\pi\)
0.107925 0.994159i \(-0.465579\pi\)
\(402\) 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 −0.899347 0.437236i \(-0.855957\pi\)
−0.0710154 + 0.997475i \(0.522624\pi\)
\(410\) 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 −0.732105 0.681191i \(-0.761462\pi\)
0.974618 0.223876i \(-0.0718712\pi\)
\(420\) 0 0
\(421\) −4.79423 17.8923i −0.233656 0.872018i −0.978750 0.205058i \(-0.934262\pi\)
0.745094 0.666960i \(-0.232405\pi\)
\(422\) 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 0.351563 0.936164i \(-0.385650\pi\)
−0.634960 + 0.772545i \(0.718984\pi\)
\(440\) 0 0
\(441\) 19.3923 + 33.5885i 0.923443 + 1.59945i
\(442\) 0 0
\(443\) 1.16025 + 4.33013i 0.0551253 + 0.205731i 0.987996 0.154482i \(-0.0493708\pi\)
−0.932870 + 0.360213i \(0.882704\pi\)
\(444\) 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 0.963747 0.266818i \(-0.0859722\pi\)
0.250802 + 0.968038i \(0.419306\pi\)
\(458\) 0 0
\(459\) −20.7846 −0.970143
\(460\) 0 0
\(461\) 4.59808 1.23205i 0.214154 0.0573823i −0.150147 0.988664i \(-0.547975\pi\)
0.364301 + 0.931281i \(0.381308\pi\)
\(462\) 0 0
\(463\) 5.33013 + 9.23205i 0.247712 + 0.429050i 0.962891 0.269892i \(-0.0869880\pi\)
−0.715179 + 0.698942i \(0.753655\pi\)
\(464\) 0 0
\(465\) 7.96410 + 29.7224i 0.369326 + 1.37834i
\(466\) 0 0
\(467\) −21.7846 21.7846i −1.00807 1.00807i −0.999967 0.00810436i \(-0.997420\pi\)
−0.00810436 0.999967i \(-0.502580\pi\)
\(468\) 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 −0.996541 0.0830995i \(-0.973518\pi\)
0.570237 + 0.821480i \(0.306851\pi\)
\(480\) 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 \(0.0491254\pi\)
−0.988114 + 0.153720i \(0.950875\pi\)
\(488\) 0 0
\(489\) −3.33975 3.33975i −0.151029 0.151029i
\(490\) 0 0
\(491\) −0.500000 0.133975i −0.0225647 0.00604619i 0.247519 0.968883i \(-0.420385\pi\)
−0.270084 + 0.962837i \(0.587051\pi\)
\(492\) 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 −0.887122 0.461534i \(-0.847299\pi\)
0.999038 + 0.0438606i \(0.0139657\pi\)
\(500\) 0 0
\(501\) −24.6962 + 14.2583i −1.10334 + 0.637015i
\(502\) 0 0
\(503\) 13.8564i 0.617827i −0.951090 0.308913i \(-0.900035\pi\)
0.951090 0.308913i \(-0.0999653\pi\)
\(504\) 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 −0.932415 0.361389i \(-0.882303\pi\)
0.988190 + 0.153236i \(0.0489693\pi\)
\(510\) 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 \(-0.630698\pi\)
0.399160 0.916881i \(-0.369302\pi\)
\(522\) 0 0
\(523\) −22.1244 + 22.1244i −0.967431 + 0.967431i −0.999486 0.0320556i \(-0.989795\pi\)
0.0320556 + 0.999486i \(0.489795\pi\)
\(524\) 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 0.306856 0.951756i \(-0.400723\pi\)
−0.951756 + 0.306856i \(0.900723\pi\)
\(542\) 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 −0.685962 0.727637i \(-0.740618\pi\)
−0.230242 + 0.973133i \(0.573952\pi\)
\(548\) 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 −0.999868 0.0162292i \(-0.994834\pi\)
−0.0162292 0.999868i \(-0.505166\pi\)
\(558\) 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 −0.922604 0.385749i \(-0.873943\pi\)
0.991873 + 0.127233i \(0.0406096\pi\)
\(564\) 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 −0.202667 0.979248i \(-0.564961\pi\)
−0.949387 + 0.314109i \(0.898294\pi\)
\(570\) 0 0
\(571\) −39.5526 10.5981i −1.65522 0.443516i −0.694155 0.719826i \(-0.744222\pi\)
−0.961068 + 0.276310i \(0.910888\pi\)
\(572\) 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 −0.998213 0.0597617i \(-0.980966\pi\)
0.834597 0.550861i \(-0.185701\pi\)
\(588\) 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 0.269688 0.962948i \(-0.413079\pi\)
0.968781 + 0.247917i \(0.0797461\pi\)
\(600\) 0 0
\(601\) −26.7679 15.4545i −1.09189 0.630401i −0.157809 0.987470i \(-0.550443\pi\)
−0.934078 + 0.357068i \(0.883776\pi\)
\(602\) 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 0.853633 0.520876i \(-0.174394\pi\)
−0.877908 + 0.478830i \(0.841061\pi\)
\(608\) 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 −0.0462032 0.998932i \(-0.514712\pi\)
0.998932 + 0.0462032i \(0.0147122\pi\)
\(614\) 0 0
\(615\) 2.59808 0.696152i 0.104765 0.0280716i
\(616\) 0 0
\(617\) 23.0885 13.3301i 0.929506 0.536651i 0.0428509 0.999081i \(-0.486356\pi\)
0.886655 + 0.462431i \(0.153023\pi\)
\(618\) 0 0
\(619\) 1.91154 + 7.13397i 0.0768314 + 0.286739i 0.993642 0.112583i \(-0.0359124\pi\)
−0.916811 + 0.399322i \(0.869246\pi\)
\(620\) 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 \(-0.895165\pi\)
0.946254 0.323425i \(-0.104835\pi\)
\(632\) 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 −0.624075 0.781365i \(-0.714524\pi\)
0.988719 + 0.149782i \(0.0478573\pi\)
\(642\) 0 0
\(643\) −7.96410 + 29.7224i −0.314074 + 1.17214i 0.610776 + 0.791804i \(0.290858\pi\)
−0.924849 + 0.380334i \(0.875809\pi\)
\(644\) 0 0
\(645\) 21.9282i 0.863422i
\(646\) 0 0
\(647\) 25.6077i 1.00674i −0.864070 0.503371i \(-0.832093\pi\)
0.864070 0.503371i \(-0.167907\pi\)
\(648\) 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 0.0296324 + 0.999561i \(0.490566\pi\)
−0.525443 + 0.850829i \(0.676100\pi\)
\(654\) 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 −0.282736 0.959198i \(-0.591242\pi\)
0.234742 + 0.972058i \(0.424575\pi\)
\(660\) 0 0
\(661\) 19.7942 + 5.30385i 0.769906 + 0.206296i 0.622330 0.782755i \(-0.286186\pi\)
0.147576 + 0.989051i \(0.452853\pi\)
\(662\) 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 −0.0931795 0.995649i \(-0.529703\pi\)
0.908847 0.417129i \(-0.136964\pi\)
\(674\) 0 0
\(675\) 5.70577 + 3.29423i 0.219615 + 0.126795i
\(676\) 0 0
\(677\) 2.34936 + 8.76795i 0.0902934 + 0.336980i 0.996264 0.0863612i \(-0.0275239\pi\)
−0.905970 + 0.423341i \(0.860857\pi\)
\(678\) 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 −0.937353 0.348382i \(-0.886731\pi\)
0.348382 + 0.937353i \(0.386731\pi\)
\(684\) 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 −0.221266 0.975213i \(-0.571019\pi\)
0.295984 + 0.955193i \(0.404352\pi\)
\(692\) 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 0.951553 0.307486i \(-0.0994878\pi\)
−0.307486 + 0.951553i \(0.599488\pi\)
\(702\) 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 0.846102 + 0.533022i \(0.178944\pi\)
−0.466235 + 0.884661i \(0.654390\pi\)
\(710\) 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 0.442139 0.896947i \(-0.354220\pi\)
−0.555709 + 0.831377i \(0.687553\pi\)
\(728\) 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 −0.612868 0.790185i \(-0.709984\pi\)
0.925852 0.377887i \(-0.123349\pi\)
\(734\) 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 0.999450 0.0331677i \(-0.0105595\pi\)
−0.0331677 + 0.999450i \(0.510560\pi\)
\(740\) 0 0
\(741\) 14.7058 8.49038i 0.540230 0.311902i
\(742\) 0 0
\(743\) −25.1147 + 14.5000i −0.921370 + 0.531953i −0.884072 0.467351i \(-0.845209\pi\)
−0.0372984 + 0.999304i \(0.511875\pi\)
\(744\) 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 0.824718 + 0.565544i \(0.191334\pi\)
0.0774160 + 0.996999i \(0.475333\pi\)
\(752\) 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 −0.678644 0.734467i \(-0.737432\pi\)
0.734467 + 0.678644i \(0.237432\pi\)
\(758\) 0 0
\(759\) −15.2942 15.2942i −0.555145 0.555145i
\(760\) 0 0
\(761\) −16.2846 + 9.40192i −0.590317 + 0.340819i −0.765223 0.643766i \(-0.777371\pi\)
0.174906 + 0.984585i \(0.444038\pi\)
\(762\) 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 0.795993 0.605305i \(-0.206949\pi\)
−0.922207 + 0.386698i \(0.873616\pi\)
\(770\) 0 0
\(771\) −21.0622 36.4808i −0.758536 1.31382i
\(772\) 0 0
\(773\) −23.5885 + 23.5885i −0.848418 + 0.848418i −0.989936 0.141518i \(-0.954802\pi\)
0.141518 + 0.989936i \(0.454802\pi\)
\(774\) 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 −0.979007 0.203828i \(-0.934662\pi\)
0.949759 + 0.312983i \(0.101328\pi\)
\(788\) 0 0
\(789\) −14.8923 8.59808i −0.530180 0.306100i
\(790\) 0 0
\(791\) 55.6410i 1.97837i
\(792\) 0 0
\(793\)