Properties

Label 576.2.bb.b.337.1
Level $576$
Weight $2$
Character 576.337
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 337.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 576.337
Dual form 576.2.bb.b.241.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.73205i q^{3} +(0.500000 + 1.86603i) q^{5} +(3.86603 - 2.23205i) q^{7} -3.00000 q^{9} +O(q^{10})\) \(q-1.73205i q^{3} +(0.500000 + 1.86603i) q^{5} +(3.86603 - 2.23205i) q^{7} -3.00000 q^{9} +(-1.86603 - 0.500000i) q^{11} +(2.23205 - 0.598076i) q^{13} +(3.23205 - 0.866025i) q^{15} +4.00000 q^{17} +(3.00000 + 3.00000i) q^{19} +(-3.86603 - 6.69615i) q^{21} +(-5.59808 - 3.23205i) q^{23} +(1.09808 - 0.633975i) q^{25} +5.19615i q^{27} +(0.232051 - 0.866025i) q^{29} +(4.59808 - 7.96410i) q^{31} +(-0.866025 + 3.23205i) q^{33} +(6.09808 + 6.09808i) q^{35} +(-4.26795 + 4.26795i) q^{37} +(-1.03590 - 3.86603i) q^{39} +(-0.696152 - 0.401924i) q^{41} +(-6.33013 - 1.69615i) q^{43} +(-1.50000 - 5.59808i) q^{45} +(0.598076 + 1.03590i) q^{47} +(6.46410 - 11.1962i) q^{49} -6.92820i q^{51} +(5.73205 - 5.73205i) q^{53} -3.73205i q^{55} +(5.19615 - 5.19615i) q^{57} +(-0.401924 - 1.50000i) q^{59} +(0.571797 - 2.13397i) q^{61} +(-11.5981 + 6.69615i) q^{63} +(2.23205 + 3.86603i) q^{65} +(-8.33013 + 2.23205i) q^{67} +(-5.59808 + 9.69615i) q^{69} +2.92820i q^{71} +7.46410i q^{73} +(-1.09808 - 1.90192i) q^{75} +(-8.33013 + 2.23205i) q^{77} +(0.866025 + 1.50000i) q^{79} +9.00000 q^{81} +(-3.79423 + 14.1603i) q^{83} +(2.00000 + 7.46410i) q^{85} +(-1.50000 - 0.401924i) q^{87} +15.8564i q^{89} +(7.29423 - 7.29423i) q^{91} +(-13.7942 - 7.96410i) q^{93} +(-4.09808 + 7.09808i) q^{95} +(-0.500000 - 0.866025i) q^{97} +(5.59808 + 1.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{5} + 12q^{7} - 12q^{9} + O(q^{10}) \) \( 4q + 2q^{5} + 12q^{7} - 12q^{9} - 4q^{11} + 2q^{13} + 6q^{15} + 16q^{17} + 12q^{19} - 12q^{21} - 12q^{23} - 6q^{25} - 6q^{29} + 8q^{31} + 14q^{35} - 24q^{37} - 18q^{39} + 18q^{41} - 8q^{43} - 6q^{45} - 8q^{47} + 12q^{49} + 16q^{53} - 12q^{59} + 30q^{61} - 36q^{63} + 2q^{65} - 16q^{67} - 12q^{69} + 6q^{75} - 16q^{77} + 36q^{81} + 16q^{83} + 8q^{85} - 6q^{87} - 2q^{91} - 24q^{93} - 6q^{95} - 2q^{97} + 12q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) 1.73205i 1.00000i
\(4\) 0 0
\(5\) 0.500000 + 1.86603i 0.223607 + 0.834512i 0.982958 + 0.183831i \(0.0588499\pi\)
−0.759351 + 0.650681i \(0.774483\pi\)
\(6\) 0 0
\(7\) 3.86603 2.23205i 1.46122 0.843636i 0.462152 0.886801i \(-0.347077\pi\)
0.999068 + 0.0431647i \(0.0137440\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) −1.86603 0.500000i −0.562628 0.150756i −0.0337145 0.999432i \(-0.510734\pi\)
−0.528913 + 0.848676i \(0.677400\pi\)
\(12\) 0 0
\(13\) 2.23205 0.598076i 0.619060 0.165876i 0.0643593 0.997927i \(-0.479500\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 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
\(21\) −3.86603 6.69615i −0.843636 1.46122i
\(22\) 0 0
\(23\) −5.59808 3.23205i −1.16728 0.673929i −0.214242 0.976781i \(-0.568728\pi\)
−0.953038 + 0.302851i \(0.902061\pi\)
\(24\) 0 0
\(25\) 1.09808 0.633975i 0.219615 0.126795i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 0.232051 0.866025i 0.0430908 0.160817i −0.941028 0.338329i \(-0.890138\pi\)
0.984119 + 0.177512i \(0.0568049\pi\)
\(30\) 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 −0.964764 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 \(-0.353327\pi\)
−0.553374 + 0.832933i \(0.686660\pi\)
\(42\) 0 0
\(43\) −6.33013 1.69615i −0.965335 0.258661i −0.258478 0.966017i \(-0.583221\pi\)
−0.706857 + 0.707356i \(0.749888\pi\)
\(44\) 0 0
\(45\) −1.50000 5.59808i −0.223607 0.834512i
\(46\) 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
\(51\) 6.92820i 0.970143i
\(52\) 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
\(59\) −0.401924 1.50000i −0.0523260 0.195283i 0.934815 0.355135i \(-0.115565\pi\)
−0.987141 + 0.159852i \(0.948898\pi\)
\(60\) 0 0
\(61\) 0.571797 2.13397i 0.0732111 0.273227i −0.919611 0.392831i \(-0.871496\pi\)
0.992822 + 0.119604i \(0.0381624\pi\)
\(62\) 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
\(67\) −8.33013 + 2.23205i −1.01769 + 0.272688i −0.728838 0.684686i \(-0.759939\pi\)
−0.288849 + 0.957375i \(0.593273\pi\)
\(68\) 0 0
\(69\) −5.59808 + 9.69615i −0.673929 + 1.16728i
\(70\) 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
\(75\) −1.09808 1.90192i −0.126795 0.219615i
\(76\) 0 0
\(77\) −8.33013 + 2.23205i −0.949306 + 0.254366i
\(78\) 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
\(83\) −3.79423 + 14.1603i −0.416471 + 1.55429i 0.365401 + 0.930850i \(0.380932\pi\)
−0.781872 + 0.623440i \(0.785735\pi\)
\(84\) 0 0
\(85\) 2.00000 + 7.46410i 0.216930 + 0.809595i
\(86\) 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
\(93\) −13.7942 7.96410i −1.43039 0.825839i
\(94\) 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
\(99\) 5.59808 + 1.50000i 0.562628 + 0.150756i
\(100\) 0 0
\(101\) 0.500000 + 0.133975i 0.0497519 + 0.0133310i 0.283609 0.958940i \(-0.408468\pi\)
−0.233857 + 0.972271i \(0.575135\pi\)
\(102\) 0 0
\(103\) 13.7942 + 7.96410i 1.35919 + 0.784726i 0.989514 0.144436i \(-0.0461369\pi\)
0.369672 + 0.929162i \(0.379470\pi\)
\(104\) 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 0.408455 + 0.912779i \(0.366068\pi\)
−0.994717 + 0.102657i \(0.967266\pi\)
\(114\) 0 0
\(115\) 3.23205 12.0622i 0.301390 1.12480i
\(116\) 0 0
\(117\) −6.69615 + 1.79423i −0.619060 + 0.165876i
\(118\) 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
\(123\) −0.696152 + 1.20577i −0.0627700 + 0.108721i
\(124\) 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
\(131\) 4.86603 1.30385i 0.425147 0.113918i −0.0399004 0.999204i \(-0.512704\pi\)
0.465047 + 0.885286i \(0.346037\pi\)
\(132\) 0 0
\(133\) 18.2942 + 4.90192i 1.58631 + 0.425051i
\(134\) 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 \(-0.657688\pi\)
0.524227 + 0.851579i \(0.324354\pi\)
\(138\) 0 0
\(139\) 4.33013 + 16.1603i 0.367277 + 1.37069i 0.864308 + 0.502962i \(0.167757\pi\)
−0.497032 + 0.867732i \(0.665577\pi\)
\(140\) 0 0
\(141\) 1.79423 1.03590i 0.151101 0.0872384i
\(142\) 0 0
\(143\) −4.46410 −0.373307
\(144\) 0 0
\(145\) 1.73205 0.143839
\(146\) 0 0
\(147\) −19.3923 11.1962i −1.59945 0.923443i
\(148\) 0 0
\(149\) −4.30385 16.0622i −0.352585 1.31586i −0.883497 0.468438i \(-0.844817\pi\)
0.530912 0.847427i \(-0.321850\pi\)
\(150\) 0 0
\(151\) −6.06218 + 3.50000i −0.493333 + 0.284826i −0.725956 0.687741i \(-0.758602\pi\)
0.232623 + 0.972567i \(0.425269\pi\)
\(152\) 0 0
\(153\) −12.0000 −0.970143
\(154\) 0 0
\(155\) 17.1603 + 4.59808i 1.37834 + 0.369326i
\(156\) 0 0
\(157\) 3.23205 0.866025i 0.257946 0.0691164i −0.127529 0.991835i \(-0.540704\pi\)
0.385474 + 0.922719i \(0.374038\pi\)
\(158\) 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
\(165\) −6.46410 −0.503230
\(166\) 0 0
\(167\) −14.2583 8.23205i −1.10334 0.637015i −0.166246 0.986084i \(-0.553165\pi\)
−0.937097 + 0.349069i \(0.886498\pi\)
\(168\) 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
\(173\) −2.03590 + 7.59808i −0.154786 + 0.577671i 0.844337 + 0.535812i \(0.179995\pi\)
−0.999124 + 0.0418586i \(0.986672\pi\)
\(174\) 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
\(187\) −7.46410 2.00000i −0.545829 0.146254i
\(188\) 0 0
\(189\) 11.5981 + 20.0885i 0.843636 + 1.46122i
\(190\) 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
\(195\) 6.69615 3.86603i 0.479521 0.276852i
\(196\) 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
\(203\) −1.03590 3.86603i −0.0727058 0.271342i
\(204\) 0 0
\(205\) 0.401924 1.50000i 0.0280716 0.104765i
\(206\) 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
\(211\) −18.5263 + 4.96410i −1.27540 + 0.341743i −0.832098 0.554629i \(-0.812860\pi\)
−0.443304 + 0.896371i \(0.646194\pi\)
\(212\) 0 0
\(213\) 5.07180 0.347514
\(214\) 0 0
\(215\) 12.6603i 0.863422i
\(216\) 0 0
\(217\) 41.0526i 2.78683i
\(218\) 0 0
\(219\) 12.9282 0.873607
\(220\) 0 0
\(221\) 8.92820 2.39230i 0.600576 0.160924i
\(222\) 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
\(227\) 5.25833 19.6244i 0.349008 1.30251i −0.538852 0.842400i \(-0.681142\pi\)
0.887860 0.460114i \(-0.152191\pi\)
\(228\) 0 0
\(229\) −4.42820 16.5263i −0.292624 1.09209i −0.943086 0.332549i \(-0.892091\pi\)
0.650462 0.759539i \(-0.274575\pi\)
\(230\) 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
\(237\) 2.59808 1.50000i 0.168763 0.0974355i
\(238\) 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
\(243\) 15.5885i 1.00000i
\(244\) 0 0
\(245\) 24.1244 + 6.46410i 1.54125 + 0.412976i
\(246\) 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 −0.185061 0.982727i \(-0.559248\pi\)
0.943597 0.331096i \(-0.107418\pi\)
\(258\) 0 0
\(259\) −6.97372 + 26.0263i −0.433326 + 1.61719i
\(260\) 0 0
\(261\) −0.696152 + 2.59808i −0.0430908 + 0.160817i
\(262\) 0 0
\(263\) −8.59808 + 4.96410i −0.530180 + 0.306100i −0.741090 0.671406i \(-0.765691\pi\)
0.210910 + 0.977506i \(0.432357\pi\)
\(264\) 0 0
\(265\) 13.5622 + 7.83013i 0.833118 + 0.481001i
\(266\) 0 0
\(267\) 27.4641 1.68078
\(268\) 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
\(275\) −2.36603 + 0.633975i −0.142677 + 0.0382301i
\(276\) 0 0
\(277\) 6.69615 + 1.79423i 0.402333 + 0.107805i 0.454310 0.890844i \(-0.349886\pi\)
−0.0519775 + 0.998648i \(0.516552\pi\)
\(278\) 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 \(-0.554324\pi\)
0.768527 + 0.639818i \(0.220990\pi\)
\(282\) 0 0
\(283\) −3.52628 13.1603i −0.209616 0.782296i −0.987993 0.154499i \(-0.950624\pi\)
0.778377 0.627797i \(-0.216043\pi\)
\(284\) 0 0
\(285\) 12.2942 + 7.09808i 0.728247 + 0.420454i
\(286\) 0 0
\(287\) −3.58846 −0.211820
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) −1.50000 + 0.866025i −0.0879316 + 0.0507673i
\(292\) 0 0
\(293\) −0.571797 2.13397i −0.0334047 0.124668i 0.947210 0.320614i \(-0.103889\pi\)
−0.980615 + 0.195945i \(0.937222\pi\)
\(294\) 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
\(299\) −14.4282 3.86603i −0.834405 0.223578i
\(300\) 0 0
\(301\) −28.2583 + 7.57180i −1.62878 + 0.436431i
\(302\) 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
\(309\) 13.7942 23.8923i 0.784726 1.35919i
\(310\) 0 0
\(311\) 9.18653 + 5.30385i 0.520921 + 0.300754i 0.737311 0.675553i \(-0.236095\pi\)
−0.216391 + 0.976307i \(0.569428\pi\)
\(312\) 0 0
\(313\) −25.1603 + 14.5263i −1.42214 + 0.821074i −0.996482 0.0838094i \(-0.973291\pi\)
−0.425660 + 0.904883i \(0.639958\pi\)
\(314\) 0 0
\(315\) −18.2942 18.2942i −1.03076 1.03076i
\(316\) 0 0
\(317\) 8.96410 33.4545i 0.503474 1.87899i 0.0273246 0.999627i \(-0.491301\pi\)
0.476150 0.879364i \(-0.342032\pi\)
\(318\) 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
\(331\) 5.06218 + 1.35641i 0.278242 + 0.0745548i 0.395242 0.918577i \(-0.370661\pi\)
−0.116999 + 0.993132i \(0.537328\pi\)
\(332\) 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
\(339\) 18.6962 + 10.7942i 1.01544 + 0.586262i
\(340\) 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
\(347\) −0.473721 1.76795i −0.0254307 0.0949085i 0.952044 0.305961i \(-0.0989776\pi\)
−0.977475 + 0.211052i \(0.932311\pi\)
\(348\) 0 0
\(349\) 1.03590 3.86603i 0.0554504 0.206944i −0.932643 0.360802i \(-0.882503\pi\)
0.988093 + 0.153858i \(0.0491698\pi\)
\(350\) 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
\(355\) −5.46410 + 1.46410i −0.290004 + 0.0777064i
\(356\) 0 0
\(357\) −15.4641 26.7846i −0.818447 1.41759i
\(358\) 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
\(363\) −6.29423 + 10.9019i −0.330361 + 0.572203i
\(364\) 0 0
\(365\) −13.9282 + 3.73205i −0.729035 + 0.195344i
\(366\) 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
\(371\) 9.36603 34.9545i 0.486260 1.81475i
\(372\) 0 0
\(373\) 0.428203 + 1.59808i 0.0221715 + 0.0827452i 0.976125 0.217209i \(-0.0696953\pi\)
−0.953954 + 0.299954i \(0.903029\pi\)
\(374\) 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
\(381\) 0.679492i 0.0348114i
\(382\) 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
\(387\) 18.9904 + 5.08846i 0.965335 + 0.258661i
\(388\) 0 0
\(389\) −8.96410 2.40192i −0.454498 0.121782i 0.0243053 0.999705i \(-0.492263\pi\)
−0.478803 + 0.877922i \(0.658929\pi\)
\(390\) 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 0.107925 + 0.994159i \(0.465579\pi\)
−0.914929 + 0.403614i \(0.867754\pi\)
\(402\) 0 0
\(403\) 5.50000 20.5263i 0.273975 1.02249i
\(404\) 0 0
\(405\) 4.50000 + 16.7942i 0.223607 + 0.834512i
\(406\) 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 \(-0.144043\pi\)
0.0710154 + 0.997475i \(0.477376\pi\)
\(410\) 0 0
\(411\) −0.571797 0.990381i −0.0282047 0.0488519i
\(412\) 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
\(419\) −18.5263 + 4.96410i −0.905068 + 0.242512i −0.681191 0.732105i \(-0.738538\pi\)
−0.223876 + 0.974618i \(0.571871\pi\)
\(420\) 0 0
\(421\) 17.8923 + 4.79423i 0.872018 + 0.233656i 0.666960 0.745094i \(-0.267595\pi\)
0.205058 + 0.978750i \(0.434262\pi\)
\(422\) 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
\(427\) −2.55256 9.52628i −0.123527 0.461009i
\(428\) 0 0
\(429\) 7.73205i 0.373307i
\(430\) 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
\(435\) 3.00000i 0.143839i
\(436\) 0 0
\(437\) −7.09808 26.4904i −0.339547 1.26721i
\(438\) 0 0
\(439\) 5.93782 3.42820i 0.283397 0.163619i −0.351563 0.936164i \(-0.614350\pi\)
0.634960 + 0.772545i \(0.281016\pi\)
\(440\) 0 0
\(441\) −19.3923 + 33.5885i −0.923443 + 1.59945i
\(442\) 0 0
\(443\) −4.33013 1.16025i −0.205731 0.0551253i 0.154482 0.987996i \(-0.450629\pi\)
−0.360213 + 0.932870i \(0.617296\pi\)
\(444\) 0 0
\(445\) −29.5885 + 7.92820i −1.40263 + 0.375833i
\(446\) 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
\(453\) 6.06218 + 10.5000i 0.284826 + 0.493333i
\(454\) 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 \(-0.914028\pi\)
−0.250802 + 0.968038i \(0.580694\pi\)
\(458\) 0 0
\(459\) 20.7846i 0.970143i
\(460\) 0 0
\(461\) −1.23205 + 4.59808i −0.0573823 + 0.214154i −0.988664 0.150147i \(-0.952025\pi\)
0.931281 + 0.364301i \(0.118692\pi\)
\(462\) 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 −0.999967 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
\(475\) 5.19615 + 1.39230i 0.238416 + 0.0638833i
\(476\) 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
\(483\) 49.9808i 2.27420i
\(484\) 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
\(491\) 0.133975 + 0.500000i 0.00604619 + 0.0225647i 0.968883 0.247519i \(-0.0796153\pi\)
−0.962837 + 0.270084i \(0.912949\pi\)
\(492\) 0 0
\(493\) 0.928203 3.46410i 0.0418042 0.156015i
\(494\) 0 0
\(495\) 11.1962i 0.503230i
\(496\) 0 0
\(497\) 6.53590 + 11.3205i 0.293175 + 0.507794i
\(498\) 0 0
\(499\) −9.33013 + 2.50000i −0.417674 + 0.111915i −0.461534 0.887122i \(-0.652701\pi\)
0.0438606 + 0.999038i \(0.486034\pi\)
\(500\) 0 0
\(501\) −14.2583 + 24.6962i −0.637015 + 1.10334i
\(502\) 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
\(507\) 6.63397 + 11.4904i 0.294625 + 0.510306i
\(508\) 0 0
\(509\) −4.69615 + 1.25833i −0.208153 + 0.0557745i −0.361389 0.932415i \(-0.617697\pi\)
0.153236 + 0.988190i \(0.451031\pi\)
\(510\) 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
\(515\) −7.96410 + 29.7224i −0.350940 + 1.30973i
\(516\) 0 0
\(517\) −0.598076 2.23205i −0.0263034 0.0981655i
\(518\) 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
\(525\) −8.49038 4.90192i −0.370551 0.213937i
\(526\) 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
\(531\) 1.20577 + 4.50000i 0.0523260 + 0.195283i
\(532\) 0 0
\(533\) −1.79423 0.480762i −0.0777167 0.0208241i
\(534\) 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
\(547\) 5.74167 21.4282i 0.245496 0.916204i −0.727637 0.685962i \(-0.759382\pi\)
0.973133 0.230242i \(-0.0739517\pi\)
\(548\) 0 0
\(549\) −1.71539 + 6.40192i −0.0732111 + 0.273227i
\(550\) 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
\(555\) −10.0981 + 17.4904i −0.428639 + 0.742425i
\(556\) 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
\(563\) −6.13397 + 1.64359i −0.258516 + 0.0692692i −0.385749 0.922604i \(-0.626057\pi\)
0.127233 + 0.991873i \(0.459390\pi\)
\(564\) 0 0
\(565\) −23.2583 6.23205i −0.978485 0.262184i
\(566\) 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 \(-0.435039\pi\)
0.949387 + 0.314109i \(0.101706\pi\)
\(570\) 0 0
\(571\) 10.5981 + 39.5526i 0.443516 + 1.65522i 0.719826 + 0.694155i \(0.244222\pi\)
−0.276310 + 0.961068i \(0.589112\pi\)
\(572\) 0 0
\(573\) −4.20577 + 2.42820i −0.175699 + 0.101440i
\(574\) 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
\(579\) −6.69615 3.86603i −0.278283 0.160667i
\(580\) 0 0
\(581\) 16.9378 + 63.2128i 0.702699 + 2.62251i
\(582\) 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
\(587\) 14.7942 + 3.96410i 0.610623 + 0.163616i 0.550861 0.834597i \(-0.314299\pi\)
0.0597617 + 0.998213i \(0.480966\pi\)
\(588\) 0 0
\(589\) 37.6865 10.0981i 1.55285 0.416084i
\(590\) 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
\(597\) 37.8564 1.54936
\(598\) 0 0
\(599\) −30.3109 17.5000i −1.23847 0.715031i −0.269688 0.962948i \(-0.586921\pi\)
−0.968781 + 0.247917i \(0.920254\pi\)
\(600\) 0 0
\(601\) 26.7679 15.4545i 1.09189 0.630401i 0.157809 0.987470i \(-0.449557\pi\)
0.934078 + 0.357068i \(0.116224\pi\)
\(602\) 0 0
\(603\) 24.9904 6.69615i 1.01769 0.272688i
\(604\) 0 0
\(605\) 3.63397 13.5622i 0.147742 0.551381i
\(606\) 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 −0.0462032 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 \(-0.513644\pi\)
−0.886655 + 0.462431i \(0.846977\pi\)
\(618\) 0 0
\(619\) −7.13397 1.91154i −0.286739 0.0768314i 0.112583 0.993642i \(-0.464088\pi\)
−0.399322 + 0.916811i \(0.630754\pi\)
\(620\) 0 0
\(621\) 16.7942 29.0885i 0.673929 1.16728i
\(622\) 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
\(627\) −12.2942 + 7.09808i −0.490984 + 0.283470i
\(628\) 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
\(635\) −0.196152 0.732051i −0.00778407 0.0290506i
\(636\) 0 0
\(637\) 7.73205 28.8564i 0.306355 1.14333i
\(638\) 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
\(643\) 29.7224 7.96410i 1.17214 0.314074i 0.380334 0.924849i \(-0.375809\pi\)
0.791804 + 0.610776i \(0.209142\pi\)
\(644\) 0 0
\(645\) −21.9282 −0.863422
\(646\) 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
\(651\) −71.1051 −2.78683
\(652\) 0 0
\(653\) 47.2846 12.6699i 1.85039 0.495810i 0.850829 0.525443i \(-0.176100\pi\)
0.999561 + 0.0296324i \(0.00943367\pi\)
\(654\) 0 0
\(655\) 4.86603 + 8.42820i 0.190131 + 0.329317i
\(656\) 0 0
\(657\) 22.3923i 0.873607i
\(658\) 0 0
\(659\) 0.330127 1.23205i 0.0128599 0.0479939i −0.959198 0.282736i \(-0.908758\pi\)
0.972058 + 0.234742i \(0.0754246\pi\)
\(660\) 0 0
\(661\) −5.30385 19.7942i −0.206296 0.769906i −0.989051 0.147576i \(-0.952853\pi\)
0.782755 0.622330i \(-0.213814\pi\)
\(662\) 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
\(669\) −23.3827 + 13.5000i −0.904027 + 0.521940i
\(670\) 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
\(675\) 3.29423 + 5.70577i 0.126795 + 0.219615i
\(676\) 0 0
\(677\) −8.76795 2.34936i −0.336980 0.0902934i 0.0863612 0.996264i \(-0.472476\pi\)
−0.423341 + 0.905970i \(0.639143\pi\)
\(678\) 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
\(691\) −0.526279 + 1.96410i −0.0200206 + 0.0747179i −0.975213 0.221266i \(-0.928981\pi\)
0.955193 + 0.295984i \(0.0956476\pi\)
\(692\) 0 0
\(693\) 24.9904 6.69615i 0.949306 0.254366i
\(694\) 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
\(699\) 15.7128 0.594313
\(700\) 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
\(707\) 2.23205 0.598076i 0.0839449 0.0224930i
\(708\) 0 0
\(709\) −37.7487 10.1147i −1.41768 0.379867i −0.533022 0.846102i \(-0.678944\pi\)
−0.884661 + 0.466235i \(0.845610\pi\)
\(710\) 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
\(715\) −2.23205 8.33013i −0.0834740 0.311529i
\(716\) 0 0
\(717\) −1.20577 0.696152i −0.0450304 0.0259983i
\(718\) 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
\(723\) −8.30385 + 4.79423i −0.308823 + 0.178299i
\(724\) 0 0
\(725\) −0.294229 1.09808i −0.0109274 0.0407815i
\(726\) 0 0
\(727\) 3.06218 1.76795i 0.113570 0.0655696i −0.442139 0.896947i \(-0.645780\pi\)
0.555709 + 0.831377i \(0.312447\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −25.3205 6.78461i −0.936513 0.250938i
\(732\) 0 0
\(733\) −31.6244 + 8.47372i −1.16807 + 0.312984i −0.790185 0.612868i \(-0.790016\pi\)
−0.377887 + 0.925852i \(0.623349\pi\)
\(734\) 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
\(741\) 8.49038 14.7058i 0.311902 0.540230i
\(742\) 0 0
\(743\) 25.1147 + 14.5000i 0.921370 + 0.531953i 0.884072 0.467351i \(-0.154791\pi\)
0.0372984 + 0.999304i \(0.488125\pi\)
\(744\) 0 0
\(745\) 27.8205 16.0622i 1.01926 0.588473i
\(746\) 0 0
\(747\) 11.3827 42.4808i 0.416471 1.55429i
\(748\) 0 0
\(749\) −15.3468 + 57.2750i −0.560759 + 2.09278i
\(750\) 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 −0.678644 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 \(-0.222629\pi\)
−0.174906 + 0.984585i \(0.555962\pi\)
\(762\) 0 0
\(763\) −10.5622 2.83013i −0.382377 0.102457i
\(764\) 0 0
\(765\) −6.00000 22.3923i −0.216930 0.809595i
\(766\) 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
\(771\) −36.4808 21.0622i −1.31382 0.758536i
\(772\) 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
\(779\) −0.882686 3.29423i −0.0316255 0.118028i
\(780\) 0 0
\(781\) 1.46410 5.46410i 0.0523897 0.195521i
\(782\) 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
\(787\) 3.06218 0.820508i 0.109155 0.0292480i −0.203828 0.979007i \(-0.565338\pi\)
0.312983 + 0.949759i \(0.398672\pi\)
\(788\) 0 0
\(789\) 8.59808 + 14.8923i 0.306100 + 0.530180i
\(790\) 0 0
\(791\) 55.6410i 1.97837i
\(792\) 0 0
\(793\) 5.10512i 0.181288i