Properties

Label 432.2.be.b.335.3
Level $432$
Weight $2$
Character 432.335
Analytic conductor $3.450$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.be (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.44953736732\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 335.3
Character \(\chi\) \(=\) 432.335
Dual form 432.2.be.b.383.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.796460 + 1.53807i) q^{3} +(1.12266 - 3.08448i) q^{5} +(-3.05005 - 0.537806i) q^{7} +(-1.73130 - 2.45002i) q^{9} +O(q^{10})\) \(q+(-0.796460 + 1.53807i) q^{3} +(1.12266 - 3.08448i) q^{5} +(-3.05005 - 0.537806i) q^{7} +(-1.73130 - 2.45002i) q^{9} +(-1.75059 + 0.637162i) q^{11} +(-3.44119 + 2.88750i) q^{13} +(3.84999 + 4.18339i) q^{15} +(-5.33058 + 3.07761i) q^{17} +(-5.61763 - 3.24334i) q^{19} +(3.25643 - 4.26285i) q^{21} +(-0.0995927 - 0.564818i) q^{23} +(-4.42344 - 3.71171i) q^{25} +(5.14721 - 0.711524i) q^{27} +(5.05288 - 6.02179i) q^{29} +(6.55127 - 1.15517i) q^{31} +(0.414275 - 3.20000i) q^{33} +(-5.08302 + 8.80406i) q^{35} +(-2.51317 - 4.35293i) q^{37} +(-1.70040 - 7.59256i) q^{39} +(4.01288 + 4.78237i) q^{41} +(-3.06074 - 8.40931i) q^{43} +(-9.50070 + 2.58964i) q^{45} +(-1.29158 + 7.32493i) q^{47} +(2.43573 + 0.886535i) q^{49} +(-0.487984 - 10.6500i) q^{51} +4.40691i q^{53} +6.11498i q^{55} +(9.46269 - 6.05710i) q^{57} +(-1.19847 - 0.436209i) q^{59} +(0.757644 - 4.29681i) q^{61} +(3.96293 + 8.40379i) q^{63} +(5.04316 + 13.8560i) q^{65} +(-3.35363 - 3.99670i) q^{67} +(0.948051 + 0.296675i) q^{69} +(2.77247 + 4.80206i) q^{71} +(-5.12137 + 8.87047i) q^{73} +(9.23195 - 3.84733i) q^{75} +(5.68206 - 1.00190i) q^{77} +(-0.530104 + 0.631754i) q^{79} +(-3.00517 + 8.48345i) q^{81} +(-5.90712 - 4.95666i) q^{83} +(3.50841 + 19.8972i) q^{85} +(5.23750 + 12.5678i) q^{87} +(-2.31943 - 1.33912i) q^{89} +(12.0487 - 6.95633i) q^{91} +(-3.44110 + 10.9963i) q^{93} +(-16.3107 + 13.6863i) q^{95} +(9.55043 - 3.47607i) q^{97} +(4.59186 + 3.18585i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + 3 q^{5} + 6 q^{9} + O(q^{10}) \) \( 36 q + 3 q^{5} + 6 q^{9} - 18 q^{11} + 9 q^{15} + 18 q^{21} - 9 q^{25} + 30 q^{29} + 27 q^{31} + 27 q^{33} + 27 q^{35} - 45 q^{39} + 18 q^{41} + 27 q^{45} + 45 q^{47} - 63 q^{51} - 9 q^{57} + 54 q^{59} - 63 q^{63} - 57 q^{65} - 63 q^{69} + 36 q^{71} + 9 q^{73} - 45 q^{75} - 81 q^{77} - 54 q^{81} - 27 q^{83} - 36 q^{85} + 45 q^{87} - 63 q^{89} + 27 q^{91} - 63 q^{93} - 72 q^{95} + 99 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).

\(n\) \(271\) \(325\) \(353\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{13}{18}\right)\)

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
\(3\) −0.796460 + 1.53807i −0.459836 + 0.888004i
\(4\) 0 0
\(5\) 1.12266 3.08448i 0.502069 1.37942i −0.387183 0.922003i \(-0.626552\pi\)
0.889251 0.457419i \(-0.151226\pi\)
\(6\) 0 0
\(7\) −3.05005 0.537806i −1.15281 0.203272i −0.435609 0.900136i \(-0.643467\pi\)
−0.717203 + 0.696864i \(0.754578\pi\)
\(8\) 0 0
\(9\) −1.73130 2.45002i −0.577101 0.816672i
\(10\) 0 0
\(11\) −1.75059 + 0.637162i −0.527822 + 0.192112i −0.592166 0.805816i \(-0.701727\pi\)
0.0643433 + 0.997928i \(0.479505\pi\)
\(12\) 0 0
\(13\) −3.44119 + 2.88750i −0.954414 + 0.800848i −0.980035 0.198823i \(-0.936288\pi\)
0.0256213 + 0.999672i \(0.491844\pi\)
\(14\) 0 0
\(15\) 3.84999 + 4.18339i 0.994063 + 1.08015i
\(16\) 0 0
\(17\) −5.33058 + 3.07761i −1.29286 + 0.746430i −0.979159 0.203093i \(-0.934901\pi\)
−0.313696 + 0.949524i \(0.601567\pi\)
\(18\) 0 0
\(19\) −5.61763 3.24334i −1.28877 0.744073i −0.310337 0.950627i \(-0.600442\pi\)
−0.978435 + 0.206554i \(0.933775\pi\)
\(20\) 0 0
\(21\) 3.25643 4.26285i 0.710610 0.930229i
\(22\) 0 0
\(23\) −0.0995927 0.564818i −0.0207665 0.117773i 0.972662 0.232224i \(-0.0746002\pi\)
−0.993429 + 0.114451i \(0.963489\pi\)
\(24\) 0 0
\(25\) −4.42344 3.71171i −0.884688 0.742342i
\(26\) 0 0
\(27\) 5.14721 0.711524i 0.990580 0.136933i
\(28\) 0 0
\(29\) 5.05288 6.02179i 0.938296 1.11822i −0.0545130 0.998513i \(-0.517361\pi\)
0.992809 0.119705i \(-0.0381949\pi\)
\(30\) 0 0
\(31\) 6.55127 1.15517i 1.17664 0.207474i 0.449065 0.893499i \(-0.351757\pi\)
0.727578 + 0.686025i \(0.240646\pi\)
\(32\) 0 0
\(33\) 0.414275 3.20000i 0.0721160 0.557048i
\(34\) 0 0
\(35\) −5.08302 + 8.80406i −0.859188 + 1.48816i
\(36\) 0 0
\(37\) −2.51317 4.35293i −0.413162 0.715618i 0.582071 0.813138i \(-0.302242\pi\)
−0.995234 + 0.0975198i \(0.968909\pi\)
\(38\) 0 0
\(39\) −1.70040 7.59256i −0.272282 1.21578i
\(40\) 0 0
\(41\) 4.01288 + 4.78237i 0.626707 + 0.746880i 0.982208 0.187796i \(-0.0601343\pi\)
−0.355501 + 0.934676i \(0.615690\pi\)
\(42\) 0 0
\(43\) −3.06074 8.40931i −0.466758 1.28241i −0.920314 0.391180i \(-0.872067\pi\)
0.453556 0.891228i \(-0.350155\pi\)
\(44\) 0 0
\(45\) −9.50070 + 2.58964i −1.41628 + 0.386041i
\(46\) 0 0
\(47\) −1.29158 + 7.32493i −0.188397 + 1.06845i 0.733116 + 0.680103i \(0.238065\pi\)
−0.921513 + 0.388347i \(0.873046\pi\)
\(48\) 0 0
\(49\) 2.43573 + 0.886535i 0.347962 + 0.126648i
\(50\) 0 0
\(51\) −0.487984 10.6500i −0.0683314 1.49130i
\(52\) 0 0
\(53\) 4.40691i 0.605335i 0.953096 + 0.302668i \(0.0978772\pi\)
−0.953096 + 0.302668i \(0.902123\pi\)
\(54\) 0 0
\(55\) 6.11498i 0.824543i
\(56\) 0 0
\(57\) 9.46269 6.05710i 1.25336 0.802283i
\(58\) 0 0
\(59\) −1.19847 0.436209i −0.156028 0.0567896i 0.262825 0.964843i \(-0.415346\pi\)
−0.418853 + 0.908054i \(0.637568\pi\)
\(60\) 0 0
\(61\) 0.757644 4.29681i 0.0970064 0.550151i −0.897108 0.441812i \(-0.854336\pi\)
0.994114 0.108339i \(-0.0345531\pi\)
\(62\) 0 0
\(63\) 3.96293 + 8.40379i 0.499283 + 1.05878i
\(64\) 0 0
\(65\) 5.04316 + 13.8560i 0.625527 + 1.71862i
\(66\) 0 0
\(67\) −3.35363 3.99670i −0.409711 0.488275i 0.521244 0.853407i \(-0.325468\pi\)
−0.930955 + 0.365133i \(0.881024\pi\)
\(68\) 0 0
\(69\) 0.948051 + 0.296675i 0.114132 + 0.0357154i
\(70\) 0 0
\(71\) 2.77247 + 4.80206i 0.329032 + 0.569900i 0.982320 0.187210i \(-0.0599444\pi\)
−0.653288 + 0.757109i \(0.726611\pi\)
\(72\) 0 0
\(73\) −5.12137 + 8.87047i −0.599411 + 1.03821i 0.393497 + 0.919326i \(0.371265\pi\)
−0.992908 + 0.118884i \(0.962068\pi\)
\(74\) 0 0
\(75\) 9.23195 3.84733i 1.06601 0.444251i
\(76\) 0 0
\(77\) 5.68206 1.00190i 0.647531 0.114177i
\(78\) 0 0
\(79\) −0.530104 + 0.631754i −0.0596414 + 0.0710778i −0.795040 0.606557i \(-0.792550\pi\)
0.735399 + 0.677634i \(0.236995\pi\)
\(80\) 0 0
\(81\) −3.00517 + 8.48345i −0.333908 + 0.942606i
\(82\) 0 0
\(83\) −5.90712 4.95666i −0.648391 0.544065i 0.258191 0.966094i \(-0.416874\pi\)
−0.906582 + 0.422029i \(0.861318\pi\)
\(84\) 0 0
\(85\) 3.50841 + 19.8972i 0.380540 + 2.15815i
\(86\) 0 0
\(87\) 5.23750 + 12.5678i 0.561519 + 1.34741i
\(88\) 0 0
\(89\) −2.31943 1.33912i −0.245859 0.141947i 0.372008 0.928230i \(-0.378670\pi\)
−0.617867 + 0.786283i \(0.712003\pi\)
\(90\) 0 0
\(91\) 12.0487 6.95633i 1.26305 0.729222i
\(92\) 0 0
\(93\) −3.44110 + 10.9963i −0.356825 + 1.14027i
\(94\) 0 0
\(95\) −16.3107 + 13.6863i −1.67344 + 1.40419i
\(96\) 0 0
\(97\) 9.55043 3.47607i 0.969699 0.352942i 0.191872 0.981420i \(-0.438544\pi\)
0.777827 + 0.628478i \(0.216322\pi\)
\(98\) 0 0
\(99\) 4.59186 + 3.18585i 0.461499 + 0.320190i
\(100\) 0 0
\(101\) 6.42237 + 1.13244i 0.639050 + 0.112682i 0.483779 0.875190i \(-0.339264\pi\)
0.155271 + 0.987872i \(0.450375\pi\)
\(102\) 0 0
\(103\) 3.66572 10.0715i 0.361194 0.992372i −0.617414 0.786638i \(-0.711820\pi\)
0.978608 0.205734i \(-0.0659581\pi\)
\(104\) 0 0
\(105\) −9.49281 14.8301i −0.926404 1.44727i
\(106\) 0 0
\(107\) 8.80586 0.851295 0.425647 0.904889i \(-0.360046\pi\)
0.425647 + 0.904889i \(0.360046\pi\)
\(108\) 0 0
\(109\) −9.44106 −0.904290 −0.452145 0.891944i \(-0.649341\pi\)
−0.452145 + 0.891944i \(0.649341\pi\)
\(110\) 0 0
\(111\) 8.69674 0.398486i 0.825458 0.0378226i
\(112\) 0 0
\(113\) 4.23372 11.6321i 0.398275 1.09425i −0.564849 0.825194i \(-0.691065\pi\)
0.963124 0.269058i \(-0.0867123\pi\)
\(114\) 0 0
\(115\) −1.85398 0.326907i −0.172885 0.0304842i
\(116\) 0 0
\(117\) 13.0322 + 3.43183i 1.20482 + 0.317273i
\(118\) 0 0
\(119\) 17.9137 6.52005i 1.64215 0.597692i
\(120\) 0 0
\(121\) −5.76790 + 4.83984i −0.524355 + 0.439986i
\(122\) 0 0
\(123\) −10.5517 + 2.36312i −0.951415 + 0.213076i
\(124\) 0 0
\(125\) −2.20134 + 1.27095i −0.196894 + 0.113677i
\(126\) 0 0
\(127\) −12.5683 7.25630i −1.11525 0.643893i −0.175070 0.984556i \(-0.556015\pi\)
−0.940185 + 0.340663i \(0.889348\pi\)
\(128\) 0 0
\(129\) 15.3718 + 1.99005i 1.35342 + 0.175214i
\(130\) 0 0
\(131\) −2.42294 13.7412i −0.211693 1.20057i −0.886553 0.462627i \(-0.846907\pi\)
0.674860 0.737946i \(-0.264204\pi\)
\(132\) 0 0
\(133\) 15.3898 + 12.9135i 1.33446 + 1.11975i
\(134\) 0 0
\(135\) 3.58388 16.6753i 0.308451 1.43518i
\(136\) 0 0
\(137\) −6.55243 + 7.80889i −0.559812 + 0.667158i −0.969507 0.245065i \(-0.921191\pi\)
0.409695 + 0.912223i \(0.365635\pi\)
\(138\) 0 0
\(139\) −14.0879 + 2.48408i −1.19492 + 0.210697i −0.735501 0.677523i \(-0.763053\pi\)
−0.459418 + 0.888220i \(0.651942\pi\)
\(140\) 0 0
\(141\) −10.2375 7.82055i −0.862156 0.658609i
\(142\) 0 0
\(143\) 4.18430 7.24742i 0.349909 0.606060i
\(144\) 0 0
\(145\) −12.9014 22.3459i −1.07141 1.85573i
\(146\) 0 0
\(147\) −3.30351 + 3.04024i −0.272469 + 0.250754i
\(148\) 0 0
\(149\) −14.2222 16.9494i −1.16513 1.38855i −0.906305 0.422624i \(-0.861109\pi\)
−0.258825 0.965924i \(-0.583335\pi\)
\(150\) 0 0
\(151\) −0.795084 2.18447i −0.0647030 0.177770i 0.903128 0.429372i \(-0.141265\pi\)
−0.967831 + 0.251602i \(0.919043\pi\)
\(152\) 0 0
\(153\) 16.7691 + 7.73173i 1.35570 + 0.625073i
\(154\) 0 0
\(155\) 3.79176 21.5041i 0.304561 1.72725i
\(156\) 0 0
\(157\) 2.76548 + 1.00655i 0.220709 + 0.0803317i 0.450008 0.893024i \(-0.351421\pi\)
−0.229299 + 0.973356i \(0.573643\pi\)
\(158\) 0 0
\(159\) −6.77812 3.50992i −0.537540 0.278355i
\(160\) 0 0
\(161\) 1.77629i 0.139991i
\(162\) 0 0
\(163\) 24.7290i 1.93692i 0.249167 + 0.968461i \(0.419843\pi\)
−0.249167 + 0.968461i \(0.580157\pi\)
\(164\) 0 0
\(165\) −9.40525 4.87033i −0.732198 0.379155i
\(166\) 0 0
\(167\) 9.45713 + 3.44211i 0.731814 + 0.266359i 0.680933 0.732346i \(-0.261575\pi\)
0.0508817 + 0.998705i \(0.483797\pi\)
\(168\) 0 0
\(169\) 1.24670 7.07037i 0.0958997 0.543874i
\(170\) 0 0
\(171\) 1.77959 + 19.3785i 0.136088 + 1.48191i
\(172\) 0 0
\(173\) 6.32967 + 17.3906i 0.481236 + 1.32218i 0.908435 + 0.418027i \(0.137278\pi\)
−0.427199 + 0.904158i \(0.640500\pi\)
\(174\) 0 0
\(175\) 11.4955 + 13.6999i 0.868982 + 1.03561i
\(176\) 0 0
\(177\) 1.62546 1.49591i 0.122177 0.112440i
\(178\) 0 0
\(179\) 8.14426 + 14.1063i 0.608731 + 1.05435i 0.991450 + 0.130488i \(0.0416544\pi\)
−0.382719 + 0.923865i \(0.625012\pi\)
\(180\) 0 0
\(181\) −5.29198 + 9.16598i −0.393350 + 0.681302i −0.992889 0.119043i \(-0.962017\pi\)
0.599539 + 0.800345i \(0.295351\pi\)
\(182\) 0 0
\(183\) 6.00536 + 4.58755i 0.443929 + 0.339121i
\(184\) 0 0
\(185\) −16.2480 + 2.86496i −1.19457 + 0.210636i
\(186\) 0 0
\(187\) 7.37071 8.78408i 0.539000 0.642355i
\(188\) 0 0
\(189\) −16.0819 0.598017i −1.16979 0.0434993i
\(190\) 0 0
\(191\) 8.48829 + 7.12252i 0.614191 + 0.515367i 0.895972 0.444112i \(-0.146481\pi\)
−0.281781 + 0.959479i \(0.590925\pi\)
\(192\) 0 0
\(193\) −2.72887 15.4762i −0.196429 1.11400i −0.910370 0.413796i \(-0.864203\pi\)
0.713941 0.700206i \(-0.246908\pi\)
\(194\) 0 0
\(195\) −25.3281 3.27900i −1.81378 0.234814i
\(196\) 0 0
\(197\) −11.8949 6.86752i −0.847476 0.489291i 0.0123223 0.999924i \(-0.496078\pi\)
−0.859799 + 0.510633i \(0.829411\pi\)
\(198\) 0 0
\(199\) −13.3305 + 7.69637i −0.944974 + 0.545581i −0.891516 0.452989i \(-0.850358\pi\)
−0.0534579 + 0.998570i \(0.517024\pi\)
\(200\) 0 0
\(201\) 8.81822 1.97490i 0.621990 0.139299i
\(202\) 0 0
\(203\) −18.6501 + 15.6493i −1.30898 + 1.09837i
\(204\) 0 0
\(205\) 19.2562 7.00869i 1.34491 0.489508i
\(206\) 0 0
\(207\) −1.21139 + 1.22188i −0.0841974 + 0.0849263i
\(208\) 0 0
\(209\) 11.9007 + 2.09841i 0.823188 + 0.145150i
\(210\) 0 0
\(211\) −0.592005 + 1.62652i −0.0407553 + 0.111974i −0.958401 0.285425i \(-0.907865\pi\)
0.917646 + 0.397400i \(0.130087\pi\)
\(212\) 0 0
\(213\) −9.59405 + 0.439601i −0.657374 + 0.0301210i
\(214\) 0 0
\(215\) −29.3745 −2.00333
\(216\) 0 0
\(217\) −20.6030 −1.39862
\(218\) 0 0
\(219\) −9.56442 14.9420i −0.646304 1.00969i
\(220\) 0 0
\(221\) 9.45692 25.9827i 0.636142 1.74778i
\(222\) 0 0
\(223\) −6.89847 1.21639i −0.461956 0.0814552i −0.0621733 0.998065i \(-0.519803\pi\)
−0.399782 + 0.916610i \(0.630914\pi\)
\(224\) 0 0
\(225\) −1.43543 + 17.2636i −0.0956950 + 1.15091i
\(226\) 0 0
\(227\) −0.456091 + 0.166003i −0.0302718 + 0.0110180i −0.357112 0.934062i \(-0.616238\pi\)
0.326840 + 0.945080i \(0.394016\pi\)
\(228\) 0 0
\(229\) 18.7833 15.7611i 1.24124 1.04152i 0.243812 0.969822i \(-0.421602\pi\)
0.997426 0.0717003i \(-0.0228425\pi\)
\(230\) 0 0
\(231\) −2.98454 + 9.53736i −0.196368 + 0.627512i
\(232\) 0 0
\(233\) −7.90560 + 4.56430i −0.517913 + 0.299017i −0.736081 0.676894i \(-0.763326\pi\)
0.218167 + 0.975911i \(0.429992\pi\)
\(234\) 0 0
\(235\) 21.1436 + 12.2073i 1.37926 + 0.796314i
\(236\) 0 0
\(237\) −0.549473 1.31850i −0.0356921 0.0856459i
\(238\) 0 0
\(239\) −3.71199 21.0517i −0.240108 1.36172i −0.831584 0.555399i \(-0.812565\pi\)
0.591475 0.806323i \(-0.298546\pi\)
\(240\) 0 0
\(241\) −6.62233 5.55679i −0.426582 0.357945i 0.404078 0.914724i \(-0.367592\pi\)
−0.830660 + 0.556780i \(0.812037\pi\)
\(242\) 0 0
\(243\) −10.6546 11.3789i −0.683495 0.729956i
\(244\) 0 0
\(245\) 5.46900 6.51770i 0.349402 0.416401i
\(246\) 0 0
\(247\) 28.6965 5.05996i 1.82591 0.321958i
\(248\) 0 0
\(249\) 12.3285 5.13777i 0.781285 0.325593i
\(250\) 0 0
\(251\) 2.06728 3.58063i 0.130485 0.226007i −0.793378 0.608729i \(-0.791680\pi\)
0.923864 + 0.382721i \(0.125013\pi\)
\(252\) 0 0
\(253\) 0.534227 + 0.925308i 0.0335866 + 0.0581736i
\(254\) 0 0
\(255\) −33.3975 10.4511i −2.09143 0.654475i
\(256\) 0 0
\(257\) 4.09081 + 4.87523i 0.255178 + 0.304109i 0.878391 0.477943i \(-0.158618\pi\)
−0.623213 + 0.782052i \(0.714173\pi\)
\(258\) 0 0
\(259\) 5.32426 + 14.6283i 0.330833 + 0.908957i
\(260\) 0 0
\(261\) −23.5016 1.95410i −1.45471 0.120956i
\(262\) 0 0
\(263\) 0.255737 1.45036i 0.0157694 0.0894328i −0.975907 0.218185i \(-0.929986\pi\)
0.991677 + 0.128753i \(0.0410973\pi\)
\(264\) 0 0
\(265\) 13.5930 + 4.94746i 0.835013 + 0.303920i
\(266\) 0 0
\(267\) 3.90699 2.50088i 0.239104 0.153051i
\(268\) 0 0
\(269\) 8.00417i 0.488023i −0.969772 0.244011i \(-0.921537\pi\)
0.969772 0.244011i \(-0.0784635\pi\)
\(270\) 0 0
\(271\) 12.8446i 0.780254i 0.920761 + 0.390127i \(0.127569\pi\)
−0.920761 + 0.390127i \(0.872431\pi\)
\(272\) 0 0
\(273\) 1.10299 + 24.0722i 0.0667561 + 1.45692i
\(274\) 0 0
\(275\) 10.1086 + 3.67923i 0.609571 + 0.221866i
\(276\) 0 0
\(277\) 2.74587 15.5726i 0.164983 0.935665i −0.784099 0.620636i \(-0.786874\pi\)
0.949082 0.315029i \(-0.102014\pi\)
\(278\) 0 0
\(279\) −14.1724 14.0508i −0.848480 0.841198i
\(280\) 0 0
\(281\) −6.37720 17.5212i −0.380432 1.04523i −0.971175 0.238368i \(-0.923388\pi\)
0.590743 0.806859i \(-0.298835\pi\)
\(282\) 0 0
\(283\) 0.664710 + 0.792171i 0.0395129 + 0.0470897i 0.785439 0.618939i \(-0.212437\pi\)
−0.745926 + 0.666029i \(0.767993\pi\)
\(284\) 0 0
\(285\) −8.05965 35.9875i −0.477412 2.13172i
\(286\) 0 0
\(287\) −9.66751 16.7446i −0.570655 0.988403i
\(288\) 0 0
\(289\) 10.4434 18.0885i 0.614316 1.06403i
\(290\) 0 0
\(291\) −2.26010 + 17.4578i −0.132489 + 1.02339i
\(292\) 0 0
\(293\) −13.3037 + 2.34580i −0.777208 + 0.137043i −0.548161 0.836373i \(-0.684672\pi\)
−0.229047 + 0.973415i \(0.573561\pi\)
\(294\) 0 0
\(295\) −2.69096 + 3.20696i −0.156674 + 0.186716i
\(296\) 0 0
\(297\) −8.55729 + 4.52519i −0.496544 + 0.262578i
\(298\) 0 0
\(299\) 1.97363 + 1.65607i 0.114138 + 0.0957732i
\(300\) 0 0
\(301\) 4.81283 + 27.2949i 0.277407 + 1.57325i
\(302\) 0 0
\(303\) −6.85693 + 8.97611i −0.393920 + 0.515664i
\(304\) 0 0
\(305\) −12.4029 7.16080i −0.710186 0.410026i
\(306\) 0 0
\(307\) −5.44502 + 3.14368i −0.310763 + 0.179419i −0.647268 0.762262i \(-0.724089\pi\)
0.336505 + 0.941682i \(0.390755\pi\)
\(308\) 0 0
\(309\) 12.5710 + 13.6596i 0.715140 + 0.777070i
\(310\) 0 0
\(311\) 24.7245 20.7464i 1.40200 1.17642i 0.441797 0.897115i \(-0.354341\pi\)
0.960203 0.279303i \(-0.0901032\pi\)
\(312\) 0 0
\(313\) −7.70071 + 2.80283i −0.435270 + 0.158425i −0.550356 0.834930i \(-0.685508\pi\)
0.115086 + 0.993356i \(0.463286\pi\)
\(314\) 0 0
\(315\) 30.3704 2.78900i 1.71118 0.157143i
\(316\) 0 0
\(317\) −0.256610 0.0452473i −0.0144127 0.00254134i 0.166437 0.986052i \(-0.446774\pi\)
−0.180850 + 0.983511i \(0.557885\pi\)
\(318\) 0 0
\(319\) −5.00866 + 13.7612i −0.280431 + 0.770478i
\(320\) 0 0
\(321\) −7.01351 + 13.5440i −0.391456 + 0.755953i
\(322\) 0 0
\(323\) 39.9269 2.22159
\(324\) 0 0
\(325\) 25.9395 1.43886
\(326\) 0 0
\(327\) 7.51943 14.5210i 0.415825 0.803013i
\(328\) 0 0
\(329\) 7.87879 21.6468i 0.434372 1.19343i
\(330\) 0 0
\(331\) 0.525724 + 0.0926993i 0.0288964 + 0.00509521i 0.188078 0.982154i \(-0.439774\pi\)
−0.159181 + 0.987249i \(0.550885\pi\)
\(332\) 0 0
\(333\) −6.31371 + 13.6936i −0.345989 + 0.750402i
\(334\) 0 0
\(335\) −16.0927 + 5.85727i −0.879240 + 0.320017i
\(336\) 0 0
\(337\) −23.8983 + 20.0530i −1.30182 + 1.09236i −0.311996 + 0.950083i \(0.600998\pi\)
−0.989827 + 0.142276i \(0.954558\pi\)
\(338\) 0 0
\(339\) 14.5189 + 15.7762i 0.788559 + 0.856847i
\(340\) 0 0
\(341\) −10.7326 + 6.19644i −0.581200 + 0.335556i
\(342\) 0 0
\(343\) 11.8229 + 6.82593i 0.638375 + 0.368566i
\(344\) 0 0
\(345\) 1.97943 2.59118i 0.106569 0.139504i
\(346\) 0 0
\(347\) −3.83765 21.7644i −0.206016 1.16837i −0.895833 0.444390i \(-0.853420\pi\)
0.689818 0.723983i \(-0.257691\pi\)
\(348\) 0 0
\(349\) −1.37320 1.15226i −0.0735059 0.0616788i 0.605294 0.796002i \(-0.293055\pi\)
−0.678800 + 0.734323i \(0.737500\pi\)
\(350\) 0 0
\(351\) −15.6580 + 17.3110i −0.835761 + 0.923995i
\(352\) 0 0
\(353\) −16.2088 + 19.3168i −0.862705 + 1.02813i 0.136592 + 0.990627i \(0.456385\pi\)
−0.999296 + 0.0375040i \(0.988059\pi\)
\(354\) 0 0
\(355\) 17.9244 3.16056i 0.951329 0.167745i
\(356\) 0 0
\(357\) −4.23925 + 32.7454i −0.224365 + 1.73307i
\(358\) 0 0
\(359\) 6.14950 10.6512i 0.324558 0.562151i −0.656865 0.754008i \(-0.728118\pi\)
0.981423 + 0.191857i \(0.0614511\pi\)
\(360\) 0 0
\(361\) 11.5385 + 19.9852i 0.607289 + 1.05186i
\(362\) 0 0
\(363\) −2.85011 12.7262i −0.149592 0.667950i
\(364\) 0 0
\(365\) 21.6113 + 25.7553i 1.13118 + 1.34809i
\(366\) 0 0
\(367\) −10.1719 27.9469i −0.530966 1.45882i −0.857923 0.513779i \(-0.828245\pi\)
0.326956 0.945039i \(-0.393977\pi\)
\(368\) 0 0
\(369\) 4.76936 18.1114i 0.248283 0.942840i
\(370\) 0 0
\(371\) 2.37006 13.4413i 0.123048 0.697837i
\(372\) 0 0
\(373\) −6.03535 2.19669i −0.312499 0.113740i 0.181010 0.983481i \(-0.442063\pi\)
−0.493508 + 0.869741i \(0.664286\pi\)
\(374\) 0 0
\(375\) −0.201520 4.39807i −0.0104065 0.227116i
\(376\) 0 0
\(377\) 35.3123i 1.81868i
\(378\) 0 0
\(379\) 32.5133i 1.67009i −0.550178 0.835047i \(-0.685440\pi\)
0.550178 0.835047i \(-0.314560\pi\)
\(380\) 0 0
\(381\) 21.1708 13.5515i 1.08461 0.694265i
\(382\) 0 0
\(383\) 19.0144 + 6.92069i 0.971593 + 0.353631i 0.778566 0.627563i \(-0.215947\pi\)
0.193027 + 0.981194i \(0.438170\pi\)
\(384\) 0 0
\(385\) 3.28867 18.6510i 0.167606 0.950543i
\(386\) 0 0
\(387\) −15.3039 + 22.0579i −0.777940 + 1.12127i
\(388\) 0 0
\(389\) −8.66645 23.8109i −0.439406 1.20726i −0.939879 0.341507i \(-0.889063\pi\)
0.500473 0.865752i \(-0.333159\pi\)
\(390\) 0 0
\(391\) 2.26918 + 2.70430i 0.114757 + 0.136762i
\(392\) 0 0
\(393\) 23.0646 + 7.21765i 1.16346 + 0.364082i
\(394\) 0 0
\(395\) 1.35351 + 2.34434i 0.0681023 + 0.117957i
\(396\) 0 0
\(397\) 3.67253 6.36102i 0.184319 0.319250i −0.759028 0.651058i \(-0.774325\pi\)
0.943347 + 0.331808i \(0.107659\pi\)
\(398\) 0 0
\(399\) −32.1192 + 13.3854i −1.60797 + 0.670107i
\(400\) 0 0
\(401\) −9.92983 + 1.75090i −0.495872 + 0.0874356i −0.415991 0.909369i \(-0.636565\pi\)
−0.0798812 + 0.996804i \(0.525454\pi\)
\(402\) 0 0
\(403\) −19.2086 + 22.8919i −0.956849 + 1.14033i
\(404\) 0 0
\(405\) 22.7933 + 18.7934i 1.13261 + 0.933853i
\(406\) 0 0
\(407\) 7.17305 + 6.01890i 0.355555 + 0.298346i
\(408\) 0 0
\(409\) −0.129387 0.733791i −0.00639778 0.0362836i 0.981442 0.191761i \(-0.0614197\pi\)
−0.987840 + 0.155477i \(0.950309\pi\)
\(410\) 0 0
\(411\) −6.79185 16.2975i −0.335017 0.803899i
\(412\) 0 0
\(413\) 3.42081 + 1.97501i 0.168327 + 0.0971838i
\(414\) 0 0
\(415\) −21.9204 + 12.6558i −1.07603 + 0.621247i
\(416\) 0 0
\(417\) 7.39976 23.6466i 0.362368 1.15798i
\(418\) 0 0
\(419\) −28.7016 + 24.0835i −1.40217 + 1.17656i −0.442039 + 0.896996i \(0.645745\pi\)
−0.960128 + 0.279561i \(0.909811\pi\)
\(420\) 0 0
\(421\) −13.2383 + 4.81836i −0.645197 + 0.234832i −0.643832 0.765167i \(-0.722657\pi\)
−0.00136448 + 0.999999i \(0.500434\pi\)
\(422\) 0 0
\(423\) 20.1823 9.51728i 0.981298 0.462746i
\(424\) 0 0
\(425\) 35.0027 + 6.17192i 1.69788 + 0.299382i
\(426\) 0 0
\(427\) −4.62171 + 12.6980i −0.223660 + 0.614501i
\(428\) 0 0
\(429\) 7.81440 + 12.2080i 0.377283 + 0.589409i
\(430\) 0 0
\(431\) 8.25286 0.397526 0.198763 0.980048i \(-0.436308\pi\)
0.198763 + 0.980048i \(0.436308\pi\)
\(432\) 0 0
\(433\) −3.81968 −0.183562 −0.0917812 0.995779i \(-0.529256\pi\)
−0.0917812 + 0.995779i \(0.529256\pi\)
\(434\) 0 0
\(435\) 44.6450 2.04564i 2.14057 0.0980810i
\(436\) 0 0
\(437\) −1.27242 + 3.49595i −0.0608682 + 0.167234i
\(438\) 0 0
\(439\) 7.25755 + 1.27970i 0.346384 + 0.0610768i 0.344134 0.938921i \(-0.388173\pi\)
0.00225021 + 0.999997i \(0.499284\pi\)
\(440\) 0 0
\(441\) −2.04497 7.50245i −0.0973796 0.357260i
\(442\) 0 0
\(443\) 28.8637 10.5055i 1.37136 0.499133i 0.451809 0.892115i \(-0.350779\pi\)
0.919546 + 0.392982i \(0.128557\pi\)
\(444\) 0 0
\(445\) −6.73443 + 5.65086i −0.319242 + 0.267876i
\(446\) 0 0
\(447\) 37.3967 8.37524i 1.76880 0.396135i
\(448\) 0 0
\(449\) −21.4724 + 12.3971i −1.01334 + 0.585055i −0.912169 0.409814i \(-0.865594\pi\)
−0.101176 + 0.994869i \(0.532260\pi\)
\(450\) 0 0
\(451\) −10.0720 5.81510i −0.474274 0.273822i
\(452\) 0 0
\(453\) 3.99312 + 0.516953i 0.187613 + 0.0242886i
\(454\) 0 0
\(455\) −7.93007 44.9737i −0.371767 2.10840i
\(456\) 0 0
\(457\) 5.08205 + 4.26434i 0.237728 + 0.199478i 0.753866 0.657028i \(-0.228187\pi\)
−0.516138 + 0.856505i \(0.672631\pi\)
\(458\) 0 0
\(459\) −25.2478 + 19.6339i −1.17847 + 0.916433i
\(460\) 0 0
\(461\) 4.80345 5.72452i 0.223719 0.266618i −0.642497 0.766289i \(-0.722101\pi\)
0.866215 + 0.499671i \(0.166546\pi\)
\(462\) 0 0
\(463\) −12.6122 + 2.22387i −0.586139 + 0.103352i −0.458850 0.888514i \(-0.651739\pi\)
−0.127288 + 0.991866i \(0.540627\pi\)
\(464\) 0 0
\(465\) 30.0548 + 22.9591i 1.39376 + 1.06470i
\(466\) 0 0
\(467\) −21.2201 + 36.7544i −0.981951 + 1.70079i −0.327180 + 0.944962i \(0.606098\pi\)
−0.654771 + 0.755827i \(0.727235\pi\)
\(468\) 0 0
\(469\) 8.07929 + 13.9937i 0.373067 + 0.646171i
\(470\) 0 0
\(471\) −3.75074 + 3.45182i −0.172825 + 0.159051i
\(472\) 0 0
\(473\) 10.7162 + 12.7711i 0.492731 + 0.587214i
\(474\) 0 0
\(475\) 12.8109 + 35.1977i 0.587805 + 1.61498i
\(476\) 0 0
\(477\) 10.7970 7.62970i 0.494361 0.349340i
\(478\) 0 0
\(479\) 1.33018 7.54383i 0.0607775 0.344687i −0.939222 0.343312i \(-0.888451\pi\)
0.999999 0.00137483i \(-0.000437621\pi\)
\(480\) 0 0
\(481\) 21.2174 + 7.72250i 0.967429 + 0.352115i
\(482\) 0 0
\(483\) −2.73205 1.41474i −0.124313 0.0643729i
\(484\) 0 0
\(485\) 33.3606i 1.51483i
\(486\) 0 0
\(487\) 26.7514i 1.21222i −0.795380 0.606111i \(-0.792729\pi\)
0.795380 0.606111i \(-0.207271\pi\)
\(488\) 0 0
\(489\) −38.0348 19.6956i −1.71999 0.890666i
\(490\) 0 0
\(491\) 28.4746 + 10.3639i 1.28504 + 0.467716i 0.892096 0.451846i \(-0.149234\pi\)
0.392944 + 0.919562i \(0.371457\pi\)
\(492\) 0 0
\(493\) −8.40206 + 47.6504i −0.378410 + 2.14607i
\(494\) 0 0
\(495\) 14.9818 10.5869i 0.673382 0.475845i
\(496\) 0 0
\(497\) −5.87360 16.1376i −0.263467 0.723870i
\(498\) 0 0
\(499\) −4.74411 5.65381i −0.212376 0.253099i 0.649331 0.760506i \(-0.275049\pi\)
−0.861707 + 0.507406i \(0.830604\pi\)
\(500\) 0 0
\(501\) −12.8264 + 11.8042i −0.573042 + 0.527373i
\(502\) 0 0
\(503\) 8.99874 + 15.5863i 0.401234 + 0.694958i 0.993875 0.110509i \(-0.0352480\pi\)
−0.592641 + 0.805467i \(0.701915\pi\)
\(504\) 0 0
\(505\) 10.7031 18.5384i 0.476283 0.824946i
\(506\) 0 0
\(507\) 9.88176 + 7.54876i 0.438864 + 0.335252i
\(508\) 0 0
\(509\) 14.1044 2.48699i 0.625167 0.110234i 0.147915 0.989000i \(-0.452744\pi\)
0.477252 + 0.878766i \(0.341633\pi\)
\(510\) 0 0
\(511\) 20.3910 24.3011i 0.902047 1.07502i
\(512\) 0 0
\(513\) −31.2228 12.6971i −1.37852 0.560589i
\(514\) 0 0
\(515\) −26.9499 22.6137i −1.18756 0.996478i
\(516\) 0 0
\(517\) −2.40614 13.6459i −0.105822 0.600145i
\(518\) 0 0
\(519\) −31.7893 4.11547i −1.39539 0.180649i
\(520\) 0 0
\(521\) 20.2534 + 11.6933i 0.887317 + 0.512293i 0.873064 0.487606i \(-0.162130\pi\)
0.0142531 + 0.999898i \(0.495463\pi\)
\(522\) 0 0
\(523\) 18.5635 10.7177i 0.811726 0.468650i −0.0358289 0.999358i \(-0.511407\pi\)
0.847555 + 0.530708i \(0.178074\pi\)
\(524\) 0 0
\(525\) −30.2270 + 6.76954i −1.31922 + 0.295447i
\(526\) 0 0
\(527\) −31.3669 + 26.3200i −1.36636 + 1.14652i
\(528\) 0 0
\(529\) 21.3038 7.75396i 0.926253 0.337129i
\(530\) 0 0
\(531\) 1.00620 + 3.69149i 0.0436656 + 0.160197i
\(532\) 0 0
\(533\) −27.6182 4.86983i −1.19628 0.210936i
\(534\) 0 0
\(535\) 9.88599 27.1615i 0.427408 1.17429i
\(536\) 0 0
\(537\) −28.1830 + 1.29135i −1.21619 + 0.0557258i
\(538\) 0 0
\(539\) −4.82884 −0.207993
\(540\) 0 0
\(541\) −23.8755 −1.02649 −0.513245 0.858242i \(-0.671557\pi\)
−0.513245 + 0.858242i \(0.671557\pi\)
\(542\) 0 0
\(543\) −9.88305 15.4398i −0.424122 0.662583i
\(544\) 0 0
\(545\) −10.5991 + 29.1208i −0.454016 + 1.24740i
\(546\) 0 0
\(547\) 21.6034 + 3.80927i 0.923696 + 0.162873i 0.615216 0.788358i \(-0.289069\pi\)
0.308480 + 0.951231i \(0.400180\pi\)
\(548\) 0 0
\(549\) −11.8390 + 5.58285i −0.505275 + 0.238270i
\(550\) 0 0
\(551\) −47.9159 + 17.4400i −2.04129 + 0.742967i
\(552\) 0 0
\(553\) 1.95661 1.64179i 0.0832034 0.0698159i
\(554\) 0 0
\(555\) 8.53436 27.2723i 0.362263 1.15765i
\(556\) 0 0
\(557\) 26.3790 15.2299i 1.11771 0.645311i 0.176896 0.984230i \(-0.443394\pi\)
0.940816 + 0.338918i \(0.110061\pi\)
\(558\) 0 0
\(559\) 34.8145 + 20.1001i 1.47249 + 0.850145i
\(560\) 0 0
\(561\) 7.64003 + 18.3328i 0.322562 + 0.774012i
\(562\) 0 0
\(563\) 4.89813 + 27.7786i 0.206431 + 1.17073i 0.895171 + 0.445722i \(0.147053\pi\)
−0.688740 + 0.725008i \(0.741836\pi\)
\(564\) 0 0
\(565\) −31.1259 26.1177i −1.30947 1.09878i
\(566\) 0 0
\(567\) 13.7284 24.2588i 0.576538 1.01877i
\(568\) 0 0
\(569\) 3.87085 4.61310i 0.162274 0.193391i −0.678780 0.734342i \(-0.737491\pi\)
0.841054 + 0.540951i \(0.181935\pi\)
\(570\) 0 0
\(571\) −34.8030 + 6.13671i −1.45646 + 0.256814i −0.845130 0.534561i \(-0.820477\pi\)
−0.611332 + 0.791374i \(0.709366\pi\)
\(572\) 0 0
\(573\) −17.7155 + 7.38276i −0.740075 + 0.308419i
\(574\) 0 0
\(575\) −1.65590 + 2.86810i −0.0690557 + 0.119608i
\(576\) 0 0
\(577\) −4.72269 8.17994i −0.196608 0.340535i 0.750818 0.660509i \(-0.229659\pi\)
−0.947426 + 0.319973i \(0.896326\pi\)
\(578\) 0 0
\(579\) 25.9769 + 8.12898i 1.07956 + 0.337829i
\(580\) 0 0
\(581\) 15.3513 + 18.2950i 0.636879 + 0.759003i
\(582\) 0 0
\(583\) −2.80792 7.71469i −0.116292 0.319510i
\(584\) 0 0
\(585\) 25.2161 36.3447i 1.04256 1.50267i
\(586\) 0 0
\(587\) −5.53066 + 31.3659i −0.228275 + 1.29461i 0.628050 + 0.778173i \(0.283853\pi\)
−0.856325 + 0.516438i \(0.827258\pi\)
\(588\) 0 0
\(589\) −40.5492 14.7587i −1.67080 0.608121i
\(590\) 0 0
\(591\) 20.0365 12.8255i 0.824192 0.527569i
\(592\) 0 0
\(593\) 26.5370i 1.08975i −0.838519 0.544873i \(-0.816578\pi\)
0.838519 0.544873i \(-0.183422\pi\)
\(594\) 0 0
\(595\) 62.5743i 2.56530i
\(596\) 0 0
\(597\) −1.22033 26.6331i −0.0499448 1.09002i
\(598\) 0 0
\(599\) 30.9021 + 11.2474i 1.26262 + 0.459558i 0.884649 0.466258i \(-0.154398\pi\)
0.377976 + 0.925816i \(0.376620\pi\)
\(600\) 0 0
\(601\) −1.31366 + 7.45015i −0.0535854 + 0.303898i −0.999808 0.0196197i \(-0.993754\pi\)
0.946222 + 0.323518i \(0.104866\pi\)
\(602\) 0 0
\(603\) −3.98583 + 15.1360i −0.162316 + 0.616384i
\(604\) 0 0
\(605\) 8.45302 + 23.2245i 0.343664 + 0.944210i
\(606\) 0 0
\(607\) −7.44129 8.86819i −0.302033 0.359949i 0.593586 0.804770i \(-0.297712\pi\)
−0.895619 + 0.444822i \(0.853267\pi\)
\(608\) 0 0
\(609\) −9.21562 41.1492i −0.373436 1.66745i
\(610\) 0 0
\(611\) −16.7062 28.9359i −0.675859 1.17062i
\(612\) 0 0
\(613\) −0.217321 + 0.376411i −0.00877751 + 0.0152031i −0.870381 0.492379i \(-0.836127\pi\)
0.861603 + 0.507582i \(0.169461\pi\)
\(614\) 0 0
\(615\) −4.55696 + 35.1995i −0.183754 + 1.41938i
\(616\) 0 0
\(617\) −8.52403 + 1.50302i −0.343165 + 0.0605092i −0.342575 0.939491i \(-0.611299\pi\)
−0.000590102 1.00000i \(0.500188\pi\)
\(618\) 0 0
\(619\) −15.5425 + 18.5228i −0.624704 + 0.744494i −0.981872 0.189547i \(-0.939298\pi\)
0.357167 + 0.934040i \(0.383743\pi\)
\(620\) 0 0
\(621\) −0.914506 2.83637i −0.0366979 0.113820i
\(622\) 0 0
\(623\) 6.35419 + 5.33180i 0.254575 + 0.213614i
\(624\) 0 0
\(625\) −3.56471 20.2165i −0.142588 0.808659i
\(626\) 0 0
\(627\) −12.7059 + 16.6328i −0.507426 + 0.664249i
\(628\) 0 0
\(629\) 26.7933 + 15.4691i 1.06832 + 0.616794i
\(630\) 0 0
\(631\) −14.3376 + 8.27784i −0.570773 + 0.329536i −0.757458 0.652884i \(-0.773559\pi\)
0.186685 + 0.982420i \(0.440226\pi\)
\(632\) 0 0
\(633\) −2.03019 2.20600i −0.0806928 0.0876806i
\(634\) 0 0
\(635\) −36.4918 + 30.6203i −1.44813 + 1.21513i
\(636\) 0 0
\(637\) −10.9417 + 3.98245i −0.433526 + 0.157790i
\(638\) 0 0
\(639\) 6.96514 15.1064i 0.275537 0.597601i
\(640\) 0 0
\(641\) −42.4598 7.48680i −1.67706 0.295711i −0.747467 0.664299i \(-0.768730\pi\)
−0.929593 + 0.368588i \(0.879841\pi\)
\(642\) 0 0
\(643\) 8.45774 23.2375i 0.333541 0.916396i −0.653642 0.756804i \(-0.726760\pi\)
0.987183 0.159592i \(-0.0510179\pi\)
\(644\) 0 0
\(645\) 23.3956 45.1800i 0.921202 1.77896i
\(646\) 0 0
\(647\) −35.4946 −1.39544 −0.697718 0.716372i \(-0.745801\pi\)
−0.697718 + 0.716372i \(0.745801\pi\)
\(648\) 0 0
\(649\) 2.37597 0.0932651
\(650\) 0 0
\(651\) 16.4094 31.6888i 0.643136 1.24198i
\(652\) 0 0
\(653\) 5.76008 15.8257i 0.225409 0.619307i −0.774503 0.632570i \(-0.782000\pi\)
0.999912 + 0.0132637i \(0.00422210\pi\)
\(654\) 0 0
\(655\) −45.1046 7.95315i −1.76238 0.310755i
\(656\) 0 0
\(657\) 30.5995 2.81004i 1.19380 0.109630i
\(658\) 0 0
\(659\) −7.79491 + 2.83712i −0.303647 + 0.110518i −0.489350 0.872088i \(-0.662766\pi\)
0.185703 + 0.982606i \(0.440544\pi\)
\(660\) 0 0
\(661\) 33.9315 28.4719i 1.31978 1.10743i 0.333433 0.942774i \(-0.391793\pi\)
0.986351 0.164657i \(-0.0526517\pi\)
\(662\) 0 0
\(663\) 32.4311 + 35.2395i 1.25952 + 1.36859i
\(664\) 0 0
\(665\) 57.1091 32.9719i 2.21459 1.27860i
\(666\) 0 0
\(667\) −3.90445 2.25423i −0.151181 0.0872843i
\(668\) 0 0
\(669\) 7.36524 9.64151i 0.284756 0.372762i
\(670\) 0 0
\(671\) 1.41144 + 8.00470i 0.0544882 + 0.309018i
\(672\) 0 0
\(673\) 17.3028 + 14.5188i 0.666975 + 0.559658i 0.912168 0.409816i \(-0.134407\pi\)
−0.245193 + 0.969474i \(0.578851\pi\)
\(674\) 0 0
\(675\) −25.4093 15.9575i −0.978006 0.614206i
\(676\) 0 0
\(677\) −5.67582 + 6.76418i −0.218139 + 0.259968i −0.864006 0.503482i \(-0.832052\pi\)
0.645866 + 0.763451i \(0.276496\pi\)
\(678\) 0 0
\(679\) −30.9988 + 5.46592i −1.18962 + 0.209763i
\(680\) 0 0
\(681\) 0.107933 0.833714i 0.00413601 0.0319480i
\(682\) 0 0
\(683\) 22.9677 39.7812i 0.878834 1.52218i 0.0262119 0.999656i \(-0.491656\pi\)
0.852622 0.522528i \(-0.175011\pi\)
\(684\) 0 0
\(685\) 16.7302 + 28.9776i 0.639229 + 1.10718i
\(686\) 0 0
\(687\) 9.28146 + 41.4431i 0.354110 + 1.58115i
\(688\) 0 0
\(689\) −12.7249 15.1650i −0.484782 0.577741i
\(690\) 0 0
\(691\) 1.35958 + 3.73542i 0.0517209 + 0.142102i 0.962863 0.269990i \(-0.0870204\pi\)
−0.911142 + 0.412092i \(0.864798\pi\)
\(692\) 0 0
\(693\) −12.2920 12.1865i −0.466936 0.462929i
\(694\) 0 0
\(695\) −8.15382 + 46.2426i −0.309292 + 1.75408i
\(696\) 0 0
\(697\) −36.1092 13.1427i −1.36773 0.497815i
\(698\) 0 0
\(699\) −0.723713 15.7946i −0.0273733 0.597408i
\(700\) 0 0
\(701\) 19.7960i 0.747684i 0.927492 + 0.373842i \(0.121960\pi\)
−0.927492 + 0.373842i \(0.878040\pi\)
\(702\) 0 0
\(703\) 32.6042i 1.22969i
\(704\) 0 0
\(705\) −35.6156 + 22.7977i −1.34136 + 0.858611i
\(706\) 0 0
\(707\) −18.9795 6.90799i −0.713799 0.259802i
\(708\) 0 0
\(709\) 0.722087 4.09516i 0.0271185 0.153797i −0.968242 0.250016i \(-0.919564\pi\)
0.995360 + 0.0962195i \(0.0306751\pi\)
\(710\) 0 0
\(711\) 2.46558 + 0.205007i 0.0924664 + 0.00768835i
\(712\) 0 0
\(713\) −1.30492 3.58523i −0.0488695 0.134268i
\(714\) 0 0
\(715\) −17.6570 21.0428i −0.660334 0.786956i
\(716\) 0 0
\(717\) 35.3354 + 11.0576i 1.31963 + 0.412952i
\(718\) 0 0
\(719\) −0.827080 1.43254i −0.0308449 0.0534249i 0.850191 0.526475i \(-0.176486\pi\)
−0.881036 + 0.473050i \(0.843153\pi\)
\(720\) 0 0
\(721\) −16.5971 + 28.7471i −0.618110 + 1.07060i
\(722\) 0 0
\(723\) 13.8211 5.75983i 0.514014 0.214210i
\(724\) 0 0
\(725\) −44.7022 + 7.88221i −1.66020 + 0.292738i
\(726\) 0 0
\(727\) 11.2040 13.3525i 0.415535 0.495215i −0.517156 0.855891i \(-0.673009\pi\)
0.932691 + 0.360676i \(0.117454\pi\)
\(728\) 0 0
\(729\) 25.9875 7.32472i 0.962499 0.271286i
\(730\) 0 0
\(731\) 42.1961 + 35.4067i 1.56068 + 1.30956i
\(732\) 0 0
\(733\) −2.08784 11.8408i −0.0771163 0.437348i −0.998781 0.0493610i \(-0.984282\pi\)
0.921665 0.387987i \(-0.126830\pi\)
\(734\) 0 0
\(735\) 5.66883 + 13.6028i 0.209098 + 0.501746i
\(736\) 0 0
\(737\) 8.41737 + 4.85977i 0.310058 + 0.179012i
\(738\) 0 0
\(739\) −19.8865 + 11.4815i −0.731538 + 0.422354i −0.818984 0.573816i \(-0.805463\pi\)
0.0874467 + 0.996169i \(0.472129\pi\)
\(740\) 0 0
\(741\) −15.0730 + 48.1671i −0.553721 + 1.76946i
\(742\) 0 0
\(743\) 15.7558 13.2207i 0.578023 0.485019i −0.306274 0.951943i \(-0.599082\pi\)
0.884297 + 0.466924i \(0.154638\pi\)
\(744\) 0 0
\(745\) −68.2468 + 24.8398i −2.50037 + 0.910060i
\(746\) 0 0
\(747\) −1.91689 + 23.0540i −0.0701352 + 0.843503i
\(748\) 0 0
\(749\) −26.8583 4.73585i −0.981382 0.173044i
\(750\) 0 0
\(751\) −12.7470 + 35.0221i −0.465145 + 1.27797i 0.456425 + 0.889762i \(0.349130\pi\)
−0.921570 + 0.388213i \(0.873093\pi\)
\(752\) 0 0
\(753\) 3.86075 + 6.03144i 0.140693 + 0.219798i
\(754\) 0 0
\(755\) −7.63058 −0.277705
\(756\) 0 0
\(757\) −13.7573 −0.500018 −0.250009 0.968244i \(-0.580434\pi\)
−0.250009 + 0.968244i \(0.580434\pi\)
\(758\) 0 0
\(759\) −1.84868 + 0.0847066i −0.0671027 + 0.00307466i
\(760\) 0 0
\(761\) −8.47595 + 23.2875i −0.307253 + 0.844171i 0.685936 + 0.727661i \(0.259393\pi\)
−0.993190 + 0.116510i \(0.962829\pi\)
\(762\) 0 0
\(763\) 28.7957 + 5.07747i 1.04248 + 0.183817i
\(764\) 0 0
\(765\) 42.6743 43.0437i 1.54289 1.55625i
\(766\) 0 0
\(767\) 5.38373 1.95952i 0.194395 0.0707541i
\(768\) 0 0
\(769\) 16.2655 13.6484i 0.586550 0.492174i −0.300541 0.953769i \(-0.597167\pi\)
0.887091 + 0.461595i \(0.152723\pi\)
\(770\) 0 0
\(771\) −10.7566 + 2.40901i −0.387390 + 0.0867584i
\(772\) 0 0
\(773\) 12.2938 7.09780i 0.442176 0.255290i −0.262344 0.964974i \(-0.584496\pi\)
0.704520 + 0.709684i \(0.251162\pi\)
\(774\) 0 0
\(775\) −33.2668 19.2066i −1.19498 0.689921i
\(776\) 0 0
\(777\) −26.7398 3.46176i −0.959286 0.124190i
\(778\) 0 0
\(779\) −7.03204 39.8807i −0.251949 1.42887i
\(780\) 0 0
\(781\) −7.91315 6.63992i −0.283155 0.237595i
\(782\) 0 0
\(783\) 21.7236 34.5906i 0.776337 1.23617i
\(784\) 0 0
\(785\) 6.20939 7.40006i 0.221623 0.264119i
\(786\) 0 0
\(787\) −27.3006 + 4.81383i −0.973160 + 0.171594i −0.637552 0.770407i \(-0.720053\pi\)
−0.335608 + 0.942002i \(0.608942\pi\)
\(788\) 0 0
\(789\) 2.02706 + 1.54849i 0.0721653 + 0.0551278i
\(790\) 0 0
\(791\) −19.1689 + 33.2015i −0.681567 + 1.18051i
\(792\) 0 0
\(793\) 9.79985 + 16.9738i 0.348003 + 0.602759i
\(794\) 0 0
\(795\) −18.4358 + 16.9665i −0.653851 + 0.601741i