Properties

Label 432.2.be.c.335.4
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 335.4
Character \(\chi\) \(=\) 432.335
Dual form 432.2.be.c.383.4

$q$-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 0.717203 0.696864i \(-0.245422\pi\)
0.435609 + 0.900136i \(0.356533\pi\)
\(8\) 0 0
\(9\) −1.73130 2.45002i −0.577101 0.816672i
\(10\) 0 0
\(11\) 1.75059 0.637162i 0.527822 0.192112i −0.0643433 0.997928i \(-0.520495\pi\)
0.592166 + 0.805816i \(0.298273\pi\)
\(12\) 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 0.978435 0.206554i \(-0.0662249\pi\)
0.310337 + 0.950627i \(0.399558\pi\)
\(20\) 0 0
\(21\) 3.25643 4.26285i 0.710610 0.930229i
\(22\) 0 0
\(23\) 0.0995927 + 0.564818i 0.0207665 + 0.117773i 0.993429 0.114451i \(-0.0365109\pi\)
−0.972662 + 0.232224i \(0.925400\pi\)
\(24\) 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 −0.727578 0.686025i \(-0.759354\pi\)
−0.449065 + 0.893499i \(0.648243\pi\)
\(32\) 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 \(0.127933\pi\)
−0.453556 + 0.891228i \(0.649845\pi\)
\(44\) 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 \(-0.761935\pi\)
0.921513 0.388347i \(-0.126954\pi\)
\(48\) 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 0.418853 0.908054i \(-0.362432\pi\)
−0.262825 + 0.964843i \(0.584654\pi\)
\(60\) 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 0.930955 0.365133i \(-0.118976\pi\)
−0.521244 + 0.853407i \(0.674532\pi\)
\(68\) 0 0
\(69\) 0.948051 + 0.296675i 0.114132 + 0.0357154i
\(70\) 0 0
\(71\) −2.77247 4.80206i −0.329032 0.569900i 0.653288 0.757109i \(-0.273389\pi\)
−0.982320 + 0.187210i \(0.940056\pi\)
\(72\) 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 −0.735399 0.677634i \(-0.763005\pi\)
0.795040 + 0.606557i \(0.207450\pi\)
\(80\) 0 0
\(81\) −3.00517 + 8.48345i −0.333908 + 0.942606i
\(82\) 0 0
\(83\) 5.90712 + 4.95666i 0.648391 + 0.544065i 0.906582 0.422029i \(-0.138682\pi\)
−0.258191 + 0.966094i \(0.583126\pi\)
\(84\) 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 \(0.288180\pi\)
−0.978608 + 0.205734i \(0.934042\pi\)
\(104\) 0 0
\(105\) −9.49281 14.8301i −0.926404 1.44727i
\(106\) 0 0
\(107\) −8.80586 −0.851295 −0.425647 0.904889i \(-0.639954\pi\)
−0.425647 + 0.904889i \(0.639954\pi\)
\(108\) 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 0.940185 0.340663i \(-0.110652\pi\)
0.175070 + 0.984556i \(0.443985\pi\)
\(128\) 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 \(0.153093\pi\)
−0.674860 + 0.737946i \(0.735796\pi\)
\(132\) 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 0.459418 0.888220i \(-0.348058\pi\)
0.735501 + 0.677523i \(0.236947\pi\)
\(140\) 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 0.967831 0.251602i \(-0.0809573\pi\)
−0.903128 + 0.429372i \(0.858735\pi\)
\(152\) 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 \(-0.580157\pi\)
0.249167 0.968461i \(-0.419843\pi\)
\(164\) 0 0
\(165\) −9.40525 4.87033i −0.732198 0.379155i
\(166\) 0 0
\(167\) −9.45713 3.44211i −0.731814 0.266359i −0.0508817 0.998705i \(-0.516203\pi\)
−0.680933 + 0.732346i \(0.738425\pi\)
\(168\) 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 \(-0.958346\pi\)
0.382719 0.923865i \(-0.374988\pi\)
\(180\) 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 0.281781 0.959479i \(-0.409075\pi\)
−0.895972 + 0.444112i \(0.853519\pi\)
\(192\) 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 0.0534579 0.998570i \(-0.482976\pi\)
0.891516 + 0.452989i \(0.149642\pi\)
\(200\) 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 −0.917646 0.397400i \(-0.869913\pi\)
0.958401 + 0.285425i \(0.0921349\pi\)
\(212\) 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 0.399782 0.916610i \(-0.369086\pi\)
0.0621733 + 0.998065i \(0.480197\pi\)
\(224\) 0 0
\(225\) −1.43543 + 17.2636i −0.0956950 + 1.15091i
\(226\) 0 0
\(227\) 0.456091 0.166003i 0.0302718 0.0110180i −0.326840 0.945080i \(-0.605984\pi\)
0.357112 + 0.934062i \(0.383762\pi\)
\(228\) 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 \(0.187435\pi\)
−0.591475 + 0.806323i \(0.701454\pi\)
\(240\) 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 −0.923864 0.382721i \(-0.874987\pi\)
0.793378 + 0.608729i \(0.208320\pi\)
\(252\) 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 −0.991677 0.128753i \(-0.958903\pi\)
0.975907 + 0.218185i \(0.0700138\pi\)
\(264\) 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 \(-0.872431\pi\)
0.920761 0.390127i \(-0.127569\pi\)
\(272\) 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 0.745926 0.666029i \(-0.232007\pi\)
−0.785439 + 0.618939i \(0.787563\pi\)
\(284\) 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 −0.336505 0.941682i \(-0.609245\pi\)
0.647268 + 0.762262i \(0.275911\pi\)
\(308\) 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 \(0.645659\pi\)
−0.960203 + 0.279303i \(0.909897\pi\)
\(312\) 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 0.159181 0.987249i \(-0.449115\pi\)
−0.188078 + 0.982154i \(0.560226\pi\)
\(332\) 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 \(0.146580\pi\)
−0.689818 + 0.723983i \(0.742309\pi\)
\(348\) 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 −0.981423 0.191857i \(-0.938549\pi\)
0.656865 + 0.754008i \(0.271882\pi\)
\(360\) 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 \(0.171755\pi\)
−0.326956 + 0.945039i \(0.606023\pi\)
\(368\) 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 \(0.314560\pi\)
−0.550178 + 0.835047i \(0.685440\pi\)
\(380\) 0 0
\(381\) 21.1708 13.5515i 1.08461 0.694265i
\(382\) 0 0
\(383\) −19.0144 6.92069i −0.971593 0.353631i −0.193027 0.981194i \(-0.561830\pi\)
−0.778566 + 0.627563i \(0.784053\pi\)
\(384\) 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 \(-0.354255\pi\)
0.960128 0.279561i \(-0.0901891\pi\)
\(420\) 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 \(-0.563692\pi\)
−0.198763 + 0.980048i \(0.563692\pi\)
\(432\) 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 −0.00225021 0.999997i \(-0.500716\pi\)
−0.344134 + 0.938921i \(0.611827\pi\)
\(440\) 0 0
\(441\) −2.04497 7.50245i −0.0973796 0.357260i
\(442\) 0 0
\(443\) −28.8637 + 10.5055i −1.37136 + 0.499133i −0.919546 0.392982i \(-0.871443\pi\)
−0.451809 + 0.892115i \(0.649221\pi\)
\(444\) 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 0.127288 0.991866i \(-0.459373\pi\)
0.458850 + 0.888514i \(0.348261\pi\)
\(464\) 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 \(-0.393902\pi\)
0.654771 0.755827i \(-0.272765\pi\)
\(468\) 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 \(0.111549\pi\)
−0.999999 + 0.00137483i \(0.999562\pi\)
\(480\) 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 \(0.207271\pi\)
−0.795380 + 0.606111i \(0.792729\pi\)
\(488\) 0 0
\(489\) −38.0348 19.6956i −1.71999 0.890666i
\(490\) 0 0
\(491\) −28.4746 10.3639i −1.28504 0.467716i −0.392944 0.919562i \(-0.628543\pi\)
−0.892096 + 0.451846i \(0.850766\pi\)
\(492\) 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 0.861707 0.507406i \(-0.169396\pi\)
−0.649331 + 0.760506i \(0.724951\pi\)
\(500\) 0 0
\(501\) −12.8264 + 11.8042i −0.573042 + 0.527373i
\(502\) 0 0
\(503\) −8.99874 15.5863i −0.401234 0.694958i 0.592641 0.805467i \(-0.298085\pi\)
−0.993875 + 0.110509i \(0.964752\pi\)
\(504\) 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 −0.847555 0.530708i \(-0.821926\pi\)
0.0358289 + 0.999358i \(0.488593\pi\)
\(524\) 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 −0.308480 0.951231i \(-0.599820\pi\)
−0.615216 + 0.788358i \(0.710931\pi\)
\(548\) 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 \(-0.852947\pi\)
0.688740 0.725008i \(-0.258164\pi\)
\(564\) 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 0.611332 0.791374i \(-0.290634\pi\)
0.845130 + 0.534561i \(0.179523\pi\)
\(572\) 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 \(-0.716147\pi\)
0.856325 0.516438i \(-0.172742\pi\)
\(588\) 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 −0.377976 0.925816i \(-0.623380\pi\)
−0.884649 + 0.466258i \(0.845602\pi\)
\(600\) 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 0.895619 0.444822i \(-0.146733\pi\)
−0.593586 + 0.804770i \(0.702288\pi\)
\(608\) 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 −0.357167 0.934040i \(-0.616257\pi\)
0.981872 + 0.189547i \(0.0607018\pi\)
\(620\) 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 −0.186685 0.982420i \(-0.559774\pi\)
0.757458 + 0.652884i \(0.226441\pi\)
\(632\) 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 \(0.273240\pi\)
−0.987183 + 0.159592i \(0.948982\pi\)
\(644\) 0 0
\(645\) 23.3956 45.1800i 0.921202 1.77896i
\(646\) 0 0
\(647\) 35.4946 1.39544 0.697718 0.716372i \(-0.254199\pi\)
0.697718 + 0.716372i \(0.254199\pi\)
\(648\) 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 −0.185703 0.982606i \(-0.559456\pi\)
0.489350 + 0.872088i \(0.337234\pi\)
\(660\) 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 \(0.508344\pi\)
−0.852622 + 0.522528i \(0.824989\pi\)
\(684\) 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 0.911142 0.412092i \(-0.135202\pi\)
−0.962863 + 0.269990i \(0.912980\pi\)
\(692\) 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 0.881036 0.473050i \(-0.156847\pi\)
−0.850191 + 0.526475i \(0.823514\pi\)
\(720\) 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 −0.932691 0.360676i \(-0.882546\pi\)
0.517156 + 0.855891i \(0.326991\pi\)
\(728\) 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 −0.0874467 0.996169i \(-0.527871\pi\)
0.818984 + 0.573816i \(0.194537\pi\)
\(740\) 0 0
\(741\) −15.0730 + 48.1671i −0.553721 + 1.76946i
\(742\) 0 0
\(743\) −15.7558 + 13.2207i −0.578023 + 0.485019i −0.884297 0.466924i \(-0.845362\pi\)
0.306274 + 0.951943i \(0.400918\pi\)
\(744\) 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 \(-0.650870\pi\)
0.921570 0.388213i \(-0.126907\pi\)
\(752\) 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 0.335608 0.942002i \(-0.391058\pi\)
0.637552 + 0.770407i \(0.279947\pi\)
\(788\) 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
\(796\)