Properties

Label 280.2.bo.a.33.1
Level $280$
Weight $2$
Character 280.33
Analytic conductor $2.236$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 280.bo (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.23581125660\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 33.1
Character \(\chi\) \(=\) 280.33
Dual form 280.2.bo.a.17.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.75887 - 0.739238i) q^{3} +(-1.04631 - 1.97617i) q^{5} +(-1.91229 + 1.82843i) q^{7} +(4.46683 + 2.57893i) q^{9} +O(q^{10})\) \(q+(-2.75887 - 0.739238i) q^{3} +(-1.04631 - 1.97617i) q^{5} +(-1.91229 + 1.82843i) q^{7} +(4.46683 + 2.57893i) q^{9} +(2.37354 + 4.11109i) q^{11} +(1.92718 - 1.92718i) q^{13} +(1.42578 + 6.22547i) q^{15} +(-1.76751 + 6.59645i) q^{17} +(0.0439918 - 0.0761960i) q^{19} +(6.62741 - 3.63077i) q^{21} +(-0.242586 + 0.0650008i) q^{23} +(-2.81047 + 4.13537i) q^{25} +(-4.35808 - 4.35808i) q^{27} -0.284886i q^{29} +(-3.69058 + 2.13075i) q^{31} +(-3.50922 - 13.0966i) q^{33} +(5.61413 + 1.86589i) q^{35} +(1.05500 + 3.93731i) q^{37} +(-6.74148 + 3.89220i) q^{39} +9.16296i q^{41} +(-6.72406 - 6.72406i) q^{43} +(0.422691 - 11.5256i) q^{45} +(6.75301 - 1.80946i) q^{47} +(0.313692 - 6.99297i) q^{49} +(9.75269 - 16.8922i) q^{51} +(-2.27886 + 8.50482i) q^{53} +(5.64073 - 8.99198i) q^{55} +(-0.177695 + 0.177695i) q^{57} +(-1.56522 - 2.71104i) q^{59} +(-4.84125 - 2.79509i) q^{61} +(-13.2573 + 3.23564i) q^{63} +(-5.82485 - 1.79199i) q^{65} +(-2.19738 - 0.588786i) q^{67} +0.717316 q^{69} -3.53569 q^{71} +(8.72777 + 2.33860i) q^{73} +(10.8107 - 9.33136i) q^{75} +(-12.0557 - 3.52174i) q^{77} +(10.7043 + 6.18015i) q^{79} +(1.06496 + 1.84456i) q^{81} +(-10.1777 + 10.1777i) q^{83} +(14.8850 - 3.40904i) q^{85} +(-0.210599 + 0.785966i) q^{87} +(-7.02336 + 12.1648i) q^{89} +(-0.161611 + 7.20903i) q^{91} +(11.7570 - 3.15027i) q^{93} +(-0.196605 - 0.00721033i) q^{95} +(-5.72716 - 5.72716i) q^{97} +24.4847i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 4q^{7} + O(q^{10}) \) \( 48q - 4q^{7} + 4q^{11} + 8q^{15} - 4q^{21} - 4q^{23} - 8q^{25} - 36q^{33} + 24q^{35} + 8q^{37} - 16q^{43} + 48q^{45} + 24q^{51} + 16q^{53} - 96q^{57} - 36q^{61} - 68q^{63} + 12q^{65} - 16q^{67} - 64q^{71} - 48q^{73} - 48q^{75} + 4q^{77} - 40q^{85} - 12q^{87} - 80q^{91} + 24q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

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
\(3\) −2.75887 0.739238i −1.59284 0.426799i −0.649967 0.759962i \(-0.725217\pi\)
−0.942869 + 0.333163i \(0.891884\pi\)
\(4\) 0 0
\(5\) −1.04631 1.97617i −0.467925 0.883768i
\(6\) 0 0
\(7\) −1.91229 + 1.82843i −0.722777 + 0.691081i
\(8\) 0 0
\(9\) 4.46683 + 2.57893i 1.48894 + 0.859643i
\(10\) 0 0
\(11\) 2.37354 + 4.11109i 0.715648 + 1.23954i 0.962709 + 0.270539i \(0.0872020\pi\)
−0.247061 + 0.969000i \(0.579465\pi\)
\(12\) 0 0
\(13\) 1.92718 1.92718i 0.534503 0.534503i −0.387406 0.921909i \(-0.626629\pi\)
0.921909 + 0.387406i \(0.126629\pi\)
\(14\) 0 0
\(15\) 1.42578 + 6.22547i 0.368136 + 1.60741i
\(16\) 0 0
\(17\) −1.76751 + 6.59645i −0.428685 + 1.59987i 0.327058 + 0.945004i \(0.393943\pi\)
−0.755742 + 0.654869i \(0.772724\pi\)
\(18\) 0 0
\(19\) 0.0439918 0.0761960i 0.0100924 0.0174806i −0.860935 0.508715i \(-0.830121\pi\)
0.871028 + 0.491234i \(0.163454\pi\)
\(20\) 0 0
\(21\) 6.62741 3.63077i 1.44622 0.792299i
\(22\) 0 0
\(23\) −0.242586 + 0.0650008i −0.0505827 + 0.0135536i −0.284022 0.958818i \(-0.591669\pi\)
0.233439 + 0.972371i \(0.425002\pi\)
\(24\) 0 0
\(25\) −2.81047 + 4.13537i −0.562093 + 0.827074i
\(26\) 0 0
\(27\) −4.35808 4.35808i −0.838714 0.838714i
\(28\) 0 0
\(29\) 0.284886i 0.0529021i −0.999650 0.0264510i \(-0.991579\pi\)
0.999650 0.0264510i \(-0.00842061\pi\)
\(30\) 0 0
\(31\) −3.69058 + 2.13075i −0.662847 + 0.382695i −0.793361 0.608752i \(-0.791671\pi\)
0.130514 + 0.991446i \(0.458337\pi\)
\(32\) 0 0
\(33\) −3.50922 13.0966i −0.610876 2.27982i
\(34\) 0 0
\(35\) 5.61413 + 1.86589i 0.948961 + 0.315393i
\(36\) 0 0
\(37\) 1.05500 + 3.93731i 0.173441 + 0.647290i 0.996812 + 0.0797867i \(0.0254239\pi\)
−0.823371 + 0.567503i \(0.807909\pi\)
\(38\) 0 0
\(39\) −6.74148 + 3.89220i −1.07950 + 0.623250i
\(40\) 0 0
\(41\) 9.16296i 1.43101i 0.698606 + 0.715507i \(0.253804\pi\)
−0.698606 + 0.715507i \(0.746196\pi\)
\(42\) 0 0
\(43\) −6.72406 6.72406i −1.02541 1.02541i −0.999669 0.0257410i \(-0.991805\pi\)
−0.0257410 0.999669i \(-0.508195\pi\)
\(44\) 0 0
\(45\) 0.422691 11.5256i 0.0630110 1.71813i
\(46\) 0 0
\(47\) 6.75301 1.80946i 0.985028 0.263937i 0.269867 0.962898i \(-0.413020\pi\)
0.715160 + 0.698960i \(0.246354\pi\)
\(48\) 0 0
\(49\) 0.313692 6.99297i 0.0448131 0.998995i
\(50\) 0 0
\(51\) 9.75269 16.8922i 1.36565 2.36537i
\(52\) 0 0
\(53\) −2.27886 + 8.50482i −0.313025 + 1.16823i 0.612788 + 0.790247i \(0.290048\pi\)
−0.925814 + 0.377980i \(0.876619\pi\)
\(54\) 0 0
\(55\) 5.64073 8.99198i 0.760596 1.21248i
\(56\) 0 0
\(57\) −0.177695 + 0.177695i −0.0235363 + 0.0235363i
\(58\) 0 0
\(59\) −1.56522 2.71104i −0.203774 0.352947i 0.745967 0.665982i \(-0.231987\pi\)
−0.949741 + 0.313036i \(0.898654\pi\)
\(60\) 0 0
\(61\) −4.84125 2.79509i −0.619858 0.357875i 0.156956 0.987606i \(-0.449832\pi\)
−0.776814 + 0.629730i \(0.783165\pi\)
\(62\) 0 0
\(63\) −13.2573 + 3.23564i −1.67026 + 0.407652i
\(64\) 0 0
\(65\) −5.82485 1.79199i −0.722484 0.222270i
\(66\) 0 0
\(67\) −2.19738 0.588786i −0.268452 0.0719316i 0.122082 0.992520i \(-0.461043\pi\)
−0.390534 + 0.920588i \(0.627710\pi\)
\(68\) 0 0
\(69\) 0.717316 0.0863547
\(70\) 0 0
\(71\) −3.53569 −0.419610 −0.209805 0.977743i \(-0.567283\pi\)
−0.209805 + 0.977743i \(0.567283\pi\)
\(72\) 0 0
\(73\) 8.72777 + 2.33860i 1.02151 + 0.273712i 0.730430 0.682987i \(-0.239319\pi\)
0.291078 + 0.956699i \(0.405986\pi\)
\(74\) 0 0
\(75\) 10.8107 9.33136i 1.24832 1.07749i
\(76\) 0 0
\(77\) −12.0557 3.52174i −1.37388 0.401339i
\(78\) 0 0
\(79\) 10.7043 + 6.18015i 1.20433 + 0.695321i 0.961515 0.274751i \(-0.0885956\pi\)
0.242816 + 0.970072i \(0.421929\pi\)
\(80\) 0 0
\(81\) 1.06496 + 1.84456i 0.118329 + 0.204951i
\(82\) 0 0
\(83\) −10.1777 + 10.1777i −1.11715 + 1.11715i −0.124989 + 0.992158i \(0.539889\pi\)
−0.992158 + 0.124989i \(0.960111\pi\)
\(84\) 0 0
\(85\) 14.8850 3.40904i 1.61451 0.369762i
\(86\) 0 0
\(87\) −0.210599 + 0.785966i −0.0225786 + 0.0842644i
\(88\) 0 0
\(89\) −7.02336 + 12.1648i −0.744474 + 1.28947i 0.205965 + 0.978559i \(0.433967\pi\)
−0.950440 + 0.310908i \(0.899367\pi\)
\(90\) 0 0
\(91\) −0.161611 + 7.20903i −0.0169414 + 0.755711i
\(92\) 0 0
\(93\) 11.7570 3.15027i 1.21914 0.326668i
\(94\) 0 0
\(95\) −0.196605 0.00721033i −0.0201713 0.000739764i
\(96\) 0 0
\(97\) −5.72716 5.72716i −0.581505 0.581505i 0.353812 0.935317i \(-0.384885\pi\)
−0.935317 + 0.353812i \(0.884885\pi\)
\(98\) 0 0
\(99\) 24.4847i 2.46081i
\(100\) 0 0
\(101\) 1.74942 1.01003i 0.174074 0.100501i −0.410432 0.911891i \(-0.634622\pi\)
0.584505 + 0.811390i \(0.301289\pi\)
\(102\) 0 0
\(103\) 1.55642 + 5.80862i 0.153358 + 0.572341i 0.999240 + 0.0389708i \(0.0124079\pi\)
−0.845882 + 0.533370i \(0.820925\pi\)
\(104\) 0 0
\(105\) −14.1093 9.29794i −1.37693 0.907386i
\(106\) 0 0
\(107\) 4.59156 + 17.1359i 0.443883 + 1.65659i 0.718870 + 0.695145i \(0.244660\pi\)
−0.274987 + 0.961448i \(0.588674\pi\)
\(108\) 0 0
\(109\) −1.79135 + 1.03423i −0.171580 + 0.0990617i −0.583331 0.812235i \(-0.698251\pi\)
0.411751 + 0.911297i \(0.364917\pi\)
\(110\) 0 0
\(111\) 11.6424i 1.10505i
\(112\) 0 0
\(113\) −3.54754 3.54754i −0.333724 0.333724i 0.520275 0.853999i \(-0.325830\pi\)
−0.853999 + 0.520275i \(0.825830\pi\)
\(114\) 0 0
\(115\) 0.382273 + 0.411380i 0.0356471 + 0.0383613i
\(116\) 0 0
\(117\) 13.5784 3.63833i 1.25533 0.336364i
\(118\) 0 0
\(119\) −8.68114 15.8461i −0.795799 1.45261i
\(120\) 0 0
\(121\) −5.76735 + 9.98935i −0.524305 + 0.908123i
\(122\) 0 0
\(123\) 6.77360 25.2794i 0.610755 2.27937i
\(124\) 0 0
\(125\) 11.1128 + 1.22706i 0.993959 + 0.109752i
\(126\) 0 0
\(127\) 11.8913 11.8913i 1.05519 1.05519i 0.0568000 0.998386i \(-0.481910\pi\)
0.998386 0.0568000i \(-0.0180897\pi\)
\(128\) 0 0
\(129\) 13.5802 + 23.5215i 1.19567 + 2.07095i
\(130\) 0 0
\(131\) −2.96850 1.71386i −0.259359 0.149741i 0.364683 0.931132i \(-0.381177\pi\)
−0.624042 + 0.781391i \(0.714511\pi\)
\(132\) 0 0
\(133\) 0.0551941 + 0.226145i 0.00478593 + 0.0196092i
\(134\) 0 0
\(135\) −4.05238 + 13.1722i −0.348774 + 1.13368i
\(136\) 0 0
\(137\) 1.12687 + 0.301944i 0.0962751 + 0.0257968i 0.306635 0.951827i \(-0.400797\pi\)
−0.210360 + 0.977624i \(0.567464\pi\)
\(138\) 0 0
\(139\) −2.74448 −0.232784 −0.116392 0.993203i \(-0.537133\pi\)
−0.116392 + 0.993203i \(0.537133\pi\)
\(140\) 0 0
\(141\) −19.9683 −1.68164
\(142\) 0 0
\(143\) 12.4970 + 3.34857i 1.04505 + 0.280021i
\(144\) 0 0
\(145\) −0.562983 + 0.298080i −0.0467532 + 0.0247542i
\(146\) 0 0
\(147\) −6.03490 + 19.0608i −0.497750 + 1.57211i
\(148\) 0 0
\(149\) −12.3425 7.12594i −1.01114 0.583780i −0.0996119 0.995026i \(-0.531760\pi\)
−0.911524 + 0.411247i \(0.865093\pi\)
\(150\) 0 0
\(151\) −5.62795 9.74790i −0.457996 0.793273i 0.540859 0.841114i \(-0.318099\pi\)
−0.998855 + 0.0478406i \(0.984766\pi\)
\(152\) 0 0
\(153\) −24.9070 + 24.9070i −2.01361 + 2.01361i
\(154\) 0 0
\(155\) 8.07222 + 5.06376i 0.648376 + 0.406731i
\(156\) 0 0
\(157\) 2.64552 9.87321i 0.211135 0.787968i −0.776356 0.630295i \(-0.782934\pi\)
0.987491 0.157673i \(-0.0503993\pi\)
\(158\) 0 0
\(159\) 12.5742 21.7791i 0.997197 1.72720i
\(160\) 0 0
\(161\) 0.345045 0.567852i 0.0271934 0.0447530i
\(162\) 0 0
\(163\) 7.34761 1.96879i 0.575509 0.154207i 0.0406871 0.999172i \(-0.487045\pi\)
0.534822 + 0.844965i \(0.320379\pi\)
\(164\) 0 0
\(165\) −22.2093 + 20.6379i −1.72899 + 1.60666i
\(166\) 0 0
\(167\) 10.7090 + 10.7090i 0.828687 + 0.828687i 0.987335 0.158648i \(-0.0507135\pi\)
−0.158648 + 0.987335i \(0.550714\pi\)
\(168\) 0 0
\(169\) 5.57198i 0.428614i
\(170\) 0 0
\(171\) 0.393008 0.226903i 0.0300541 0.0173517i
\(172\) 0 0
\(173\) −2.15020 8.02465i −0.163477 0.610103i −0.998230 0.0594785i \(-0.981056\pi\)
0.834753 0.550625i \(-0.185610\pi\)
\(174\) 0 0
\(175\) −2.18681 13.0468i −0.165308 0.986242i
\(176\) 0 0
\(177\) 2.31414 + 8.63647i 0.173941 + 0.649157i
\(178\) 0 0
\(179\) −0.609128 + 0.351680i −0.0455284 + 0.0262858i −0.522591 0.852583i \(-0.675035\pi\)
0.477063 + 0.878869i \(0.341701\pi\)
\(180\) 0 0
\(181\) 14.2928i 1.06238i 0.847253 + 0.531189i \(0.178255\pi\)
−0.847253 + 0.531189i \(0.821745\pi\)
\(182\) 0 0
\(183\) 11.2901 + 11.2901i 0.834591 + 0.834591i
\(184\) 0 0
\(185\) 6.67692 6.20451i 0.490897 0.456164i
\(186\) 0 0
\(187\) −31.3138 + 8.39051i −2.28989 + 0.613575i
\(188\) 0 0
\(189\) 16.3024 + 0.365463i 1.18582 + 0.0265836i
\(190\) 0 0
\(191\) 8.49789 14.7188i 0.614886 1.06501i −0.375519 0.926815i \(-0.622535\pi\)
0.990405 0.138199i \(-0.0441313\pi\)
\(192\) 0 0
\(193\) 3.89171 14.5240i 0.280131 1.04546i −0.672193 0.740376i \(-0.734648\pi\)
0.952324 0.305088i \(-0.0986858\pi\)
\(194\) 0 0
\(195\) 14.7453 + 9.24984i 1.05593 + 0.662395i
\(196\) 0 0
\(197\) −2.18377 + 2.18377i −0.155587 + 0.155587i −0.780608 0.625021i \(-0.785091\pi\)
0.625021 + 0.780608i \(0.285091\pi\)
\(198\) 0 0
\(199\) −1.06910 1.85173i −0.0757863 0.131266i 0.825642 0.564195i \(-0.190813\pi\)
−0.901428 + 0.432929i \(0.857480\pi\)
\(200\) 0 0
\(201\) 5.62704 + 3.24877i 0.396900 + 0.229151i
\(202\) 0 0
\(203\) 0.520895 + 0.544785i 0.0365596 + 0.0382364i
\(204\) 0 0
\(205\) 18.1075 9.58730i 1.26468 0.669606i
\(206\) 0 0
\(207\) −1.25122 0.335265i −0.0869661 0.0233025i
\(208\) 0 0
\(209\) 0.417665 0.0288905
\(210\) 0 0
\(211\) 8.59667 0.591819 0.295910 0.955216i \(-0.404377\pi\)
0.295910 + 0.955216i \(0.404377\pi\)
\(212\) 0 0
\(213\) 9.75453 + 2.61372i 0.668370 + 0.179089i
\(214\) 0 0
\(215\) −6.25240 + 20.3233i −0.426410 + 1.38604i
\(216\) 0 0
\(217\) 3.16151 10.8226i 0.214617 0.734684i
\(218\) 0 0
\(219\) −22.3500 12.9038i −1.51028 0.871958i
\(220\) 0 0
\(221\) 9.30621 + 16.1188i 0.626004 + 1.08427i
\(222\) 0 0
\(223\) −7.64095 + 7.64095i −0.511676 + 0.511676i −0.915040 0.403364i \(-0.867841\pi\)
0.403364 + 0.915040i \(0.367841\pi\)
\(224\) 0 0
\(225\) −23.2187 + 11.2240i −1.54791 + 0.748268i
\(226\) 0 0
\(227\) −0.106829 + 0.398693i −0.00709052 + 0.0264622i −0.969380 0.245564i \(-0.921027\pi\)
0.962290 + 0.272026i \(0.0876936\pi\)
\(228\) 0 0
\(229\) 6.96704 12.0673i 0.460395 0.797427i −0.538586 0.842571i \(-0.681041\pi\)
0.998981 + 0.0451435i \(0.0143745\pi\)
\(230\) 0 0
\(231\) 30.6568 + 18.6281i 2.01707 + 1.22564i
\(232\) 0 0
\(233\) 2.40099 0.643344i 0.157294 0.0421469i −0.179313 0.983792i \(-0.557387\pi\)
0.336607 + 0.941645i \(0.390721\pi\)
\(234\) 0 0
\(235\) −10.6415 11.4518i −0.694178 0.747033i
\(236\) 0 0
\(237\) −24.9633 24.9633i −1.62154 1.62154i
\(238\) 0 0
\(239\) 10.7870i 0.697753i −0.937169 0.348877i \(-0.886563\pi\)
0.937169 0.348877i \(-0.113437\pi\)
\(240\) 0 0
\(241\) −4.35718 + 2.51562i −0.280671 + 0.162045i −0.633727 0.773557i \(-0.718476\pi\)
0.353056 + 0.935602i \(0.385142\pi\)
\(242\) 0 0
\(243\) 3.21100 + 11.9836i 0.205985 + 0.768748i
\(244\) 0 0
\(245\) −14.1475 + 6.69691i −0.903850 + 0.427850i
\(246\) 0 0
\(247\) −0.0620633 0.231623i −0.00394899 0.0147378i
\(248\) 0 0
\(249\) 35.6027 20.5552i 2.25623 1.30263i
\(250\) 0 0
\(251\) 3.62098i 0.228554i −0.993449 0.114277i \(-0.963545\pi\)
0.993449 0.114277i \(-0.0364552\pi\)
\(252\) 0 0
\(253\) −0.843011 0.843011i −0.0529997 0.0529997i
\(254\) 0 0
\(255\) −43.5860 1.59848i −2.72946 0.100101i
\(256\) 0 0
\(257\) 21.4562 5.74916i 1.33840 0.358623i 0.482559 0.875864i \(-0.339708\pi\)
0.855840 + 0.517241i \(0.173041\pi\)
\(258\) 0 0
\(259\) −9.21656 5.60028i −0.572689 0.347985i
\(260\) 0 0
\(261\) 0.734702 1.27254i 0.0454769 0.0787683i
\(262\) 0 0
\(263\) 0.415825 1.55188i 0.0256409 0.0956930i −0.951920 0.306348i \(-0.900893\pi\)
0.977561 + 0.210655i \(0.0675596\pi\)
\(264\) 0 0
\(265\) 19.1913 4.39528i 1.17891 0.270000i
\(266\) 0 0
\(267\) 28.3692 28.3692i 1.73617 1.73617i
\(268\) 0 0
\(269\) −11.9154 20.6380i −0.726493 1.25832i −0.958357 0.285574i \(-0.907816\pi\)
0.231864 0.972748i \(-0.425518\pi\)
\(270\) 0 0
\(271\) −16.9698 9.79753i −1.03084 0.595158i −0.113617 0.993525i \(-0.536244\pi\)
−0.917226 + 0.398367i \(0.869577\pi\)
\(272\) 0 0
\(273\) 5.77505 19.7693i 0.349522 1.19649i
\(274\) 0 0
\(275\) −23.6716 1.73861i −1.42745 0.104842i
\(276\) 0 0
\(277\) −12.9270 3.46378i −0.776709 0.208119i −0.151376 0.988476i \(-0.548370\pi\)
−0.625333 + 0.780358i \(0.715037\pi\)
\(278\) 0 0
\(279\) −21.9803 −1.31592
\(280\) 0 0
\(281\) −11.6570 −0.695398 −0.347699 0.937606i \(-0.613037\pi\)
−0.347699 + 0.937606i \(0.613037\pi\)
\(282\) 0 0
\(283\) −21.9998 5.89484i −1.30775 0.350412i −0.463378 0.886161i \(-0.653363\pi\)
−0.844377 + 0.535749i \(0.820029\pi\)
\(284\) 0 0
\(285\) 0.537079 + 0.165230i 0.0318138 + 0.00978740i
\(286\) 0 0
\(287\) −16.7538 17.5222i −0.988947 1.03430i
\(288\) 0 0
\(289\) −25.6666 14.8186i −1.50980 0.871683i
\(290\) 0 0
\(291\) 11.5668 + 20.0342i 0.678056 + 1.17443i
\(292\) 0 0
\(293\) 21.4186 21.4186i 1.25129 1.25129i 0.296143 0.955144i \(-0.404300\pi\)
0.955144 0.296143i \(-0.0957005\pi\)
\(294\) 0 0
\(295\) −3.71975 + 5.92972i −0.216572 + 0.345241i
\(296\) 0 0
\(297\) 7.57239 28.2605i 0.439394 1.63984i
\(298\) 0 0
\(299\) −0.342239 + 0.592775i −0.0197922 + 0.0342810i
\(300\) 0 0
\(301\) 25.1528 + 0.563871i 1.44978 + 0.0325010i
\(302\) 0 0
\(303\) −5.57307 + 1.49330i −0.320165 + 0.0857878i
\(304\) 0 0
\(305\) −0.458121 + 12.4916i −0.0262319 + 0.715269i
\(306\) 0 0
\(307\) 3.23542 + 3.23542i 0.184655 + 0.184655i 0.793381 0.608726i \(-0.208319\pi\)
−0.608726 + 0.793381i \(0.708319\pi\)
\(308\) 0 0
\(309\) 17.1758i 0.977098i
\(310\) 0 0
\(311\) −9.07682 + 5.24050i −0.514699 + 0.297162i −0.734763 0.678324i \(-0.762707\pi\)
0.220064 + 0.975485i \(0.429373\pi\)
\(312\) 0 0
\(313\) 5.51996 + 20.6008i 0.312007 + 1.16443i 0.926744 + 0.375693i \(0.122595\pi\)
−0.614737 + 0.788732i \(0.710738\pi\)
\(314\) 0 0
\(315\) 20.2654 + 22.8131i 1.14182 + 1.28537i
\(316\) 0 0
\(317\) 7.88745 + 29.4364i 0.443003 + 1.65331i 0.721155 + 0.692774i \(0.243611\pi\)
−0.278152 + 0.960537i \(0.589722\pi\)
\(318\) 0 0
\(319\) 1.17119 0.676188i 0.0655742 0.0378593i
\(320\) 0 0
\(321\) 50.6701i 2.82813i
\(322\) 0 0
\(323\) 0.424867 + 0.424867i 0.0236402 + 0.0236402i
\(324\) 0 0
\(325\) 2.55333 + 13.3859i 0.141633 + 0.742514i
\(326\) 0 0
\(327\) 5.70664 1.52909i 0.315578 0.0845589i
\(328\) 0 0
\(329\) −9.60522 + 15.8076i −0.529553 + 0.871502i
\(330\) 0 0
\(331\) −2.65492 + 4.59846i −0.145928 + 0.252754i −0.929719 0.368271i \(-0.879950\pi\)
0.783791 + 0.621025i \(0.213283\pi\)
\(332\) 0 0
\(333\) −5.44154 + 20.3081i −0.298194 + 1.11288i
\(334\) 0 0
\(335\) 1.13560 + 4.95844i 0.0620446 + 0.270908i
\(336\) 0 0
\(337\) 6.43088 6.43088i 0.350312 0.350312i −0.509913 0.860226i \(-0.670323\pi\)
0.860226 + 0.509913i \(0.170323\pi\)
\(338\) 0 0
\(339\) 7.16473 + 12.4097i 0.389135 + 0.674001i
\(340\) 0 0
\(341\) −17.5194 10.1148i −0.948730 0.547750i
\(342\) 0 0
\(343\) 12.1863 + 13.9461i 0.657997 + 0.753020i
\(344\) 0 0
\(345\) −0.750536 1.41753i −0.0404075 0.0763175i
\(346\) 0 0
\(347\) 21.5856 + 5.78384i 1.15877 + 0.310493i 0.786476 0.617621i \(-0.211903\pi\)
0.372298 + 0.928113i \(0.378570\pi\)
\(348\) 0 0
\(349\) 32.6644 1.74849 0.874244 0.485487i \(-0.161358\pi\)
0.874244 + 0.485487i \(0.161358\pi\)
\(350\) 0 0
\(351\) −16.7976 −0.896589
\(352\) 0 0
\(353\) 23.3607 + 6.25948i 1.24336 + 0.333158i 0.819770 0.572694i \(-0.194101\pi\)
0.423594 + 0.905852i \(0.360768\pi\)
\(354\) 0 0
\(355\) 3.69944 + 6.98712i 0.196346 + 0.370838i
\(356\) 0 0
\(357\) 12.2362 + 50.1348i 0.647606 + 2.65341i
\(358\) 0 0
\(359\) 30.6942 + 17.7213i 1.61998 + 0.935293i 0.986924 + 0.161184i \(0.0515311\pi\)
0.633051 + 0.774110i \(0.281802\pi\)
\(360\) 0 0
\(361\) 9.49613 + 16.4478i 0.499796 + 0.865673i
\(362\) 0 0
\(363\) 23.2959 23.2959i 1.22272 1.22272i
\(364\) 0 0
\(365\) −4.51051 19.6944i −0.236091 1.03085i
\(366\) 0 0
\(367\) −3.51883 + 13.1325i −0.183682 + 0.685509i 0.811227 + 0.584731i \(0.198800\pi\)
−0.994909 + 0.100778i \(0.967867\pi\)
\(368\) 0 0
\(369\) −23.6306 + 40.9294i −1.23016 + 2.13070i
\(370\) 0 0
\(371\) −11.1926 20.4304i −0.581092 1.06069i
\(372\) 0 0
\(373\) −16.6387 + 4.45833i −0.861519 + 0.230843i −0.662417 0.749135i \(-0.730469\pi\)
−0.199102 + 0.979979i \(0.563803\pi\)
\(374\) 0 0
\(375\) −29.7517 11.6003i −1.53637 0.599037i
\(376\) 0 0
\(377\) −0.549027 0.549027i −0.0282763 0.0282763i
\(378\) 0 0
\(379\) 3.68014i 0.189036i −0.995523 0.0945181i \(-0.969869\pi\)
0.995523 0.0945181i \(-0.0301310\pi\)
\(380\) 0 0
\(381\) −41.5972 + 24.0162i −2.13109 + 1.23039i
\(382\) 0 0
\(383\) 5.85380 + 21.8467i 0.299115 + 1.11631i 0.937894 + 0.346923i \(0.112774\pi\)
−0.638778 + 0.769391i \(0.720560\pi\)
\(384\) 0 0
\(385\) 5.65450 + 27.5089i 0.288180 + 1.40199i
\(386\) 0 0
\(387\) −12.6944 47.3761i −0.645293 2.40826i
\(388\) 0 0
\(389\) −1.31599 + 0.759787i −0.0667234 + 0.0385227i −0.532991 0.846121i \(-0.678932\pi\)
0.466267 + 0.884644i \(0.345599\pi\)
\(390\) 0 0
\(391\) 1.71510i 0.0867362i
\(392\) 0 0
\(393\) 6.92277 + 6.92277i 0.349207 + 0.349207i
\(394\) 0 0
\(395\) 1.01294 27.6199i 0.0509664 1.38971i
\(396\) 0 0
\(397\) 1.58354 0.424309i 0.0794757 0.0212954i −0.218862 0.975756i \(-0.570234\pi\)
0.298338 + 0.954460i \(0.403568\pi\)
\(398\) 0 0
\(399\) 0.0149013 0.664706i 0.000745996 0.0332769i
\(400\) 0 0
\(401\) 1.21896 2.11129i 0.0608717 0.105433i −0.833984 0.551789i \(-0.813945\pi\)
0.894855 + 0.446356i \(0.147279\pi\)
\(402\) 0 0
\(403\) −3.00605 + 11.2187i −0.149742 + 0.558845i
\(404\) 0 0
\(405\) 2.53088 4.03451i 0.125760 0.200477i
\(406\) 0 0
\(407\) −13.6825 + 13.6825i −0.678219 + 0.678219i
\(408\) 0 0
\(409\) 8.03235 + 13.9124i 0.397174 + 0.687925i 0.993376 0.114909i \(-0.0366576\pi\)
−0.596202 + 0.802834i \(0.703324\pi\)
\(410\) 0 0
\(411\) −2.88569 1.66605i −0.142340 0.0821803i
\(412\) 0 0
\(413\) 7.95008 + 2.32239i 0.391198 + 0.114277i
\(414\) 0 0
\(415\) 30.7618 + 9.46378i 1.51004 + 0.464558i
\(416\) 0 0
\(417\) 7.57168 + 2.02883i 0.370787 + 0.0993521i
\(418\) 0 0
\(419\) 1.04323 0.0509652 0.0254826 0.999675i \(-0.491888\pi\)
0.0254826 + 0.999675i \(0.491888\pi\)
\(420\) 0 0
\(421\) −12.8512 −0.626331 −0.313165 0.949699i \(-0.601389\pi\)
−0.313165 + 0.949699i \(0.601389\pi\)
\(422\) 0 0
\(423\) 34.8310 + 9.33295i 1.69354 + 0.453784i
\(424\) 0 0
\(425\) −22.3112 25.8484i −1.08225 1.25383i
\(426\) 0 0
\(427\) 14.3685 3.50685i 0.695340 0.169708i
\(428\) 0 0
\(429\) −32.0023 18.4765i −1.54509 0.892056i
\(430\) 0 0
\(431\) 6.50366 + 11.2647i 0.313270 + 0.542600i 0.979068 0.203532i \(-0.0652421\pi\)
−0.665798 + 0.746132i \(0.731909\pi\)
\(432\) 0 0
\(433\) −23.8441 + 23.8441i −1.14587 + 1.14587i −0.158518 + 0.987356i \(0.550672\pi\)
−0.987356 + 0.158518i \(0.949328\pi\)
\(434\) 0 0
\(435\) 1.77355 0.406186i 0.0850352 0.0194751i
\(436\) 0 0
\(437\) −0.00571900 + 0.0213436i −0.000273577 + 0.00102100i
\(438\) 0 0
\(439\) −3.55919 + 6.16470i −0.169871 + 0.294225i −0.938374 0.345621i \(-0.887668\pi\)
0.768503 + 0.639846i \(0.221002\pi\)
\(440\) 0 0
\(441\) 19.4356 30.4274i 0.925503 1.44893i
\(442\) 0 0
\(443\) −14.6235 + 3.91835i −0.694783 + 0.186166i −0.588892 0.808211i \(-0.700436\pi\)
−0.105890 + 0.994378i \(0.533769\pi\)
\(444\) 0 0
\(445\) 31.3883 + 1.15114i 1.48795 + 0.0545693i
\(446\) 0 0
\(447\) 28.7836 + 28.7836i 1.36142 + 1.36142i
\(448\) 0 0
\(449\) 23.7583i 1.12122i −0.828079 0.560612i \(-0.810566\pi\)
0.828079 0.560612i \(-0.189434\pi\)
\(450\) 0 0
\(451\) −37.6697 + 21.7486i −1.77380 + 1.02410i
\(452\) 0 0
\(453\) 8.32079 + 31.0536i 0.390945 + 1.45903i
\(454\) 0 0
\(455\) 14.4153 7.22352i 0.675801 0.338644i
\(456\) 0 0
\(457\) −7.12346 26.5851i −0.333221 1.24360i −0.905785 0.423738i \(-0.860718\pi\)
0.572563 0.819861i \(-0.305949\pi\)
\(458\) 0 0
\(459\) 36.4508 21.0449i 1.70138 0.982292i
\(460\) 0 0
\(461\) 12.0569i 0.561545i 0.959774 + 0.280773i \(0.0905907\pi\)
−0.959774 + 0.280773i \(0.909409\pi\)
\(462\) 0 0
\(463\) −19.7680 19.7680i −0.918695 0.918695i 0.0782395 0.996935i \(-0.475070\pi\)
−0.996935 + 0.0782395i \(0.975070\pi\)
\(464\) 0 0
\(465\) −18.5269 19.9376i −0.859165 0.924582i
\(466\) 0 0
\(467\) −21.6402 + 5.79848i −1.00139 + 0.268322i −0.722028 0.691864i \(-0.756790\pi\)
−0.279362 + 0.960186i \(0.590123\pi\)
\(468\) 0 0
\(469\) 5.27857 2.89182i 0.243742 0.133532i
\(470\) 0 0
\(471\) −14.5973 + 25.2833i −0.672609 + 1.16499i
\(472\) 0 0
\(473\) 11.6834 43.6030i 0.537203 2.00487i
\(474\) 0 0
\(475\) 0.191461 + 0.396069i 0.00878485 + 0.0181729i
\(476\) 0 0
\(477\) −32.1126 + 32.1126i −1.47034 + 1.47034i
\(478\) 0 0
\(479\) 3.69565 + 6.40106i 0.168859 + 0.292472i 0.938019 0.346584i \(-0.112658\pi\)
−0.769160 + 0.639056i \(0.779325\pi\)
\(480\) 0 0
\(481\) 9.62107 + 5.55473i 0.438683 + 0.253274i
\(482\) 0 0
\(483\) −1.37171 + 1.31156i −0.0624152 + 0.0596781i
\(484\) 0 0
\(485\) −5.32543 + 17.3102i −0.241815 + 0.786016i
\(486\) 0 0
\(487\) −31.5188 8.44544i −1.42825 0.382699i −0.539849 0.841762i \(-0.681519\pi\)
−0.888404 + 0.459062i \(0.848186\pi\)
\(488\) 0 0
\(489\) −21.7265 −0.982507
\(490\) 0 0
\(491\) −14.1324 −0.637785 −0.318893 0.947791i \(-0.603311\pi\)
−0.318893 + 0.947791i \(0.603311\pi\)
\(492\) 0 0
\(493\) 1.87924 + 0.503540i 0.0846366 + 0.0226783i
\(494\) 0 0
\(495\) 48.3859 25.6186i 2.17478 1.15147i
\(496\) 0 0
\(497\) 6.76127 6.46477i 0.303284 0.289984i
\(498\) 0 0
\(499\) 6.51132 + 3.75931i 0.291487 + 0.168290i 0.638612 0.769529i \(-0.279509\pi\)
−0.347125 + 0.937819i \(0.612842\pi\)
\(500\) 0 0
\(501\) −21.6283 37.4613i −0.966280 1.67365i
\(502\) 0 0
\(503\) 13.8563 13.8563i 0.617822 0.617822i −0.327150 0.944972i \(-0.606088\pi\)
0.944972 + 0.327150i \(0.106088\pi\)
\(504\) 0 0
\(505\) −3.82642 2.40034i −0.170273 0.106814i
\(506\) 0 0
\(507\) 4.11902 15.3724i 0.182932 0.682711i
\(508\) 0 0
\(509\) −14.3898 + 24.9239i −0.637818 + 1.10473i 0.348092 + 0.937460i \(0.386830\pi\)
−0.985911 + 0.167274i \(0.946504\pi\)
\(510\) 0 0
\(511\) −20.9660 + 11.4860i −0.927480 + 0.508112i
\(512\) 0 0
\(513\) −0.523789 + 0.140349i −0.0231258 + 0.00619655i
\(514\) 0 0
\(515\) 9.85031 9.15336i 0.434056 0.403345i
\(516\) 0 0
\(517\) 23.4674 + 23.4674i 1.03209 + 1.03209i
\(518\) 0 0
\(519\) 23.7285i 1.04157i
\(520\) 0 0
\(521\) 16.1832 9.34339i 0.709000 0.409342i −0.101690 0.994816i \(-0.532425\pi\)
0.810691 + 0.585475i \(0.199092\pi\)
\(522\) 0 0
\(523\) 7.01477 + 26.1795i 0.306735 + 1.14475i 0.931442 + 0.363890i \(0.118552\pi\)
−0.624707 + 0.780859i \(0.714782\pi\)
\(524\) 0 0
\(525\) −3.61152 + 37.6109i −0.157619 + 1.64148i
\(526\) 0 0
\(527\) −7.53227 28.1108i −0.328111 1.22453i
\(528\) 0 0
\(529\) −19.8640 + 11.4685i −0.863650 + 0.498629i
\(530\) 0 0
\(531\) 16.1463i 0.700691i
\(532\) 0 0
\(533\) 17.6586 + 17.6586i 0.764881 + 0.764881i
\(534\) 0 0
\(535\) 29.0592 27.0032i 1.25634 1.16745i
\(536\) 0 0
\(537\) 1.94048 0.519951i 0.0837380 0.0224375i
\(538\) 0 0
\(539\) 29.4933 15.3085i 1.27036 0.659382i
\(540\) 0 0
\(541\) 0.346702 0.600506i 0.0149059 0.0258178i −0.858476 0.512853i \(-0.828588\pi\)
0.873382 + 0.487036i \(0.161922\pi\)
\(542\) 0 0
\(543\) 10.5658 39.4321i 0.453422 1.69219i
\(544\) 0 0
\(545\) 3.91813 + 2.45787i 0.167834 + 0.105283i
\(546\) 0 0
\(547\) 15.8425 15.8425i 0.677377 0.677377i −0.282029 0.959406i \(-0.591007\pi\)
0.959406 + 0.282029i \(0.0910074\pi\)
\(548\) 0 0
\(549\) −14.4167 24.9704i −0.615290 1.06571i
\(550\) 0 0
\(551\) −0.0217072 0.0125327i −0.000924758 0.000533910i
\(552\) 0 0
\(553\) −31.7697 + 7.75389i −1.35099 + 0.329729i
\(554\) 0 0
\(555\) −23.0074 + 12.1816i −0.976610 + 0.517081i
\(556\) 0 0
\(557\) −6.88206 1.84404i −0.291602 0.0781346i 0.110052 0.993926i \(-0.464898\pi\)
−0.401655 + 0.915791i \(0.631565\pi\)
\(558\) 0 0
\(559\) −25.9169 −1.09617
\(560\) 0 0
\(561\) 92.5935 3.90930
\(562\) 0 0
\(563\) 9.00304 + 2.41236i 0.379433 + 0.101669i 0.443494 0.896277i \(-0.353739\pi\)
−0.0640613 + 0.997946i \(0.520405\pi\)
\(564\) 0 0
\(565\) −3.29869 + 10.7223i −0.138777 + 0.451092i
\(566\) 0 0
\(567\) −5.40915 1.58013i −0.227163 0.0663592i
\(568\) 0 0
\(569\) 30.8192 + 17.7935i 1.29201 + 0.745941i 0.979010 0.203812i \(-0.0653333\pi\)
0.312998 + 0.949754i \(0.398667\pi\)
\(570\) 0 0
\(571\) 10.9925 + 19.0395i 0.460020 + 0.796778i 0.998961 0.0455656i \(-0.0145090\pi\)
−0.538942 + 0.842343i \(0.681176\pi\)
\(572\) 0 0
\(573\) −34.3253 + 34.3253i −1.43396 + 1.43396i
\(574\) 0 0
\(575\) 0.412978 1.18587i 0.0172224 0.0494540i
\(576\) 0 0
\(577\) 2.05870 7.68316i 0.0857047 0.319854i −0.909742 0.415174i \(-0.863721\pi\)
0.995447 + 0.0953198i \(0.0303874\pi\)
\(578\) 0 0
\(579\) −21.4734 + 37.1931i −0.892406 + 1.54569i
\(580\) 0 0
\(581\) 0.853489 38.0719i 0.0354087 1.57949i
\(582\) 0 0
\(583\) −40.3730 + 10.8179i −1.67208 + 0.448032i
\(584\) 0 0
\(585\) −21.3972 23.0264i −0.884666 0.952025i
\(586\) 0 0
\(587\) 9.97309 + 9.97309i 0.411633 + 0.411633i 0.882307 0.470674i \(-0.155989\pi\)
−0.470674 + 0.882307i \(0.655989\pi\)
\(588\) 0 0
\(589\) 0.374943i 0.0154493i
\(590\) 0 0
\(591\) 7.63908 4.41043i 0.314230 0.181421i
\(592\) 0 0
\(593\) −9.91736 37.0121i −0.407257 1.51990i −0.799854 0.600194i \(-0.795090\pi\)
0.392597 0.919711i \(-0.371577\pi\)
\(594\) 0 0
\(595\) −22.2313 + 33.7353i −0.911395 + 1.38301i
\(596\) 0 0
\(597\) 1.58063 + 5.89901i 0.0646910 + 0.241430i
\(598\) 0 0
\(599\) 6.66956 3.85067i 0.272511 0.157334i −0.357517 0.933907i \(-0.616377\pi\)
0.630028 + 0.776572i \(0.283043\pi\)
\(600\) 0 0
\(601\) 6.91584i 0.282103i −0.990002 0.141051i \(-0.954952\pi\)
0.990002 0.141051i \(-0.0450483\pi\)
\(602\) 0 0
\(603\) −8.29689 8.29689i −0.337875 0.337875i
\(604\) 0 0
\(605\) 25.7751 + 0.945279i 1.04791 + 0.0384310i
\(606\) 0 0
\(607\) 41.6534 11.1610i 1.69066 0.453011i 0.720101 0.693870i \(-0.244096\pi\)
0.970560 + 0.240858i \(0.0774290\pi\)
\(608\) 0 0
\(609\) −1.03436 1.88806i −0.0419143 0.0765080i
\(610\) 0 0
\(611\) 9.52709 16.5014i 0.385425 0.667575i
\(612\) 0 0
\(613\) 9.35702 34.9209i 0.377927 1.41044i −0.471095 0.882083i \(-0.656141\pi\)
0.849021 0.528359i \(-0.177192\pi\)
\(614\) 0 0
\(615\) −57.0437 + 13.0644i −2.30022 + 0.526807i
\(616\) 0 0
\(617\) −21.4356 + 21.4356i −0.862966 + 0.862966i −0.991682 0.128715i \(-0.958915\pi\)
0.128715 + 0.991682i \(0.458915\pi\)
\(618\) 0 0
\(619\) 13.5728 + 23.5088i 0.545538 + 0.944900i 0.998573 + 0.0534071i \(0.0170081\pi\)
−0.453035 + 0.891493i \(0.649659\pi\)
\(620\) 0 0
\(621\) 1.34049 + 0.773932i 0.0537920 + 0.0310568i
\(622\) 0 0
\(623\) −8.81182 36.1043i −0.353038 1.44649i
\(624\) 0 0
\(625\) −9.20257 23.2446i −0.368103 0.929785i
\(626\) 0 0
\(627\) −1.15228 0.308754i −0.0460178 0.0123304i
\(628\) 0 0
\(629\) −27.8370 −1.10993
\(630\) 0 0
\(631\) 32.0140 1.27446 0.637229 0.770675i \(-0.280081\pi\)
0.637229 + 0.770675i \(0.280081\pi\)
\(632\) 0 0
\(633\) −23.7171 6.35499i −0.942672 0.252588i
\(634\) 0 0
\(635\) −35.9413 11.0572i −1.42629 0.438792i
\(636\) 0 0
\(637\) −12.8721 14.0812i −0.510013 0.557919i
\(638\) 0 0
\(639\) −15.7934 9.11830i −0.624776 0.360714i
\(640\) 0 0
\(641\) 11.3718 + 19.6966i 0.449160 + 0.777968i 0.998332 0.0577415i \(-0.0183899\pi\)
−0.549171 + 0.835710i \(0.685057\pi\)
\(642\) 0 0
\(643\) 14.6427 14.6427i 0.577453 0.577453i −0.356748 0.934201i \(-0.616114\pi\)
0.934201 + 0.356748i \(0.116114\pi\)
\(644\) 0 0
\(645\) 32.2734 51.4475i 1.27076 2.02574i
\(646\) 0 0
\(647\) 5.67864 21.1930i 0.223250 0.833181i −0.759848 0.650101i \(-0.774727\pi\)
0.983098 0.183080i \(-0.0586068\pi\)
\(648\) 0 0
\(649\) 7.43020 12.8695i 0.291661 0.505172i
\(650\) 0 0
\(651\) −16.7227 + 27.5210i −0.655413 + 1.07863i
\(652\) 0 0
\(653\) −39.3632 + 10.5473i −1.54040 + 0.412750i −0.926396 0.376551i \(-0.877110\pi\)
−0.614007 + 0.789301i \(0.710443\pi\)
\(654\) 0 0
\(655\) −0.280905 + 7.65949i −0.0109759 + 0.299281i
\(656\) 0 0
\(657\) 32.9544 + 32.9544i 1.28567 + 1.28567i
\(658\) 0 0
\(659\) 14.1384i 0.550755i −0.961336 0.275378i \(-0.911197\pi\)
0.961336 0.275378i \(-0.0888029\pi\)
\(660\) 0 0
\(661\) −14.9892 + 8.65401i −0.583011 + 0.336602i −0.762329 0.647189i \(-0.775944\pi\)
0.179318 + 0.983791i \(0.442611\pi\)
\(662\) 0 0
\(663\) −13.7590 51.3493i −0.534356 1.99424i
\(664\) 0 0
\(665\) 0.389149 0.345690i 0.0150906 0.0134053i
\(666\) 0 0
\(667\) 0.0185178 + 0.0691095i 0.000717014 + 0.00267593i
\(668\) 0 0
\(669\) 26.7289 15.4319i 1.03340 0.596633i
\(670\) 0 0
\(671\) 26.5370i 1.02445i
\(672\) 0 0
\(673\) 14.1900 + 14.1900i 0.546983 + 0.546983i 0.925567 0.378584i \(-0.123589\pi\)
−0.378584 + 0.925567i \(0.623589\pi\)
\(674\) 0 0
\(675\) 30.2705 5.77405i 1.16511 0.222243i
\(676\) 0 0
\(677\) 11.9446 3.20054i 0.459068 0.123007i −0.0218715 0.999761i \(-0.506962\pi\)
0.480939 + 0.876754i \(0.340296\pi\)
\(678\) 0 0
\(679\) 21.4237 + 0.480272i 0.822166 + 0.0184312i
\(680\) 0 0
\(681\) 0.589458 1.02097i 0.0225881 0.0391237i
\(682\) 0 0
\(683\) −3.36173 + 12.5461i −0.128633 + 0.480065i −0.999943 0.0106680i \(-0.996604\pi\)
0.871310 + 0.490733i \(0.163271\pi\)
\(684\) 0 0
\(685\) −0.582366 2.54281i −0.0222511 0.0971559i
\(686\) 0 0
\(687\) −28.1418 + 28.1418i −1.07368 + 1.07368i
\(688\) 0 0
\(689\) 11.9985 + 20.7821i 0.457108 + 0.791733i
\(690\) 0 0
\(691\) 36.3838 + 21.0062i 1.38411 + 0.799114i 0.992643 0.121080i \(-0.0386359\pi\)
0.391463 + 0.920194i \(0.371969\pi\)
\(692\) 0 0
\(693\) −44.7686 46.8218i −1.70062 1.77861i
\(694\) 0 0
\(695\) 2.87158 + 5.42356i 0.108925 + 0.205727i
\(696\) 0 0
\(697\) −60.4430 16.1956i −2.28944 0.613454i
\(698\) 0 0
\(699\) −7.09962 −0.268532
\(700\) 0 0
\(701\) 13.5398 0.511390 0.255695 0.966757i \(-0.417696\pi\)
0.255695 + 0.966757i \(0.417696\pi\)
\(702\) 0 0
\(703\) 0.346419 + 0.0928226i 0.0130654 + 0.00350087i
\(704\) 0 0
\(705\) 20.8931 + 39.4607i 0.786879 + 1.48618i
\(706\) 0 0
\(707\) −1.49863 + 5.13015i −0.0563617 + 0.192939i
\(708\) 0 0
\(709\) 10.4976 + 6.06080i 0.394246 + 0.227618i 0.683998 0.729484i \(-0.260240\pi\)
−0.289752 + 0.957102i \(0.593573\pi\)
\(710\) 0 0
\(711\) 31.8763 + 55.2114i 1.19546 + 2.07059i
\(712\) 0 0
\(713\) 0.756782 0.756782i 0.0283417 0.0283417i
\(714\) 0 0
\(715\) −6.45845 28.1998i −0.241532 1.05461i
\(716\) 0 0
\(717\) −7.97416 + 29.7600i −0.297801 + 1.11141i
\(718\) 0 0
\(719\) 11.1933 19.3874i 0.417441 0.723030i −0.578240 0.815867i \(-0.696260\pi\)
0.995681 + 0.0928372i \(0.0295936\pi\)
\(720\) 0 0
\(721\) −13.5970 8.26196i −0.506378 0.307692i
\(722\) 0 0
\(723\) 13.8806 3.71928i 0.516224 0.138322i
\(724\) 0 0
\(725\) 1.17811 + 0.800663i 0.0437539 + 0.0297359i
\(726\) 0 0
\(727\) −27.0366 27.0366i −1.00273 1.00273i −0.999996 0.00273448i \(-0.999130\pi\)
−0.00273448 0.999996i \(-0.500870\pi\)
\(728\) 0 0
\(729\) 41.8247i 1.54906i
\(730\) 0 0
\(731\) 56.2398 32.4700i 2.08010 1.20095i
\(732\) 0 0
\(733\) −2.92004 10.8977i −0.107854 0.402517i 0.890799 0.454397i \(-0.150145\pi\)
−0.998653 + 0.0518799i \(0.983479\pi\)
\(734\) 0 0
\(735\) 43.9817 8.01758i 1.62229 0.295733i
\(736\) 0 0
\(737\) −2.79501 10.4311i −0.102955 0.384235i
\(738\) 0 0
\(739\) 24.8452 14.3444i 0.913944 0.527666i 0.0322460 0.999480i \(-0.489734\pi\)
0.881698 + 0.471814i \(0.156401\pi\)
\(740\) 0 0
\(741\) 0.684899i 0.0251604i
\(742\) 0 0
\(743\) −11.3200 11.3200i −0.415290 0.415290i 0.468287 0.883577i \(-0.344871\pi\)
−0.883577 + 0.468287i \(0.844871\pi\)
\(744\) 0 0
\(745\) −1.16795 + 31.8468i −0.0427905 + 1.16677i
\(746\) 0 0
\(747\) −71.7096 + 19.2145i −2.62372 + 0.703023i
\(748\) 0 0
\(749\) −40.1122 24.3735i −1.46567 0.890588i
\(750\) 0 0
\(751\) −1.31034 + 2.26958i −0.0478151 + 0.0828182i −0.888942 0.458019i \(-0.848559\pi\)
0.841127 + 0.540837i \(0.181893\pi\)
\(752\) 0 0
\(753\) −2.67677 + 9.98983i −0.0975468 + 0.364050i
\(754\) 0 0
\(755\) −13.3749 + 21.3211i −0.486762 + 0.775955i
\(756\) 0 0
\(757\) −11.9396 + 11.9396i −0.433953 + 0.433953i −0.889971 0.456017i \(-0.849275\pi\)
0.456017 + 0.889971i \(0.349275\pi\)
\(758\) 0 0
\(759\) 1.70258 + 2.94895i 0.0617996 + 0.107040i
\(760\) 0 0
\(761\) 17.1993 + 9.93004i 0.623475 + 0.359964i 0.778221 0.627991i \(-0.216122\pi\)
−0.154745 + 0.987954i \(0.549456\pi\)
\(762\) 0 0
\(763\) 1.53455 5.25311i 0.0555543 0.190175i
\(764\) 0 0
\(765\) 75.2807 + 23.1598i 2.72178 + 0.837346i
\(766\) 0 0
\(767\) −8.24110 2.20820i −0.297569 0.0797333i
\(768\) 0 0
\(769\) −4.79436 −0.172889 −0.0864445 0.996257i \(-0.527551\pi\)
−0.0864445 + 0.996257i \(0.527551\pi\)
\(770\) 0 0
\(771\) −63.4448 −2.28491
\(772\) 0 0
\(773\) −25.0979 6.72495i −0.902707 0.241880i −0.222529 0.974926i \(-0.571431\pi\)
−0.680179 + 0.733046i \(0.738098\pi\)
\(774\) 0 0
\(775\) 1.56077 21.2503i 0.0560646 0.763334i
\(776\) 0 0
\(777\) 21.2874 + 22.2637i 0.763681 + 0.798706i
\(778\) 0 0
\(779\) 0.698181 + 0.403095i 0.0250149 + 0.0144424i
\(780\) 0 0
\(781\) −8.39210 14.5355i −0.300293 0.520123i
\(782\) 0 0
\(783\) −1.24156 + 1.24156i −0.0443697 + 0.0443697i
\(784\) 0 0
\(785\) −22.2791 + 5.10247i −0.795177 + 0.182115i
\(786\) 0 0
\(787\) −1.22159 + 4.55904i −0.0435450 + 0.162512i −0.984275 0.176646i \(-0.943475\pi\)
0.940730 + 0.339158i \(0.110142\pi\)
\(788\) 0 0
\(789\) −2.29442 + 3.97405i −0.0816834 + 0.141480i
\(790\) 0 0
\(791\) 13.2703 + 0.297492i 0.471839 + 0.0105776i
\(792\) 0 0
\(793\) −14.7166 + 3.94330i −0.522601 + 0.140031i
\(794\) 0 0
\(795\) −56.1956 2.06093i −1.99305 0.0730936i
\(796\) 0 0
\(797\) 6.20691 + 6.20691i