Properties

Label 280.2.bo.a.17.1
Level $280$
Weight $2$
Character 280.17
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 17.1
Character \(\chi\) \(=\) 280.17
Dual form 280.2.bo.a.33.1

$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

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

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 −0.942869 0.333163i \(-0.891884\pi\)
−0.649967 + 0.759962i \(0.725217\pi\)
\(4\) 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 −0.247061 0.969000i \(-0.579465\pi\)
0.962709 0.270539i \(-0.0872020\pi\)
\(12\) 0 0
\(13\) 1.92718 + 1.92718i 0.534503 + 0.534503i 0.921909 0.387406i \(-0.126629\pi\)
−0.387406 + 0.921909i \(0.626629\pi\)
\(14\) 0 0
\(15\) 1.42578 6.22547i 0.368136 1.60741i
\(16\) 0 0
\(17\) −1.76751 6.59645i −0.428685 1.59987i −0.755742 0.654869i \(-0.772724\pi\)
0.327058 0.945004i \(-0.393943\pi\)
\(18\) 0 0
\(19\) 0.0439918 + 0.0761960i 0.0100924 + 0.0174806i 0.871028 0.491234i \(-0.163454\pi\)
−0.860935 + 0.508715i \(0.830121\pi\)
\(20\) 0 0
\(21\) 6.62741 + 3.63077i 1.44622 + 0.792299i
\(22\) 0 0
\(23\) −0.242586 0.0650008i −0.0505827 0.0135536i 0.233439 0.972371i \(-0.425002\pi\)
−0.284022 + 0.958818i \(0.591669\pi\)
\(24\) 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 \(0.00842061\pi\)
−0.999650 + 0.0264510i \(0.991579\pi\)
\(30\) 0 0
\(31\) −3.69058 2.13075i −0.662847 0.382695i 0.130514 0.991446i \(-0.458337\pi\)
−0.793361 + 0.608752i \(0.791671\pi\)
\(32\) 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 −0.823371 0.567503i \(-0.807909\pi\)
0.996812 0.0797867i \(-0.0254239\pi\)
\(38\) 0 0
\(39\) −6.74148 3.89220i −1.07950 0.623250i
\(40\) 0 0
\(41\) 9.16296i 1.43101i −0.698606 0.715507i \(-0.746196\pi\)
0.698606 0.715507i \(-0.253804\pi\)
\(42\) 0 0
\(43\) −6.72406 + 6.72406i −1.02541 + 1.02541i −0.0257410 + 0.999669i \(0.508195\pi\)
−0.999669 + 0.0257410i \(0.991805\pi\)
\(44\) 0 0
\(45\) 0.422691 + 11.5256i 0.0630110 + 1.71813i
\(46\) 0 0
\(47\) 6.75301 + 1.80946i 0.985028 + 0.263937i 0.715160 0.698960i \(-0.246354\pi\)
0.269867 + 0.962898i \(0.413020\pi\)
\(48\) 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 −0.925814 0.377980i \(-0.876619\pi\)
0.612788 0.790247i \(-0.290048\pi\)
\(54\) 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 −0.949741 0.313036i \(-0.898654\pi\)
0.745967 + 0.665982i \(0.231987\pi\)
\(60\) 0 0
\(61\) −4.84125 + 2.79509i −0.619858 + 0.357875i −0.776814 0.629730i \(-0.783165\pi\)
0.156956 + 0.987606i \(0.449832\pi\)
\(62\) 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 −0.390534 0.920588i \(-0.627710\pi\)
0.122082 + 0.992520i \(0.461043\pi\)
\(68\) 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 0.291078 0.956699i \(-0.405986\pi\)
0.730430 + 0.682987i \(0.239319\pi\)
\(74\) 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 0.242816 0.970072i \(-0.421929\pi\)
0.961515 + 0.274751i \(0.0885956\pi\)
\(80\) 0 0
\(81\) 1.06496 1.84456i 0.118329 0.204951i
\(82\) 0 0
\(83\) −10.1777 10.1777i −1.11715 1.11715i −0.992158 0.124989i \(-0.960111\pi\)
−0.124989 0.992158i \(-0.539889\pi\)
\(84\) 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 −0.950440 0.310908i \(-0.899367\pi\)
0.205965 0.978559i \(-0.433967\pi\)
\(90\) 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 −0.935317 0.353812i \(-0.884885\pi\)
0.353812 + 0.935317i \(0.384885\pi\)
\(98\) 0 0
\(99\) 24.4847i 2.46081i
\(100\) 0 0
\(101\) 1.74942 + 1.01003i 0.174074 + 0.100501i 0.584505 0.811390i \(-0.301289\pi\)
−0.410432 + 0.911891i \(0.634622\pi\)
\(102\) 0 0
\(103\) 1.55642 5.80862i 0.153358 0.572341i −0.845882 0.533370i \(-0.820925\pi\)
0.999240 0.0389708i \(-0.0124079\pi\)
\(104\) 0 0
\(105\) −14.1093 + 9.29794i −1.37693 + 0.907386i
\(106\) 0 0
\(107\) 4.59156 17.1359i 0.443883 1.65659i −0.274987 0.961448i \(-0.588674\pi\)
0.718870 0.695145i \(-0.244660\pi\)
\(108\) 0 0
\(109\) −1.79135 1.03423i −0.171580 0.0990617i 0.411751 0.911297i \(-0.364917\pi\)
−0.583331 + 0.812235i \(0.698251\pi\)
\(110\) 0 0
\(111\) 11.6424i 1.10505i
\(112\) 0 0
\(113\) −3.54754 + 3.54754i −0.333724 + 0.333724i −0.853999 0.520275i \(-0.825830\pi\)
0.520275 + 0.853999i \(0.325830\pi\)
\(114\) 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 0.998386 + 0.0568000i \(0.0180897\pi\)
0.0568000 + 0.998386i \(0.481910\pi\)
\(128\) 0 0
\(129\) 13.5802 23.5215i 1.19567 2.07095i
\(130\) 0 0
\(131\) −2.96850 + 1.71386i −0.259359 + 0.149741i −0.624042 0.781391i \(-0.714511\pi\)
0.364683 + 0.931132i \(0.381177\pi\)
\(132\) 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 −0.210360 0.977624i \(-0.567464\pi\)
0.306635 + 0.951827i \(0.400797\pi\)
\(138\) 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 −0.911524 0.411247i \(-0.865093\pi\)
−0.0996119 + 0.995026i \(0.531760\pi\)
\(150\) 0 0
\(151\) −5.62795 + 9.74790i −0.457996 + 0.793273i −0.998855 0.0478406i \(-0.984766\pi\)
0.540859 + 0.841114i \(0.318099\pi\)
\(152\) 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 0.987491 + 0.157673i \(0.0503993\pi\)
−0.776356 + 0.630295i \(0.782934\pi\)
\(158\) 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 0.534822 0.844965i \(-0.320379\pi\)
0.0406871 + 0.999172i \(0.487045\pi\)
\(164\) 0 0
\(165\) −22.2093 20.6379i −1.72899 1.60666i
\(166\) 0 0
\(167\) 10.7090 10.7090i 0.828687 0.828687i −0.158648 0.987335i \(-0.550714\pi\)
0.987335 + 0.158648i \(0.0507135\pi\)
\(168\) 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 0.834753 + 0.550625i \(0.185610\pi\)
−0.998230 + 0.0594785i \(0.981056\pi\)
\(174\) 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 0.477063 0.878869i \(-0.341701\pi\)
−0.522591 + 0.852583i \(0.675035\pi\)
\(180\) 0 0
\(181\) 14.2928i 1.06238i −0.847253 0.531189i \(-0.821745\pi\)
0.847253 0.531189i \(-0.178255\pi\)
\(182\) 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 0.990405 + 0.138199i \(0.0441313\pi\)
−0.375519 + 0.926815i \(0.622535\pi\)
\(192\) 0 0
\(193\) 3.89171 + 14.5240i 0.280131 + 1.04546i 0.952324 + 0.305088i \(0.0986858\pi\)
−0.672193 + 0.740376i \(0.734648\pi\)
\(194\) 0 0
\(195\) 14.7453 9.24984i 1.05593 0.662395i
\(196\) 0 0
\(197\) −2.18377 2.18377i −0.155587 0.155587i 0.625021 0.780608i \(-0.285091\pi\)
−0.780608 + 0.625021i \(0.785091\pi\)
\(198\) 0 0
\(199\) −1.06910 + 1.85173i −0.0757863 + 0.131266i −0.901428 0.432929i \(-0.857480\pi\)
0.825642 + 0.564195i \(0.190813\pi\)
\(200\) 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 0.403364 0.915040i \(-0.367841\pi\)
−0.915040 + 0.403364i \(0.867841\pi\)
\(224\) 0 0
\(225\) −23.2187 11.2240i −1.54791 0.748268i
\(226\) 0 0
\(227\) −0.106829 0.398693i −0.00709052 0.0264622i 0.962290 0.272026i \(-0.0876936\pi\)
−0.969380 + 0.245564i \(0.921027\pi\)
\(228\) 0 0
\(229\) 6.96704 + 12.0673i 0.460395 + 0.797427i 0.998981 0.0451435i \(-0.0143745\pi\)
−0.538586 + 0.842571i \(0.681041\pi\)
\(230\) 0 0
\(231\) 30.6568 18.6281i 2.01707 1.22564i
\(232\) 0 0
\(233\) 2.40099 + 0.643344i 0.157294 + 0.0421469i 0.336607 0.941645i \(-0.390721\pi\)
−0.179313 + 0.983792i \(0.557387\pi\)
\(234\) 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 \(0.113437\pi\)
−0.937169 + 0.348877i \(0.886563\pi\)
\(240\) 0 0
\(241\) −4.35718 2.51562i −0.280671 0.162045i 0.353056 0.935602i \(-0.385142\pi\)
−0.633727 + 0.773557i \(0.718476\pi\)
\(242\) 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 \(0.0364552\pi\)
−0.993449 + 0.114277i \(0.963545\pi\)
\(252\) 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 0.855840 0.517241i \(-0.173041\pi\)
0.482559 + 0.875864i \(0.339708\pi\)
\(258\) 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 0.977561 0.210655i \(-0.0675596\pi\)
−0.951920 + 0.306348i \(0.900893\pi\)
\(264\) 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 0.231864 + 0.972748i \(0.425518\pi\)
−0.958357 + 0.285574i \(0.907816\pi\)
\(270\) 0 0
\(271\) −16.9698 + 9.79753i −1.03084 + 0.595158i −0.917226 0.398367i \(-0.869577\pi\)
−0.113617 + 0.993525i \(0.536244\pi\)
\(272\) 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 −0.625333 0.780358i \(-0.715037\pi\)
−0.151376 + 0.988476i \(0.548370\pi\)
\(278\) 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 −0.844377 0.535749i \(-0.820029\pi\)
−0.463378 + 0.886161i \(0.653363\pi\)
\(284\) 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 0.955144 + 0.296143i \(0.0957005\pi\)
0.296143 + 0.955144i \(0.404300\pi\)
\(294\) 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 −0.608726 0.793381i \(-0.708319\pi\)
0.793381 + 0.608726i \(0.208319\pi\)
\(308\) 0 0
\(309\) 17.1758i 0.977098i
\(310\) 0 0
\(311\) −9.07682 5.24050i −0.514699 0.297162i 0.220064 0.975485i \(-0.429373\pi\)
−0.734763 + 0.678324i \(0.762707\pi\)
\(312\) 0 0
\(313\) 5.51996 20.6008i 0.312007 1.16443i −0.614737 0.788732i \(-0.710738\pi\)
0.926744 0.375693i \(-0.122595\pi\)
\(314\) 0 0
\(315\) 20.2654 22.8131i 1.14182 1.28537i
\(316\) 0 0
\(317\) 7.88745 29.4364i 0.443003 1.65331i −0.278152 0.960537i \(-0.589722\pi\)
0.721155 0.692774i \(-0.243611\pi\)
\(318\) 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 0.783791 0.621025i \(-0.213283\pi\)
−0.929719 + 0.368271i \(0.879950\pi\)
\(332\) 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 0.860226 0.509913i \(-0.170323\pi\)
−0.509913 + 0.860226i \(0.670323\pi\)
\(338\) 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 0.372298 0.928113i \(-0.378570\pi\)
0.786476 + 0.617621i \(0.211903\pi\)
\(348\) 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 0.423594 0.905852i \(-0.360768\pi\)
0.819770 + 0.572694i \(0.194101\pi\)
\(354\) 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 0.633051 0.774110i \(-0.281802\pi\)
0.986924 0.161184i \(-0.0515311\pi\)
\(360\) 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 −0.994909 0.100778i \(-0.967867\pi\)
0.811227 0.584731i \(-0.198800\pi\)
\(368\) 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 −0.199102 0.979979i \(-0.563803\pi\)
−0.662417 + 0.749135i \(0.730469\pi\)
\(374\) 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 \(0.0301310\pi\)
−0.995523 + 0.0945181i \(0.969869\pi\)
\(380\) 0 0
\(381\) −41.5972 24.0162i −2.13109 1.23039i
\(382\) 0 0
\(383\) 5.85380 21.8467i 0.299115 1.11631i −0.638778 0.769391i \(-0.720560\pi\)
0.937894 0.346923i \(-0.112774\pi\)
\(384\) 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 0.466267 0.884644i \(-0.345599\pi\)
−0.532991 + 0.846121i \(0.678932\pi\)
\(390\) 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 0.298338 0.954460i \(-0.403568\pi\)
−0.218862 + 0.975756i \(0.570234\pi\)
\(398\) 0 0
\(399\) 0.0149013 + 0.664706i 0.000745996 + 0.0332769i
\(400\) 0 0
\(401\) 1.21896 + 2.11129i 0.0608717 + 0.105433i 0.894855 0.446356i \(-0.147279\pi\)
−0.833984 + 0.551789i \(0.813945\pi\)
\(402\) 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 −0.596202 0.802834i \(-0.703324\pi\)
0.993376 + 0.114909i \(0.0366576\pi\)
\(410\) 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 −0.665798 0.746132i \(-0.731909\pi\)
0.979068 + 0.203532i \(0.0652421\pi\)
\(432\) 0 0
\(433\) −23.8441 23.8441i −1.14587 1.14587i −0.987356 0.158518i \(-0.949328\pi\)
−0.158518 0.987356i \(-0.550672\pi\)
\(434\) 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 0.768503 0.639846i \(-0.221002\pi\)
−0.938374 + 0.345621i \(0.887668\pi\)
\(440\) 0 0
\(441\) 19.4356 + 30.4274i 0.925503 + 1.44893i
\(442\) 0 0
\(443\) −14.6235 3.91835i −0.694783 0.186166i −0.105890 0.994378i \(-0.533769\pi\)
−0.588892 + 0.808211i \(0.700436\pi\)
\(444\) 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 \(0.189434\pi\)
−0.828079 + 0.560612i \(0.810566\pi\)
\(450\) 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 0.572563 + 0.819861i \(0.305949\pi\)
−0.905785 + 0.423738i \(0.860718\pi\)
\(458\) 0 0
\(459\) 36.4508 + 21.0449i 1.70138 + 0.982292i
\(460\) 0 0
\(461\) 12.0569i 0.561545i −0.959774 0.280773i \(-0.909409\pi\)
0.959774 0.280773i \(-0.0905907\pi\)
\(462\) 0 0
\(463\) −19.7680 + 19.7680i −0.918695 + 0.918695i −0.996935 0.0782395i \(-0.975070\pi\)
0.0782395 + 0.996935i \(0.475070\pi\)
\(464\) 0 0
\(465\) −18.5269 + 19.9376i −0.859165 + 0.924582i
\(466\) 0 0
\(467\) −21.6402 5.79848i −1.00139 0.268322i −0.279362 0.960186i \(-0.590123\pi\)
−0.722028 + 0.691864i \(0.756790\pi\)
\(468\) 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 −0.769160 0.639056i \(-0.779325\pi\)
0.938019 + 0.346584i \(0.112658\pi\)
\(480\) 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 −0.888404 0.459062i \(-0.848186\pi\)
−0.539849 + 0.841762i \(0.681519\pi\)
\(488\) 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 −0.347125 0.937819i \(-0.612842\pi\)
0.638612 + 0.769529i \(0.279509\pi\)
\(500\) 0 0
\(501\) −21.6283 + 37.4613i −0.966280 + 1.67365i
\(502\) 0 0
\(503\) 13.8563 + 13.8563i 0.617822 + 0.617822i 0.944972 0.327150i \(-0.106088\pi\)
−0.327150 + 0.944972i \(0.606088\pi\)
\(504\) 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 −0.985911 0.167274i \(-0.946504\pi\)
0.348092 0.937460i \(-0.386830\pi\)
\(510\) 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 0.810691 0.585475i \(-0.199092\pi\)
−0.101690 + 0.994816i \(0.532425\pi\)
\(522\) 0 0
\(523\) 7.01477 26.1795i 0.306735 1.14475i −0.624707 0.780859i \(-0.714782\pi\)
0.931442 0.363890i \(-0.118552\pi\)
\(524\) 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 0.873382 0.487036i \(-0.161922\pi\)
−0.858476 + 0.512853i \(0.828588\pi\)
\(542\) 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 0.959406 0.282029i \(-0.0910074\pi\)
−0.282029 + 0.959406i \(0.591007\pi\)
\(548\) 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 −0.401655 0.915791i \(-0.631565\pi\)
0.110052 + 0.993926i \(0.464898\pi\)
\(558\) 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 −0.0640613 0.997946i \(-0.520405\pi\)
0.443494 + 0.896277i \(0.353739\pi\)
\(564\) 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 0.312998 0.949754i \(-0.398667\pi\)
0.979010 + 0.203812i \(0.0653333\pi\)
\(570\) 0 0
\(571\) 10.9925 19.0395i 0.460020 0.796778i −0.538942 0.842343i \(-0.681176\pi\)
0.998961 + 0.0455656i \(0.0145090\pi\)
\(572\) 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 0.995447 0.0953198i \(-0.0303874\pi\)
−0.909742 + 0.415174i \(0.863721\pi\)
\(578\) 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 −0.470674 0.882307i \(-0.655989\pi\)
0.882307 + 0.470674i \(0.155989\pi\)
\(588\) 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 0.392597 + 0.919711i \(0.371577\pi\)
−0.799854 + 0.600194i \(0.795090\pi\)
\(594\) 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 0.630028 0.776572i \(-0.283043\pi\)
−0.357517 + 0.933907i \(0.616377\pi\)
\(600\) 0 0
\(601\) 6.91584i 0.282103i 0.990002 + 0.141051i \(0.0450483\pi\)
−0.990002 + 0.141051i \(0.954952\pi\)
\(602\) 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 0.970560 0.240858i \(-0.0774290\pi\)
0.720101 + 0.693870i \(0.244096\pi\)
\(608\) 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 0.849021 + 0.528359i \(0.177192\pi\)
−0.471095 + 0.882083i \(0.656141\pi\)
\(614\) 0 0
\(615\) −57.0437 13.0644i −2.30022 0.526807i
\(616\) 0 0
\(617\) −21.4356 21.4356i −0.862966 0.862966i 0.128715 0.991682i \(-0.458915\pi\)
−0.991682 + 0.128715i \(0.958915\pi\)
\(618\) 0 0
\(619\) 13.5728 23.5088i 0.545538 0.944900i −0.453035 0.891493i \(-0.649659\pi\)
0.998573 0.0534071i \(-0.0170081\pi\)
\(620\) 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 −0.549171 0.835710i \(-0.685057\pi\)
0.998332 + 0.0577415i \(0.0183899\pi\)
\(642\) 0 0
\(643\) 14.6427 + 14.6427i 0.577453 + 0.577453i 0.934201 0.356748i \(-0.116114\pi\)
−0.356748 + 0.934201i \(0.616114\pi\)
\(644\) 0 0
\(645\) 32.2734 + 51.4475i 1.27076 + 2.02574i
\(646\) 0 0
\(647\) 5.67864 + 21.1930i 0.223250 + 0.833181i 0.983098 + 0.183080i \(0.0586068\pi\)
−0.759848 + 0.650101i \(0.774727\pi\)
\(648\) 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 −0.614007 0.789301i \(-0.710443\pi\)
−0.926396 + 0.376551i \(0.877110\pi\)
\(654\) 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 \(0.0888029\pi\)
−0.961336 + 0.275378i \(0.911197\pi\)
\(660\) 0 0
\(661\) −14.9892 8.65401i −0.583011 0.336602i 0.179318 0.983791i \(-0.442611\pi\)
−0.762329 + 0.647189i \(0.775944\pi\)
\(662\) 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 −0.378584 0.925567i \(-0.623589\pi\)
0.925567 + 0.378584i \(0.123589\pi\)
\(674\) 0 0
\(675\) 30.2705 + 5.77405i 1.16511 + 0.222243i
\(676\) 0 0
\(677\) 11.9446 + 3.20054i 0.459068 + 0.123007i 0.480939 0.876754i \(-0.340296\pi\)
−0.0218715 + 0.999761i \(0.506962\pi\)
\(678\) 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 0.871310 0.490733i \(-0.163271\pi\)
−0.999943 + 0.0106680i \(0.996604\pi\)
\(684\) 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 0.391463 0.920194i \(-0.371969\pi\)
0.992643 + 0.121080i \(0.0386359\pi\)
\(692\) 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 −0.289752 0.957102i \(-0.593573\pi\)
0.683998 + 0.729484i \(0.260240\pi\)
\(710\) 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 0.995681 0.0928372i \(-0.0295936\pi\)
−0.578240 + 0.815867i \(0.696260\pi\)
\(720\) 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 −0.00273448 + 0.999996i \(0.500870\pi\)
−0.999996 + 0.00273448i \(0.999130\pi\)
\(728\) 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 −0.998653 0.0518799i \(-0.983479\pi\)
0.890799 + 0.454397i \(0.150145\pi\)
\(734\) 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 0.881698 0.471814i \(-0.156401\pi\)
0.0322460 + 0.999480i \(0.489734\pi\)
\(740\) 0 0
\(741\) 0.684899i 0.0251604i
\(742\) 0 0
\(743\) −11.3200 + 11.3200i −0.415290 + 0.415290i −0.883577 0.468287i \(-0.844871\pi\)
0.468287 + 0.883577i \(0.344871\pi\)
\(744\) 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 0.841127 0.540837i \(-0.181893\pi\)
−0.888942 + 0.458019i \(0.848559\pi\)
\(752\) 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 0.456017 0.889971i \(-0.349275\pi\)
−0.889971 + 0.456017i \(0.849275\pi\)
\(758\) 0 0
\(759\) 1.70258 2.94895i 0.0617996 0.107040i
\(760\) 0 0
\(761\) 17.1993 9.93004i 0.623475 0.359964i −0.154745 0.987954i \(-0.549456\pi\)
0.778221 + 0.627991i \(0.216122\pi\)
\(762\) 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 −0.680179 0.733046i \(-0.738098\pi\)
−0.222529 + 0.974926i \(0.571431\pi\)
\(774\) 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 0.940730 0.339158i \(-0.110142\pi\)
−0.984275 + 0.176646i \(0.943475\pi\)
\(788\) 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 0.219860