Properties

Label 804.2.s.b.5.19
Level 804
Weight 2
Character 804.5
Analytic conductor 6.420
Analytic rank 0
Dimension 200
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.s (of order \(22\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(200\)
Relative dimension: \(20\) over \(\Q(\zeta_{22})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 5.19
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.19

$q$-expansion

\(f(q)\) \(=\) \(q+(1.61142 + 0.635084i) q^{3} +(-2.05430 + 0.603197i) q^{5} +(-2.91035 - 2.52183i) q^{7} +(2.19334 + 2.04677i) q^{9} +O(q^{10})\) \(q+(1.61142 + 0.635084i) q^{3} +(-2.05430 + 0.603197i) q^{5} +(-2.91035 - 2.52183i) q^{7} +(2.19334 + 2.04677i) q^{9} +(-5.36557 + 1.57547i) q^{11} +(3.44974 + 5.36790i) q^{13} +(-3.69342 - 0.332650i) q^{15} +(0.764837 + 0.109967i) q^{17} +(-5.19155 - 5.99137i) q^{19} +(-3.08821 - 5.91204i) q^{21} +(-4.69664 + 2.14488i) q^{23} +(-0.349969 + 0.224911i) q^{25} +(2.23451 + 4.69116i) q^{27} +8.43272i q^{29} +(-1.76539 + 2.74699i) q^{31} +(-9.64674 - 0.868839i) q^{33} +(7.49988 + 3.42508i) q^{35} -5.40444 q^{37} +(2.14991 + 10.8408i) q^{39} +(1.28169 - 8.91433i) q^{41} +(0.443176 + 0.0637191i) q^{43} +(-5.74038 - 2.88167i) q^{45} +(-3.17052 + 1.44793i) q^{47} +(1.11429 + 7.75005i) q^{49} +(1.16263 + 0.662939i) q^{51} +(0.119970 + 0.834409i) q^{53} +(10.0722 - 6.47299i) q^{55} +(-4.56074 - 12.9517i) q^{57} +(6.01354 - 9.35726i) q^{59} +(2.74338 - 9.34309i) q^{61} +(-1.22177 - 11.4880i) q^{63} +(-10.3247 - 8.94641i) q^{65} +(7.35766 + 3.58676i) q^{67} +(-8.93042 + 0.473545i) q^{69} +(-7.24102 + 1.04110i) q^{71} +(6.32300 + 1.85660i) q^{73} +(-0.706783 + 0.140167i) q^{75} +(19.5887 + 8.94588i) q^{77} +(1.27332 + 1.98132i) q^{79} +(0.621459 + 8.97852i) q^{81} +(2.86458 + 9.75587i) q^{83} +(-1.63754 + 0.235442i) q^{85} +(-5.35549 + 13.5886i) q^{87} +(3.49281 + 1.59511i) q^{89} +(3.49699 - 24.3221i) q^{91} +(-4.58935 + 3.30539i) q^{93} +(14.2790 + 9.17653i) q^{95} +1.22491i q^{97} +(-14.9931 - 7.52655i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{22}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.61142 + 0.635084i 0.930353 + 0.366666i
\(4\) 0 0
\(5\) −2.05430 + 0.603197i −0.918711 + 0.269758i −0.706703 0.707510i \(-0.749818\pi\)
−0.212007 + 0.977268i \(0.568000\pi\)
\(6\) 0 0
\(7\) −2.91035 2.52183i −1.10001 0.953162i −0.100879 0.994899i \(-0.532166\pi\)
−0.999129 + 0.0417366i \(0.986711\pi\)
\(8\) 0 0
\(9\) 2.19334 + 2.04677i 0.731113 + 0.682257i
\(10\) 0 0
\(11\) −5.36557 + 1.57547i −1.61778 + 0.475023i −0.960421 0.278554i \(-0.910145\pi\)
−0.657360 + 0.753577i \(0.728327\pi\)
\(12\) 0 0
\(13\) 3.44974 + 5.36790i 0.956786 + 1.48879i 0.870292 + 0.492536i \(0.163930\pi\)
0.0864941 + 0.996252i \(0.472434\pi\)
\(14\) 0 0
\(15\) −3.69342 0.332650i −0.953636 0.0858898i
\(16\) 0 0
\(17\) 0.764837 + 0.109967i 0.185500 + 0.0266709i 0.234439 0.972131i \(-0.424675\pi\)
−0.0489385 + 0.998802i \(0.515584\pi\)
\(18\) 0 0
\(19\) −5.19155 5.99137i −1.19102 1.37451i −0.909893 0.414844i \(-0.863836\pi\)
−0.281130 0.959670i \(-0.590709\pi\)
\(20\) 0 0
\(21\) −3.08821 5.91204i −0.673903 1.29011i
\(22\) 0 0
\(23\) −4.69664 + 2.14488i −0.979316 + 0.447239i −0.839750 0.542974i \(-0.817298\pi\)
−0.139567 + 0.990213i \(0.544571\pi\)
\(24\) 0 0
\(25\) −0.349969 + 0.224911i −0.0699937 + 0.0449822i
\(26\) 0 0
\(27\) 2.23451 + 4.69116i 0.430032 + 0.902813i
\(28\) 0 0
\(29\) 8.43272i 1.56592i 0.622074 + 0.782959i \(0.286290\pi\)
−0.622074 + 0.782959i \(0.713710\pi\)
\(30\) 0 0
\(31\) −1.76539 + 2.74699i −0.317073 + 0.493375i −0.962808 0.270187i \(-0.912915\pi\)
0.645735 + 0.763561i \(0.276551\pi\)
\(32\) 0 0
\(33\) −9.64674 0.868839i −1.67928 0.151245i
\(34\) 0 0
\(35\) 7.49988 + 3.42508i 1.26771 + 0.578944i
\(36\) 0 0
\(37\) −5.40444 −0.888484 −0.444242 0.895907i \(-0.646527\pi\)
−0.444242 + 0.895907i \(0.646527\pi\)
\(38\) 0 0
\(39\) 2.14991 + 10.8408i 0.344261 + 1.73592i
\(40\) 0 0
\(41\) 1.28169 8.91433i 0.200166 1.39218i −0.603623 0.797270i \(-0.706277\pi\)
0.803789 0.594915i \(-0.202814\pi\)
\(42\) 0 0
\(43\) 0.443176 + 0.0637191i 0.0675837 + 0.00971707i 0.176024 0.984386i \(-0.443676\pi\)
−0.108440 + 0.994103i \(0.534586\pi\)
\(44\) 0 0
\(45\) −5.74038 2.88167i −0.855725 0.429573i
\(46\) 0 0
\(47\) −3.17052 + 1.44793i −0.462467 + 0.211202i −0.633002 0.774150i \(-0.718178\pi\)
0.170535 + 0.985352i \(0.445450\pi\)
\(48\) 0 0
\(49\) 1.11429 + 7.75005i 0.159184 + 1.10715i
\(50\) 0 0
\(51\) 1.16263 + 0.662939i 0.162801 + 0.0928300i
\(52\) 0 0
\(53\) 0.119970 + 0.834409i 0.0164791 + 0.114615i 0.996401 0.0847686i \(-0.0270151\pi\)
−0.979922 + 0.199384i \(0.936106\pi\)
\(54\) 0 0
\(55\) 10.0722 6.47299i 1.35813 0.872818i
\(56\) 0 0
\(57\) −4.56074 12.9517i −0.604084 1.71549i
\(58\) 0 0
\(59\) 6.01354 9.35726i 0.782897 1.21821i −0.188808 0.982014i \(-0.560462\pi\)
0.971705 0.236197i \(-0.0759012\pi\)
\(60\) 0 0
\(61\) 2.74338 9.34309i 0.351254 1.19626i −0.574618 0.818422i \(-0.694849\pi\)
0.925872 0.377838i \(-0.123332\pi\)
\(62\) 0 0
\(63\) −1.22177 11.4880i −0.153928 1.44736i
\(64\) 0 0
\(65\) −10.3247 8.94641i −1.28062 1.10967i
\(66\) 0 0
\(67\) 7.35766 + 3.58676i 0.898881 + 0.438192i
\(68\) 0 0
\(69\) −8.93042 + 0.473545i −1.07510 + 0.0570081i
\(70\) 0 0
\(71\) −7.24102 + 1.04110i −0.859351 + 0.123556i −0.557882 0.829920i \(-0.688386\pi\)
−0.301469 + 0.953476i \(0.597477\pi\)
\(72\) 0 0
\(73\) 6.32300 + 1.85660i 0.740051 + 0.217298i 0.629965 0.776624i \(-0.283069\pi\)
0.110086 + 0.993922i \(0.464887\pi\)
\(74\) 0 0
\(75\) −0.706783 + 0.140167i −0.0816123 + 0.0161850i
\(76\) 0 0
\(77\) 19.5887 + 8.94588i 2.23234 + 1.01948i
\(78\) 0 0
\(79\) 1.27332 + 1.98132i 0.143259 + 0.222916i 0.905467 0.424417i \(-0.139521\pi\)
−0.762208 + 0.647332i \(0.775885\pi\)
\(80\) 0 0
\(81\) 0.621459 + 8.97852i 0.0690510 + 0.997613i
\(82\) 0 0
\(83\) 2.86458 + 9.75587i 0.314429 + 1.07085i 0.953424 + 0.301635i \(0.0975323\pi\)
−0.638995 + 0.769211i \(0.720650\pi\)
\(84\) 0 0
\(85\) −1.63754 + 0.235442i −0.177616 + 0.0255373i
\(86\) 0 0
\(87\) −5.35549 + 13.5886i −0.574168 + 1.45686i
\(88\) 0 0
\(89\) 3.49281 + 1.59511i 0.370238 + 0.169082i 0.591840 0.806055i \(-0.298402\pi\)
−0.221603 + 0.975137i \(0.571129\pi\)
\(90\) 0 0
\(91\) 3.49699 24.3221i 0.366584 2.54965i
\(92\) 0 0
\(93\) −4.58935 + 3.30539i −0.475893 + 0.342753i
\(94\) 0 0
\(95\) 14.2790 + 9.17653i 1.46499 + 0.941493i
\(96\) 0 0
\(97\) 1.22491i 0.124371i 0.998065 + 0.0621853i \(0.0198070\pi\)
−0.998065 + 0.0621853i \(0.980193\pi\)
\(98\) 0 0
\(99\) −14.9931 7.52655i −1.50687 0.756446i
\(100\) 0 0
\(101\) 1.40427 + 1.62061i 0.139730 + 0.161257i 0.821301 0.570495i \(-0.193248\pi\)
−0.681571 + 0.731752i \(0.738703\pi\)
\(102\) 0 0
\(103\) −2.30070 1.47857i −0.226695 0.145688i 0.422364 0.906426i \(-0.361201\pi\)
−0.649058 + 0.760739i \(0.724837\pi\)
\(104\) 0 0
\(105\) 9.91023 + 10.2823i 0.967140 + 1.00345i
\(106\) 0 0
\(107\) −0.573320 + 1.95255i −0.0554249 + 0.188760i −0.982552 0.185986i \(-0.940452\pi\)
0.927127 + 0.374746i \(0.122270\pi\)
\(108\) 0 0
\(109\) 8.11037 + 12.6200i 0.776832 + 1.20877i 0.973586 + 0.228322i \(0.0733237\pi\)
−0.196754 + 0.980453i \(0.563040\pi\)
\(110\) 0 0
\(111\) −8.70881 3.43227i −0.826604 0.325777i
\(112\) 0 0
\(113\) −18.3068 5.37535i −1.72216 0.505671i −0.736790 0.676121i \(-0.763659\pi\)
−0.985366 + 0.170451i \(0.945478\pi\)
\(114\) 0 0
\(115\) 8.35451 7.23922i 0.779062 0.675061i
\(116\) 0 0
\(117\) −3.42042 + 18.8345i −0.316218 + 1.74125i
\(118\) 0 0
\(119\) −1.94862 2.24883i −0.178630 0.206150i
\(120\) 0 0
\(121\) 17.0534 10.9596i 1.55031 0.996325i
\(122\) 0 0
\(123\) 7.72668 13.5507i 0.696691 1.22183i
\(124\) 0 0
\(125\) 7.59364 8.76353i 0.679196 0.783834i
\(126\) 0 0
\(127\) 2.98832 3.44871i 0.265171 0.306024i −0.607512 0.794310i \(-0.707832\pi\)
0.872683 + 0.488287i \(0.162378\pi\)
\(128\) 0 0
\(129\) 0.673675 + 0.384132i 0.0593138 + 0.0338209i
\(130\) 0 0
\(131\) −2.81078 + 1.28364i −0.245579 + 0.112152i −0.534402 0.845230i \(-0.679463\pi\)
0.288824 + 0.957382i \(0.406736\pi\)
\(132\) 0 0
\(133\) 30.5292i 2.64721i
\(134\) 0 0
\(135\) −7.42005 8.28919i −0.638616 0.713420i
\(136\) 0 0
\(137\) −3.57227 7.82217i −0.305199 0.668293i 0.693436 0.720518i \(-0.256096\pi\)
−0.998635 + 0.0522248i \(0.983369\pi\)
\(138\) 0 0
\(139\) 4.95108 + 16.8618i 0.419945 + 1.43020i 0.849705 + 0.527259i \(0.176780\pi\)
−0.429759 + 0.902943i \(0.641402\pi\)
\(140\) 0 0
\(141\) −6.02858 + 0.319672i −0.507698 + 0.0269212i
\(142\) 0 0
\(143\) −26.9668 23.3669i −2.25508 1.95404i
\(144\) 0 0
\(145\) −5.08659 17.3233i −0.422418 1.43863i
\(146\) 0 0
\(147\) −3.12634 + 13.1962i −0.257856 + 1.08841i
\(148\) 0 0
\(149\) −10.0243 + 8.68614i −0.821226 + 0.711596i −0.960386 0.278674i \(-0.910105\pi\)
0.139160 + 0.990270i \(0.455560\pi\)
\(150\) 0 0
\(151\) −1.31762 + 9.16424i −0.107226 + 0.745775i 0.863285 + 0.504717i \(0.168403\pi\)
−0.970511 + 0.241057i \(0.922506\pi\)
\(152\) 0 0
\(153\) 1.45247 + 1.80664i 0.117425 + 0.146058i
\(154\) 0 0
\(155\) 1.96965 6.70802i 0.158206 0.538802i
\(156\) 0 0
\(157\) 2.04478 + 4.47745i 0.163192 + 0.357340i 0.973508 0.228653i \(-0.0734321\pi\)
−0.810316 + 0.585992i \(0.800705\pi\)
\(158\) 0 0
\(159\) −0.336598 + 1.42077i −0.0266940 + 0.112675i
\(160\) 0 0
\(161\) 19.0779 + 5.60177i 1.50355 + 0.441481i
\(162\) 0 0
\(163\) 7.70377 0.603406 0.301703 0.953402i \(-0.402445\pi\)
0.301703 + 0.953402i \(0.402445\pi\)
\(164\) 0 0
\(165\) 20.3414 4.03402i 1.58357 0.314048i
\(166\) 0 0
\(167\) −13.1265 + 11.3742i −1.01576 + 0.880161i −0.992825 0.119576i \(-0.961847\pi\)
−0.0229352 + 0.999737i \(0.507301\pi\)
\(168\) 0 0
\(169\) −11.5133 + 25.2105i −0.885636 + 1.93927i
\(170\) 0 0
\(171\) 0.876135 23.7670i 0.0669997 1.81751i
\(172\) 0 0
\(173\) 2.04209 3.17755i 0.155257 0.241585i −0.754908 0.655831i \(-0.772318\pi\)
0.910165 + 0.414246i \(0.135955\pi\)
\(174\) 0 0
\(175\) 1.58572 + 0.227992i 0.119869 + 0.0172346i
\(176\) 0 0
\(177\) 15.6330 11.2594i 1.17505 0.846305i
\(178\) 0 0
\(179\) 2.71308 5.94082i 0.202785 0.444037i −0.780729 0.624870i \(-0.785152\pi\)
0.983514 + 0.180833i \(0.0578792\pi\)
\(180\) 0 0
\(181\) −3.14530 6.88725i −0.233788 0.511925i 0.755982 0.654592i \(-0.227160\pi\)
−0.989771 + 0.142667i \(0.954432\pi\)
\(182\) 0 0
\(183\) 10.3544 13.3134i 0.765417 0.984151i
\(184\) 0 0
\(185\) 11.1023 3.25994i 0.816260 0.239675i
\(186\) 0 0
\(187\) −4.27704 + 0.614945i −0.312768 + 0.0449693i
\(188\) 0 0
\(189\) 5.32709 19.2880i 0.387489 1.40299i
\(190\) 0 0
\(191\) 1.20933 2.64807i 0.0875041 0.191607i −0.860821 0.508908i \(-0.830049\pi\)
0.948325 + 0.317301i \(0.102777\pi\)
\(192\) 0 0
\(193\) 4.28043 + 2.75087i 0.308112 + 0.198012i 0.685554 0.728021i \(-0.259560\pi\)
−0.377442 + 0.926033i \(0.623196\pi\)
\(194\) 0 0
\(195\) −10.9557 20.9735i −0.784554 1.50194i
\(196\) 0 0
\(197\) −0.0858349 0.596995i −0.00611548 0.0425341i 0.986535 0.163549i \(-0.0522942\pi\)
−0.992651 + 0.121015i \(0.961385\pi\)
\(198\) 0 0
\(199\) −6.87755 + 7.93711i −0.487536 + 0.562647i −0.945206 0.326475i \(-0.894139\pi\)
0.457669 + 0.889123i \(0.348684\pi\)
\(200\) 0 0
\(201\) 9.57838 + 10.4525i 0.675607 + 0.737262i
\(202\) 0 0
\(203\) 21.2659 24.5422i 1.49257 1.72252i
\(204\) 0 0
\(205\) 2.74413 + 19.0858i 0.191658 + 1.33301i
\(206\) 0 0
\(207\) −14.6914 4.90849i −1.02112 0.341163i
\(208\) 0 0
\(209\) 37.2949 + 23.9679i 2.57974 + 1.65790i
\(210\) 0 0
\(211\) 4.15574 9.09981i 0.286093 0.626457i −0.710955 0.703238i \(-0.751737\pi\)
0.997048 + 0.0767810i \(0.0244642\pi\)
\(212\) 0 0
\(213\) −12.3295 2.92100i −0.844803 0.200144i
\(214\) 0 0
\(215\) −0.948852 + 0.136424i −0.0647111 + 0.00930406i
\(216\) 0 0
\(217\) 12.0653 3.54270i 0.819049 0.240494i
\(218\) 0 0
\(219\) 9.00990 + 7.00739i 0.608832 + 0.473515i
\(220\) 0 0
\(221\) 2.04820 + 4.48493i 0.137777 + 0.301689i
\(222\) 0 0
\(223\) 4.61874 10.1136i 0.309294 0.677259i −0.689604 0.724186i \(-0.742216\pi\)
0.998898 + 0.0469270i \(0.0149428\pi\)
\(224\) 0 0
\(225\) −1.22794 0.222999i −0.0818627 0.0148666i
\(226\) 0 0
\(227\) −16.6970 2.40067i −1.10822 0.159338i −0.436185 0.899857i \(-0.643671\pi\)
−0.672035 + 0.740519i \(0.734580\pi\)
\(228\) 0 0
\(229\) −9.00592 + 14.0135i −0.595128 + 0.926037i 0.404805 + 0.914403i \(0.367340\pi\)
−0.999932 + 0.0116336i \(0.996297\pi\)
\(230\) 0 0
\(231\) 25.8843 + 26.8560i 1.70306 + 1.76700i
\(232\) 0 0
\(233\) 5.65669 12.3864i 0.370582 0.811461i −0.628842 0.777533i \(-0.716471\pi\)
0.999424 0.0339285i \(-0.0108019\pi\)
\(234\) 0 0
\(235\) 5.63981 4.88692i 0.367900 0.318787i
\(236\) 0 0
\(237\) 0.793541 + 4.00139i 0.0515460 + 0.259918i
\(238\) 0 0
\(239\) 5.75934 0.372540 0.186270 0.982499i \(-0.440360\pi\)
0.186270 + 0.982499i \(0.440360\pi\)
\(240\) 0 0
\(241\) −11.5227 3.38337i −0.742242 0.217942i −0.111316 0.993785i \(-0.535507\pi\)
−0.630926 + 0.775843i \(0.717325\pi\)
\(242\) 0 0
\(243\) −4.70068 + 14.8628i −0.301549 + 0.953451i
\(244\) 0 0
\(245\) −6.96389 15.2488i −0.444906 0.974209i
\(246\) 0 0
\(247\) 14.2516 48.5364i 0.906806 3.08830i
\(248\) 0 0
\(249\) −1.57975 + 17.5400i −0.100113 + 1.11155i
\(250\) 0 0
\(251\) −0.484711 + 3.37124i −0.0305947 + 0.212791i −0.999384 0.0350948i \(-0.988827\pi\)
0.968789 + 0.247886i \(0.0797358\pi\)
\(252\) 0 0
\(253\) 21.8209 18.9079i 1.37187 1.18873i
\(254\) 0 0
\(255\) −2.78828 0.660577i −0.174609 0.0413669i
\(256\) 0 0
\(257\) −7.42734 25.2952i −0.463305 1.57787i −0.777736 0.628591i \(-0.783632\pi\)
0.314431 0.949280i \(-0.398186\pi\)
\(258\) 0 0
\(259\) 15.7288 + 13.6291i 0.977339 + 0.846869i
\(260\) 0 0
\(261\) −17.2599 + 18.4958i −1.06836 + 1.14486i
\(262\) 0 0
\(263\) 6.36513 + 21.6777i 0.392491 + 1.33670i 0.884674 + 0.466210i \(0.154381\pi\)
−0.492183 + 0.870492i \(0.663801\pi\)
\(264\) 0 0
\(265\) −0.749767 1.64176i −0.0460578 0.100853i
\(266\) 0 0
\(267\) 4.61535 + 4.78863i 0.282455 + 0.293059i
\(268\) 0 0
\(269\) 19.6323i 1.19700i 0.801123 + 0.598500i \(0.204236\pi\)
−0.801123 + 0.598500i \(0.795764\pi\)
\(270\) 0 0
\(271\) −18.3397 + 8.37545i −1.11406 + 0.508773i −0.885445 0.464745i \(-0.846146\pi\)
−0.228612 + 0.973518i \(0.573419\pi\)
\(272\) 0 0
\(273\) 21.0817 36.9722i 1.27592 2.23766i
\(274\) 0 0
\(275\) 1.52344 1.75814i 0.0918669 0.106020i
\(276\) 0 0
\(277\) −2.81170 + 3.24488i −0.168939 + 0.194966i −0.833906 0.551907i \(-0.813900\pi\)
0.664967 + 0.746873i \(0.268446\pi\)
\(278\) 0 0
\(279\) −9.49456 + 2.41175i −0.568424 + 0.144387i
\(280\) 0 0
\(281\) 2.96094 1.90288i 0.176635 0.113516i −0.449336 0.893363i \(-0.648339\pi\)
0.625971 + 0.779847i \(0.284703\pi\)
\(282\) 0 0
\(283\) 2.64597 + 3.05361i 0.157286 + 0.181518i 0.828923 0.559362i \(-0.188954\pi\)
−0.671637 + 0.740880i \(0.734408\pi\)
\(284\) 0 0
\(285\) 17.1815 + 23.8556i 1.01775 + 1.41308i
\(286\) 0 0
\(287\) −26.2106 + 22.7116i −1.54716 + 1.34062i
\(288\) 0 0
\(289\) −15.7385 4.62124i −0.925794 0.271838i
\(290\) 0 0
\(291\) −0.777919 + 1.97384i −0.0456024 + 0.115708i
\(292\) 0 0
\(293\) −8.56693 13.3304i −0.500485 0.778771i 0.495469 0.868625i \(-0.334996\pi\)
−0.995955 + 0.0898548i \(0.971360\pi\)
\(294\) 0 0
\(295\) −6.70935 + 22.8500i −0.390634 + 1.33038i
\(296\) 0 0
\(297\) −19.3802 21.6503i −1.12456 1.25628i
\(298\) 0 0
\(299\) −27.7157 17.8118i −1.60284 1.03008i
\(300\) 0 0
\(301\) −1.12911 1.30306i −0.0650807 0.0751071i
\(302\) 0 0
\(303\) 1.23364 + 3.50332i 0.0708708 + 0.201260i
\(304\) 0 0
\(305\) 20.8483i 1.19377i
\(306\) 0 0
\(307\) 8.05757 + 5.17828i 0.459870 + 0.295540i 0.749989 0.661450i \(-0.230059\pi\)
−0.290119 + 0.956990i \(0.593695\pi\)
\(308\) 0 0
\(309\) −2.76837 3.84373i −0.157487 0.218662i
\(310\) 0 0
\(311\) 2.80597 19.5159i 0.159112 1.10665i −0.741163 0.671325i \(-0.765725\pi\)
0.900275 0.435322i \(-0.143366\pi\)
\(312\) 0 0
\(313\) 26.7398 + 12.2117i 1.51142 + 0.690245i 0.986927 0.161167i \(-0.0515259\pi\)
0.524498 + 0.851412i \(0.324253\pi\)
\(314\) 0 0
\(315\) 9.43942 + 22.8629i 0.531851 + 1.28818i
\(316\) 0 0
\(317\) 5.12090 0.736274i 0.287618 0.0413533i 0.00300432 0.999995i \(-0.499044\pi\)
0.284614 + 0.958642i \(0.408135\pi\)
\(318\) 0 0
\(319\) −13.2855 45.2464i −0.743847 2.53331i
\(320\) 0 0
\(321\) −2.16389 + 2.78226i −0.120776 + 0.155291i
\(322\) 0 0
\(323\) −3.31184 5.15332i −0.184276 0.286738i
\(324\) 0 0
\(325\) −2.41460 1.10271i −0.133938 0.0611675i
\(326\) 0 0
\(327\) 5.05445 + 25.4868i 0.279512 + 1.40942i
\(328\) 0 0
\(329\) 12.8787 + 3.78154i 0.710027 + 0.208483i
\(330\) 0 0
\(331\) −26.9910 + 3.88072i −1.48356 + 0.213303i −0.836007 0.548719i \(-0.815116\pi\)
−0.647551 + 0.762022i \(0.724207\pi\)
\(332\) 0 0
\(333\) −11.8538 11.0616i −0.649582 0.606174i
\(334\) 0 0
\(335\) −17.2784 2.93016i −0.944017 0.160092i
\(336\) 0 0
\(337\) −17.4251 15.0990i −0.949207 0.822493i 0.0350227 0.999387i \(-0.488850\pi\)
−0.984230 + 0.176894i \(0.943395\pi\)
\(338\) 0 0
\(339\) −26.0861 20.2883i −1.41680 1.10191i
\(340\) 0 0
\(341\) 5.14449 17.5205i 0.278590 0.948789i
\(342\) 0 0
\(343\) 1.72751 2.68805i 0.0932766 0.145141i
\(344\) 0 0
\(345\) 18.0601 6.35960i 0.972324 0.342390i
\(346\) 0 0
\(347\) −10.3251 + 6.63554i −0.554280 + 0.356214i −0.787601 0.616185i \(-0.788677\pi\)
0.233321 + 0.972400i \(0.425041\pi\)
\(348\) 0 0
\(349\) −3.49322 24.2959i −0.186988 1.30053i −0.839754 0.542968i \(-0.817301\pi\)
0.652766 0.757560i \(-0.273609\pi\)
\(350\) 0 0
\(351\) −17.4732 + 28.1779i −0.932649 + 1.50403i
\(352\) 0 0
\(353\) 3.07084 + 21.3582i 0.163444 + 1.13678i 0.892079 + 0.451879i \(0.149246\pi\)
−0.728635 + 0.684902i \(0.759845\pi\)
\(354\) 0 0
\(355\) 14.2472 6.50649i 0.756165 0.345329i
\(356\) 0 0
\(357\) −1.71185 4.86135i −0.0906008 0.257290i
\(358\) 0 0
\(359\) 19.9608 + 2.86993i 1.05349 + 0.151469i 0.647235 0.762291i \(-0.275925\pi\)
0.406255 + 0.913760i \(0.366834\pi\)
\(360\) 0 0
\(361\) −6.24031 + 43.4023i −0.328437 + 2.28433i
\(362\) 0 0
\(363\) 34.4405 6.83011i 1.80766 0.358488i
\(364\) 0 0
\(365\) −14.1092 −0.738510
\(366\) 0 0
\(367\) 5.59358 + 2.55450i 0.291983 + 0.133344i 0.556021 0.831168i \(-0.312327\pi\)
−0.264039 + 0.964512i \(0.585055\pi\)
\(368\) 0 0
\(369\) 21.0568 16.9288i 1.09617 0.881279i
\(370\) 0 0
\(371\) 1.75508 2.73096i 0.0911194 0.141785i
\(372\) 0 0
\(373\) 9.15585i 0.474072i −0.971501 0.237036i \(-0.923824\pi\)
0.971501 0.237036i \(-0.0761759\pi\)
\(374\) 0 0
\(375\) 17.8021 9.29912i 0.919297 0.480204i
\(376\) 0 0
\(377\) −45.2660 + 29.0907i −2.33132 + 1.49825i
\(378\) 0 0
\(379\) 8.36305 3.81928i 0.429581 0.196183i −0.188877 0.982001i \(-0.560485\pi\)
0.618458 + 0.785818i \(0.287758\pi\)
\(380\) 0 0
\(381\) 7.00566 3.65948i 0.358911 0.187481i
\(382\) 0 0
\(383\) 13.2261 + 15.2638i 0.675824 + 0.779942i 0.985276 0.170973i \(-0.0546910\pi\)
−0.309452 + 0.950915i \(0.600146\pi\)
\(384\) 0 0
\(385\) −45.6373 6.56165i −2.32589 0.334413i
\(386\) 0 0
\(387\) 0.841617 + 1.04684i 0.0427818 + 0.0532137i
\(388\) 0 0
\(389\) −3.16294 4.92163i −0.160367 0.249536i 0.751766 0.659430i \(-0.229202\pi\)
−0.912133 + 0.409893i \(0.865566\pi\)
\(390\) 0 0
\(391\) −3.82803 + 1.12401i −0.193592 + 0.0568437i
\(392\) 0 0
\(393\) −5.34455 + 0.283400i −0.269597 + 0.0142957i
\(394\) 0 0
\(395\) −3.81089 3.30216i −0.191747 0.166150i
\(396\) 0 0
\(397\) −1.73367 + 0.509053i −0.0870107 + 0.0255486i −0.324948 0.945732i \(-0.605347\pi\)
0.237937 + 0.971280i \(0.423529\pi\)
\(398\) 0 0
\(399\) −19.3886 + 49.1952i −0.970642 + 2.46284i
\(400\) 0 0
\(401\) −23.9896 −1.19798 −0.598992 0.800755i \(-0.704432\pi\)
−0.598992 + 0.800755i \(0.704432\pi\)
\(402\) 0 0
\(403\) −20.8357 −1.03790
\(404\) 0 0
\(405\) −6.69247 18.0697i −0.332552 0.897891i
\(406\) 0 0
\(407\) 28.9979 8.51455i 1.43737 0.422050i
\(408\) 0 0
\(409\) 6.86757 + 5.95079i 0.339580 + 0.294247i 0.807910 0.589306i \(-0.200599\pi\)
−0.468330 + 0.883553i \(0.655144\pi\)
\(410\) 0 0
\(411\) −0.788682 14.8735i −0.0389028 0.733655i
\(412\) 0 0
\(413\) −41.0989 + 12.0677i −2.02235 + 0.593814i
\(414\) 0 0
\(415\) −11.7694 18.3136i −0.577738 0.898977i
\(416\) 0 0
\(417\) −2.73041 + 30.3158i −0.133709 + 1.48457i
\(418\) 0 0
\(419\) 30.2736 + 4.35269i 1.47896 + 0.212643i 0.834082 0.551641i \(-0.185998\pi\)
0.644880 + 0.764284i \(0.276907\pi\)
\(420\) 0 0
\(421\) 11.1131 + 12.8253i 0.541622 + 0.625065i 0.958910 0.283709i \(-0.0915651\pi\)
−0.417289 + 0.908774i \(0.637020\pi\)
\(422\) 0 0
\(423\) −9.91759 3.31353i −0.482210 0.161109i
\(424\) 0 0
\(425\) −0.292402 + 0.133535i −0.0141836 + 0.00647742i
\(426\) 0 0
\(427\) −31.5459 + 20.2733i −1.52661 + 0.981094i
\(428\) 0 0
\(429\) −28.6149 54.7800i −1.38154 2.64480i
\(430\) 0 0
\(431\) 15.4336i 0.743410i 0.928351 + 0.371705i \(0.121227\pi\)
−0.928351 + 0.371705i \(0.878773\pi\)
\(432\) 0 0
\(433\) −12.6950 + 19.7538i −0.610084 + 0.949309i 0.389516 + 0.921020i \(0.372642\pi\)
−0.999600 + 0.0282893i \(0.990994\pi\)
\(434\) 0 0
\(435\) 2.80514 31.1456i 0.134496 1.49332i
\(436\) 0 0
\(437\) 37.2336 + 17.0040i 1.78112 + 0.813412i
\(438\) 0 0
\(439\) −36.2970 −1.73236 −0.866180 0.499733i \(-0.833432\pi\)
−0.866180 + 0.499733i \(0.833432\pi\)
\(440\) 0 0
\(441\) −13.4186 + 19.2792i −0.638979 + 0.918055i
\(442\) 0 0
\(443\) 1.80487 12.5531i 0.0857518 0.596417i −0.900956 0.433911i \(-0.857133\pi\)
0.986708 0.162506i \(-0.0519577\pi\)
\(444\) 0 0
\(445\) −8.13745 1.16999i −0.385752 0.0554628i
\(446\) 0 0
\(447\) −21.6698 + 7.63071i −1.02495 + 0.360920i
\(448\) 0 0
\(449\) 9.35902 4.27412i 0.441680 0.201708i −0.182147 0.983271i \(-0.558305\pi\)
0.623826 + 0.781563i \(0.285577\pi\)
\(450\) 0 0
\(451\) 7.16731 + 49.8497i 0.337495 + 2.34733i
\(452\) 0 0
\(453\) −7.94329 + 13.9306i −0.373208 + 0.654518i
\(454\) 0 0
\(455\) 7.48715 + 52.0743i 0.351003 + 2.44128i
\(456\) 0 0
\(457\) −17.7520 + 11.4085i −0.830403 + 0.533668i −0.885406 0.464818i \(-0.846120\pi\)
0.0550027 + 0.998486i \(0.482483\pi\)
\(458\) 0 0
\(459\) 1.19317 + 3.83369i 0.0556923 + 0.178942i
\(460\) 0 0
\(461\) −19.4412 + 30.2511i −0.905468 + 1.40894i 0.00708430 + 0.999975i \(0.497745\pi\)
−0.912552 + 0.408960i \(0.865891\pi\)
\(462\) 0 0
\(463\) 7.61122 25.9214i 0.353723 1.20467i −0.570011 0.821637i \(-0.693061\pi\)
0.923734 0.383034i \(-0.125121\pi\)
\(464\) 0 0
\(465\) 7.43409 9.55854i 0.344748 0.443267i
\(466\) 0 0
\(467\) 28.5506 + 24.7392i 1.32116 + 1.14479i 0.978707 + 0.205261i \(0.0658044\pi\)
0.342457 + 0.939534i \(0.388741\pi\)
\(468\) 0 0
\(469\) −12.3681 28.9935i −0.571108 1.33879i
\(470\) 0 0
\(471\) 0.451445 + 8.51366i 0.0208015 + 0.392289i
\(472\) 0 0
\(473\) −2.47828 + 0.356323i −0.113951 + 0.0163837i
\(474\) 0 0
\(475\) 3.16440 + 0.929153i 0.145193 + 0.0426325i
\(476\) 0 0
\(477\) −1.44471 + 2.07569i −0.0661487 + 0.0950394i
\(478\) 0 0
\(479\) −29.6370 13.5348i −1.35415 0.618420i −0.399661 0.916663i \(-0.630872\pi\)
−0.954490 + 0.298243i \(0.903600\pi\)
\(480\) 0 0
\(481\) −18.6439 29.0105i −0.850089 1.32276i
\(482\) 0 0
\(483\) 27.1848 + 21.1428i 1.23695 + 0.962032i
\(484\) 0 0
\(485\) −0.738860 2.51633i −0.0335499 0.114261i
\(486\) 0 0
\(487\) 2.23477 0.321312i 0.101267 0.0145600i −0.0914949 0.995806i \(-0.529165\pi\)
0.192762 + 0.981246i \(0.438255\pi\)
\(488\) 0 0
\(489\) 12.4140 + 4.89254i 0.561381 + 0.221248i
\(490\) 0 0
\(491\) 3.36878 + 1.53847i 0.152031 + 0.0694303i 0.489977 0.871735i \(-0.337005\pi\)
−0.337946 + 0.941165i \(0.609732\pi\)
\(492\) 0 0
\(493\) −0.927321 + 6.44966i −0.0417645 + 0.290478i
\(494\) 0 0
\(495\) 35.3404 + 6.41797i 1.58843 + 0.288466i
\(496\) 0 0
\(497\) 23.6994 + 15.2307i 1.06306 + 0.683188i
\(498\) 0 0
\(499\) 8.44924i 0.378240i 0.981954 + 0.189120i \(0.0605635\pi\)
−0.981954 + 0.189120i \(0.939436\pi\)
\(500\) 0 0
\(501\) −28.3759 + 9.99214i −1.26774 + 0.446416i
\(502\) 0 0
\(503\) 3.25435 + 3.75572i 0.145104 + 0.167459i 0.823649 0.567100i \(-0.191935\pi\)
−0.678545 + 0.734559i \(0.737389\pi\)
\(504\) 0 0
\(505\) −3.86234 2.48218i −0.171872 0.110455i
\(506\) 0 0
\(507\) −34.5635 + 33.3128i −1.53502 + 1.47948i
\(508\) 0 0
\(509\) 3.15472 10.7440i 0.139831 0.476219i −0.859563 0.511029i \(-0.829264\pi\)
0.999394 + 0.0348099i \(0.0110826\pi\)
\(510\) 0 0
\(511\) −13.7201 21.3489i −0.606941 0.944418i
\(512\) 0 0
\(513\) 16.5059 37.7422i 0.728751 1.66636i
\(514\) 0 0
\(515\) 5.61819 + 1.64965i 0.247567 + 0.0726923i
\(516\) 0 0
\(517\) 14.7305 12.7640i 0.647845 0.561361i
\(518\) 0 0
\(519\) 5.30867 3.82347i 0.233025 0.167832i
\(520\) 0 0
\(521\) −2.87894 3.32248i −0.126129 0.145560i 0.689173 0.724597i \(-0.257974\pi\)
−0.815301 + 0.579037i \(0.803429\pi\)
\(522\) 0 0
\(523\) −5.19011 + 3.33548i −0.226948 + 0.145850i −0.649174 0.760640i \(-0.724885\pi\)
0.422226 + 0.906491i \(0.361249\pi\)
\(524\) 0 0
\(525\) 2.41046 + 1.37445i 0.105201 + 0.0599861i
\(526\) 0 0
\(527\) −1.65231 + 1.90687i −0.0719759 + 0.0830646i
\(528\) 0 0
\(529\) 2.39607 2.76522i 0.104177 0.120227i
\(530\) 0 0
\(531\) 32.3419 8.21528i 1.40352 0.356513i
\(532\) 0 0
\(533\) 52.2728 23.8722i 2.26418 1.03402i
\(534\) 0 0
\(535\) 4.35694i 0.188367i
\(536\) 0 0
\(537\) 8.14482 7.85011i 0.351475 0.338757i
\(538\) 0 0
\(539\) −18.1888 39.8279i −0.783447 1.71551i
\(540\) 0 0
\(541\) −4.93169 16.7958i −0.212030 0.722108i −0.994985 0.100029i \(-0.968107\pi\)
0.782955 0.622079i \(-0.213712\pi\)
\(542\) 0 0
\(543\) −0.694417 13.0958i −0.0298003 0.561993i
\(544\) 0 0
\(545\) −24.2734 21.0331i −1.03976 0.900957i
\(546\) 0 0
\(547\) −6.70920 22.8494i −0.286865 0.976971i −0.969270 0.245998i \(-0.920884\pi\)
0.682406 0.730974i \(-0.260934\pi\)
\(548\) 0 0
\(549\) 25.1403 14.8775i 1.07296 0.634955i
\(550\) 0 0
\(551\) 50.5235 43.7789i 2.15238 1.86504i
\(552\) 0 0
\(553\) 1.29076 8.97740i 0.0548885 0.381758i
\(554\) 0 0
\(555\) 19.9608 + 1.79778i 0.847290 + 0.0763117i
\(556\) 0 0
\(557\) −10.2018 + 34.7442i −0.432264 + 1.47216i 0.399347 + 0.916800i \(0.369237\pi\)
−0.831612 + 0.555358i \(0.812581\pi\)
\(558\) 0 0
\(559\) 1.18681 + 2.59874i 0.0501965 + 0.109915i
\(560\) 0 0
\(561\) −7.28264 1.72534i −0.307473 0.0728440i
\(562\) 0 0
\(563\) 4.92173 + 1.44515i 0.207426 + 0.0609059i 0.383795 0.923418i \(-0.374617\pi\)
−0.176369 + 0.984324i \(0.556435\pi\)
\(564\) 0 0
\(565\) 40.8500 1.71857
\(566\) 0 0
\(567\) 20.8336 27.6978i 0.874930 1.16320i
\(568\) 0 0
\(569\) −24.4368 + 21.1746i −1.02445 + 0.887687i −0.993726 0.111841i \(-0.964325\pi\)
−0.0307191 + 0.999528i \(0.509780\pi\)
\(570\) 0 0
\(571\) −1.79742 + 3.93581i −0.0752198 + 0.164708i −0.943506 0.331355i \(-0.892494\pi\)
0.868286 + 0.496063i \(0.165222\pi\)
\(572\) 0 0
\(573\) 3.63048 3.49911i 0.151666 0.146178i
\(574\) 0 0
\(575\) 1.16127 1.80697i 0.0484282 0.0753557i
\(576\) 0 0
\(577\) 12.8650 + 1.84971i 0.535577 + 0.0770043i 0.404796 0.914407i \(-0.367342\pi\)
0.130781 + 0.991411i \(0.458252\pi\)
\(578\) 0 0
\(579\) 5.15054 + 7.15123i 0.214049 + 0.297195i
\(580\) 0 0
\(581\) 16.2657 35.6169i 0.674815 1.47764i
\(582\) 0 0
\(583\) −1.95830 4.28807i −0.0811044 0.177594i
\(584\) 0 0
\(585\) −4.33432 40.7548i −0.179202 1.68500i
\(586\) 0 0
\(587\) 10.5178 3.08830i 0.434116 0.127468i −0.0573709 0.998353i \(-0.518272\pi\)
0.491487 + 0.870885i \(0.336454\pi\)
\(588\) 0 0
\(589\) 25.6233 3.68408i 1.05579 0.151800i
\(590\) 0 0
\(591\) 0.240826 1.01652i 0.00990624 0.0418141i
\(592\) 0 0
\(593\) 6.86975 15.0427i 0.282107 0.617728i −0.714536 0.699599i \(-0.753362\pi\)
0.996643 + 0.0818707i \(0.0260895\pi\)
\(594\) 0 0
\(595\) 5.35954 + 3.44437i 0.219720 + 0.141205i
\(596\) 0 0
\(597\) −16.1233 + 8.42219i −0.659884 + 0.344697i
\(598\) 0 0
\(599\) −5.87718 40.8767i −0.240135 1.67018i −0.651456 0.758686i \(-0.725842\pi\)
0.411321 0.911490i \(-0.365067\pi\)
\(600\) 0 0
\(601\) −16.6168 + 19.1768i −0.677812 + 0.782236i −0.985577 0.169226i \(-0.945873\pi\)
0.307766 + 0.951462i \(0.400419\pi\)
\(602\) 0 0
\(603\) 8.79656 + 22.9264i 0.358224 + 0.933636i
\(604\) 0 0
\(605\) −28.4221 + 32.8008i −1.15552 + 1.33354i
\(606\) 0 0
\(607\) 2.41607 + 16.8041i 0.0980651 + 0.682058i 0.978250 + 0.207428i \(0.0665092\pi\)
−0.880185 + 0.474630i \(0.842582\pi\)
\(608\) 0 0
\(609\) 49.8546 26.0420i 2.02021 1.05528i
\(610\) 0 0
\(611\) −18.7098 12.0241i −0.756917 0.486441i
\(612\) 0 0
\(613\) 5.03209 11.0187i 0.203244 0.445043i −0.780372 0.625315i \(-0.784970\pi\)
0.983617 + 0.180272i \(0.0576978\pi\)
\(614\) 0 0
\(615\) −7.69915 + 32.4980i −0.310460 + 1.31044i
\(616\) 0 0
\(617\) −9.54492 + 1.37235i −0.384264 + 0.0552488i −0.331740 0.943371i \(-0.607636\pi\)
−0.0525240 + 0.998620i \(0.516727\pi\)
\(618\) 0 0
\(619\) −38.3872 + 11.2715i −1.54291 + 0.453040i −0.938973 0.343990i \(-0.888221\pi\)
−0.603940 + 0.797030i \(0.706403\pi\)
\(620\) 0 0
\(621\) −20.5567 17.2399i −0.824911 0.691813i
\(622\) 0 0
\(623\) −6.14269 13.4506i −0.246102 0.538888i
\(624\) 0 0
\(625\) −9.44940 + 20.6913i −0.377976 + 0.827652i
\(626\) 0 0
\(627\) 44.8760 + 62.3077i 1.79217 + 2.48833i
\(628\) 0 0
\(629\) −4.13352 0.594310i −0.164814 0.0236967i
\(630\) 0 0
\(631\) −12.1271 + 18.8702i −0.482774 + 0.751210i −0.994134 0.108156i \(-0.965505\pi\)
0.511360 + 0.859366i \(0.329142\pi\)
\(632\) 0 0
\(633\) 12.4758 12.0244i 0.495868 0.477925i
\(634\) 0 0
\(635\) −4.05866 + 8.88723i −0.161063 + 0.352679i
\(636\) 0 0
\(637\) −37.7575 + 32.7171i −1.49601 + 1.29630i
\(638\) 0 0
\(639\) −18.0129 12.5372i −0.712579 0.495965i
\(640\) 0 0
\(641\) −44.6524 −1.76366 −0.881831 0.471565i \(-0.843689\pi\)
−0.881831 + 0.471565i \(0.843689\pi\)
\(642\) 0 0
\(643\) −10.6277 3.12056i −0.419114 0.123063i 0.0653743 0.997861i \(-0.479176\pi\)
−0.484488 + 0.874798i \(0.660994\pi\)
\(644\) 0 0
\(645\) −1.61564 0.382764i −0.0636157 0.0150713i
\(646\) 0 0
\(647\) 6.78193 + 14.8504i 0.266625 + 0.583828i 0.994833 0.101529i \(-0.0323735\pi\)
−0.728207 + 0.685357i \(0.759646\pi\)
\(648\) 0 0
\(649\) −17.5240 + 59.6812i −0.687877 + 2.34269i
\(650\) 0 0
\(651\) 21.6922 + 1.95372i 0.850185 + 0.0765725i
\(652\) 0 0
\(653\) 3.18187 22.1304i 0.124516 0.866029i −0.827823 0.560989i \(-0.810421\pi\)
0.952340 0.305040i \(-0.0986699\pi\)
\(654\) 0 0
\(655\) 4.99989 4.33243i 0.195362 0.169282i
\(656\) 0 0
\(657\) 10.0684 + 17.0139i 0.392807 + 0.663774i
\(658\) 0 0
\(659\) 10.0400 + 34.1930i 0.391101 + 1.33197i 0.886269 + 0.463171i \(0.153288\pi\)
−0.495168 + 0.868797i \(0.664893\pi\)
\(660\) 0 0
\(661\) 3.86237 + 3.34676i 0.150229 + 0.130174i 0.726733 0.686920i \(-0.241038\pi\)
−0.576504 + 0.817094i \(0.695583\pi\)
\(662\) 0 0
\(663\) 0.452199 + 8.52788i 0.0175620 + 0.331195i
\(664\) 0 0
\(665\) −18.4151 62.7160i −0.714106 2.43202i
\(666\) 0 0
\(667\) −18.0872 39.6054i −0.700339 1.53353i
\(668\) 0 0
\(669\) 13.8657 13.3640i 0.536080 0.516683i
\(670\) 0 0
\(671\) 54.4531i 2.10214i
\(672\) 0 0
\(673\) −2.83398 + 1.29423i −0.109242 + 0.0498890i −0.469286 0.883046i \(-0.655489\pi\)
0.360045 + 0.932935i \(0.382761\pi\)
\(674\) 0 0
\(675\) −1.83710 1.13919i −0.0707101 0.0438475i
\(676\) 0 0
\(677\) 15.1871 17.5269i 0.583689 0.673613i −0.384705 0.923040i \(-0.625697\pi\)
0.968394 + 0.249427i \(0.0802421\pi\)
\(678\) 0 0
\(679\) 3.08901 3.56491i 0.118545 0.136809i
\(680\) 0 0
\(681\) −25.3812 14.4725i −0.972611 0.554587i
\(682\) 0 0
\(683\) 22.4208 14.4090i 0.857909 0.551344i −0.0361235 0.999347i \(-0.511501\pi\)
0.894032 + 0.448003i \(0.147865\pi\)
\(684\) 0 0
\(685\) 12.0568 + 13.9143i 0.460667 + 0.531638i
\(686\) 0 0
\(687\) −23.4120 + 16.8621i −0.893225 + 0.643328i
\(688\) 0 0
\(689\) −4.06516 + 3.52248i −0.154870 + 0.134196i
\(690\) 0 0
\(691\) −37.8298 11.1078i −1.43911 0.422562i −0.533187 0.845997i \(-0.679006\pi\)
−0.905926 + 0.423435i \(0.860824\pi\)
\(692\) 0 0
\(693\) 24.6546 + 59.7150i 0.936549 + 2.26839i
\(694\) 0 0
\(695\) −20.3420 31.6528i −0.771616 1.20066i
\(696\) 0 0
\(697\) 1.96056 6.67707i 0.0742617 0.252912i
\(698\) 0 0
\(699\) 16.9817 16.3672i 0.642307 0.619066i
\(700\) 0 0
\(701\) 26.6339 + 17.1166i 1.00595 + 0.646483i 0.936341 0.351091i \(-0.114189\pi\)
0.0696066 + 0.997575i \(0.477826\pi\)
\(702\) 0 0
\(703\) 28.0574 + 32.3800i 1.05820 + 1.22123i
\(704\) 0 0
\(705\) 12.1917 4.29312i 0.459166 0.161688i
\(706\) 0 0
\(707\) 8.25788i 0.310570i
\(708\) 0 0
\(709\) −27.0527 17.3857i −1.01599 0.652935i −0.0770512 0.997027i \(-0.524550\pi\)
−0.938936 + 0.344092i \(0.888187\pi\)
\(710\) 0 0
\(711\) −1.26249 + 6.95188i −0.0473471 + 0.260716i
\(712\) 0 0
\(713\) 2.39940 16.6882i 0.0898582 0.624977i
\(714\) 0 0
\(715\) 69.4927 + 31.7363i 2.59888 + 1.18687i
\(716\) 0 0
\(717\) 9.28070 + 3.65766i 0.346594 + 0.136598i
\(718\) 0 0
\(719\) 10.6376 1.52946i 0.396717 0.0570393i 0.0589305 0.998262i \(-0.481231\pi\)
0.337786 + 0.941223i \(0.390322\pi\)
\(720\) 0 0
\(721\) 2.96713 + 10.1051i 0.110502 + 0.376334i
\(722\) 0 0
\(723\) −16.4192 12.7699i −0.610635 0.474917i
\(724\) 0 0
\(725\) −1.89661 2.95119i −0.0704385 0.109604i
\(726\) 0 0
\(727\) −4.85499 2.21720i −0.180062 0.0822314i 0.323344 0.946281i \(-0.395193\pi\)
−0.503406 + 0.864050i \(0.667920\pi\)
\(728\) 0 0
\(729\) −17.0139 + 20.9649i −0.630144 + 0.776478i
\(730\) 0 0
\(731\) 0.331951 + 0.0974695i 0.0122776 + 0.00360504i
\(732\) 0 0
\(733\) 27.6536 3.97598i 1.02141 0.146856i 0.388795 0.921324i \(-0.372891\pi\)
0.632613 + 0.774468i \(0.281982\pi\)
\(734\) 0 0
\(735\) −1.53748 28.9948i −0.0567108 1.06949i
\(736\) 0 0
\(737\) −45.1289 7.65321i −1.66234 0.281909i
\(738\) 0 0
\(739\) −10.7060 9.27680i −0.393826 0.341252i 0.435328 0.900272i \(-0.356632\pi\)
−0.829155 + 0.559019i \(0.811178\pi\)
\(740\) 0 0
\(741\) 53.7899 69.1615i 1.97602 2.54071i
\(742\) 0 0
\(743\) −11.1004 + 37.8045i −0.407234 + 1.38691i 0.459517 + 0.888169i \(0.348023\pi\)
−0.866751 + 0.498742i \(0.833796\pi\)
\(744\) 0 0
\(745\) 15.3535 23.8906i 0.562510 0.875283i
\(746\) 0 0
\(747\) −13.6850 + 27.2610i −0.500709 + 0.997430i
\(748\) 0 0
\(749\) 6.59255 4.23677i 0.240887 0.154808i
\(750\) 0 0
\(751\) −1.92313 13.3756i −0.0701758 0.488084i −0.994353 0.106120i \(-0.966157\pi\)
0.924177 0.381963i \(-0.124752\pi\)
\(752\) 0 0
\(753\) −2.92209 + 5.12465i −0.106487 + 0.186753i
\(754\) 0 0
\(755\) −2.82105 19.6209i −0.102669 0.714076i
\(756\) 0 0
\(757\) 36.5661 16.6992i 1.32902 0.606942i 0.380828 0.924646i \(-0.375639\pi\)
0.948190 + 0.317704i \(0.102912\pi\)
\(758\) 0 0
\(759\) 47.1708 16.6105i 1.71219 0.602922i
\(760\) 0 0
\(761\) 1.08944 + 0.156638i 0.0394923 + 0.00567813i 0.162033 0.986785i \(-0.448195\pi\)
−0.122540 + 0.992464i \(0.539104\pi\)
\(762\) 0 0
\(763\) 8.22145 57.1815i 0.297637 2.07011i
\(764\) 0 0
\(765\) −4.07357 2.83526i −0.147280 0.102509i
\(766\) 0 0
\(767\) 70.9740 2.56272
\(768\) 0 0
\(769\) 32.1287 + 14.6727i 1.15859 + 0.529111i 0.899577 0.436763i \(-0.143875\pi\)
0.259014 + 0.965874i \(0.416602\pi\)
\(770\) 0 0
\(771\) 4.09602 45.4781i 0.147514 1.63785i
\(772\) 0 0
\(773\) −9.47518 + 14.7437i −0.340798 + 0.530293i −0.968776 0.247939i \(-0.920247\pi\)
0.627977 + 0.778232i \(0.283883\pi\)
\(774\) 0 0
\(775\) 1.35842i 0.0487958i
\(776\) 0 0