Properties

Label 1148.2.ba.a.113.2
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.2
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.19

$q$-expansion

\(f(q)\) \(=\) \(q-2.81622i q^{3} +(1.10836 + 3.41119i) q^{5} +(0.587785 + 0.809017i) q^{7} -4.93108 q^{9} +O(q^{10})\) \(q-2.81622i q^{3} +(1.10836 + 3.41119i) q^{5} +(0.587785 + 0.809017i) q^{7} -4.93108 q^{9} +(-0.213839 - 0.0694806i) q^{11} +(-3.07430 + 4.23140i) q^{13} +(9.60667 - 3.12140i) q^{15} +(-3.00515 - 0.976434i) q^{17} +(2.68046 + 3.68934i) q^{19} +(2.27837 - 1.65533i) q^{21} +(3.82515 + 2.77914i) q^{23} +(-6.36269 + 4.62277i) q^{25} +5.43835i q^{27} +(-0.396882 + 0.128955i) q^{29} +(-1.43283 + 4.40979i) q^{31} +(-0.195673 + 0.602218i) q^{33} +(-2.10823 + 2.90174i) q^{35} +(0.846662 + 2.60576i) q^{37} +(11.9166 + 8.65788i) q^{39} +(4.14062 + 4.88418i) q^{41} +(0.388402 + 0.282190i) q^{43} +(-5.46544 - 16.8209i) q^{45} +(-4.40935 + 6.06894i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-2.74985 + 8.46317i) q^{51} +(-1.20312 + 0.390916i) q^{53} -0.806457i q^{55} +(10.3900 - 7.54877i) q^{57} +(-8.96171 - 6.51107i) q^{59} +(9.89239 - 7.18725i) q^{61} +(-2.89842 - 3.98933i) q^{63} +(-17.8416 - 5.79708i) q^{65} +(-6.70062 + 2.17716i) q^{67} +(7.82666 - 10.7725i) q^{69} +(11.1052 + 3.60829i) q^{71} -3.44830 q^{73} +(13.0187 + 17.9187i) q^{75} +(-0.0694806 - 0.213839i) q^{77} -12.1848i q^{79} +0.522330 q^{81} +15.1285 q^{83} -11.3334i q^{85} +(0.363165 + 1.11771i) q^{87} +(4.68737 + 6.45161i) q^{89} -5.23030 q^{91} +(12.4189 + 4.03515i) q^{93} +(-9.61413 + 13.2327i) q^{95} +(7.28078 - 2.36567i) q^{97} +(1.05446 + 0.342615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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
\(3\) 2.81622i 1.62594i −0.582303 0.812972i \(-0.697848\pi\)
0.582303 0.812972i \(-0.302152\pi\)
\(4\) 0 0
\(5\) 1.10836 + 3.41119i 0.495676 + 1.52553i 0.815901 + 0.578191i \(0.196241\pi\)
−0.320226 + 0.947341i \(0.603759\pi\)
\(6\) 0 0
\(7\) 0.587785 + 0.809017i 0.222162 + 0.305780i
\(8\) 0 0
\(9\) −4.93108 −1.64369
\(10\) 0 0
\(11\) −0.213839 0.0694806i −0.0644750 0.0209492i 0.276602 0.960985i \(-0.410792\pi\)
−0.341077 + 0.940035i \(0.610792\pi\)
\(12\) 0 0
\(13\) −3.07430 + 4.23140i −0.852656 + 1.17358i 0.130615 + 0.991433i \(0.458305\pi\)
−0.983271 + 0.182147i \(0.941695\pi\)
\(14\) 0 0
\(15\) 9.60667 3.12140i 2.48043 0.805941i
\(16\) 0 0
\(17\) −3.00515 0.976434i −0.728857 0.236820i −0.0789980 0.996875i \(-0.525172\pi\)
−0.649859 + 0.760055i \(0.725172\pi\)
\(18\) 0 0
\(19\) 2.68046 + 3.68934i 0.614941 + 0.846393i 0.996972 0.0777561i \(-0.0247755\pi\)
−0.382032 + 0.924149i \(0.624776\pi\)
\(20\) 0 0
\(21\) 2.27837 1.65533i 0.497181 0.361223i
\(22\) 0 0
\(23\) 3.82515 + 2.77914i 0.797600 + 0.579490i 0.910209 0.414149i \(-0.135921\pi\)
−0.112609 + 0.993639i \(0.535921\pi\)
\(24\) 0 0
\(25\) −6.36269 + 4.62277i −1.27254 + 0.924553i
\(26\) 0 0
\(27\) 5.43835i 1.04661i
\(28\) 0 0
\(29\) −0.396882 + 0.128955i −0.0736991 + 0.0239463i −0.345635 0.938369i \(-0.612336\pi\)
0.271935 + 0.962316i \(0.412336\pi\)
\(30\) 0 0
\(31\) −1.43283 + 4.40979i −0.257343 + 0.792021i 0.736016 + 0.676964i \(0.236705\pi\)
−0.993359 + 0.115057i \(0.963295\pi\)
\(32\) 0 0
\(33\) −0.195673 + 0.602218i −0.0340622 + 0.104833i
\(34\) 0 0
\(35\) −2.10823 + 2.90174i −0.356357 + 0.490483i
\(36\) 0 0
\(37\) 0.846662 + 2.60576i 0.139190 + 0.428384i 0.996218 0.0868860i \(-0.0276916\pi\)
−0.857028 + 0.515270i \(0.827692\pi\)
\(38\) 0 0
\(39\) 11.9166 + 8.65788i 1.90818 + 1.38637i
\(40\) 0 0
\(41\) 4.14062 + 4.88418i 0.646657 + 0.762781i
\(42\) 0 0
\(43\) 0.388402 + 0.282190i 0.0592307 + 0.0430336i 0.617007 0.786958i \(-0.288345\pi\)
−0.557776 + 0.829992i \(0.688345\pi\)
\(44\) 0 0
\(45\) −5.46544 16.8209i −0.814739 2.50751i
\(46\) 0 0
\(47\) −4.40935 + 6.06894i −0.643169 + 0.885247i −0.998780 0.0493877i \(-0.984273\pi\)
0.355610 + 0.934634i \(0.384273\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) −2.74985 + 8.46317i −0.385056 + 1.18508i
\(52\) 0 0
\(53\) −1.20312 + 0.390916i −0.165261 + 0.0536964i −0.390479 0.920612i \(-0.627691\pi\)
0.225218 + 0.974308i \(0.427691\pi\)
\(54\) 0 0
\(55\) 0.806457i 0.108743i
\(56\) 0 0
\(57\) 10.3900 7.54877i 1.37619 0.999859i
\(58\) 0 0
\(59\) −8.96171 6.51107i −1.16672 0.847668i −0.176104 0.984372i \(-0.556349\pi\)
−0.990612 + 0.136703i \(0.956349\pi\)
\(60\) 0 0
\(61\) 9.89239 7.18725i 1.26659 0.920232i 0.267530 0.963550i \(-0.413793\pi\)
0.999061 + 0.0433171i \(0.0137926\pi\)
\(62\) 0 0
\(63\) −2.89842 3.98933i −0.365166 0.502608i
\(64\) 0 0
\(65\) −17.8416 5.79708i −2.21298 0.719039i
\(66\) 0 0
\(67\) −6.70062 + 2.17716i −0.818612 + 0.265983i −0.688241 0.725482i \(-0.741617\pi\)
−0.130371 + 0.991465i \(0.541617\pi\)
\(68\) 0 0
\(69\) 7.82666 10.7725i 0.942219 1.29685i
\(70\) 0 0
\(71\) 11.1052 + 3.60829i 1.31794 + 0.428226i 0.881788 0.471646i \(-0.156340\pi\)
0.436155 + 0.899871i \(0.356340\pi\)
\(72\) 0 0
\(73\) −3.44830 −0.403593 −0.201796 0.979428i \(-0.564678\pi\)
−0.201796 + 0.979428i \(0.564678\pi\)
\(74\) 0 0
\(75\) 13.0187 + 17.9187i 1.50327 + 2.06908i
\(76\) 0 0
\(77\) −0.0694806 0.213839i −0.00791805 0.0243693i
\(78\) 0 0
\(79\) 12.1848i 1.37090i −0.728119 0.685450i \(-0.759605\pi\)
0.728119 0.685450i \(-0.240395\pi\)
\(80\) 0 0
\(81\) 0.522330 0.0580367
\(82\) 0 0
\(83\) 15.1285 1.66057 0.830284 0.557341i \(-0.188178\pi\)
0.830284 + 0.557341i \(0.188178\pi\)
\(84\) 0 0
\(85\) 11.3334i 1.22928i
\(86\) 0 0
\(87\) 0.363165 + 1.11771i 0.0389353 + 0.119831i
\(88\) 0 0
\(89\) 4.68737 + 6.45161i 0.496860 + 0.683870i 0.981635 0.190769i \(-0.0610983\pi\)
−0.484774 + 0.874639i \(0.661098\pi\)
\(90\) 0 0
\(91\) −5.23030 −0.548285
\(92\) 0 0
\(93\) 12.4189 + 4.03515i 1.28778 + 0.418426i
\(94\) 0 0
\(95\) −9.61413 + 13.2327i −0.986389 + 1.35765i
\(96\) 0 0
\(97\) 7.28078 2.36567i 0.739252 0.240197i 0.0849018 0.996389i \(-0.472942\pi\)
0.654350 + 0.756192i \(0.272942\pi\)
\(98\) 0 0
\(99\) 1.05446 + 0.342615i 0.105977 + 0.0344341i
\(100\) 0 0
\(101\) 5.70889 + 7.85762i 0.568056 + 0.781862i 0.992323 0.123675i \(-0.0394681\pi\)
−0.424267 + 0.905537i \(0.639468\pi\)
\(102\) 0 0
\(103\) 7.78404 5.65544i 0.766984 0.557247i −0.134060 0.990973i \(-0.542802\pi\)
0.901045 + 0.433727i \(0.142802\pi\)
\(104\) 0 0
\(105\) 8.17192 + 5.93725i 0.797498 + 0.579416i
\(106\) 0 0
\(107\) 4.43447 3.22183i 0.428696 0.311466i −0.352431 0.935838i \(-0.614645\pi\)
0.781127 + 0.624372i \(0.214645\pi\)
\(108\) 0 0
\(109\) 14.3127i 1.37091i −0.728115 0.685455i \(-0.759603\pi\)
0.728115 0.685455i \(-0.240397\pi\)
\(110\) 0 0
\(111\) 7.33838 2.38439i 0.696529 0.226316i
\(112\) 0 0
\(113\) −3.56698 + 10.9780i −0.335554 + 1.03273i 0.630895 + 0.775868i \(0.282688\pi\)
−0.966449 + 0.256860i \(0.917312\pi\)
\(114\) 0 0
\(115\) −5.24051 + 16.1286i −0.488680 + 1.50400i
\(116\) 0 0
\(117\) 15.1596 20.8654i 1.40151 1.92901i
\(118\) 0 0
\(119\) −0.976434 3.00515i −0.0895095 0.275482i
\(120\) 0 0
\(121\) −8.85829 6.43592i −0.805299 0.585084i
\(122\) 0 0
\(123\) 13.7549 11.6609i 1.24024 1.05143i
\(124\) 0 0
\(125\) −8.31266 6.03950i −0.743507 0.540189i
\(126\) 0 0
\(127\) 2.64540 + 8.14171i 0.234742 + 0.722460i 0.997156 + 0.0753706i \(0.0240140\pi\)
−0.762414 + 0.647089i \(0.775986\pi\)
\(128\) 0 0
\(129\) 0.794709 1.09382i 0.0699702 0.0963058i
\(130\) 0 0
\(131\) 0.682712 2.10117i 0.0596489 0.183580i −0.916792 0.399365i \(-0.869231\pi\)
0.976441 + 0.215784i \(0.0692308\pi\)
\(132\) 0 0
\(133\) −1.40920 + 4.33708i −0.122193 + 0.376073i
\(134\) 0 0
\(135\) −18.5513 + 6.02767i −1.59664 + 0.518780i
\(136\) 0 0
\(137\) 5.43989i 0.464761i −0.972625 0.232381i \(-0.925349\pi\)
0.972625 0.232381i \(-0.0746515\pi\)
\(138\) 0 0
\(139\) −7.07087 + 5.13729i −0.599743 + 0.435739i −0.845788 0.533520i \(-0.820869\pi\)
0.246045 + 0.969259i \(0.420869\pi\)
\(140\) 0 0
\(141\) 17.0915 + 12.4177i 1.43936 + 1.04576i
\(142\) 0 0
\(143\) 0.951406 0.691237i 0.0795606 0.0578041i
\(144\) 0 0
\(145\) −0.879779 1.21091i −0.0730617 0.100561i
\(146\) 0 0
\(147\) 2.67838 + 0.870259i 0.220909 + 0.0717778i
\(148\) 0 0
\(149\) −10.5188 + 3.41778i −0.861737 + 0.279995i −0.706354 0.707859i \(-0.749661\pi\)
−0.155383 + 0.987854i \(0.549661\pi\)
\(150\) 0 0
\(151\) 12.0773 16.6229i 0.982834 1.35275i 0.0475449 0.998869i \(-0.484860\pi\)
0.935289 0.353885i \(-0.115140\pi\)
\(152\) 0 0
\(153\) 14.8187 + 4.81488i 1.19802 + 0.389260i
\(154\) 0 0
\(155\) −16.6307 −1.33581
\(156\) 0 0
\(157\) −9.77240 13.4506i −0.779922 1.07347i −0.995290 0.0969381i \(-0.969095\pi\)
0.215368 0.976533i \(-0.430905\pi\)
\(158\) 0 0
\(159\) 1.10090 + 3.38824i 0.0873074 + 0.268705i
\(160\) 0 0
\(161\) 4.72815i 0.372630i
\(162\) 0 0
\(163\) 16.7104 1.30886 0.654428 0.756124i \(-0.272909\pi\)
0.654428 + 0.756124i \(0.272909\pi\)
\(164\) 0 0
\(165\) −2.27116 −0.176810
\(166\) 0 0
\(167\) 5.98742i 0.463321i 0.972797 + 0.231660i \(0.0744158\pi\)
−0.972797 + 0.231660i \(0.925584\pi\)
\(168\) 0 0
\(169\) −4.43627 13.6534i −0.341252 1.05026i
\(170\) 0 0
\(171\) −13.2176 18.1925i −1.01077 1.39121i
\(172\) 0 0
\(173\) −20.3113 −1.54424 −0.772120 0.635477i \(-0.780804\pi\)
−0.772120 + 0.635477i \(0.780804\pi\)
\(174\) 0 0
\(175\) −7.47979 2.43033i −0.565419 0.183716i
\(176\) 0 0
\(177\) −18.3366 + 25.2381i −1.37826 + 1.89701i
\(178\) 0 0
\(179\) −22.4093 + 7.28123i −1.67495 + 0.544225i −0.983921 0.178602i \(-0.942843\pi\)
−0.691029 + 0.722827i \(0.742843\pi\)
\(180\) 0 0
\(181\) −12.8254 4.16721i −0.953302 0.309747i −0.209245 0.977863i \(-0.567101\pi\)
−0.744057 + 0.668117i \(0.767101\pi\)
\(182\) 0 0
\(183\) −20.2408 27.8591i −1.49625 2.05941i
\(184\) 0 0
\(185\) −7.95034 + 5.77626i −0.584521 + 0.424679i
\(186\) 0 0
\(187\) 0.574777 + 0.417600i 0.0420319 + 0.0305379i
\(188\) 0 0
\(189\) −4.39972 + 3.19658i −0.320032 + 0.232517i
\(190\) 0 0
\(191\) 24.7883i 1.79362i −0.442416 0.896810i \(-0.645879\pi\)
0.442416 0.896810i \(-0.354121\pi\)
\(192\) 0 0
\(193\) −8.55539 + 2.77982i −0.615831 + 0.200095i −0.600288 0.799784i \(-0.704947\pi\)
−0.0155423 + 0.999879i \(0.504947\pi\)
\(194\) 0 0
\(195\) −16.3258 + 50.2458i −1.16912 + 3.59818i
\(196\) 0 0
\(197\) −4.18408 + 12.8773i −0.298103 + 0.917468i 0.684058 + 0.729428i \(0.260214\pi\)
−0.982161 + 0.188040i \(0.939786\pi\)
\(198\) 0 0
\(199\) 2.74535 3.77865i 0.194613 0.267861i −0.700548 0.713606i \(-0.747061\pi\)
0.895160 + 0.445744i \(0.147061\pi\)
\(200\) 0 0
\(201\) 6.13137 + 18.8704i 0.432474 + 1.33102i
\(202\) 0 0
\(203\) −0.337608 0.245286i −0.0236954 0.0172157i
\(204\) 0 0
\(205\) −12.0716 + 19.5379i −0.843115 + 1.36459i
\(206\) 0 0
\(207\) −18.8622 13.7042i −1.31101 0.952505i
\(208\) 0 0
\(209\) −0.316851 0.975167i −0.0219170 0.0674537i
\(210\) 0 0
\(211\) −5.81663 + 8.00590i −0.400433 + 0.551149i −0.960853 0.277060i \(-0.910640\pi\)
0.560420 + 0.828209i \(0.310640\pi\)
\(212\) 0 0
\(213\) 10.1617 31.2746i 0.696271 2.14290i
\(214\) 0 0
\(215\) −0.532115 + 1.63768i −0.0362900 + 0.111689i
\(216\) 0 0
\(217\) −4.40979 + 1.43283i −0.299356 + 0.0972666i
\(218\) 0 0
\(219\) 9.71116i 0.656219i
\(220\) 0 0
\(221\) 13.3704 9.71418i 0.899392 0.653446i
\(222\) 0 0
\(223\) 15.2615 + 11.0881i 1.02198 + 0.742515i 0.966689 0.255955i \(-0.0823900\pi\)
0.0552953 + 0.998470i \(0.482390\pi\)
\(224\) 0 0
\(225\) 31.3750 22.7952i 2.09166 1.51968i
\(226\) 0 0
\(227\) 11.2478 + 15.4812i 0.746542 + 1.02753i 0.998215 + 0.0597145i \(0.0190190\pi\)
−0.251674 + 0.967812i \(0.580981\pi\)
\(228\) 0 0
\(229\) −11.8359 3.84572i −0.782139 0.254132i −0.109386 0.993999i \(-0.534888\pi\)
−0.672753 + 0.739867i \(0.734888\pi\)
\(230\) 0 0
\(231\) −0.602218 + 0.195673i −0.0396230 + 0.0128743i
\(232\) 0 0
\(233\) 6.79638 9.35441i 0.445246 0.612828i −0.526122 0.850409i \(-0.676355\pi\)
0.971368 + 0.237581i \(0.0763545\pi\)
\(234\) 0 0
\(235\) −25.5895 8.31454i −1.66928 0.542381i
\(236\) 0 0
\(237\) −34.3151 −2.22901
\(238\) 0 0
\(239\) −3.84320 5.28971i −0.248596 0.342163i 0.666423 0.745574i \(-0.267824\pi\)
−0.915019 + 0.403411i \(0.867824\pi\)
\(240\) 0 0
\(241\) 8.15022 + 25.0838i 0.525002 + 1.61579i 0.764312 + 0.644847i \(0.223079\pi\)
−0.239310 + 0.970943i \(0.576921\pi\)
\(242\) 0 0
\(243\) 14.8441i 0.952247i
\(244\) 0 0
\(245\) −3.58674 −0.229149
\(246\) 0 0
\(247\) −23.8516 −1.51764
\(248\) 0 0
\(249\) 42.6051i 2.69999i
\(250\) 0 0
\(251\) 7.18170 + 22.1030i 0.453305 + 1.39513i 0.873114 + 0.487516i \(0.162097\pi\)
−0.419810 + 0.907612i \(0.637903\pi\)
\(252\) 0 0
\(253\) −0.624872 0.860063i −0.0392854 0.0540717i
\(254\) 0 0
\(255\) −31.9174 −1.99874
\(256\) 0 0
\(257\) 13.3030 + 4.32241i 0.829819 + 0.269625i 0.692969 0.720967i \(-0.256302\pi\)
0.136850 + 0.990592i \(0.456302\pi\)
\(258\) 0 0
\(259\) −1.61045 + 2.21659i −0.100068 + 0.137732i
\(260\) 0 0
\(261\) 1.95706 0.635887i 0.121139 0.0393604i
\(262\) 0 0
\(263\) −5.95221 1.93399i −0.367029 0.119255i 0.119695 0.992811i \(-0.461808\pi\)
−0.486724 + 0.873556i \(0.661808\pi\)
\(264\) 0 0
\(265\) −2.66698 3.67078i −0.163831 0.225495i
\(266\) 0 0
\(267\) 18.1692 13.2007i 1.11193 0.807867i
\(268\) 0 0
\(269\) 17.4003 + 12.6421i 1.06092 + 0.770800i 0.974258 0.225438i \(-0.0723812\pi\)
0.0866582 + 0.996238i \(0.472381\pi\)
\(270\) 0 0
\(271\) −7.50412 + 5.45207i −0.455843 + 0.331189i −0.791898 0.610653i \(-0.790907\pi\)
0.336055 + 0.941842i \(0.390907\pi\)
\(272\) 0 0
\(273\) 14.7297i 0.891480i
\(274\) 0 0
\(275\) 1.68179 0.546446i 0.101416 0.0329519i
\(276\) 0 0
\(277\) −6.06768 + 18.6744i −0.364572 + 1.12204i 0.585677 + 0.810545i \(0.300829\pi\)
−0.950249 + 0.311492i \(0.899171\pi\)
\(278\) 0 0
\(279\) 7.06539 21.7450i 0.422994 1.30184i
\(280\) 0 0
\(281\) 17.6892 24.3470i 1.05525 1.45242i 0.171076 0.985258i \(-0.445276\pi\)
0.884170 0.467164i \(-0.154724\pi\)
\(282\) 0 0
\(283\) −7.18655 22.1179i −0.427196 1.31477i −0.900876 0.434077i \(-0.857074\pi\)
0.473679 0.880697i \(-0.342926\pi\)
\(284\) 0 0
\(285\) 37.2662 + 27.0755i 2.20746 + 1.60381i
\(286\) 0 0
\(287\) −1.51759 + 6.22069i −0.0895804 + 0.367195i
\(288\) 0 0
\(289\) −5.67576 4.12368i −0.333868 0.242569i
\(290\) 0 0
\(291\) −6.66224 20.5043i −0.390548 1.20198i
\(292\) 0 0
\(293\) −2.62647 + 3.61503i −0.153440 + 0.211192i −0.878816 0.477161i \(-0.841666\pi\)
0.725376 + 0.688353i \(0.241666\pi\)
\(294\) 0 0
\(295\) 12.2777 37.7868i 0.714833 2.20003i
\(296\) 0 0
\(297\) 0.377860 1.16293i 0.0219257 0.0674802i
\(298\) 0 0
\(299\) −23.5193 + 7.64189i −1.36016 + 0.441942i
\(300\) 0 0
\(301\) 0.480091i 0.0276720i
\(302\) 0 0
\(303\) 22.1288 16.0775i 1.27126 0.923628i
\(304\) 0 0
\(305\) 35.4815 + 25.7788i 2.03166 + 1.47609i
\(306\) 0 0
\(307\) −12.4056 + 9.01318i −0.708023 + 0.514409i −0.882535 0.470246i \(-0.844165\pi\)
0.174512 + 0.984655i \(0.444165\pi\)
\(308\) 0 0
\(309\) −15.9269 21.9215i −0.906052 1.24707i
\(310\) 0 0
\(311\) 9.99483 + 3.24752i 0.566755 + 0.184150i 0.578358 0.815783i \(-0.303694\pi\)
−0.0116035 + 0.999933i \(0.503694\pi\)
\(312\) 0 0
\(313\) 27.2840 8.86510i 1.54218 0.501085i 0.590204 0.807254i \(-0.299047\pi\)
0.951977 + 0.306169i \(0.0990473\pi\)
\(314\) 0 0
\(315\) 10.3959 14.3087i 0.585741 0.806204i
\(316\) 0 0
\(317\) 14.2729 + 4.63755i 0.801647 + 0.260471i 0.681056 0.732231i \(-0.261521\pi\)
0.120591 + 0.992702i \(0.461521\pi\)
\(318\) 0 0
\(319\) 0.0938288 0.00525341
\(320\) 0 0
\(321\) −9.07338 12.4884i −0.506426 0.697036i
\(322\) 0 0
\(323\) −4.45281 13.7043i −0.247761 0.762530i
\(324\) 0 0
\(325\) 41.1349i 2.28175i
\(326\) 0 0
\(327\) −40.3077 −2.22902
\(328\) 0 0
\(329\) −7.50163 −0.413578
\(330\) 0 0
\(331\) 26.5738i 1.46063i −0.683112 0.730313i \(-0.739374\pi\)
0.683112 0.730313i \(-0.260626\pi\)
\(332\) 0 0
\(333\) −4.17496 12.8492i −0.228787 0.704132i
\(334\) 0 0
\(335\) −14.8535 20.4440i −0.811532 1.11698i
\(336\) 0 0
\(337\) −26.3291 −1.43424 −0.717119 0.696951i \(-0.754540\pi\)
−0.717119 + 0.696951i \(0.754540\pi\)
\(338\) 0 0
\(339\) 30.9166 + 10.0454i 1.67916 + 0.545591i
\(340\) 0 0
\(341\) 0.612789 0.843432i 0.0331844 0.0456744i
\(342\) 0 0
\(343\) −0.951057 + 0.309017i −0.0513522 + 0.0166853i
\(344\) 0 0
\(345\) 45.4218 + 14.7584i 2.44543 + 0.794567i
\(346\) 0 0
\(347\) 11.3889 + 15.6755i 0.611388 + 0.841503i 0.996691 0.0812871i \(-0.0259031\pi\)
−0.385303 + 0.922790i \(0.625903\pi\)
\(348\) 0 0
\(349\) 9.87461 7.17432i 0.528576 0.384033i −0.291249 0.956647i \(-0.594071\pi\)
0.819825 + 0.572615i \(0.194071\pi\)
\(350\) 0 0
\(351\) −23.0119 16.7191i −1.22828 0.892399i
\(352\) 0 0
\(353\) 2.11741 1.53839i 0.112698 0.0818801i −0.530009 0.847992i \(-0.677811\pi\)
0.642707 + 0.766112i \(0.277811\pi\)
\(354\) 0 0
\(355\) 41.8813i 2.22283i
\(356\) 0 0
\(357\) −8.46317 + 2.74985i −0.447918 + 0.145538i
\(358\) 0 0
\(359\) 1.03472 3.18454i 0.0546104 0.168074i −0.920031 0.391845i \(-0.871837\pi\)
0.974642 + 0.223771i \(0.0718369\pi\)
\(360\) 0 0
\(361\) −0.555034 + 1.70822i −0.0292123 + 0.0899063i
\(362\) 0 0
\(363\) −18.1250 + 24.9469i −0.951314 + 1.30937i
\(364\) 0 0
\(365\) −3.82197 11.7628i −0.200051 0.615694i
\(366\) 0 0
\(367\) 21.6390 + 15.7217i 1.12955 + 0.820665i 0.985629 0.168925i \(-0.0540294\pi\)
0.143919 + 0.989589i \(0.454029\pi\)
\(368\) 0 0
\(369\) −20.4178 24.0843i −1.06291 1.25378i
\(370\) 0 0
\(371\) −1.02343 0.743566i −0.0531339 0.0386040i
\(372\) 0 0
\(373\) 11.0333 + 33.9570i 0.571282 + 1.75823i 0.648504 + 0.761211i \(0.275395\pi\)
−0.0772217 + 0.997014i \(0.524605\pi\)
\(374\) 0 0
\(375\) −17.0085 + 23.4103i −0.878318 + 1.20890i
\(376\) 0 0
\(377\) 0.674472 2.07581i 0.0347371 0.106910i
\(378\) 0 0
\(379\) 6.83014 21.0210i 0.350841 1.07978i −0.607541 0.794288i \(-0.707844\pi\)
0.958382 0.285489i \(-0.0921560\pi\)
\(380\) 0 0
\(381\) 22.9288 7.45003i 1.17468 0.381677i
\(382\) 0 0
\(383\) 1.35520i 0.0692474i −0.999400 0.0346237i \(-0.988977\pi\)
0.999400 0.0346237i \(-0.0110233\pi\)
\(384\) 0 0
\(385\) 0.652438 0.474024i 0.0332513 0.0241585i
\(386\) 0 0
\(387\) −1.91524 1.39150i −0.0973571 0.0707341i
\(388\) 0 0
\(389\) 19.7815 14.3721i 1.00296 0.728693i 0.0402387 0.999190i \(-0.487188\pi\)
0.962721 + 0.270497i \(0.0871882\pi\)
\(390\) 0 0
\(391\) −8.78153 12.0867i −0.444101 0.611253i
\(392\) 0 0
\(393\) −5.91736 1.92267i −0.298491 0.0969857i
\(394\) 0 0
\(395\) 41.5648 13.5052i 2.09135 0.679522i
\(396\) 0 0
\(397\) 3.70117 5.09423i 0.185756 0.255672i −0.705975 0.708237i \(-0.749491\pi\)
0.891731 + 0.452565i \(0.149491\pi\)
\(398\) 0 0
\(399\) 12.2142 + 3.96862i 0.611473 + 0.198680i
\(400\) 0 0
\(401\) 24.2022 1.20860 0.604301 0.796756i \(-0.293453\pi\)
0.604301 + 0.796756i \(0.293453\pi\)
\(402\) 0 0
\(403\) −14.2547 19.6199i −0.710075 0.977334i
\(404\) 0 0
\(405\) 0.578932 + 1.78177i 0.0287674 + 0.0885369i
\(406\) 0 0
\(407\) 0.616040i 0.0305360i
\(408\) 0 0
\(409\) −14.7138 −0.727549 −0.363774 0.931487i \(-0.618512\pi\)
−0.363774 + 0.931487i \(0.618512\pi\)
\(410\) 0 0
\(411\) −15.3199 −0.755676
\(412\) 0 0
\(413\) 11.0773i 0.545078i
\(414\) 0 0
\(415\) 16.7679 + 51.6062i 0.823103 + 2.53325i
\(416\) 0 0
\(417\) 14.4677 + 19.9131i 0.708487 + 0.975149i
\(418\) 0 0
\(419\) 13.8648 0.677342 0.338671 0.940905i \(-0.390023\pi\)
0.338671 + 0.940905i \(0.390023\pi\)
\(420\) 0 0
\(421\) −5.75433 1.86970i −0.280449 0.0911234i 0.165415 0.986224i \(-0.447104\pi\)
−0.445864 + 0.895101i \(0.647104\pi\)
\(422\) 0 0
\(423\) 21.7429 29.9265i 1.05717 1.45507i
\(424\) 0 0
\(425\) 23.6347 7.67938i 1.14645 0.372505i
\(426\) 0 0
\(427\) 11.6292 + 3.77856i 0.562777 + 0.182857i
\(428\) 0 0
\(429\) −1.94667 2.67937i −0.0939863 0.129361i
\(430\) 0 0
\(431\) −5.11074 + 3.71317i −0.246176 + 0.178857i −0.704030 0.710170i \(-0.748618\pi\)
0.457855 + 0.889027i \(0.348618\pi\)
\(432\) 0 0
\(433\) −28.8183 20.9377i −1.38492 1.00620i −0.996401 0.0847597i \(-0.972988\pi\)
−0.388516 0.921442i \(-0.627012\pi\)
\(434\) 0 0
\(435\) −3.41019 + 2.47765i −0.163506 + 0.118794i
\(436\) 0 0
\(437\) 21.5617i 1.03143i
\(438\) 0 0
\(439\) 9.11777 2.96254i 0.435168 0.141395i −0.0832374 0.996530i \(-0.526526\pi\)
0.518405 + 0.855135i \(0.326526\pi\)
\(440\) 0 0
\(441\) 1.52379 4.68974i 0.0725614 0.223321i
\(442\) 0 0
\(443\) 0.0918636 0.282727i 0.00436457 0.0134328i −0.948851 0.315726i \(-0.897752\pi\)
0.953215 + 0.302293i \(0.0977521\pi\)
\(444\) 0 0
\(445\) −16.8124 + 23.1403i −0.796984 + 1.09695i
\(446\) 0 0
\(447\) 9.62521 + 29.6233i 0.455257 + 1.40114i
\(448\) 0 0
\(449\) −18.8419 13.6894i −0.889203 0.646044i 0.0464672 0.998920i \(-0.485204\pi\)
−0.935670 + 0.352876i \(0.885204\pi\)
\(450\) 0 0
\(451\) −0.546072 1.33212i −0.0257135 0.0627272i
\(452\) 0 0
\(453\) −46.8138 34.0122i −2.19950 1.59803i
\(454\) 0 0
\(455\) −5.79708 17.8416i −0.271771 0.836426i
\(456\) 0 0
\(457\) 14.9801 20.6184i 0.700741 0.964487i −0.299206 0.954189i \(-0.596722\pi\)
0.999947 0.0102988i \(-0.00327828\pi\)
\(458\) 0 0
\(459\) 5.31019 16.3431i 0.247858 0.762830i
\(460\) 0 0
\(461\) −6.53726 + 20.1196i −0.304471 + 0.937064i 0.675404 + 0.737448i \(0.263969\pi\)
−0.979874 + 0.199616i \(0.936031\pi\)
\(462\) 0 0
\(463\) 9.94406 3.23102i 0.462140 0.150158i −0.0686878 0.997638i \(-0.521881\pi\)
0.530827 + 0.847480i \(0.321881\pi\)
\(464\) 0 0
\(465\) 46.8358i 2.17196i
\(466\) 0 0
\(467\) −24.4593 + 17.7707i −1.13184 + 0.822330i −0.985962 0.166972i \(-0.946601\pi\)
−0.145879 + 0.989302i \(0.546601\pi\)
\(468\) 0 0
\(469\) −5.69989 4.14121i −0.263197 0.191223i
\(470\) 0 0
\(471\) −37.8797 + 27.5212i −1.74540 + 1.26811i
\(472\) 0 0
\(473\) −0.0634488 0.0873298i −0.00291738 0.00401543i
\(474\) 0 0
\(475\) −34.1099 11.0830i −1.56507 0.508522i
\(476\) 0 0
\(477\) 5.93266 1.92764i 0.271638 0.0882605i
\(478\) 0 0
\(479\) 19.5030 26.8435i 0.891114 1.22651i −0.0821029 0.996624i \(-0.526164\pi\)
0.973217 0.229889i \(-0.0738364\pi\)
\(480\) 0 0
\(481\) −13.6289 4.42830i −0.621425 0.201913i
\(482\) 0 0
\(483\) 13.3155 0.605876
\(484\) 0 0
\(485\) 16.1395 + 22.2141i 0.732858 + 1.00869i
\(486\) 0 0
\(487\) −2.89232 8.90163i −0.131063 0.403371i 0.863894 0.503674i \(-0.168019\pi\)
−0.994957 + 0.100303i \(0.968019\pi\)
\(488\) 0 0
\(489\) 47.0600i 2.12813i
\(490\) 0 0
\(491\) 12.9066 0.582466 0.291233 0.956652i \(-0.405935\pi\)
0.291233 + 0.956652i \(0.405935\pi\)
\(492\) 0 0
\(493\) 1.31861 0.0593871
\(494\) 0 0
\(495\) 3.97671i 0.178740i
\(496\) 0 0
\(497\) 3.60829 + 11.1052i 0.161854 + 0.498136i
\(498\) 0 0
\(499\) −4.10437 5.64918i −0.183737 0.252892i 0.707206 0.707008i \(-0.249955\pi\)
−0.890943 + 0.454115i \(0.849955\pi\)
\(500\) 0 0
\(501\) 16.8619 0.753334
\(502\) 0 0
\(503\) 41.0672 + 13.3435i 1.83110 + 0.594959i 0.999198 + 0.0400303i \(0.0127454\pi\)
0.831898 + 0.554929i \(0.187255\pi\)
\(504\) 0 0
\(505\) −20.4763 + 28.1832i −0.911185 + 1.25414i
\(506\) 0 0
\(507\) −38.4511 + 12.4935i −1.70767 + 0.554856i
\(508\) 0 0
\(509\) 16.8407 + 5.47188i 0.746452 + 0.242537i 0.657454 0.753495i \(-0.271633\pi\)
0.0889982 + 0.996032i \(0.471633\pi\)
\(510\) 0 0
\(511\) −2.02686 2.78973i −0.0896629 0.123410i
\(512\) 0 0
\(513\) −20.0639 + 14.5773i −0.885844 + 0.643604i
\(514\) 0 0
\(515\) 27.9193 + 20.2846i 1.23027 + 0.893846i
\(516\) 0 0
\(517\) 1.36457 0.991415i 0.0600135 0.0436024i
\(518\) 0 0
\(519\) 57.2011i 2.51085i
\(520\) 0 0
\(521\) 1.13142 0.367619i 0.0495682 0.0161057i −0.284128 0.958786i \(-0.591704\pi\)
0.333696 + 0.942681i \(0.391704\pi\)
\(522\) 0 0
\(523\) 3.72967 11.4787i 0.163087 0.501930i −0.835803 0.549029i \(-0.814998\pi\)
0.998890 + 0.0470989i \(0.0149976\pi\)
\(524\) 0 0
\(525\) −6.84434 + 21.0647i −0.298712 + 0.919340i
\(526\) 0 0
\(527\) 8.61173 11.8530i 0.375133 0.516326i
\(528\) 0 0
\(529\) −0.199190 0.613043i −0.00866043 0.0266541i
\(530\) 0 0
\(531\) 44.1909 + 32.1066i 1.91772 + 1.39331i
\(532\) 0 0
\(533\) −33.3964 + 2.50524i −1.44656 + 0.108514i
\(534\) 0 0
\(535\) 15.9053 + 11.5559i 0.687646 + 0.499604i
\(536\) 0 0
\(537\) 20.5055 + 63.1095i 0.884879 + 2.72338i
\(538\) 0 0
\(539\) 0.132160 0.181903i 0.00569253 0.00783510i
\(540\) 0 0
\(541\) −3.68004 + 11.3260i −0.158217 + 0.486943i −0.998473 0.0552481i \(-0.982405\pi\)
0.840255 + 0.542191i \(0.182405\pi\)
\(542\) 0 0
\(543\) −11.7358 + 36.1190i −0.503631 + 1.55002i
\(544\) 0 0
\(545\) 48.8235 15.8637i 2.09137 0.679527i
\(546\) 0 0
\(547\) 24.3251i 1.04007i 0.854146 + 0.520033i \(0.174080\pi\)
−0.854146 + 0.520033i \(0.825920\pi\)
\(548\) 0 0
\(549\) −48.7802 + 35.4409i −2.08189 + 1.51258i
\(550\) 0 0
\(551\) −1.53959 1.11857i −0.0655885 0.0476529i
\(552\) 0 0
\(553\) 9.85774 7.16207i 0.419194 0.304562i
\(554\) 0 0
\(555\) 16.2672 + 22.3899i 0.690504 + 0.950398i
\(556\) 0 0
\(557\) −37.6344 12.2282i −1.59462 0.518124i −0.628852 0.777525i \(-0.716475\pi\)
−0.965770 + 0.259401i \(0.916475\pi\)
\(558\) 0 0
\(559\) −2.38812 + 0.775948i −0.101007 + 0.0328191i
\(560\) 0 0
\(561\) 1.17605 1.61870i 0.0496530 0.0683415i
\(562\) 0 0
\(563\) −29.1783 9.48062i −1.22972 0.399560i −0.379107 0.925353i \(-0.623769\pi\)
−0.850613 + 0.525792i \(0.823769\pi\)
\(564\) 0 0
\(565\) −41.4018 −1.74179
\(566\) 0 0
\(567\) 0.307018 + 0.422574i 0.0128935 + 0.0177464i
\(568\) 0 0
\(569\) 8.12477 + 25.0055i 0.340608 + 1.04828i 0.963893 + 0.266290i \(0.0857977\pi\)
−0.623285 + 0.781995i \(0.714202\pi\)
\(570\) 0 0
\(571\) 34.5365i 1.44531i 0.691211 + 0.722653i \(0.257078\pi\)
−0.691211 + 0.722653i \(0.742922\pi\)
\(572\) 0 0
\(573\) −69.8093 −2.91633
\(574\) 0 0
\(575\) −37.1856 −1.55075
\(576\) 0 0
\(577\) 24.1300i 1.00455i −0.864709 0.502273i \(-0.832497\pi\)
0.864709 0.502273i \(-0.167503\pi\)
\(578\) 0 0
\(579\) 7.82856 + 24.0938i 0.325344 + 1.00131i
\(580\) 0 0
\(581\) 8.89230 + 12.2392i 0.368915 + 0.507768i
\(582\) 0 0
\(583\) 0.284435 0.0117801
\(584\) 0 0
\(585\) 87.9783 + 28.5859i 3.63746 + 1.18188i
\(586\) 0 0
\(587\) −13.0777 + 18.0000i −0.539776 + 0.742938i −0.988581 0.150692i \(-0.951850\pi\)
0.448804 + 0.893630i \(0.351850\pi\)
\(588\) 0 0
\(589\) −20.1098 + 6.53409i −0.828612 + 0.269232i
\(590\) 0 0
\(591\) 36.2652 + 11.7833i 1.49175 + 0.484700i
\(592\) 0 0
\(593\) −11.8651 16.3309i −0.487241 0.670630i 0.492635 0.870236i \(-0.336034\pi\)
−0.979876 + 0.199606i \(0.936034\pi\)
\(594\) 0 0
\(595\) 9.16892 6.66161i 0.375889 0.273099i
\(596\) 0 0
\(597\) −10.6415 7.73150i −0.435527 0.316429i
\(598\) 0 0
\(599\) 11.7519 8.53827i 0.480170 0.348864i −0.321221 0.947004i \(-0.604093\pi\)
0.801392 + 0.598140i \(0.204093\pi\)
\(600\) 0 0
\(601\) 32.6497i 1.33181i −0.746037 0.665905i \(-0.768046\pi\)
0.746037 0.665905i \(-0.231954\pi\)
\(602\) 0 0
\(603\) 33.0413 10.7358i 1.34555 0.437195i
\(604\) 0 0
\(605\) 12.1360 37.3507i 0.493398 1.51852i
\(606\) 0 0
\(607\) 5.36027 16.4972i 0.217566 0.669601i −0.781395 0.624037i \(-0.785492\pi\)
0.998961 0.0455639i \(-0.0145085\pi\)
\(608\) 0 0
\(609\) −0.690780 + 0.950777i −0.0279918 + 0.0385274i
\(610\) 0 0
\(611\) −12.1245 37.3155i −0.490506 1.50962i
\(612\) 0 0
\(613\) −9.33601 6.78301i −0.377078 0.273963i 0.383062 0.923723i \(-0.374870\pi\)
−0.760140 + 0.649760i \(0.774870\pi\)
\(614\) 0 0
\(615\) 55.0231 + 33.9962i 2.21874 + 1.37086i
\(616\) 0 0
\(617\) −20.8528 15.1504i −0.839501 0.609933i 0.0827305 0.996572i \(-0.473636\pi\)
−0.922231 + 0.386639i \(0.873636\pi\)
\(618\) 0 0
\(619\) 1.35463 + 4.16914i 0.0544474 + 0.167572i 0.974582 0.224030i \(-0.0719212\pi\)
−0.920135 + 0.391601i \(0.871921\pi\)
\(620\) 0 0
\(621\) −15.1139 + 20.8025i −0.606501 + 0.834777i
\(622\) 0 0
\(623\) −2.46430 + 7.58433i −0.0987300 + 0.303860i
\(624\) 0 0
\(625\) −0.763206 + 2.34891i −0.0305282 + 0.0939563i
\(626\) 0 0
\(627\) −2.74628 + 0.892321i −0.109676 + 0.0356359i
\(628\) 0 0
\(629\) 8.65742i 0.345194i
\(630\) 0 0
\(631\) 35.8654 26.0577i 1.42778 1.03734i 0.437354 0.899289i \(-0.355916\pi\)
0.990425 0.138053i \(-0.0440843\pi\)
\(632\) 0 0
\(633\) 22.5464 + 16.3809i 0.896137 + 0.651082i
\(634\) 0 0
\(635\) −24.8409 + 18.0480i −0.985781 + 0.716212i
\(636\) 0 0
\(637\) −3.07430 4.23140i −0.121808 0.167654i
\(638\) 0 0
\(639\) −54.7606 17.7928i −2.16630 0.703872i
\(640\) 0 0
\(641\) 15.5795 5.06209i 0.615353 0.199940i 0.0152771 0.999883i \(-0.495137\pi\)
0.600076 + 0.799943i \(0.295137\pi\)
\(642\) 0 0
\(643\) 1.76286 2.42637i 0.0695205 0.0956867i −0.772841 0.634600i \(-0.781165\pi\)
0.842361 + 0.538913i \(0.181165\pi\)
\(644\) 0 0
\(645\) 4.61207 + 1.49855i 0.181600 + 0.0590055i
\(646\) 0 0
\(647\) 46.5087 1.82845 0.914223 0.405211i \(-0.132802\pi\)
0.914223 + 0.405211i \(0.132802\pi\)
\(648\) 0 0
\(649\) 1.46397 + 2.01499i 0.0574660 + 0.0790952i
\(650\) 0 0
\(651\) 4.03515 + 12.4189i 0.158150 + 0.486736i
\(652\) 0 0
\(653\) 9.17878i 0.359193i 0.983740 + 0.179597i \(0.0574792\pi\)
−0.983740 + 0.179597i \(0.942521\pi\)
\(654\) 0 0
\(655\) 7.92420 0.309624
\(656\) 0 0
\(657\) 17.0038 0.663383
\(658\) 0 0
\(659\) 37.4362i 1.45831i −0.684349 0.729154i \(-0.739914\pi\)
0.684349 0.729154i \(-0.260086\pi\)
\(660\) 0 0
\(661\) −3.78564 11.6510i −0.147244 0.453172i 0.850048 0.526705i \(-0.176573\pi\)
−0.997293 + 0.0735330i \(0.976573\pi\)
\(662\) 0 0
\(663\) −27.3572 37.6540i −1.06247 1.46236i
\(664\) 0 0
\(665\) −16.3565 −0.634279
\(666\) 0 0
\(667\) −1.87652 0.609717i −0.0726590 0.0236084i
\(668\) 0 0
\(669\) 31.2265 42.9796i 1.20729 1.66169i
\(670\) 0 0
\(671\) −2.61476 + 0.849586i −0.100942 + 0.0327979i
\(672\) 0 0
\(673\) −1.86293 0.605304i −0.0718108 0.0233328i 0.272891 0.962045i \(-0.412020\pi\)
−0.344702 + 0.938712i \(0.612020\pi\)
\(674\) 0 0
\(675\) −25.1402 34.6025i −0.967648 1.33185i
\(676\) 0 0
\(677\) −13.8596 + 10.0696i −0.532668 + 0.387006i −0.821355 0.570418i \(-0.806781\pi\)
0.288687 + 0.957424i \(0.406781\pi\)
\(678\) 0 0
\(679\) 6.19341 + 4.49977i 0.237681 + 0.172685i
\(680\) 0 0
\(681\) 43.5986 31.6762i 1.67070 1.21384i
\(682\) 0 0
\(683\) 15.3586i 0.587680i −0.955855 0.293840i \(-0.905067\pi\)
0.955855 0.293840i \(-0.0949333\pi\)
\(684\) 0 0
\(685\) 18.5565 6.02938i 0.709008 0.230371i
\(686\) 0 0
\(687\) −10.8304 + 33.3325i −0.413205 + 1.27171i
\(688\) 0 0
\(689\) 2.04461 6.29266i 0.0778934 0.239731i
\(690\) 0 0
\(691\) 12.1798 16.7641i 0.463342 0.637735i −0.511856 0.859071i \(-0.671042\pi\)
0.975198 + 0.221336i \(0.0710418\pi\)
\(692\) 0 0
\(693\) 0.342615 + 1.05446i 0.0130149 + 0.0400556i
\(694\) 0 0
\(695\) −25.3614 18.4261i −0.962012 0.698943i
\(696\) 0 0
\(697\) −7.67413 18.7208i −0.290679 0.709100i
\(698\) 0 0
\(699\) −26.3441 19.1401i −0.996424 0.723945i
\(700\) 0 0
\(701\) −2.35289 7.24147i −0.0888676 0.273506i 0.896739 0.442559i \(-0.145929\pi\)
−0.985607 + 0.169053i \(0.945929\pi\)
\(702\) 0 0
\(703\) −7.34409 + 10.1083i −0.276987 + 0.381241i
\(704\) 0 0
\(705\) −23.4155 + 72.0656i −0.881881 + 2.71415i
\(706\) 0 0
\(707\) −3.00134 + 9.23718i −0.112877 + 0.347400i
\(708\) 0 0
\(709\) 45.4560 14.7696i 1.70714 0.554682i 0.717284 0.696780i \(-0.245385\pi\)
0.989853 + 0.142098i \(0.0453848\pi\)
\(710\) 0 0
\(711\) 60.0844i 2.25334i
\(712\) 0 0
\(713\) −17.7362 + 12.8861i −0.664225 + 0.482588i
\(714\) 0 0
\(715\) 3.41245 + 2.47929i 0.127618 + 0.0927201i
\(716\) 0 0
\(717\) −14.8970 + 10.8233i −0.556337 + 0.404203i
\(718\) 0 0
\(719\) −7.56657 10.4145i −0.282185 0.388395i 0.644271 0.764797i \(-0.277161\pi\)
−0.926456 + 0.376403i \(0.877161\pi\)
\(720\) 0 0
\(721\) 9.15069 + 2.97324i 0.340789 + 0.110729i
\(722\) 0 0
\(723\) 70.6415 22.9528i 2.62718 0.853624i
\(724\) 0 0
\(725\) 1.92911 2.65519i 0.0716453 0.0986113i
\(726\) 0 0
\(727\) −34.9096 11.3428i −1.29472 0.420681i −0.420981 0.907069i \(-0.638314\pi\)
−0.873743 + 0.486388i \(0.838314\pi\)
\(728\) 0 0
\(729\) 43.3711 1.60634
\(730\) 0 0
\(731\) −0.891666 1.22727i −0.0329795 0.0453924i
\(732\) 0 0
\(733\) −6.00841 18.4920i −0.221926 0.683017i −0.998589 0.0531013i \(-0.983089\pi\)
0.776663 0.629916i \(-0.216911\pi\)
\(734\) 0 0
\(735\) 10.1010i 0.372583i
\(736\) 0 0
\(737\) 1.58413 0.0583521
\(738\) 0 0
\(739\) 19.9961 0.735569 0.367784 0.929911i \(-0.380116\pi\)
0.367784 + 0.929911i \(0.380116\pi\)
\(740\) 0 0
\(741\) 67.1714i 2.46760i
\(742\) 0 0
\(743\) 15.4902 + 47.6740i 0.568281 + 1.74899i 0.657996 + 0.753021i \(0.271404\pi\)
−0.0897153 + 0.995967i \(0.528596\pi\)
\(744\) 0 0
\(745\) −23.3174 32.0937i −0.854284 1.17582i
\(746\) 0 0
\(747\) −74.5999 −2.72947
\(748\) 0 0
\(749\) 5.21303 + 1.69382i 0.190480 + 0.0618907i
\(750\) 0 0
\(751\) 12.5232 17.2368i 0.456980 0.628979i −0.516899 0.856046i \(-0.672914\pi\)
0.973879 + 0.227068i \(0.0729138\pi\)
\(752\) 0 0
\(753\) 62.2468 20.2252i 2.26840 0.737048i
\(754\) 0 0
\(755\) 70.0900 + 22.7736i 2.55084 + 0.828817i
\(756\) 0 0
\(757\) −3.08626 4.24787i −0.112172 0.154391i 0.749240 0.662299i \(-0.230419\pi\)
−0.861412 + 0.507908i \(0.830419\pi\)
\(758\) 0 0
\(759\) −2.42212 + 1.75978i −0.0879176 + 0.0638758i
\(760\) 0 0
\(761\) 21.4646 + 15.5949i 0.778090 + 0.565315i 0.904405 0.426675i \(-0.140315\pi\)
−0.126315 + 0.991990i \(0.540315\pi\)
\(762\) 0 0
\(763\) 11.5792 8.41281i 0.419196 0.304564i
\(764\) 0 0
\(765\) 55.8860i 2.02056i
\(766\) 0 0
\(767\) 55.1019 17.9037i 1.98961 0.646465i
\(768\) 0 0
\(769\) −10.4719 + 32.2292i −0.377626 + 1.16221i 0.564063 + 0.825731i \(0.309237\pi\)
−0.941690 + 0.336483i \(0.890763\pi\)
\(770\) 0 0
\(771\) 12.1729 37.4642i 0.438395 1.34924i
\(772\) 0 0
\(773\) −13.8034 + 18.9987i −0.496473 + 0.683337i −0.981565 0.191126i \(-0.938786\pi\)
0.485092 + 0.874463i \(0.338786\pi\)
\(774\) 0 0
\(775\) −11.2688 34.6817i −0.404786 1.24580i
\(776\) 0 0
\(777\) 6.24240 + 4.53537i 0.223945 + 0.162706i
\(778\) 0 0
\(779\) −6.92062 + 28.3680i −0.247957 + 1.01639i
\(780\) 0 0
\(781\) −2.12402 1.54319i −0.0760034 0.0552197i
\(782\) 0 0
\(783\) −0.701301 2.15838i −0.0250625 0.0771343i
\(784\) 0 0
\(785\) 35.0511 48.2437i 1.25103 1.72189i
\(786\) 0 0
\(787\) 6.24017 19.2053i 0.222438 0.684594i −0.776104 0.630606i \(-0.782807\pi\)
0.998542 0.0539884i \(-0.0171934\pi\)
\(788\) 0 0
\(789\) −5.44654 + 16.7627i −0.193902 + 0.596769i
\(790\) 0 0
\(791\) −10.9780 + 3.56698i −0.390334 + 0.126827i
\(792\) 0 0
\(793\) 63.9544i 2.27109i
\(794\) 0 0
\(795\) −10.3377 + 7.51080i −0.366641 + 0.266381i
\(796\) 0 0
\(797\) −2.41203 1.75244i −0.0854385 0.0620747