Properties

Label 804.2.s.b.5.18
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 5.18
Character \(\chi\) = 804.5
Dual form 804.2.s.b.161.18

$q$-expansion

\(f(q)\) \(=\) \(q+(1.54953 + 0.773916i) q^{3} +(3.03558 - 0.891328i) q^{5} +(-1.25477 - 1.08727i) q^{7} +(1.80211 + 2.39842i) q^{9} +O(q^{10})\) \(q+(1.54953 + 0.773916i) q^{3} +(3.03558 - 0.891328i) q^{5} +(-1.25477 - 1.08727i) q^{7} +(1.80211 + 2.39842i) q^{9} +(-1.88696 + 0.554063i) q^{11} +(-0.265744 - 0.413506i) q^{13} +(5.39355 + 0.968143i) q^{15} +(2.11532 + 0.304138i) q^{17} +(4.38841 + 5.06450i) q^{19} +(-1.10286 - 2.65584i) q^{21} +(5.82102 - 2.65837i) q^{23} +(4.21404 - 2.70820i) q^{25} +(0.936257 + 5.11111i) q^{27} -9.06475i q^{29} +(-3.35609 + 5.22218i) q^{31} +(-3.35271 - 0.601812i) q^{33} +(-4.77808 - 2.18207i) q^{35} -7.61322 q^{37} +(-0.0917608 - 0.846405i) q^{39} +(0.191141 - 1.32941i) q^{41} +(-3.41972 - 0.491681i) q^{43} +(7.60823 + 5.67433i) q^{45} +(4.53234 - 2.06985i) q^{47} +(-0.603899 - 4.20021i) q^{49} +(3.04239 + 2.10835i) q^{51} +(0.353730 + 2.46024i) q^{53} +(-5.23419 + 3.36381i) q^{55} +(2.88050 + 11.2439i) q^{57} +(-1.69949 + 2.64446i) q^{59} +(2.44051 - 8.31163i) q^{61} +(0.346481 - 4.96884i) q^{63} +(-1.17526 - 1.01837i) q^{65} +(-8.02999 + 1.58723i) q^{67} +(11.0772 + 0.385743i) q^{69} +(-15.3838 + 2.21185i) q^{71} +(5.08429 + 1.49288i) q^{73} +(8.62572 - 0.935135i) q^{75} +(2.97012 + 1.35641i) q^{77} +(-1.14758 - 1.78567i) q^{79} +(-2.50480 + 8.64442i) q^{81} +(2.84309 + 9.68269i) q^{83} +(6.69233 - 0.962212i) q^{85} +(7.01535 - 14.0461i) q^{87} +(-4.82981 - 2.20570i) q^{89} +(-0.116143 + 0.807790i) q^{91} +(-9.24190 + 5.49461i) q^{93} +(17.8355 + 11.4622i) q^{95} +13.2013i q^{97} +(-4.72939 - 3.52724i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 200q - 10q^{9} + O(q^{10}) \) \( 200q - 10q^{9} + 2q^{15} + 6q^{19} - 10q^{21} - 20q^{25} - 44q^{31} - 5q^{33} + 78q^{39} - 22q^{43} - 22q^{45} - 16q^{49} + 36q^{55} + 66q^{57} + 176q^{61} + 132q^{63} + 46q^{67} - 26q^{73} - 165q^{75} - 44q^{79} + 42q^{81} - 66q^{87} - 20q^{91} + 84q^{93} - 55q^{99} + O(q^{100}) \)

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
\(3\) 1.54953 + 0.773916i 0.894624 + 0.446820i
\(4\) 0 0
\(5\) 3.03558 0.891328i 1.35755 0.398614i 0.479655 0.877457i \(-0.340762\pi\)
0.877900 + 0.478843i \(0.158944\pi\)
\(6\) 0 0
\(7\) −1.25477 1.08727i −0.474259 0.410948i 0.384661 0.923058i \(-0.374318\pi\)
−0.858920 + 0.512110i \(0.828864\pi\)
\(8\) 0 0
\(9\) 1.80211 + 2.39842i 0.600703 + 0.799472i
\(10\) 0 0
\(11\) −1.88696 + 0.554063i −0.568941 + 0.167056i −0.553536 0.832825i \(-0.686722\pi\)
−0.0154049 + 0.999881i \(0.504904\pi\)
\(12\) 0 0
\(13\) −0.265744 0.413506i −0.0737042 0.114686i 0.802445 0.596726i \(-0.203532\pi\)
−0.876149 + 0.482040i \(0.839896\pi\)
\(14\) 0 0
\(15\) 5.39355 + 0.968143i 1.39261 + 0.249974i
\(16\) 0 0
\(17\) 2.11532 + 0.304138i 0.513042 + 0.0737642i 0.393973 0.919122i \(-0.371100\pi\)
0.119068 + 0.992886i \(0.462009\pi\)
\(18\) 0 0
\(19\) 4.38841 + 5.06450i 1.00677 + 1.16188i 0.986778 + 0.162076i \(0.0518189\pi\)
0.0199928 + 0.999800i \(0.493636\pi\)
\(20\) 0 0
\(21\) −1.10286 2.65584i −0.240664 0.579552i
\(22\) 0 0
\(23\) 5.82102 2.65837i 1.21377 0.554309i 0.297440 0.954740i \(-0.403867\pi\)
0.916327 + 0.400432i \(0.131140\pi\)
\(24\) 0 0
\(25\) 4.21404 2.70820i 0.842809 0.541640i
\(26\) 0 0
\(27\) 0.936257 + 5.11111i 0.180183 + 0.983633i
\(28\) 0 0
\(29\) 9.06475i 1.68328i −0.540038 0.841641i \(-0.681590\pi\)
0.540038 0.841641i \(-0.318410\pi\)
\(30\) 0 0
\(31\) −3.35609 + 5.22218i −0.602772 + 0.937931i 0.397026 + 0.917808i \(0.370042\pi\)
−0.999797 + 0.0201238i \(0.993594\pi\)
\(32\) 0 0
\(33\) −3.35271 0.601812i −0.583632 0.104762i
\(34\) 0 0
\(35\) −4.77808 2.18207i −0.807642 0.368838i
\(36\) 0 0
\(37\) −7.61322 −1.25161 −0.625803 0.779981i \(-0.715228\pi\)
−0.625803 + 0.779981i \(0.715228\pi\)
\(38\) 0 0
\(39\) −0.0917608 0.846405i −0.0146935 0.135533i
\(40\) 0 0
\(41\) 0.191141 1.32941i 0.0298512 0.207619i −0.969437 0.245340i \(-0.921100\pi\)
0.999288 + 0.0377203i \(0.0120096\pi\)
\(42\) 0 0
\(43\) −3.41972 0.491681i −0.521502 0.0749807i −0.123463 0.992349i \(-0.539400\pi\)
−0.398039 + 0.917369i \(0.630309\pi\)
\(44\) 0 0
\(45\) 7.60823 + 5.67433i 1.13417 + 0.845879i
\(46\) 0 0
\(47\) 4.53234 2.06985i 0.661110 0.301919i −0.0564606 0.998405i \(-0.517982\pi\)
0.717570 + 0.696486i \(0.245254\pi\)
\(48\) 0 0
\(49\) −0.603899 4.20021i −0.0862713 0.600030i
\(50\) 0 0
\(51\) 3.04239 + 2.10835i 0.426020 + 0.295229i
\(52\) 0 0
\(53\) 0.353730 + 2.46024i 0.0485885 + 0.337941i 0.999587 + 0.0287444i \(0.00915089\pi\)
−0.950998 + 0.309196i \(0.899940\pi\)
\(54\) 0 0
\(55\) −5.23419 + 3.36381i −0.705778 + 0.453576i
\(56\) 0 0
\(57\) 2.88050 + 11.2439i 0.381532 + 1.48929i
\(58\) 0 0
\(59\) −1.69949 + 2.64446i −0.221255 + 0.344280i −0.934081 0.357061i \(-0.883779\pi\)
0.712826 + 0.701341i \(0.247415\pi\)
\(60\) 0 0
\(61\) 2.44051 8.31163i 0.312476 1.06419i −0.642197 0.766539i \(-0.721977\pi\)
0.954673 0.297656i \(-0.0962047\pi\)
\(62\) 0 0
\(63\) 0.346481 4.96884i 0.0436524 0.626015i
\(64\) 0 0
\(65\) −1.17526 1.01837i −0.145773 0.126313i
\(66\) 0 0
\(67\) −8.02999 + 1.58723i −0.981019 + 0.193911i
\(68\) 0 0
\(69\) 11.0772 + 0.385743i 1.33354 + 0.0464380i
\(70\) 0 0
\(71\) −15.3838 + 2.21185i −1.82572 + 0.262499i −0.967878 0.251419i \(-0.919103\pi\)
−0.857840 + 0.513917i \(0.828194\pi\)
\(72\) 0 0
\(73\) 5.08429 + 1.49288i 0.595071 + 0.174729i 0.565380 0.824830i \(-0.308729\pi\)
0.0296911 + 0.999559i \(0.490548\pi\)
\(74\) 0 0
\(75\) 8.62572 0.935135i 0.996012 0.107980i
\(76\) 0 0
\(77\) 2.97012 + 1.35641i 0.338477 + 0.154577i
\(78\) 0 0
\(79\) −1.14758 1.78567i −0.129113 0.200904i 0.770678 0.637225i \(-0.219918\pi\)
−0.899791 + 0.436321i \(0.856281\pi\)
\(80\) 0 0
\(81\) −2.50480 + 8.64442i −0.278312 + 0.960491i
\(82\) 0 0
\(83\) 2.84309 + 9.68269i 0.312070 + 1.06281i 0.954930 + 0.296830i \(0.0959294\pi\)
−0.642860 + 0.765984i \(0.722252\pi\)
\(84\) 0 0
\(85\) 6.69233 0.962212i 0.725886 0.104367i
\(86\) 0 0
\(87\) 7.01535 14.0461i 0.752124 1.50590i
\(88\) 0 0
\(89\) −4.82981 2.20570i −0.511959 0.233804i 0.142647 0.989774i \(-0.454438\pi\)
−0.654607 + 0.755970i \(0.727166\pi\)
\(90\) 0 0
\(91\) −0.116143 + 0.807790i −0.0121751 + 0.0846794i
\(92\) 0 0
\(93\) −9.24190 + 5.49461i −0.958341 + 0.569765i
\(94\) 0 0
\(95\) 17.8355 + 11.4622i 1.82989 + 1.17600i
\(96\) 0 0
\(97\) 13.2013i 1.34039i 0.742186 + 0.670194i \(0.233789\pi\)
−0.742186 + 0.670194i \(0.766211\pi\)
\(98\) 0 0
\(99\) −4.72939 3.52724i −0.475321 0.354501i
\(100\) 0 0
\(101\) 7.61191 + 8.78461i 0.757413 + 0.874102i 0.995265 0.0971999i \(-0.0309886\pi\)
−0.237852 + 0.971302i \(0.576443\pi\)
\(102\) 0 0
\(103\) −11.4173 7.33743i −1.12498 0.722978i −0.160471 0.987041i \(-0.551301\pi\)
−0.964506 + 0.264062i \(0.914938\pi\)
\(104\) 0 0
\(105\) −5.71505 7.07903i −0.557732 0.690842i
\(106\) 0 0
\(107\) 0.0498318 0.169712i 0.00481742 0.0164066i −0.957049 0.289926i \(-0.906369\pi\)
0.961867 + 0.273519i \(0.0881876\pi\)
\(108\) 0 0
\(109\) −8.55064 13.3050i −0.819002 1.27439i −0.958763 0.284207i \(-0.908270\pi\)
0.139761 0.990185i \(-0.455367\pi\)
\(110\) 0 0
\(111\) −11.7969 5.89199i −1.11972 0.559243i
\(112\) 0 0
\(113\) 2.48008 + 0.728216i 0.233306 + 0.0685048i 0.396296 0.918123i \(-0.370296\pi\)
−0.162990 + 0.986628i \(0.552114\pi\)
\(114\) 0 0
\(115\) 15.3007 13.2582i 1.42680 1.23633i
\(116\) 0 0
\(117\) 0.512859 1.38255i 0.0474139 0.127817i
\(118\) 0 0
\(119\) −2.32357 2.68154i −0.213001 0.245817i
\(120\) 0 0
\(121\) −6.00014 + 3.85606i −0.545467 + 0.350551i
\(122\) 0 0
\(123\) 1.32503 1.91204i 0.119474 0.172403i
\(124\) 0 0
\(125\) 0.0191479 0.0220978i 0.00171264 0.00197649i
\(126\) 0 0
\(127\) −8.82859 + 10.1887i −0.783411 + 0.904104i −0.997351 0.0727426i \(-0.976825\pi\)
0.213940 + 0.976847i \(0.431370\pi\)
\(128\) 0 0
\(129\) −4.91845 3.40845i −0.433045 0.300097i
\(130\) 0 0
\(131\) 6.01060 2.74495i 0.525149 0.239827i −0.135157 0.990824i \(-0.543154\pi\)
0.660306 + 0.750997i \(0.270427\pi\)
\(132\) 0 0
\(133\) 11.1262i 0.964761i
\(134\) 0 0
\(135\) 7.39776 + 14.6807i 0.636698 + 1.26351i
\(136\) 0 0
\(137\) −4.98287 10.9110i −0.425716 0.932187i −0.994003 0.109357i \(-0.965121\pi\)
0.568287 0.822830i \(-0.307606\pi\)
\(138\) 0 0
\(139\) −1.49570 5.09389i −0.126864 0.432058i 0.871426 0.490528i \(-0.163196\pi\)
−0.998289 + 0.0584699i \(0.981378\pi\)
\(140\) 0 0
\(141\) 8.62490 + 0.300346i 0.726348 + 0.0252937i
\(142\) 0 0
\(143\) 0.730558 + 0.633032i 0.0610923 + 0.0529368i
\(144\) 0 0
\(145\) −8.07966 27.5168i −0.670980 2.28515i
\(146\) 0 0
\(147\) 2.31485 6.97573i 0.190925 0.575349i
\(148\) 0 0
\(149\) 6.69588 5.80202i 0.548548 0.475320i −0.335939 0.941884i \(-0.609054\pi\)
0.884487 + 0.466564i \(0.154508\pi\)
\(150\) 0 0
\(151\) 0.234723 1.63254i 0.0191015 0.132854i −0.978039 0.208421i \(-0.933168\pi\)
0.997141 + 0.0755670i \(0.0240767\pi\)
\(152\) 0 0
\(153\) 3.08260 + 5.62152i 0.249213 + 0.454473i
\(154\) 0 0
\(155\) −5.53302 + 18.8438i −0.444423 + 1.51357i
\(156\) 0 0
\(157\) 3.06444 + 6.71020i 0.244569 + 0.535532i 0.991613 0.129243i \(-0.0412547\pi\)
−0.747044 + 0.664775i \(0.768527\pi\)
\(158\) 0 0
\(159\) −1.35591 + 4.08599i −0.107530 + 0.324040i
\(160\) 0 0
\(161\) −10.1944 2.99335i −0.803432 0.235909i
\(162\) 0 0
\(163\) −18.5314 −1.45149 −0.725745 0.687963i \(-0.758505\pi\)
−0.725745 + 0.687963i \(0.758505\pi\)
\(164\) 0 0
\(165\) −10.7139 + 1.16151i −0.834072 + 0.0904238i
\(166\) 0 0
\(167\) 0.789841 0.684402i 0.0611198 0.0529606i −0.623765 0.781612i \(-0.714398\pi\)
0.684885 + 0.728651i \(0.259852\pi\)
\(168\) 0 0
\(169\) 5.30003 11.6054i 0.407694 0.892726i
\(170\) 0 0
\(171\) −4.23838 + 19.6520i −0.324117 + 1.50283i
\(172\) 0 0
\(173\) −5.09001 + 7.92020i −0.386986 + 0.602162i −0.979023 0.203749i \(-0.934687\pi\)
0.592037 + 0.805911i \(0.298324\pi\)
\(174\) 0 0
\(175\) −8.23219 1.18361i −0.622295 0.0894726i
\(176\) 0 0
\(177\) −4.68002 + 2.78242i −0.351771 + 0.209140i
\(178\) 0 0
\(179\) 1.21859 2.66834i 0.0910818 0.199441i −0.858609 0.512632i \(-0.828671\pi\)
0.949690 + 0.313191i \(0.101398\pi\)
\(180\) 0 0
\(181\) 3.89978 + 8.53932i 0.289868 + 0.634723i 0.997408 0.0719506i \(-0.0229224\pi\)
−0.707540 + 0.706673i \(0.750195\pi\)
\(182\) 0 0
\(183\) 10.2142 10.9904i 0.755052 0.812433i
\(184\) 0 0
\(185\) −23.1106 + 6.78587i −1.69912 + 0.498907i
\(186\) 0 0
\(187\) −4.16005 + 0.598125i −0.304213 + 0.0437392i
\(188\) 0 0
\(189\) 4.38234 7.43123i 0.318769 0.540543i
\(190\) 0 0
\(191\) 0.522401 1.14390i 0.0377996 0.0827696i −0.889790 0.456370i \(-0.849149\pi\)
0.927590 + 0.373600i \(0.121877\pi\)
\(192\) 0 0
\(193\) −2.79049 1.79334i −0.200864 0.129087i 0.436342 0.899781i \(-0.356274\pi\)
−0.637206 + 0.770693i \(0.719910\pi\)
\(194\) 0 0
\(195\) −1.03297 2.48755i −0.0739727 0.178137i
\(196\) 0 0
\(197\) −2.73971 19.0551i −0.195197 1.35762i −0.817989 0.575235i \(-0.804911\pi\)
0.622792 0.782388i \(-0.285998\pi\)
\(198\) 0 0
\(199\) −15.6841 + 18.1004i −1.11181 + 1.28310i −0.156444 + 0.987687i \(0.550003\pi\)
−0.955369 + 0.295414i \(0.904542\pi\)
\(200\) 0 0
\(201\) −13.6711 3.75507i −0.964286 0.264862i
\(202\) 0 0
\(203\) −9.85579 + 11.3742i −0.691741 + 0.798311i
\(204\) 0 0
\(205\) −0.604719 4.20592i −0.0422354 0.293754i
\(206\) 0 0
\(207\) 16.8660 + 9.17056i 1.17227 + 0.637398i
\(208\) 0 0
\(209\) −11.0868 7.12507i −0.766892 0.492851i
\(210\) 0 0
\(211\) 5.24189 11.4781i 0.360867 0.790188i −0.638915 0.769278i \(-0.720616\pi\)
0.999781 0.0209101i \(-0.00665639\pi\)
\(212\) 0 0
\(213\) −25.5495 8.47840i −1.75062 0.580931i
\(214\) 0 0
\(215\) −10.8191 + 1.55555i −0.737856 + 0.106088i
\(216\) 0 0
\(217\) 9.88903 2.90368i 0.671311 0.197115i
\(218\) 0 0
\(219\) 6.72292 + 6.24808i 0.454293 + 0.422206i
\(220\) 0 0
\(221\) −0.436372 0.955522i −0.0293536 0.0642754i
\(222\) 0 0
\(223\) −8.49959 + 18.6115i −0.569175 + 1.24632i 0.378061 + 0.925781i \(0.376591\pi\)
−0.947236 + 0.320538i \(0.896136\pi\)
\(224\) 0 0
\(225\) 14.0896 + 5.22656i 0.939304 + 0.348437i
\(226\) 0 0
\(227\) 0.499215 + 0.0717763i 0.0331341 + 0.00476396i 0.158862 0.987301i \(-0.449218\pi\)
−0.125728 + 0.992065i \(0.540127\pi\)
\(228\) 0 0
\(229\) 9.32943 14.5169i 0.616506 0.959302i −0.382864 0.923805i \(-0.625062\pi\)
0.999370 0.0354972i \(-0.0113015\pi\)
\(230\) 0 0
\(231\) 3.55256 + 4.40042i 0.233741 + 0.289527i
\(232\) 0 0
\(233\) −3.47909 + 7.61814i −0.227923 + 0.499081i −0.988696 0.149937i \(-0.952093\pi\)
0.760773 + 0.649018i \(0.224820\pi\)
\(234\) 0 0
\(235\) 11.9134 10.3230i 0.777144 0.673399i
\(236\) 0 0
\(237\) −0.396257 3.65509i −0.0257397 0.237424i
\(238\) 0 0
\(239\) 22.3180 1.44363 0.721814 0.692087i \(-0.243308\pi\)
0.721814 + 0.692087i \(0.243308\pi\)
\(240\) 0 0
\(241\) 6.56454 + 1.92752i 0.422859 + 0.124163i 0.486237 0.873827i \(-0.338369\pi\)
−0.0633779 + 0.997990i \(0.520187\pi\)
\(242\) 0 0
\(243\) −10.5713 + 11.4563i −0.678151 + 0.734923i
\(244\) 0 0
\(245\) −5.57695 12.2118i −0.356298 0.780185i
\(246\) 0 0
\(247\) 0.928005 3.16050i 0.0590476 0.201098i
\(248\) 0 0
\(249\) −3.08811 + 17.2040i −0.195701 + 1.09026i
\(250\) 0 0
\(251\) −1.72705 + 12.0119i −0.109010 + 0.758183i 0.859845 + 0.510555i \(0.170560\pi\)
−0.968855 + 0.247628i \(0.920349\pi\)
\(252\) 0 0
\(253\) −9.51115 + 8.24146i −0.597961 + 0.518136i
\(254\) 0 0
\(255\) 11.1147 + 3.68832i 0.696028 + 0.230972i
\(256\) 0 0
\(257\) −4.41723 15.0437i −0.275539 0.938400i −0.974715 0.223451i \(-0.928268\pi\)
0.699176 0.714950i \(-0.253550\pi\)
\(258\) 0 0
\(259\) 9.55285 + 8.27759i 0.593585 + 0.514344i
\(260\) 0 0
\(261\) 21.7410 16.3357i 1.34574 1.01115i
\(262\) 0 0
\(263\) −5.74550 19.5674i −0.354282 1.20658i −0.923245 0.384212i \(-0.874473\pi\)
0.568963 0.822363i \(-0.307345\pi\)
\(264\) 0 0
\(265\) 3.26666 + 7.15299i 0.200669 + 0.439405i
\(266\) 0 0
\(267\) −5.77693 7.15568i −0.353543 0.437920i
\(268\) 0 0
\(269\) 13.4572i 0.820497i 0.911974 + 0.410249i \(0.134558\pi\)
−0.911974 + 0.410249i \(0.865442\pi\)
\(270\) 0 0
\(271\) 29.4231 13.4371i 1.78733 0.816245i 0.816168 0.577815i \(-0.196095\pi\)
0.971160 0.238430i \(-0.0766326\pi\)
\(272\) 0 0
\(273\) −0.805128 + 1.16181i −0.0487286 + 0.0703161i
\(274\) 0 0
\(275\) −6.45123 + 7.44512i −0.389024 + 0.448958i
\(276\) 0 0
\(277\) 11.6975 13.4996i 0.702834 0.811114i −0.286298 0.958141i \(-0.592425\pi\)
0.989133 + 0.147026i \(0.0469702\pi\)
\(278\) 0 0
\(279\) −18.5730 + 1.36163i −1.11194 + 0.0815189i
\(280\) 0 0
\(281\) −19.2147 + 12.3486i −1.14626 + 0.736654i −0.968890 0.247491i \(-0.920394\pi\)
−0.177366 + 0.984145i \(0.556758\pi\)
\(282\) 0 0
\(283\) −2.67257 3.08431i −0.158868 0.183343i 0.670735 0.741697i \(-0.265979\pi\)
−0.829603 + 0.558354i \(0.811433\pi\)
\(284\) 0 0
\(285\) 18.7660 + 31.5643i 1.11160 + 1.86971i
\(286\) 0 0
\(287\) −1.68526 + 1.46029i −0.0994779 + 0.0861981i
\(288\) 0 0
\(289\) −11.9293 3.50275i −0.701722 0.206044i
\(290\) 0 0
\(291\) −10.2167 + 20.4558i −0.598913 + 1.19914i
\(292\) 0 0
\(293\) 5.44028 + 8.46524i 0.317825 + 0.494545i 0.963004 0.269486i \(-0.0868539\pi\)
−0.645180 + 0.764031i \(0.723218\pi\)
\(294\) 0 0
\(295\) −2.80187 + 9.54230i −0.163131 + 0.555574i
\(296\) 0 0
\(297\) −4.59856 9.12573i −0.266835 0.529529i
\(298\) 0 0
\(299\) −2.64615 1.70058i −0.153031 0.0983471i
\(300\) 0 0
\(301\) 3.75638 + 4.33509i 0.216514 + 0.249870i
\(302\) 0 0
\(303\) 4.99636 + 19.5030i 0.287034 + 1.12042i
\(304\) 0 0
\(305\) 27.4060i 1.56926i
\(306\) 0 0
\(307\) −11.2516 7.23094i −0.642161 0.412692i 0.178633 0.983916i \(-0.442832\pi\)
−0.820794 + 0.571224i \(0.806469\pi\)
\(308\) 0 0
\(309\) −12.0129 20.2056i −0.683389 1.14946i
\(310\) 0 0
\(311\) 3.74884 26.0738i 0.212577 1.47851i −0.551928 0.833892i \(-0.686108\pi\)
0.764506 0.644617i \(-0.222983\pi\)
\(312\) 0 0
\(313\) 8.46340 + 3.86511i 0.478380 + 0.218469i 0.639986 0.768387i \(-0.278940\pi\)
−0.161606 + 0.986855i \(0.551667\pi\)
\(314\) 0 0
\(315\) −3.37709 15.3922i −0.190278 0.867250i
\(316\) 0 0
\(317\) 29.9478 4.30584i 1.68203 0.241840i 0.765971 0.642875i \(-0.222259\pi\)
0.916063 + 0.401035i \(0.131349\pi\)
\(318\) 0 0
\(319\) 5.02244 + 17.1048i 0.281202 + 0.957688i
\(320\) 0 0
\(321\) 0.208559 0.224408i 0.0116406 0.0125252i
\(322\) 0 0
\(323\) 7.74261 + 12.0477i 0.430811 + 0.670354i
\(324\) 0 0
\(325\) −2.23971 1.02284i −0.124237 0.0567371i
\(326\) 0 0
\(327\) −2.95251 27.2341i −0.163274 1.50605i
\(328\) 0 0
\(329\) −7.93753 2.33067i −0.437610 0.128494i
\(330\) 0 0
\(331\) −24.4599 + 3.51681i −1.34444 + 0.193301i −0.776681 0.629894i \(-0.783098\pi\)
−0.567758 + 0.823195i \(0.692189\pi\)
\(332\) 0 0
\(333\) −13.7198 18.2597i −0.751843 1.00062i
\(334\) 0 0
\(335\) −22.9610 + 11.9755i −1.25449 + 0.654293i
\(336\) 0 0
\(337\) −6.09098 5.27786i −0.331797 0.287503i 0.472990 0.881068i \(-0.343175\pi\)
−0.804786 + 0.593565i \(0.797720\pi\)
\(338\) 0 0
\(339\) 3.27939 + 3.04777i 0.178112 + 0.165532i
\(340\) 0 0
\(341\) 3.43941 11.7135i 0.186254 0.634324i
\(342\) 0 0
\(343\) −10.0924 + 15.7040i −0.544937 + 0.847938i
\(344\) 0 0
\(345\) 33.9697 8.70248i 1.82887 0.468526i
\(346\) 0 0
\(347\) 18.3774 11.8104i 0.986551 0.634018i 0.0553285 0.998468i \(-0.482379\pi\)
0.931223 + 0.364450i \(0.118743\pi\)
\(348\) 0 0
\(349\) 3.30080 + 22.9575i 0.176688 + 1.22889i 0.864362 + 0.502870i \(0.167723\pi\)
−0.687674 + 0.726019i \(0.741368\pi\)
\(350\) 0 0
\(351\) 1.86467 1.74539i 0.0995286 0.0931623i
\(352\) 0 0
\(353\) 4.36249 + 30.3418i 0.232192 + 1.61493i 0.688588 + 0.725152i \(0.258231\pi\)
−0.456397 + 0.889776i \(0.650860\pi\)
\(354\) 0 0
\(355\) −44.7273 + 20.4263i −2.37388 + 1.08411i
\(356\) 0 0
\(357\) −1.52516 5.95339i −0.0807202 0.315087i
\(358\) 0 0
\(359\) 32.0809 + 4.61254i 1.69317 + 0.243441i 0.920324 0.391156i \(-0.127925\pi\)
0.772843 + 0.634597i \(0.218834\pi\)
\(360\) 0 0
\(361\) −3.68700 + 25.6436i −0.194052 + 1.34966i
\(362\) 0 0
\(363\) −12.2817 + 1.33149i −0.644621 + 0.0698849i
\(364\) 0 0
\(365\) 16.7644 0.877491
\(366\) 0 0
\(367\) 20.5231 + 9.37259i 1.07130 + 0.489245i 0.871401 0.490571i \(-0.163212\pi\)
0.199897 + 0.979817i \(0.435939\pi\)
\(368\) 0 0
\(369\) 3.53294 1.93731i 0.183918 0.100852i
\(370\) 0 0
\(371\) 2.23109 3.47164i 0.115832 0.180239i
\(372\) 0 0
\(373\) 27.4560i 1.42162i −0.703386 0.710808i \(-0.748330\pi\)
0.703386 0.710808i \(-0.251670\pi\)
\(374\) 0 0
\(375\) 0.0467721 0.0194225i 0.00241530 0.00100297i
\(376\) 0 0
\(377\) −3.74833 + 2.40890i −0.193049 + 0.124065i
\(378\) 0 0
\(379\) 24.4741 11.1769i 1.25715 0.574121i 0.328298 0.944574i \(-0.393525\pi\)
0.928851 + 0.370454i \(0.120798\pi\)
\(380\) 0 0
\(381\) −21.5654 + 8.95521i −1.10483 + 0.458789i
\(382\) 0 0
\(383\) 1.40639 + 1.62306i 0.0718631 + 0.0829344i 0.790543 0.612407i \(-0.209799\pi\)
−0.718680 + 0.695341i \(0.755253\pi\)
\(384\) 0 0
\(385\) 10.2251 + 1.47014i 0.521117 + 0.0749254i
\(386\) 0 0
\(387\) −4.98345 9.08797i −0.253323 0.461967i
\(388\) 0 0
\(389\) −13.8927 21.6175i −0.704388 1.09605i −0.990455 0.137839i \(-0.955984\pi\)
0.286066 0.958210i \(-0.407652\pi\)
\(390\) 0 0
\(391\) 13.1219 3.85293i 0.663601 0.194851i
\(392\) 0 0
\(393\) 11.4380 + 0.398306i 0.576970 + 0.0200919i
\(394\) 0 0
\(395\) −5.07520 4.39769i −0.255361 0.221272i
\(396\) 0 0
\(397\) −18.8203 + 5.52612i −0.944561 + 0.277348i −0.717521 0.696537i \(-0.754723\pi\)
−0.227041 + 0.973885i \(0.572905\pi\)
\(398\) 0 0
\(399\) 8.61071 17.2404i 0.431075 0.863098i
\(400\) 0 0
\(401\) 35.2908 1.76234 0.881169 0.472801i \(-0.156757\pi\)
0.881169 + 0.472801i \(0.156757\pi\)
\(402\) 0 0
\(403\) 3.05126 0.151994
\(404\) 0 0
\(405\) 0.101469 + 28.4735i 0.00504202 + 1.41486i
\(406\) 0 0
\(407\) 14.3659 4.21820i 0.712089 0.209088i
\(408\) 0 0
\(409\) 17.4769 + 15.1438i 0.864178 + 0.748815i 0.969362 0.245638i \(-0.0789975\pi\)
−0.105183 + 0.994453i \(0.533543\pi\)
\(410\) 0 0
\(411\) 0.723040 20.7632i 0.0356649 1.02418i
\(412\) 0 0
\(413\) 5.00771 1.47040i 0.246413 0.0723535i
\(414\) 0 0
\(415\) 17.2609 + 26.8585i 0.847305 + 1.31843i
\(416\) 0 0
\(417\) 1.62460 9.05070i 0.0795570 0.443215i
\(418\) 0 0
\(419\) 3.08530 + 0.443600i 0.150727 + 0.0216713i 0.217265 0.976113i \(-0.430286\pi\)
−0.0665382 + 0.997784i \(0.521195\pi\)
\(420\) 0 0
\(421\) 5.87434 + 6.77935i 0.286298 + 0.330406i 0.880621 0.473821i \(-0.157126\pi\)
−0.594323 + 0.804226i \(0.702580\pi\)
\(422\) 0 0
\(423\) 13.1321 + 7.14034i 0.638506 + 0.347175i
\(424\) 0 0
\(425\) 9.73773 4.44707i 0.472350 0.215715i
\(426\) 0 0
\(427\) −12.0992 + 7.77571i −0.585523 + 0.376293i
\(428\) 0 0
\(429\) 0.642111 + 1.54629i 0.0310014 + 0.0746558i
\(430\) 0 0
\(431\) 9.40488i 0.453017i 0.974009 + 0.226508i \(0.0727311\pi\)
−0.974009 + 0.226508i \(0.927269\pi\)
\(432\) 0 0
\(433\) 8.59786 13.3785i 0.413187 0.642931i −0.570817 0.821077i \(-0.693374\pi\)
0.984004 + 0.178146i \(0.0570100\pi\)
\(434\) 0 0
\(435\) 8.77597 48.8912i 0.420776 2.34415i
\(436\) 0 0
\(437\) 39.0084 + 17.8145i 1.86602 + 0.852184i
\(438\) 0 0
\(439\) 33.0069 1.57533 0.787667 0.616101i \(-0.211289\pi\)
0.787667 + 0.616101i \(0.211289\pi\)
\(440\) 0 0
\(441\) 8.98556 9.01764i 0.427884 0.429411i
\(442\) 0 0
\(443\) 4.12806 28.7113i 0.196130 1.36411i −0.619252 0.785192i \(-0.712564\pi\)
0.815382 0.578923i \(-0.196527\pi\)
\(444\) 0 0
\(445\) −16.6273 2.39065i −0.788210 0.113328i
\(446\) 0 0
\(447\) 14.8658 3.80837i 0.703127 0.180130i
\(448\) 0 0
\(449\) 5.06841 2.31467i 0.239193 0.109236i −0.292212 0.956353i \(-0.594391\pi\)
0.531405 + 0.847118i \(0.321664\pi\)
\(450\) 0 0
\(451\) 0.375902 + 2.61446i 0.0177005 + 0.123110i
\(452\) 0 0
\(453\) 1.62716 2.34802i 0.0764505 0.110319i
\(454\) 0 0
\(455\) 0.367445 + 2.55564i 0.0172261 + 0.119810i
\(456\) 0 0
\(457\) 27.5754 17.7216i 1.28992 0.828982i 0.297844 0.954615i \(-0.403732\pi\)
0.992077 + 0.125633i \(0.0400961\pi\)
\(458\) 0 0
\(459\) 0.426007 + 11.0964i 0.0198843 + 0.517936i
\(460\) 0 0
\(461\) −10.4093 + 16.1972i −0.484810 + 0.754379i −0.994360 0.106062i \(-0.966176\pi\)
0.509549 + 0.860441i \(0.329812\pi\)
\(462\) 0 0
\(463\) 3.57771 12.1846i 0.166270 0.566265i −0.833632 0.552320i \(-0.813743\pi\)
0.999903 0.0139452i \(-0.00443904\pi\)
\(464\) 0 0
\(465\) −23.1571 + 24.9169i −1.07388 + 1.15550i
\(466\) 0 0
\(467\) 9.15972 + 7.93694i 0.423861 + 0.367278i 0.840516 0.541787i \(-0.182252\pi\)
−0.416654 + 0.909065i \(0.636797\pi\)
\(468\) 0 0
\(469\) 11.8015 + 6.73912i 0.544944 + 0.311184i
\(470\) 0 0
\(471\) −0.444666 + 12.7693i −0.0204891 + 0.588378i
\(472\) 0 0
\(473\) 6.72530 0.966953i 0.309230 0.0444605i
\(474\) 0 0
\(475\) 32.2086 + 9.45731i 1.47783 + 0.433931i
\(476\) 0 0
\(477\) −5.26323 + 5.28202i −0.240987 + 0.241847i
\(478\) 0 0
\(479\) 10.5795 + 4.83151i 0.483391 + 0.220757i 0.642178 0.766556i \(-0.278031\pi\)
−0.158787 + 0.987313i \(0.550758\pi\)
\(480\) 0 0
\(481\) 2.02317 + 3.14811i 0.0922485 + 0.143541i
\(482\) 0 0
\(483\) −13.4800 12.5279i −0.613360 0.570039i
\(484\) 0 0
\(485\) 11.7667 + 40.0736i 0.534298 + 1.81965i
\(486\) 0 0
\(487\) 19.4795 2.80073i 0.882702 0.126913i 0.313967 0.949434i \(-0.398342\pi\)
0.568735 + 0.822521i \(0.307433\pi\)
\(488\) 0 0
\(489\) −28.7150 14.3417i −1.29854 0.648556i
\(490\) 0 0
\(491\) −13.2953 6.07174i −0.600006 0.274014i 0.0921686 0.995743i \(-0.470620\pi\)
−0.692175 + 0.721730i \(0.743347\pi\)
\(492\) 0 0
\(493\) 2.75693 19.1749i 0.124166 0.863593i
\(494\) 0 0
\(495\) −17.5004 6.49181i −0.786584 0.291785i
\(496\) 0 0
\(497\) 21.7080 + 13.9509i 0.973737 + 0.625783i
\(498\) 0 0
\(499\) 28.0049i 1.25367i 0.779152 + 0.626835i \(0.215650\pi\)
−0.779152 + 0.626835i \(0.784350\pi\)
\(500\) 0 0
\(501\) 1.75355 0.449233i 0.0783431 0.0200702i
\(502\) 0 0
\(503\) −19.7335 22.7737i −0.879874 1.01543i −0.999744 0.0226388i \(-0.992793\pi\)
0.119870 0.992790i \(-0.461752\pi\)
\(504\) 0 0
\(505\) 30.9366 + 19.8817i 1.37666 + 0.884725i
\(506\) 0 0
\(507\) 17.1942 13.8812i 0.763621 0.616488i
\(508\) 0 0
\(509\) −9.53776 + 32.4826i −0.422754 + 1.43977i 0.422969 + 0.906144i \(0.360988\pi\)
−0.845723 + 0.533622i \(0.820830\pi\)
\(510\) 0 0
\(511\) −4.75646 7.40120i −0.210414 0.327410i
\(512\) 0 0
\(513\) −21.7765 + 27.1713i −0.961457 + 1.19964i
\(514\) 0 0
\(515\) −41.1981 12.0969i −1.81541 0.533051i
\(516\) 0 0
\(517\) −7.40553 + 6.41693i −0.325695 + 0.282216i
\(518\) 0 0
\(519\) −14.0167 + 8.33339i −0.615265 + 0.365795i
\(520\) 0 0
\(521\) −1.50801 1.74034i −0.0660672 0.0762457i 0.721754 0.692150i \(-0.243336\pi\)
−0.787821 + 0.615904i \(0.788791\pi\)
\(522\) 0 0
\(523\) −17.2890 + 11.1110i −0.755994 + 0.485848i −0.860988 0.508625i \(-0.830154\pi\)
0.104994 + 0.994473i \(0.466518\pi\)
\(524\) 0 0
\(525\) −11.8400 8.20507i −0.516742 0.358099i
\(526\) 0 0
\(527\) −8.68749 + 10.0259i −0.378433 + 0.436735i
\(528\) 0 0
\(529\) 11.7555 13.5666i 0.511111 0.589853i
\(530\) 0 0
\(531\) −9.40520 + 0.689519i −0.408151 + 0.0299226i
\(532\) 0 0
\(533\) −0.600515 + 0.274246i −0.0260112 + 0.0118789i
\(534\) 0 0
\(535\) 0.559590i 0.0241932i
\(536\) 0 0
\(537\) 3.95332 3.19160i 0.170598 0.137728i
\(538\) 0 0
\(539\) 3.46671 + 7.59105i 0.149322 + 0.326969i
\(540\) 0 0
\(541\) 4.57439 + 15.5790i 0.196669 + 0.669792i 0.997485 + 0.0708815i \(0.0225812\pi\)
−0.800816 + 0.598910i \(0.795601\pi\)
\(542\) 0 0
\(543\) −0.565877 + 16.2501i −0.0242841 + 0.697357i
\(544\) 0 0
\(545\) −37.8153 32.7672i −1.61983 1.40359i
\(546\) 0 0
\(547\) −0.529705 1.80401i −0.0226485 0.0771338i 0.947393 0.320072i \(-0.103707\pi\)
−0.970042 + 0.242938i \(0.921889\pi\)
\(548\) 0 0
\(549\) 24.3328 9.12509i 1.03850 0.389449i
\(550\) 0 0
\(551\) 45.9084 39.7799i 1.95576 1.69468i
\(552\) 0 0
\(553\) −0.501547 + 3.48834i −0.0213280 + 0.148339i
\(554\) 0 0
\(555\) −41.0623 7.37069i −1.74300 0.312868i
\(556\) 0 0
\(557\) −6.93447 + 23.6166i −0.293823 + 1.00067i 0.671802 + 0.740731i \(0.265521\pi\)
−0.965625 + 0.259939i \(0.916298\pi\)
\(558\) 0 0
\(559\) 0.705457 + 1.54473i 0.0298376 + 0.0653353i
\(560\) 0 0
\(561\) −6.90904 2.29271i −0.291700 0.0967985i
\(562\) 0 0
\(563\) −33.1018 9.71955i −1.39507 0.409630i −0.504083 0.863655i \(-0.668170\pi\)
−0.890989 + 0.454025i \(0.849988\pi\)
\(564\) 0 0
\(565\) 8.17756 0.344033
\(566\) 0 0
\(567\) 12.5417 8.12338i 0.526703 0.341150i
\(568\) 0 0
\(569\) −24.9932 + 21.6567i −1.04777 + 0.907897i −0.995873 0.0907554i \(-0.971072\pi\)
−0.0518959 + 0.998653i \(0.516526\pi\)
\(570\) 0 0
\(571\) −14.8373 + 32.4892i −0.620922 + 1.35963i 0.293925 + 0.955828i \(0.405038\pi\)
−0.914847 + 0.403800i \(0.867689\pi\)
\(572\) 0 0
\(573\) 1.69476 1.36821i 0.0707995 0.0571580i
\(574\) 0 0
\(575\) 17.3306 26.9670i 0.722737 1.12460i
\(576\) 0 0
\(577\) 9.17105 + 1.31860i 0.381796 + 0.0548940i 0.330541 0.943792i \(-0.392769\pi\)
0.0512549 + 0.998686i \(0.483678\pi\)
\(578\) 0 0
\(579\) −2.93607 4.93845i −0.122019 0.205235i
\(580\) 0 0
\(581\) 6.96022 15.2408i 0.288759 0.632294i
\(582\) 0 0
\(583\) −2.03060 4.44640i −0.0840991 0.184151i
\(584\) 0 0
\(585\) 0.324525 4.65397i 0.0134174 0.192418i
\(586\) 0 0
\(587\) 16.8520 4.94820i 0.695557 0.204234i 0.0852039 0.996364i \(-0.472846\pi\)
0.610353 + 0.792130i \(0.291028\pi\)
\(588\) 0 0
\(589\) −41.1756 + 5.92016i −1.69661 + 0.243936i
\(590\) 0 0
\(591\) 10.5018 31.6469i 0.431986 1.30178i
\(592\) 0 0
\(593\) −1.40647 + 3.07974i −0.0577569 + 0.126470i −0.936310 0.351175i \(-0.885782\pi\)
0.878553 + 0.477645i \(0.158509\pi\)
\(594\) 0 0
\(595\) −9.44353 6.06899i −0.387147 0.248804i
\(596\) 0 0
\(597\) −38.3111 + 15.9090i −1.56797 + 0.651112i
\(598\) 0 0
\(599\) −1.19705 8.32568i −0.0489102 0.340178i −0.999553 0.0298910i \(-0.990484\pi\)
0.950643 0.310287i \(-0.100425\pi\)
\(600\) 0 0
\(601\) 6.82435 7.87571i 0.278371 0.321257i −0.599297 0.800527i \(-0.704553\pi\)
0.877668 + 0.479270i \(0.159098\pi\)
\(602\) 0 0
\(603\) −18.2778 16.3989i −0.744328 0.667815i
\(604\) 0 0
\(605\) −14.7769 + 17.0535i −0.600768 + 0.693323i
\(606\) 0 0
\(607\) 3.16796 + 22.0337i 0.128584 + 0.894319i 0.947352 + 0.320194i \(0.103748\pi\)
−0.818768 + 0.574124i \(0.805343\pi\)
\(608\) 0 0
\(609\) −24.0745 + 9.99714i −0.975549 + 0.405104i
\(610\) 0 0
\(611\) −2.06034 1.32410i −0.0833523 0.0535673i
\(612\) 0 0
\(613\) −4.49055 + 9.83293i −0.181372 + 0.397148i −0.978379 0.206822i \(-0.933688\pi\)
0.797007 + 0.603970i \(0.206415\pi\)
\(614\) 0 0
\(615\) 2.31799 6.98521i 0.0934704 0.281671i
\(616\) 0 0
\(617\) −26.6415 + 3.83047i −1.07255 + 0.154209i −0.655891 0.754856i \(-0.727707\pi\)
−0.416655 + 0.909065i \(0.636798\pi\)
\(618\) 0 0
\(619\) 10.5222 3.08959i 0.422922 0.124181i −0.0633442 0.997992i \(-0.520177\pi\)
0.486266 + 0.873811i \(0.338358\pi\)
\(620\) 0 0
\(621\) 19.0372 + 27.2629i 0.763936 + 1.09402i
\(622\) 0 0
\(623\) 3.66213 + 8.01894i 0.146720 + 0.321272i
\(624\) 0 0
\(625\) −10.3661 + 22.6987i −0.414646 + 0.907948i
\(626\) 0 0
\(627\) −11.6652 19.6208i −0.465864 0.783579i
\(628\) 0 0
\(629\) −16.1044 2.31547i −0.642126 0.0923237i
\(630\) 0 0
\(631\) 3.61806 5.62981i 0.144033 0.224119i −0.761740 0.647882i \(-0.775655\pi\)
0.905773 + 0.423763i \(0.139291\pi\)
\(632\) 0 0
\(633\) 17.0056 13.7290i 0.675912 0.545678i
\(634\) 0 0
\(635\) −17.7184 + 38.7979i −0.703134 + 1.53965i
\(636\) 0 0
\(637\) −1.57633 + 1.36590i −0.0624564 + 0.0541188i
\(638\) 0 0
\(639\) −33.0282 32.9107i −1.30658 1.30193i
\(640\) 0 0
\(641\) 38.4911 1.52031 0.760153 0.649744i \(-0.225124\pi\)
0.760153 + 0.649744i \(0.225124\pi\)
\(642\) 0 0
\(643\) −17.8153 5.23103i −0.702565 0.206292i −0.0891106 0.996022i \(-0.528402\pi\)
−0.613455 + 0.789730i \(0.710221\pi\)
\(644\) 0 0
\(645\) −17.9684 5.96268i −0.707505 0.234780i
\(646\) 0 0
\(647\) −6.81847 14.9304i −0.268062 0.586973i 0.726955 0.686685i \(-0.240935\pi\)
−0.995016 + 0.0997123i \(0.968208\pi\)
\(648\) 0 0
\(649\) 1.74168 5.93163i 0.0683671 0.232837i
\(650\) 0 0
\(651\) 17.5706 + 3.15392i 0.688645 + 0.123612i
\(652\) 0 0
\(653\) −2.92846 + 20.3679i −0.114599 + 0.797056i 0.848748 + 0.528798i \(0.177357\pi\)
−0.963347 + 0.268258i \(0.913552\pi\)
\(654\) 0 0
\(655\) 15.7990 13.6899i 0.617320 0.534911i
\(656\) 0 0
\(657\) 5.58189 + 14.8846i 0.217770 + 0.580703i
\(658\) 0 0
\(659\) −7.65218 26.0609i −0.298087 1.01519i −0.963276 0.268515i \(-0.913467\pi\)
0.665189 0.746675i \(-0.268351\pi\)
\(660\) 0 0
\(661\) −0.502433 0.435361i −0.0195424 0.0169336i 0.645035 0.764153i \(-0.276843\pi\)
−0.664577 + 0.747220i \(0.731388\pi\)
\(662\) 0 0
\(663\) 0.0633198 1.81833i 0.00245914 0.0706181i
\(664\) 0 0
\(665\) −9.91706 33.7744i −0.384567 1.30972i
\(666\) 0 0
\(667\) −24.0975 52.7661i −0.933057 2.04311i
\(668\) 0 0
\(669\) −27.5741 + 22.2612i −1.06608 + 0.860667i
\(670\) 0 0
\(671\) 17.0359i 0.657665i
\(672\) 0 0
\(673\) −25.8441 + 11.8026i −0.996218 + 0.454958i −0.845705 0.533650i \(-0.820820\pi\)
−0.150513 + 0.988608i \(0.548093\pi\)
\(674\) 0 0
\(675\) 17.7873 + 19.0029i 0.684635 + 0.731420i
\(676\) 0 0
\(677\) −16.5731 + 19.1264i −0.636956 + 0.735086i −0.978834 0.204658i \(-0.934392\pi\)
0.341878 + 0.939744i \(0.388937\pi\)
\(678\) 0 0
\(679\) 14.3533 16.5646i 0.550830 0.635691i
\(680\) 0 0
\(681\) 0.718002 + 0.497570i 0.0275139 + 0.0190669i
\(682\) 0 0
\(683\) −8.34714 + 5.36438i −0.319395 + 0.205262i −0.690507 0.723325i \(-0.742613\pi\)
0.371113 + 0.928588i \(0.378976\pi\)
\(684\) 0 0
\(685\) −24.8512 28.6798i −0.949515 1.09580i
\(686\) 0 0
\(687\) 25.6911 15.2742i 0.980177 0.582747i
\(688\) 0 0
\(689\) 0.923324 0.800065i 0.0351758 0.0304800i
\(690\) 0 0
\(691\) 34.4370 + 10.1116i 1.31005 + 0.384664i 0.860891 0.508789i \(-0.169907\pi\)
0.449156 + 0.893454i \(0.351725\pi\)
\(692\) 0 0
\(693\) 2.09925 + 9.56799i 0.0797439 + 0.363458i
\(694\) 0 0
\(695\) −9.08065 14.1298i −0.344449 0.535973i
\(696\) 0 0
\(697\) 0.808649 2.75401i 0.0306298 0.104315i
\(698\) 0 0
\(699\) −11.2868 + 9.11204i −0.426904 + 0.344649i
\(700\) 0 0
\(701\) −16.4770 10.5891i −0.622329 0.399946i 0.191134 0.981564i \(-0.438784\pi\)
−0.813462 + 0.581618i \(0.802420\pi\)
\(702\) 0 0
\(703\) −33.4099 38.5571i −1.26008 1.45421i
\(704\) 0 0
\(705\) 26.4493 6.77589i 0.996139 0.255195i
\(706\) 0 0
\(707\) 19.2989i 0.725808i
\(708\) 0 0
\(709\) −1.83525 1.17944i −0.0689242 0.0442949i 0.505725 0.862695i \(-0.331225\pi\)
−0.574649 + 0.818400i \(0.694861\pi\)
\(710\) 0 0
\(711\) 2.21472 5.97036i 0.0830584 0.223906i
\(712\) 0 0
\(713\) −5.65338 + 39.3202i −0.211721 + 1.47255i
\(714\) 0 0
\(715\) 2.78191 + 1.27046i 0.104037 + 0.0475123i
\(716\) 0 0
\(717\) 34.5824 + 17.2722i 1.29150 + 0.645043i
\(718\) 0 0
\(719\) 38.6622 5.55878i 1.44186 0.207308i 0.623412 0.781893i \(-0.285746\pi\)
0.818444 + 0.574586i \(0.194837\pi\)
\(720\) 0 0
\(721\) 6.34832 + 21.6204i 0.236424 + 0.805186i
\(722\) 0 0
\(723\) 8.68023 + 8.06716i 0.322821 + 0.300021i
\(724\) 0 0
\(725\) −24.5492 38.1992i −0.911733 1.41868i
\(726\) 0 0
\(727\) 32.1464 + 14.6808i 1.19224 + 0.544480i 0.909898 0.414833i \(-0.136160\pi\)
0.282346 + 0.959313i \(0.408887\pi\)
\(728\) 0 0
\(729\) −25.2468 + 9.57062i −0.935068 + 0.354468i
\(730\) 0 0
\(731\) −7.08427 2.08013i −0.262021 0.0769364i
\(732\) 0 0
\(733\) 38.3382 5.51219i 1.41605 0.203598i 0.608575 0.793496i \(-0.291742\pi\)
0.807477 + 0.589899i \(0.200832\pi\)
\(734\) 0 0
\(735\) 0.809244 23.2387i 0.0298494 0.857173i
\(736\) 0 0
\(737\) 14.2729 7.44416i 0.525748 0.274209i
\(738\) 0 0
\(739\) −29.6209 25.6666i −1.08962 0.944162i −0.0909584 0.995855i \(-0.528993\pi\)
−0.998663 + 0.0516923i \(0.983538\pi\)
\(740\) 0 0
\(741\) 3.88393 4.17910i 0.142680 0.153523i
\(742\) 0 0
\(743\) −1.52119 + 5.18069i −0.0558070 + 0.190061i −0.982679 0.185317i \(-0.940669\pi\)
0.926872 + 0.375378i \(0.122487\pi\)
\(744\) 0 0
\(745\) 15.1544 23.5807i 0.555215 0.863931i
\(746\) 0 0
\(747\) −18.0996 + 24.2682i −0.662228 + 0.887927i
\(748\) 0 0
\(749\) −0.247049 + 0.158769i −0.00902698 + 0.00580129i
\(750\) 0 0
\(751\) 1.94020 + 13.4944i 0.0707988 + 0.492416i 0.994111 + 0.108366i \(0.0345619\pi\)
−0.923312 + 0.384050i \(0.874529\pi\)
\(752\) 0 0
\(753\) −11.9723 + 17.2762i −0.436295 + 0.629580i
\(754\) 0 0
\(755\) −0.742604 5.16492i −0.0270261 0.187971i
\(756\) 0 0
\(757\) −25.7166 + 11.7444i −0.934685 + 0.426857i −0.823739 0.566970i \(-0.808116\pi\)
−0.110947 + 0.993826i \(0.535388\pi\)
\(758\) 0 0
\(759\) −21.1160 + 5.40959i −0.766464 + 0.196356i
\(760\) 0 0
\(761\) −23.0095 3.30826i −0.834093 0.119924i −0.287980 0.957636i \(-0.592984\pi\)
−0.546113 + 0.837712i \(0.683893\pi\)
\(762\) 0 0
\(763\) −3.73703 + 25.9916i −0.135290 + 0.940959i
\(764\) 0 0
\(765\) 14.3681 + 14.3170i 0.519480 + 0.517632i
\(766\) 0 0
\(767\) 1.54513 0.0557915
\(768\) 0 0
\(769\) 27.0155 + 12.3376i 0.974203 + 0.444904i 0.837936 0.545769i \(-0.183762\pi\)
0.136267 + 0.990672i \(0.456490\pi\)
\(770\) 0 0
\(771\) 4.79791 26.7293i 0.172792 0.962632i
\(772\) 0 0
\(773\) −20.4015 + 31.7453i −0.733791 + 1.14180i 0.250988 + 0.967990i \(0.419244\pi\)
−0.984779 + 0.173811i \(0.944392\pi\)
\(774\) 0 0
\(775\) 31.0955i 1.11698i
\(776\) 0 0