Properties

Label 144.3.o.a.79.4
Level $144$
Weight $3$
Character 144.79
Analytic conductor $3.924$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.92371580679\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.856615824.2
Defining polynomial: \(x^{8} + 11 x^{6} + 36 x^{4} + 32 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.4
Root \(-2.33086i\) of defining polynomial
Character \(\chi\) \(=\) 144.79
Dual form 144.3.o.a.31.4

$q$-expansion

\(f(q)\) \(=\) \(q+(2.89248 - 0.795973i) q^{3} +(0.355304 + 0.615405i) q^{5} +(2.70480 + 1.56162i) q^{7} +(7.73285 - 4.60467i) q^{9} +O(q^{10})\) \(q+(2.89248 - 0.795973i) q^{3} +(0.355304 + 0.615405i) q^{5} +(2.70480 + 1.56162i) q^{7} +(7.73285 - 4.60467i) q^{9} +(14.3822 + 8.30359i) q^{11} +(-9.17743 - 15.8958i) q^{13} +(1.51756 + 1.49723i) q^{15} -9.69321 q^{17} +8.20686i q^{19} +(9.06659 + 2.36400i) q^{21} +(1.94815 - 1.12477i) q^{23} +(12.2475 - 21.2133i) q^{25} +(18.7019 - 19.4740i) q^{27} +(-20.8217 + 36.0642i) q^{29} +(-21.6298 + 12.4879i) q^{31} +(48.2097 + 12.5701i) q^{33} +2.21940i q^{35} -40.3888 q^{37} +(-39.1981 - 38.6732i) q^{39} +(25.6944 + 44.5040i) q^{41} +(-56.6621 - 32.7139i) q^{43} +(5.58126 + 3.12278i) q^{45} +(29.2894 + 16.9102i) q^{47} +(-19.6227 - 33.9875i) q^{49} +(-28.0374 + 7.71554i) q^{51} -90.6691 q^{53} +11.8012i q^{55} +(6.53244 + 23.7382i) q^{57} +(-66.2243 + 38.2346i) q^{59} +(1.35822 - 2.35250i) q^{61} +(28.1066 - 0.378955i) q^{63} +(6.52157 - 11.2957i) q^{65} +(-34.5422 + 19.9429i) q^{67} +(4.73970 - 4.80403i) q^{69} -102.923i q^{71} +38.1741 q^{73} +(18.5404 - 71.1078i) q^{75} +(25.9341 + 44.9192i) q^{77} +(94.4994 + 54.5593i) q^{79} +(38.5940 - 71.2145i) q^{81} +(113.503 + 65.5311i) q^{83} +(-3.44404 - 5.96526i) q^{85} +(-31.5201 + 120.888i) q^{87} +38.0903 q^{89} -57.3266i q^{91} +(-52.6235 + 53.3378i) q^{93} +(-5.05055 + 2.91593i) q^{95} +(-12.1961 + 21.1243i) q^{97} +(149.451 - 2.01501i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 3q^{3} + 3q^{5} + 3q^{7} - 3q^{9} + O(q^{10}) \) \( 8q - 3q^{3} + 3q^{5} + 3q^{7} - 3q^{9} + 18q^{11} + 5q^{13} - 21q^{15} + 6q^{17} - 33q^{21} - 81q^{23} - 23q^{25} + 108q^{27} + 69q^{29} + 45q^{31} + 72q^{33} - 20q^{37} - 141q^{39} + 54q^{41} - 117q^{45} + 207q^{47} + 41q^{49} - 141q^{51} - 252q^{53} - 273q^{57} - 306q^{59} + 7q^{61} + 441q^{63} + 93q^{65} + 12q^{67} + 189q^{69} + 74q^{73} - 387q^{75} + 207q^{77} + 33q^{79} + 117q^{81} + 549q^{83} - 30q^{85} - 87q^{87} - 168q^{89} - 27q^{93} - 684q^{95} - 10q^{97} + 585q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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
\(3\) 2.89248 0.795973i 0.964159 0.265324i
\(4\) 0 0
\(5\) 0.355304 + 0.615405i 0.0710609 + 0.123081i 0.899367 0.437195i \(-0.144028\pi\)
−0.828306 + 0.560277i \(0.810695\pi\)
\(6\) 0 0
\(7\) 2.70480 + 1.56162i 0.386401 + 0.223088i 0.680599 0.732656i \(-0.261719\pi\)
−0.294199 + 0.955744i \(0.595053\pi\)
\(8\) 0 0
\(9\) 7.73285 4.60467i 0.859206 0.511630i
\(10\) 0 0
\(11\) 14.3822 + 8.30359i 1.30748 + 0.754872i 0.981674 0.190566i \(-0.0610325\pi\)
0.325802 + 0.945438i \(0.394366\pi\)
\(12\) 0 0
\(13\) −9.17743 15.8958i −0.705956 1.22275i −0.966345 0.257248i \(-0.917184\pi\)
0.260389 0.965504i \(-0.416149\pi\)
\(14\) 0 0
\(15\) 1.51756 + 1.49723i 0.101170 + 0.0998156i
\(16\) 0 0
\(17\) −9.69321 −0.570189 −0.285095 0.958499i \(-0.592025\pi\)
−0.285095 + 0.958499i \(0.592025\pi\)
\(18\) 0 0
\(19\) 8.20686i 0.431940i 0.976400 + 0.215970i \(0.0692913\pi\)
−0.976400 + 0.215970i \(0.930709\pi\)
\(20\) 0 0
\(21\) 9.06659 + 2.36400i 0.431742 + 0.112571i
\(22\) 0 0
\(23\) 1.94815 1.12477i 0.0847022 0.0489028i −0.457051 0.889441i \(-0.651094\pi\)
0.541753 + 0.840538i \(0.317761\pi\)
\(24\) 0 0
\(25\) 12.2475 21.2133i 0.489901 0.848533i
\(26\) 0 0
\(27\) 18.7019 19.4740i 0.692663 0.721261i
\(28\) 0 0
\(29\) −20.8217 + 36.0642i −0.717989 + 1.24359i 0.243806 + 0.969824i \(0.421604\pi\)
−0.961795 + 0.273770i \(0.911729\pi\)
\(30\) 0 0
\(31\) −21.6298 + 12.4879i −0.697734 + 0.402837i −0.806503 0.591230i \(-0.798642\pi\)
0.108769 + 0.994067i \(0.465309\pi\)
\(32\) 0 0
\(33\) 48.2097 + 12.5701i 1.46090 + 0.380911i
\(34\) 0 0
\(35\) 2.21940i 0.0634115i
\(36\) 0 0
\(37\) −40.3888 −1.09159 −0.545794 0.837919i \(-0.683772\pi\)
−0.545794 + 0.837919i \(0.683772\pi\)
\(38\) 0 0
\(39\) −39.1981 38.6732i −1.00508 0.991620i
\(40\) 0 0
\(41\) 25.6944 + 44.5040i 0.626692 + 1.08546i 0.988211 + 0.153098i \(0.0489251\pi\)
−0.361519 + 0.932365i \(0.617742\pi\)
\(42\) 0 0
\(43\) −56.6621 32.7139i −1.31772 0.760787i −0.334360 0.942445i \(-0.608520\pi\)
−0.983362 + 0.181658i \(0.941854\pi\)
\(44\) 0 0
\(45\) 5.58126 + 3.12278i 0.124028 + 0.0693951i
\(46\) 0 0
\(47\) 29.2894 + 16.9102i 0.623179 + 0.359793i 0.778106 0.628133i \(-0.216181\pi\)
−0.154927 + 0.987926i \(0.549514\pi\)
\(48\) 0 0
\(49\) −19.6227 33.9875i −0.400463 0.693622i
\(50\) 0 0
\(51\) −28.0374 + 7.71554i −0.549753 + 0.151285i
\(52\) 0 0
\(53\) −90.6691 −1.71074 −0.855369 0.518019i \(-0.826670\pi\)
−0.855369 + 0.518019i \(0.826670\pi\)
\(54\) 0 0
\(55\) 11.8012i 0.214567i
\(56\) 0 0
\(57\) 6.53244 + 23.7382i 0.114604 + 0.416459i
\(58\) 0 0
\(59\) −66.2243 + 38.2346i −1.12245 + 0.648045i −0.942024 0.335545i \(-0.891080\pi\)
−0.180422 + 0.983589i \(0.557746\pi\)
\(60\) 0 0
\(61\) 1.35822 2.35250i 0.0222659 0.0385656i −0.854678 0.519159i \(-0.826245\pi\)
0.876944 + 0.480593i \(0.159579\pi\)
\(62\) 0 0
\(63\) 28.1066 0.378955i 0.446136 0.00601516i
\(64\) 0 0
\(65\) 6.52157 11.2957i 0.100332 0.173780i
\(66\) 0 0
\(67\) −34.5422 + 19.9429i −0.515555 + 0.297656i −0.735114 0.677943i \(-0.762871\pi\)
0.219559 + 0.975599i \(0.429538\pi\)
\(68\) 0 0
\(69\) 4.73970 4.80403i 0.0686913 0.0696237i
\(70\) 0 0
\(71\) 102.923i 1.44962i −0.688950 0.724809i \(-0.741928\pi\)
0.688950 0.724809i \(-0.258072\pi\)
\(72\) 0 0
\(73\) 38.1741 0.522933 0.261466 0.965213i \(-0.415794\pi\)
0.261466 + 0.965213i \(0.415794\pi\)
\(74\) 0 0
\(75\) 18.5404 71.1078i 0.247206 0.948103i
\(76\) 0 0
\(77\) 25.9341 + 44.9192i 0.336806 + 0.583366i
\(78\) 0 0
\(79\) 94.4994 + 54.5593i 1.19620 + 0.690624i 0.959705 0.281010i \(-0.0906694\pi\)
0.236491 + 0.971634i \(0.424003\pi\)
\(80\) 0 0
\(81\) 38.5940 71.2145i 0.476470 0.879191i
\(82\) 0 0
\(83\) 113.503 + 65.5311i 1.36751 + 0.789531i 0.990609 0.136723i \(-0.0436570\pi\)
0.376899 + 0.926254i \(0.376990\pi\)
\(84\) 0 0
\(85\) −3.44404 5.96526i −0.0405181 0.0701795i
\(86\) 0 0
\(87\) −31.5201 + 120.888i −0.362300 + 1.38952i
\(88\) 0 0
\(89\) 38.0903 0.427981 0.213991 0.976836i \(-0.431354\pi\)
0.213991 + 0.976836i \(0.431354\pi\)
\(90\) 0 0
\(91\) 57.3266i 0.629963i
\(92\) 0 0
\(93\) −52.6235 + 53.3378i −0.565844 + 0.573525i
\(94\) 0 0
\(95\) −5.05055 + 2.91593i −0.0531636 + 0.0306940i
\(96\) 0 0
\(97\) −12.1961 + 21.1243i −0.125733 + 0.217776i −0.922019 0.387144i \(-0.873462\pi\)
0.796286 + 0.604920i \(0.206795\pi\)
\(98\) 0 0
\(99\) 149.451 2.01501i 1.50961 0.0203537i
\(100\) 0 0
\(101\) 98.1305 169.967i 0.971589 1.68284i 0.280829 0.959758i \(-0.409391\pi\)
0.690760 0.723084i \(-0.257276\pi\)
\(102\) 0 0
\(103\) 104.472 60.3172i 1.01430 0.585604i 0.101849 0.994800i \(-0.467524\pi\)
0.912446 + 0.409196i \(0.134191\pi\)
\(104\) 0 0
\(105\) 1.76658 + 6.41957i 0.0168246 + 0.0611387i
\(106\) 0 0
\(107\) 6.52440i 0.0609757i 0.999535 + 0.0304878i \(0.00970609\pi\)
−0.999535 + 0.0304878i \(0.990294\pi\)
\(108\) 0 0
\(109\) 38.0272 0.348873 0.174437 0.984668i \(-0.444190\pi\)
0.174437 + 0.984668i \(0.444190\pi\)
\(110\) 0 0
\(111\) −116.824 + 32.1484i −1.05247 + 0.289625i
\(112\) 0 0
\(113\) −53.5086 92.6795i −0.473527 0.820173i 0.526014 0.850476i \(-0.323686\pi\)
−0.999541 + 0.0303032i \(0.990353\pi\)
\(114\) 0 0
\(115\) 1.38437 + 0.799268i 0.0120380 + 0.00695016i
\(116\) 0 0
\(117\) −144.163 80.6607i −1.23216 0.689408i
\(118\) 0 0
\(119\) −26.2182 15.1371i −0.220321 0.127203i
\(120\) 0 0
\(121\) 77.3992 + 134.059i 0.639662 + 1.10793i
\(122\) 0 0
\(123\) 109.744 + 108.275i 0.892231 + 0.880282i
\(124\) 0 0
\(125\) 35.1716 0.281373
\(126\) 0 0
\(127\) 101.437i 0.798713i 0.916796 + 0.399357i \(0.130766\pi\)
−0.916796 + 0.399357i \(0.869234\pi\)
\(128\) 0 0
\(129\) −189.933 49.5226i −1.47235 0.383896i
\(130\) 0 0
\(131\) −162.820 + 94.0042i −1.24290 + 0.717589i −0.969684 0.244363i \(-0.921421\pi\)
−0.273217 + 0.961952i \(0.588088\pi\)
\(132\) 0 0
\(133\) −12.8160 + 22.1979i −0.0963608 + 0.166902i
\(134\) 0 0
\(135\) 18.6293 + 4.59004i 0.137995 + 0.0340003i
\(136\) 0 0
\(137\) 31.3271 54.2601i 0.228665 0.396059i −0.728748 0.684782i \(-0.759897\pi\)
0.957413 + 0.288723i \(0.0932307\pi\)
\(138\) 0 0
\(139\) 40.5801 23.4289i 0.291943 0.168553i −0.346875 0.937911i \(-0.612757\pi\)
0.638818 + 0.769358i \(0.279424\pi\)
\(140\) 0 0
\(141\) 98.1791 + 25.5989i 0.696305 + 0.181553i
\(142\) 0 0
\(143\) 304.822i 2.13163i
\(144\) 0 0
\(145\) −29.5922 −0.204084
\(146\) 0 0
\(147\) −83.8113 82.6889i −0.570145 0.562510i
\(148\) 0 0
\(149\) 53.9860 + 93.5064i 0.362322 + 0.627560i 0.988343 0.152247i \(-0.0486508\pi\)
−0.626021 + 0.779806i \(0.715317\pi\)
\(150\) 0 0
\(151\) −2.75240 1.58910i −0.0182278 0.0105238i 0.490858 0.871239i \(-0.336683\pi\)
−0.509086 + 0.860716i \(0.670017\pi\)
\(152\) 0 0
\(153\) −74.9562 + 44.6340i −0.489910 + 0.291726i
\(154\) 0 0
\(155\) −15.3703 8.87405i −0.0991632 0.0572519i
\(156\) 0 0
\(157\) 128.215 + 222.075i 0.816656 + 1.41449i 0.908133 + 0.418683i \(0.137508\pi\)
−0.0914764 + 0.995807i \(0.529159\pi\)
\(158\) 0 0
\(159\) −262.258 + 72.1702i −1.64942 + 0.453901i
\(160\) 0 0
\(161\) 7.02582 0.0436386
\(162\) 0 0
\(163\) 201.100i 1.23374i −0.787065 0.616870i \(-0.788400\pi\)
0.787065 0.616870i \(-0.211600\pi\)
\(164\) 0 0
\(165\) 9.39345 + 34.1347i 0.0569300 + 0.206877i
\(166\) 0 0
\(167\) −110.689 + 63.9062i −0.662807 + 0.382672i −0.793346 0.608771i \(-0.791663\pi\)
0.130538 + 0.991443i \(0.458329\pi\)
\(168\) 0 0
\(169\) −83.9505 + 145.407i −0.496749 + 0.860394i
\(170\) 0 0
\(171\) 37.7899 + 63.4624i 0.220993 + 0.371125i
\(172\) 0 0
\(173\) 100.718 174.448i 0.582183 1.00837i −0.413037 0.910714i \(-0.635532\pi\)
0.995220 0.0976562i \(-0.0311346\pi\)
\(174\) 0 0
\(175\) 66.2543 38.2519i 0.378596 0.218582i
\(176\) 0 0
\(177\) −161.119 + 163.306i −0.910275 + 0.922630i
\(178\) 0 0
\(179\) 5.83187i 0.0325803i −0.999867 0.0162901i \(-0.994814\pi\)
0.999867 0.0162901i \(-0.00518554\pi\)
\(180\) 0 0
\(181\) 132.737 0.733353 0.366677 0.930348i \(-0.380496\pi\)
0.366677 + 0.930348i \(0.380496\pi\)
\(182\) 0 0
\(183\) 2.05608 7.88566i 0.0112354 0.0430910i
\(184\) 0 0
\(185\) −14.3503 24.8555i −0.0775693 0.134354i
\(186\) 0 0
\(187\) −139.410 80.4885i −0.745509 0.430420i
\(188\) 0 0
\(189\) 80.9960 23.4682i 0.428551 0.124170i
\(190\) 0 0
\(191\) −36.0843 20.8333i −0.188923 0.109075i 0.402555 0.915396i \(-0.368122\pi\)
−0.591478 + 0.806321i \(0.701455\pi\)
\(192\) 0 0
\(193\) −69.1927 119.845i −0.358511 0.620960i 0.629201 0.777242i \(-0.283382\pi\)
−0.987712 + 0.156283i \(0.950049\pi\)
\(194\) 0 0
\(195\) 9.87242 37.8635i 0.0506278 0.194172i
\(196\) 0 0
\(197\) −109.421 −0.555438 −0.277719 0.960662i \(-0.589578\pi\)
−0.277719 + 0.960662i \(0.589578\pi\)
\(198\) 0 0
\(199\) 87.0243i 0.437308i 0.975802 + 0.218654i \(0.0701666\pi\)
−0.975802 + 0.218654i \(0.929833\pi\)
\(200\) 0 0
\(201\) −84.0385 + 85.1792i −0.418102 + 0.423777i
\(202\) 0 0
\(203\) −112.637 + 65.0311i −0.554863 + 0.320350i
\(204\) 0 0
\(205\) −18.2587 + 31.6249i −0.0890666 + 0.154268i
\(206\) 0 0
\(207\) 9.88559 17.6682i 0.0477565 0.0853538i
\(208\) 0 0
\(209\) −68.1464 + 118.033i −0.326059 + 0.564751i
\(210\) 0 0
\(211\) −244.383 + 141.095i −1.15821 + 0.668695i −0.950875 0.309574i \(-0.899814\pi\)
−0.207339 + 0.978269i \(0.566480\pi\)
\(212\) 0 0
\(213\) −81.9239 297.702i −0.384619 1.39766i
\(214\) 0 0
\(215\) 46.4935i 0.216249i
\(216\) 0 0
\(217\) −78.0057 −0.359473
\(218\) 0 0
\(219\) 110.418 30.3855i 0.504190 0.138747i
\(220\) 0 0
\(221\) 88.9588 + 154.081i 0.402529 + 0.697200i
\(222\) 0 0
\(223\) 255.359 + 147.432i 1.14511 + 0.661129i 0.947691 0.319190i \(-0.103411\pi\)
0.197419 + 0.980319i \(0.436744\pi\)
\(224\) 0 0
\(225\) −2.97208 220.435i −0.0132092 0.979712i
\(226\) 0 0
\(227\) 124.390 + 71.8164i 0.547972 + 0.316372i 0.748304 0.663356i \(-0.230869\pi\)
−0.200332 + 0.979728i \(0.564202\pi\)
\(228\) 0 0
\(229\) −141.426 244.958i −0.617583 1.06968i −0.989925 0.141590i \(-0.954779\pi\)
0.372343 0.928095i \(-0.378555\pi\)
\(230\) 0 0
\(231\) 110.768 + 109.285i 0.479516 + 0.473094i
\(232\) 0 0
\(233\) −25.9127 −0.111213 −0.0556067 0.998453i \(-0.517709\pi\)
−0.0556067 + 0.998453i \(0.517709\pi\)
\(234\) 0 0
\(235\) 24.0331i 0.102269i
\(236\) 0 0
\(237\) 316.765 + 82.5925i 1.33656 + 0.348491i
\(238\) 0 0
\(239\) 310.807 179.444i 1.30045 0.750813i 0.319966 0.947429i \(-0.396328\pi\)
0.980481 + 0.196616i \(0.0629951\pi\)
\(240\) 0 0
\(241\) 87.7048 151.909i 0.363920 0.630328i −0.624682 0.780879i \(-0.714771\pi\)
0.988602 + 0.150551i \(0.0481048\pi\)
\(242\) 0 0
\(243\) 54.9476 236.706i 0.226122 0.974099i
\(244\) 0 0
\(245\) 13.9441 24.1518i 0.0569145 0.0985789i
\(246\) 0 0
\(247\) 130.454 75.3179i 0.528156 0.304931i
\(248\) 0 0
\(249\) 380.466 + 99.2017i 1.52798 + 0.398401i
\(250\) 0 0
\(251\) 410.044i 1.63364i 0.576891 + 0.816821i \(0.304266\pi\)
−0.576891 + 0.816821i \(0.695734\pi\)
\(252\) 0 0
\(253\) 37.3583 0.147661
\(254\) 0 0
\(255\) −14.7100 14.5130i −0.0576863 0.0569137i
\(256\) 0 0
\(257\) −86.4280 149.698i −0.336296 0.582481i 0.647437 0.762119i \(-0.275841\pi\)
−0.983733 + 0.179638i \(0.942507\pi\)
\(258\) 0 0
\(259\) −109.244 63.0719i −0.421790 0.243521i
\(260\) 0 0
\(261\) 5.05276 + 374.756i 0.0193592 + 1.43585i
\(262\) 0 0
\(263\) 132.696 + 76.6118i 0.504546 + 0.291300i 0.730589 0.682818i \(-0.239246\pi\)
−0.226043 + 0.974117i \(0.572579\pi\)
\(264\) 0 0
\(265\) −32.2151 55.7983i −0.121567 0.210559i
\(266\) 0 0
\(267\) 110.175 30.3189i 0.412642 0.113554i
\(268\) 0 0
\(269\) 12.6752 0.0471198 0.0235599 0.999722i \(-0.492500\pi\)
0.0235599 + 0.999722i \(0.492500\pi\)
\(270\) 0 0
\(271\) 40.7101i 0.150222i 0.997175 + 0.0751108i \(0.0239311\pi\)
−0.997175 + 0.0751108i \(0.976069\pi\)
\(272\) 0 0
\(273\) −45.6305 165.816i −0.167145 0.607385i
\(274\) 0 0
\(275\) 352.293 203.397i 1.28107 0.739624i
\(276\) 0 0
\(277\) 184.143 318.945i 0.664776 1.15143i −0.314570 0.949234i \(-0.601860\pi\)
0.979346 0.202191i \(-0.0648063\pi\)
\(278\) 0 0
\(279\) −109.757 + 196.165i −0.393394 + 0.703101i
\(280\) 0 0
\(281\) −238.310 + 412.765i −0.848078 + 1.46891i 0.0348433 + 0.999393i \(0.488907\pi\)
−0.882921 + 0.469521i \(0.844427\pi\)
\(282\) 0 0
\(283\) 150.052 86.6323i 0.530217 0.306121i −0.210888 0.977510i \(-0.567635\pi\)
0.741105 + 0.671389i \(0.234302\pi\)
\(284\) 0 0
\(285\) −12.2876 + 12.4544i −0.0431143 + 0.0436995i
\(286\) 0 0
\(287\) 160.499i 0.559231i
\(288\) 0 0
\(289\) −195.042 −0.674884
\(290\) 0 0
\(291\) −18.4626 + 70.8094i −0.0634455 + 0.243331i
\(292\) 0 0
\(293\) −2.91833 5.05470i −0.00996017 0.0172515i 0.861002 0.508601i \(-0.169837\pi\)
−0.870963 + 0.491349i \(0.836504\pi\)
\(294\) 0 0
\(295\) −47.0596 27.1699i −0.159524 0.0921013i
\(296\) 0 0
\(297\) 430.680 124.787i 1.45010 0.420160i
\(298\) 0 0
\(299\) −35.7580 20.6449i −0.119592 0.0690465i
\(300\) 0 0
\(301\) −102.173 176.969i −0.339446 0.587937i
\(302\) 0 0
\(303\) 148.551 569.735i 0.490268 1.88031i
\(304\) 0 0
\(305\) 1.93032 0.00632893
\(306\) 0 0
\(307\) 371.717i 1.21080i 0.795920 + 0.605402i \(0.206988\pi\)
−0.795920 + 0.605402i \(0.793012\pi\)
\(308\) 0 0
\(309\) 254.173 257.623i 0.822567 0.833733i
\(310\) 0 0
\(311\) −193.964 + 111.985i −0.623679 + 0.360081i −0.778300 0.627892i \(-0.783918\pi\)
0.154621 + 0.987974i \(0.450584\pi\)
\(312\) 0 0
\(313\) 79.0960 136.998i 0.252703 0.437694i −0.711566 0.702619i \(-0.752014\pi\)
0.964269 + 0.264925i \(0.0853472\pi\)
\(314\) 0 0
\(315\) 10.2196 + 17.1623i 0.0324432 + 0.0544835i
\(316\) 0 0
\(317\) −206.428 + 357.543i −0.651191 + 1.12790i 0.331643 + 0.943405i \(0.392397\pi\)
−0.982834 + 0.184491i \(0.940936\pi\)
\(318\) 0 0
\(319\) −598.925 + 345.789i −1.87751 + 1.08398i
\(320\) 0 0
\(321\) 5.19325 + 18.8717i 0.0161783 + 0.0587903i
\(322\) 0 0
\(323\) 79.5508i 0.246287i
\(324\) 0 0
\(325\) −449.603 −1.38339
\(326\) 0 0
\(327\) 109.993 30.2686i 0.336370 0.0925646i
\(328\) 0 0
\(329\) 52.8147 + 91.4778i 0.160531 + 0.278048i
\(330\) 0 0
\(331\) −126.937 73.2871i −0.383495 0.221411i 0.295843 0.955237i \(-0.404400\pi\)
−0.679338 + 0.733826i \(0.737733\pi\)
\(332\) 0 0
\(333\) −312.320 + 185.977i −0.937899 + 0.558489i
\(334\) 0 0
\(335\) −24.5460 14.1716i −0.0732716 0.0423034i
\(336\) 0 0
\(337\) −47.3499 82.0124i −0.140504 0.243360i 0.787182 0.616720i \(-0.211539\pi\)
−0.927687 + 0.373360i \(0.878206\pi\)
\(338\) 0 0
\(339\) −228.543 225.482i −0.674167 0.665139i
\(340\) 0 0
\(341\) −414.779 −1.21636
\(342\) 0 0
\(343\) 275.611i 0.803532i
\(344\) 0 0
\(345\) 4.64046 + 1.20994i 0.0134506 + 0.00350708i
\(346\) 0 0
\(347\) −81.3438 + 46.9639i −0.234420 + 0.135343i −0.612609 0.790386i \(-0.709880\pi\)
0.378189 + 0.925728i \(0.376547\pi\)
\(348\) 0 0
\(349\) −115.579 + 200.188i −0.331171 + 0.573605i −0.982742 0.184983i \(-0.940777\pi\)
0.651571 + 0.758588i \(0.274110\pi\)
\(350\) 0 0
\(351\) −481.191 118.560i −1.37091 0.337777i
\(352\) 0 0
\(353\) −48.9623 + 84.8052i −0.138703 + 0.240241i −0.927006 0.375046i \(-0.877627\pi\)
0.788303 + 0.615288i \(0.210960\pi\)
\(354\) 0 0
\(355\) 63.3393 36.5690i 0.178421 0.103011i
\(356\) 0 0
\(357\) −87.8844 22.9147i −0.246175 0.0641869i
\(358\) 0 0
\(359\) 244.287i 0.680465i 0.940341 + 0.340233i \(0.110506\pi\)
−0.940341 + 0.340233i \(0.889494\pi\)
\(360\) 0 0
\(361\) 293.647 0.813428
\(362\) 0 0
\(363\) 330.583 + 326.156i 0.910697 + 0.898501i
\(364\) 0 0
\(365\) 13.5634 + 23.4925i 0.0371601 + 0.0643631i
\(366\) 0 0
\(367\) −368.327 212.654i −1.00362 0.579438i −0.0942999 0.995544i \(-0.530061\pi\)
−0.909316 + 0.416106i \(0.863395\pi\)
\(368\) 0 0
\(369\) 403.617 + 225.829i 1.09381 + 0.612002i
\(370\) 0 0
\(371\) −245.242 141.591i −0.661030 0.381646i
\(372\) 0 0
\(373\) 44.8567 + 77.6941i 0.120259 + 0.208295i 0.919870 0.392224i \(-0.128294\pi\)
−0.799611 + 0.600519i \(0.794961\pi\)
\(374\) 0 0
\(375\) 101.733 27.9957i 0.271288 0.0746551i
\(376\) 0 0
\(377\) 764.359 2.02748
\(378\) 0 0
\(379\) 406.140i 1.07161i −0.844342 0.535805i \(-0.820008\pi\)
0.844342 0.535805i \(-0.179992\pi\)
\(380\) 0 0
\(381\) 80.7408 + 293.403i 0.211918 + 0.770087i
\(382\) 0 0
\(383\) 280.901 162.178i 0.733423 0.423442i −0.0862502 0.996274i \(-0.527488\pi\)
0.819673 + 0.572832i \(0.194155\pi\)
\(384\) 0 0
\(385\) −18.4290 + 31.9200i −0.0478675 + 0.0829090i
\(386\) 0 0
\(387\) −588.796 + 7.93860i −1.52144 + 0.0205132i
\(388\) 0 0
\(389\) −28.6761 + 49.6685i −0.0737176 + 0.127683i −0.900528 0.434798i \(-0.856820\pi\)
0.826810 + 0.562481i \(0.190153\pi\)
\(390\) 0 0
\(391\) −18.8838 + 10.9026i −0.0482963 + 0.0278839i
\(392\) 0 0
\(393\) −396.128 + 401.505i −1.00796 + 1.02164i
\(394\) 0 0
\(395\) 77.5406i 0.196305i
\(396\) 0 0
\(397\) 194.475 0.489861 0.244931 0.969541i \(-0.421235\pi\)
0.244931 + 0.969541i \(0.421235\pi\)
\(398\) 0 0
\(399\) −19.4010 + 74.4082i −0.0486240 + 0.186487i
\(400\) 0 0
\(401\) −163.943 283.958i −0.408836 0.708124i 0.585924 0.810366i \(-0.300732\pi\)
−0.994760 + 0.102242i \(0.967398\pi\)
\(402\) 0 0
\(403\) 397.011 + 229.215i 0.985140 + 0.568771i
\(404\) 0 0
\(405\) 57.5384 1.55184i 0.142070 0.00383170i
\(406\) 0 0
\(407\) −580.881 335.372i −1.42723 0.824009i
\(408\) 0 0
\(409\) −36.6786 63.5292i −0.0896787 0.155328i 0.817697 0.575649i \(-0.195251\pi\)
−0.907375 + 0.420321i \(0.861917\pi\)
\(410\) 0 0
\(411\) 47.4233 181.882i 0.115385 0.442534i
\(412\) 0 0
\(413\) −238.832 −0.578285
\(414\) 0 0
\(415\) 93.1340i 0.224419i
\(416\) 0 0
\(417\) 98.7282 100.068i 0.236758 0.239972i
\(418\) 0 0
\(419\) 557.390 321.809i 1.33029 0.768041i 0.344943 0.938624i \(-0.387898\pi\)
0.985343 + 0.170582i \(0.0545649\pi\)
\(420\) 0 0
\(421\) −280.151 + 485.236i −0.665441 + 1.15258i 0.313724 + 0.949514i \(0.398423\pi\)
−0.979165 + 0.203064i \(0.934910\pi\)
\(422\) 0 0
\(423\) 304.357 4.10358i 0.719520 0.00970112i
\(424\) 0 0
\(425\) −118.718 + 205.625i −0.279336 + 0.483824i
\(426\) 0 0
\(427\) 7.34742 4.24204i 0.0172071 0.00993451i
\(428\) 0 0
\(429\) −242.631 881.692i −0.565572 2.05523i
\(430\) 0 0
\(431\) 536.437i 1.24463i 0.782765 + 0.622317i \(0.213809\pi\)
−0.782765 + 0.622317i \(0.786191\pi\)
\(432\) 0 0
\(433\) 281.999 0.651268 0.325634 0.945496i \(-0.394422\pi\)
0.325634 + 0.945496i \(0.394422\pi\)
\(434\) 0 0
\(435\) −85.5947 + 23.5546i −0.196769 + 0.0541484i
\(436\) 0 0
\(437\) 9.23079 + 15.9882i 0.0211231 + 0.0365863i
\(438\) 0 0
\(439\) 87.2604 + 50.3798i 0.198771 + 0.114760i 0.596082 0.802924i \(-0.296723\pi\)
−0.397311 + 0.917684i \(0.630057\pi\)
\(440\) 0 0
\(441\) −308.241 172.464i −0.698958 0.391076i
\(442\) 0 0
\(443\) −519.799 300.106i −1.17336 0.677440i −0.218891 0.975749i \(-0.570244\pi\)
−0.954469 + 0.298309i \(0.903577\pi\)
\(444\) 0 0
\(445\) 13.5337 + 23.4410i 0.0304127 + 0.0526764i
\(446\) 0 0
\(447\) 230.582 + 227.494i 0.515843 + 0.508935i
\(448\) 0 0
\(449\) 639.843 1.42504 0.712520 0.701651i \(-0.247554\pi\)
0.712520 + 0.701651i \(0.247554\pi\)
\(450\) 0 0
\(451\) 853.422i 1.89229i
\(452\) 0 0
\(453\) −9.22612 2.40559i −0.0203667 0.00531036i
\(454\) 0 0
\(455\) 35.2791 20.3684i 0.0775365 0.0447657i
\(456\) 0 0
\(457\) 86.7721 150.294i 0.189873 0.328870i −0.755334 0.655339i \(-0.772526\pi\)
0.945208 + 0.326469i \(0.105859\pi\)
\(458\) 0 0
\(459\) −181.282 + 188.766i −0.394949 + 0.411255i
\(460\) 0 0
\(461\) 361.655 626.406i 0.784502 1.35880i −0.144794 0.989462i \(-0.546252\pi\)
0.929296 0.369336i \(-0.120415\pi\)
\(462\) 0 0
\(463\) 643.880 371.744i 1.39067 0.802903i 0.397280 0.917698i \(-0.369954\pi\)
0.993389 + 0.114794i \(0.0366210\pi\)
\(464\) 0 0
\(465\) −51.5217 13.4336i −0.110799 0.0288895i
\(466\) 0 0
\(467\) 98.0700i 0.210000i −0.994472 0.105000i \(-0.966516\pi\)
0.994472 0.105000i \(-0.0334842\pi\)
\(468\) 0 0
\(469\) −124.573 −0.265614
\(470\) 0 0
\(471\) 547.625 + 540.291i 1.16269 + 1.14711i
\(472\) 0 0
\(473\) −543.285 940.997i −1.14859 1.98942i
\(474\) 0 0
\(475\) 174.095 + 100.514i 0.366515 + 0.211608i
\(476\) 0 0
\(477\) −701.131 + 417.501i −1.46988 + 0.875265i
\(478\) 0 0
\(479\) 293.648 + 169.538i 0.613043 + 0.353941i 0.774156 0.632995i \(-0.218175\pi\)
−0.161112 + 0.986936i \(0.551508\pi\)
\(480\) 0 0
\(481\) 370.665 + 642.011i 0.770614 + 1.33474i
\(482\) 0 0
\(483\) 20.3220 5.59236i 0.0420746 0.0115784i
\(484\) 0 0
\(485\) −17.3334 −0.0357389
\(486\) 0 0
\(487\) 777.718i 1.59696i −0.602023 0.798479i \(-0.705638\pi\)
0.602023 0.798479i \(-0.294362\pi\)
\(488\) 0 0
\(489\) −160.070 581.676i −0.327341 1.18952i
\(490\) 0 0
\(491\) −52.0054 + 30.0254i −0.105917 + 0.0611514i −0.552023 0.833829i \(-0.686144\pi\)
0.446106 + 0.894980i \(0.352811\pi\)
\(492\) 0 0
\(493\) 201.829 349.578i 0.409390 0.709084i
\(494\) 0 0
\(495\) 54.3407 + 91.2570i 0.109779 + 0.184358i
\(496\) 0 0
\(497\) 160.726 278.386i 0.323393 0.560133i
\(498\) 0 0
\(499\) 250.110 144.401i 0.501222 0.289381i −0.227996 0.973662i \(-0.573217\pi\)
0.729218 + 0.684281i \(0.239884\pi\)
\(500\) 0 0
\(501\) −269.297 + 272.953i −0.537520 + 0.544816i
\(502\) 0 0
\(503\) 567.389i 1.12801i 0.825772 + 0.564005i \(0.190740\pi\)
−0.825772 + 0.564005i \(0.809260\pi\)
\(504\) 0 0
\(505\) 139.465 0.276168
\(506\) 0 0
\(507\) −127.085 + 487.408i −0.250661 + 0.961357i
\(508\) 0 0
\(509\) 158.283 + 274.155i 0.310970 + 0.538615i 0.978573 0.205902i \(-0.0660130\pi\)
−0.667603 + 0.744517i \(0.732680\pi\)
\(510\) 0 0
\(511\) 103.253 + 59.6134i 0.202061 + 0.116660i
\(512\) 0 0
\(513\) 159.821 + 153.484i 0.311541 + 0.299189i
\(514\) 0 0
\(515\) 74.2390 + 42.8619i 0.144153 + 0.0832271i
\(516\) 0 0
\(517\) 280.831 + 486.414i 0.543194 + 0.940840i
\(518\) 0 0
\(519\) 152.468 584.756i 0.293772 1.12670i
\(520\) 0 0
\(521\) 597.419 1.14668 0.573339 0.819318i \(-0.305648\pi\)
0.573339 + 0.819318i \(0.305648\pi\)
\(522\) 0 0
\(523\) 630.846i 1.20621i −0.797663 0.603103i \(-0.793931\pi\)
0.797663 0.603103i \(-0.206069\pi\)
\(524\) 0 0
\(525\) 161.191 163.379i 0.307031 0.311199i
\(526\) 0 0
\(527\) 209.662 121.048i 0.397840 0.229693i
\(528\) 0 0
\(529\) −261.970 + 453.745i −0.495217 + 0.857741i
\(530\) 0 0
\(531\) −336.045 + 600.604i −0.632853 + 1.13108i
\(532\) 0 0
\(533\) 471.617 816.865i 0.884835 1.53258i
\(534\) 0 0
\(535\) −4.01515 + 2.31815i −0.00750495 + 0.00433299i
\(536\) 0 0
\(537\) −4.64201 16.8685i −0.00864434 0.0314126i
\(538\) 0 0
\(539\) 651.755i 1.20919i
\(540\) 0 0
\(541\) −144.808 −0.267667 −0.133834 0.991004i \(-0.542729\pi\)
−0.133834 + 0.991004i \(0.542729\pi\)
\(542\) 0 0
\(543\) 383.939 105.655i 0.707069 0.194577i
\(544\) 0 0
\(545\) 13.5112 + 23.4022i 0.0247913 + 0.0429397i
\(546\) 0 0
\(547\) 679.104 + 392.081i 1.24151 + 0.716784i 0.969401 0.245484i \(-0.0789468\pi\)
0.272105 + 0.962268i \(0.412280\pi\)
\(548\) 0 0
\(549\) −0.329596 24.4457i −0.000600357 0.0445277i
\(550\) 0 0
\(551\) −295.974 170.881i −0.537158 0.310128i
\(552\) 0 0
\(553\) 170.402 + 295.144i 0.308140 + 0.533715i
\(554\) 0 0
\(555\) −61.2923 60.4714i −0.110436 0.108958i
\(556\) 0 0
\(557\) 92.1884 0.165509 0.0827544 0.996570i \(-0.473628\pi\)
0.0827544 + 0.996570i \(0.473628\pi\)
\(558\) 0 0
\(559\) 1200.92i 2.14833i
\(560\) 0 0
\(561\) −467.307 121.844i −0.832990 0.217191i
\(562\) 0 0
\(563\) 141.939 81.9485i 0.252112 0.145557i −0.368619 0.929581i \(-0.620169\pi\)
0.620731 + 0.784024i \(0.286836\pi\)
\(564\) 0 0
\(565\) 38.0237 65.8589i 0.0672985 0.116564i
\(566\) 0 0
\(567\) 215.599 132.352i 0.380245 0.233425i
\(568\) 0 0
\(569\) −352.219 + 610.061i −0.619014 + 1.07216i 0.370652 + 0.928772i \(0.379134\pi\)
−0.989666 + 0.143392i \(0.954199\pi\)
\(570\) 0 0
\(571\) 413.817 238.917i 0.724723 0.418419i −0.0917653 0.995781i \(-0.529251\pi\)
0.816489 + 0.577361i \(0.195918\pi\)
\(572\) 0 0
\(573\) −120.956 31.5377i −0.211092 0.0550396i
\(574\) 0 0
\(575\) 55.1023i 0.0958301i
\(576\) 0 0
\(577\) −21.5525 −0.0373527 −0.0186764 0.999826i \(-0.505945\pi\)
−0.0186764 + 0.999826i \(0.505945\pi\)
\(578\) 0 0
\(579\) −295.532 291.574i −0.510418 0.503582i
\(580\) 0 0
\(581\) 204.669 + 354.498i 0.352271 + 0.610151i
\(582\) 0 0
\(583\) −1304.02 752.879i −2.23675 1.29139i
\(584\) 0 0
\(585\) −1.58257 117.378i −0.00270526 0.200645i
\(586\) 0 0
\(587\) −686.177 396.164i −1.16896 0.674897i −0.215522 0.976499i \(-0.569145\pi\)
−0.953434 + 0.301602i \(0.902479\pi\)
\(588\) 0 0
\(589\) −102.487 177.512i −0.174001 0.301379i
\(590\) 0 0
\(591\) −316.498 + 87.0964i −0.535530 + 0.147371i
\(592\) 0 0
\(593\) −571.777 −0.964211 −0.482105 0.876113i \(-0.660128\pi\)
−0.482105 + 0.876113i \(0.660128\pi\)
\(594\) 0 0
\(595\) 21.5131i 0.0361565i
\(596\) 0 0
\(597\) 69.2690 + 251.716i 0.116028 + 0.421635i
\(598\) 0 0
\(599\) −803.662 + 463.994i −1.34167 + 0.774615i −0.987053 0.160396i \(-0.948723\pi\)
−0.354620 + 0.935011i \(0.615390\pi\)
\(600\) 0 0
\(601\) −66.4316 + 115.063i −0.110535 + 0.191452i −0.915986 0.401210i \(-0.868590\pi\)
0.805451 + 0.592662i \(0.201923\pi\)
\(602\) 0 0
\(603\) −175.279 + 313.271i −0.290678 + 0.519521i
\(604\) 0 0
\(605\) −55.0005 + 95.2637i −0.0909100 + 0.157461i
\(606\) 0 0
\(607\) −480.102 + 277.187i −0.790942 + 0.456651i −0.840294 0.542131i \(-0.817618\pi\)
0.0493520 + 0.998781i \(0.484284\pi\)
\(608\) 0 0
\(609\) −274.037 + 277.757i −0.449979 + 0.456087i
\(610\) 0 0
\(611\) 620.771i 1.01599i
\(612\) 0 0
\(613\) 1096.88 1.78937 0.894684 0.446700i \(-0.147401\pi\)
0.894684 + 0.446700i \(0.147401\pi\)
\(614\) 0 0
\(615\) −27.6402 + 106.008i −0.0449434 + 0.172370i
\(616\) 0 0
\(617\) −311.636 539.770i −0.505083 0.874829i −0.999983 0.00587917i \(-0.998129\pi\)
0.494900 0.868950i \(-0.335205\pi\)
\(618\) 0 0
\(619\) 613.432 + 354.165i 0.991005 + 0.572157i 0.905575 0.424187i \(-0.139440\pi\)
0.0854305 + 0.996344i \(0.472773\pi\)
\(620\) 0 0
\(621\) 14.5304 58.9736i 0.0233984 0.0949656i
\(622\) 0 0
\(623\) 103.027 + 59.4826i 0.165372 + 0.0954777i
\(624\) 0 0
\(625\) −293.691 508.688i −0.469906 0.813901i
\(626\) 0 0
\(627\) −103.161 + 395.650i −0.164531 + 0.631021i
\(628\) 0 0
\(629\) 391.497 0.622412
\(630\) 0 0
\(631\) 1142.86i 1.81119i −0.424139 0.905597i \(-0.639423\pi\)
0.424139 0.905597i \(-0.360577\pi\)
\(632\) 0 0
\(633\) −594.565 + 602.636i −0.939282 + 0.952031i
\(634\) 0 0
\(635\) −62.4246 + 36.0409i −0.0983065 + 0.0567573i
\(636\) 0 0
\(637\) −360.172 + 623.836i −0.565419 + 0.979334i
\(638\) 0 0
\(639\) −473.926 795.888i −0.741668 1.24552i
\(640\) 0 0
\(641\) −138.542 + 239.961i −0.216134 + 0.374354i −0.953623 0.301005i \(-0.902678\pi\)
0.737489 + 0.675359i \(0.236011\pi\)
\(642\) 0 0
\(643\) −737.236 + 425.644i −1.14656 + 0.661965i −0.948046 0.318133i \(-0.896944\pi\)
−0.198511 + 0.980099i \(0.563611\pi\)
\(644\) 0 0
\(645\) −37.0076 134.481i −0.0573761 0.208498i
\(646\) 0 0
\(647\) 706.622i 1.09215i 0.837736 + 0.546076i \(0.183879\pi\)
−0.837736 + 0.546076i \(0.816121\pi\)
\(648\) 0 0
\(649\) −1269.94 −1.95676
\(650\) 0 0
\(651\) −225.630 + 62.0904i −0.346589 + 0.0953770i
\(652\) 0 0
\(653\) −390.342 676.092i −0.597767 1.03536i −0.993150 0.116846i \(-0.962722\pi\)
0.395383 0.918516i \(-0.370612\pi\)
\(654\) 0 0
\(655\) −115.701 66.8002i −0.176643 0.101985i
\(656\) 0 0
\(657\) 295.195 175.779i 0.449307 0.267548i
\(658\) 0 0
\(659\) 491.322 + 283.665i 0.745557 + 0.430447i 0.824086 0.566465i \(-0.191689\pi\)
−0.0785296 + 0.996912i \(0.525023\pi\)
\(660\) 0 0
\(661\) 46.9164 + 81.2615i 0.0709778 + 0.122937i 0.899330 0.437270i \(-0.144055\pi\)
−0.828352 + 0.560208i \(0.810721\pi\)
\(662\) 0 0
\(663\) 379.956 + 374.868i 0.573086 + 0.565411i
\(664\) 0 0
\(665\) −18.2143 −0.0273899
\(666\) 0 0
\(667\) 93.6780i 0.140447i
\(668\) 0 0
\(669\) 855.973 + 223.184i 1.27948 + 0.333608i
\(670\) 0 0
\(671\) 39.0684 22.5562i 0.0582241 0.0336157i
\(672\) 0 0
\(673\) 100.742 174.490i 0.149691 0.259272i −0.781422 0.624003i \(-0.785505\pi\)
0.931113 + 0.364730i \(0.118839\pi\)
\(674\) 0 0
\(675\) −184.057 635.238i −0.272677 0.941094i
\(676\) 0 0
\(677\) −336.988 + 583.680i −0.497766 + 0.862157i −0.999997 0.00257723i \(-0.999180\pi\)
0.502230 + 0.864734i \(0.332513\pi\)
\(678\) 0 0
\(679\) −65.9763 + 38.0914i −0.0971668 + 0.0560993i
\(680\) 0 0
\(681\) 416.958 + 108.716i 0.612273 + 0.159642i
\(682\) 0 0
\(683\) 155.633i 0.227867i 0.993488 + 0.113933i \(0.0363450\pi\)
−0.993488 + 0.113933i \(0.963655\pi\)
\(684\) 0 0
\(685\) 44.5226 0.0649965
\(686\) 0 0
\(687\) −604.053 595.963i −0.879262 0.867487i
\(688\) 0 0
\(689\) 832.110 + 1441.26i 1.20771 + 2.09181i
\(690\) 0 0
\(691\) −693.263 400.255i −1.00327 0.579241i −0.0940588 0.995567i \(-0.529984\pi\)
−0.909215 + 0.416326i \(0.863318\pi\)
\(692\) 0 0
\(693\) 407.382 + 227.935i 0.587853 + 0.328911i
\(694\) 0 0
\(695\) 28.8366 + 16.6488i 0.0414915 + 0.0239551i
\(696\) 0 0
\(697\) −249.061 431.387i −0.357333 0.618919i
\(698\) 0 0
\(699\) −74.9520 + 20.6258i −0.107228 + 0.0295077i
\(700\) 0 0
\(701\) −488.317 −0.696601 −0.348300 0.937383i \(-0.613241\pi\)
−0.348300 + 0.937383i \(0.613241\pi\)
\(702\) 0 0
\(703\) 331.465i 0.471501i
\(704\) 0 0
\(705\) 19.1297 + 69.5153i 0.0271344 + 0.0986033i
\(706\) 0 0
\(707\) 530.848 306.485i 0.750845 0.433501i
\(708\) 0 0
\(709\) 358.633 621.170i 0.505829 0.876121i −0.494149 0.869377i \(-0.664520\pi\)
0.999977 0.00674353i \(-0.00214655\pi\)
\(710\) 0 0
\(711\) 981.978 13.2398i 1.38112 0.0186214i
\(712\) 0 0
\(713\) −28.0920 + 48.6568i −0.0393997 + 0.0682423i
\(714\) 0 0
\(715\) 187.589 108.305i 0.262363 0.151475i
\(716\) 0 0
\(717\) 756.169 766.433i 1.05463 1.06894i
\(718\) 0 0
\(719\) 512.219i 0.712404i −0.934409 0.356202i \(-0.884071\pi\)
0.934409 0.356202i \(-0.115929\pi\)
\(720\) 0 0
\(721\) 376.770 0.522566
\(722\) 0 0
\(723\) 132.768 509.204i 0.183636 0.704294i
\(724\) 0 0
\(725\) 510.028 + 883.394i 0.703487 + 1.21848i
\(726\) 0 0
\(727\) 574.499 + 331.687i 0.790232 + 0.456241i 0.840044 0.542518i \(-0.182529\pi\)
−0.0498122 + 0.998759i \(0.515862\pi\)
\(728\) 0 0
\(729\) −29.4770 728.404i −0.0404349 0.999182i
\(730\) 0 0
\(731\) 549.237 + 317.102i 0.751351 + 0.433793i
\(732\) 0 0
\(733\) −146.883 254.408i −0.200386 0.347078i 0.748267 0.663398i \(-0.230886\pi\)
−0.948653 + 0.316320i \(0.897553\pi\)
\(734\) 0 0
\(735\) 21.1087 80.9577i 0.0287193 0.110147i
\(736\) 0 0
\(737\) −662.392 −0.898768
\(738\) 0 0
\(739\) 1335.27i 1.80686i 0.428736 + 0.903430i \(0.358959\pi\)
−0.428736 + 0.903430i \(0.641041\pi\)
\(740\) 0 0
\(741\) 317.385 321.694i 0.428320 0.434134i
\(742\) 0 0
\(743\) −488.188 + 281.855i −0.657050 + 0.379348i −0.791152 0.611620i \(-0.790518\pi\)
0.134102 + 0.990968i \(0.457185\pi\)
\(744\) 0 0
\(745\) −38.3629 + 66.4465i −0.0514938 + 0.0891899i
\(746\) 0 0
\(747\) 1179.45 15.9023i 1.57892 0.0212882i
\(748\) 0 0
\(749\) −10.1886 + 17.6472i −0.0136030 + 0.0235610i
\(750\) 0 0
\(751\) −591.407 + 341.449i −0.787493 + 0.454659i −0.839079 0.544009i \(-0.816906\pi\)
0.0515861 + 0.998669i \(0.483572\pi\)
\(752\) 0 0
\(753\) 326.384 + 1186.04i 0.433445 + 1.57509i
\(754\) 0 0
\(755\) 2.25845i 0.00299133i
\(756\) 0 0
\(757\) −534.746 −0.706401 −0.353201 0.935548i \(-0.614907\pi\)
−0.353201 + 0.935548i \(0.614907\pi\)
\(758\) 0 0
\(759\) 108.058 29.7362i 0.142369 0.0391782i
\(760\) 0 0
\(761\) −416.191 720.863i −0.546900 0.947258i −0.998485 0.0550300i \(-0.982475\pi\)
0.451585 0.892228i \(-0.350859\pi\)
\(762\) 0 0
\(763\) 102.856 + 59.3840i 0.134805 + 0.0778296i
\(764\) 0 0
\(765\) −54.1003 30.2698i −0.0707194 0.0395683i
\(766\) 0 0
\(767\) 1215.54 + 701.791i 1.58480 + 0.914982i
\(768\) 0 0
\(769\) −351.020 607.985i −0.456464 0.790618i 0.542308 0.840180i \(-0.317551\pi\)
−0.998771 + 0.0495620i \(0.984217\pi\)
\(770\) 0 0
\(771\) −369.146 364.203i −0.478789 0.472377i
\(772\) 0 0
\(773\) −472.477 −0.611225 −0.305612 0.952156i \(-0.598861\pi\)
−0.305612 + 0.952156i \(0.598861\pi\)
\(774\) 0 0
\(775\) 611.785i 0.789400i
\(776\) 0 0
\(777\) −366.189 95.4790i −0.471285 0.122882i
\(778\) 0 0
\(779\) −365.238 + 210.870i −0.468855 + 0.270693i
\(780\) 0 0
\(781\) 854.630 1480.26i 1.09428 1.89534i
\(782\) 0 0
\(783\) 312.911 + 1079.95i 0.399631 + 1.37925i
\(784\) 0 0
\(785\) −91.1107 + 157.808i −0.116065 + 0.201030i
\(786\) 0 0
\(787\) 556.186 321.114i 0.706717 0.408023i −0.103127 0.994668i \(-0.532885\pi\)
0.809844 + 0.586645i \(0.199552\pi\)
\(788\) 0 0
\(789\) 444.800 + 115.976i 0.563752 + 0.146991i
\(790\) 0 0
\(791\) 334.240i 0.422554i
\(792\) 0 0
\(793\) −49.8598 −0.0628749
\(794\) 0 0