Properties

Label 324.3.o.a.5.1
Level $324$
Weight $3$
Character 324.5
Analytic conductor $8.828$
Analytic rank $0$
Dimension $324$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 324.o (of order \(54\), degree \(18\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.82836056527\)
Analytic rank: \(0\)
Dimension: \(324\)
Relative dimension: \(18\) over \(\Q(\zeta_{54})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label 5.1
Character \(\chi\) \(=\) 324.5
Dual form 324.3.o.a.65.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.85677 + 0.915910i) q^{3} +(-4.55987 + 3.39470i) q^{5} +(9.74231 - 6.40762i) q^{7} +(7.32222 - 5.23308i) q^{9} +O(q^{10})\) \(q+(-2.85677 + 0.915910i) q^{3} +(-4.55987 + 3.39470i) q^{5} +(9.74231 - 6.40762i) q^{7} +(7.32222 - 5.23308i) q^{9} +(0.713033 - 6.10039i) q^{11} +(4.08156 + 13.6334i) q^{13} +(9.91723 - 13.8743i) q^{15} +(-21.2831 - 3.75278i) q^{17} +(6.10801 + 34.6402i) q^{19} +(-21.9627 + 27.2281i) q^{21} +(-11.5087 + 17.4982i) q^{23} +(2.09835 - 7.00898i) q^{25} +(-16.1248 + 21.6562i) q^{27} +(4.94737 - 4.66760i) q^{29} +(-2.02555 + 34.7774i) q^{31} +(3.55044 + 18.0805i) q^{33} +(-22.6717 + 62.2901i) q^{35} +(14.3291 - 5.21535i) q^{37} +(-24.1470 - 35.2090i) q^{39} +(-0.792837 + 3.34524i) q^{41} +(-5.34616 - 12.3938i) q^{43} +(-15.6236 + 48.7188i) q^{45} +(29.6405 - 1.72636i) q^{47} +(34.4471 - 79.8574i) q^{49} +(64.2379 - 8.77257i) q^{51} +(58.2609 + 33.6369i) q^{53} +(17.4576 + 30.2375i) q^{55} +(-49.1765 - 93.3646i) q^{57} +(5.87325 + 50.2489i) q^{59} +(-19.7711 - 9.92944i) q^{61} +(37.8037 - 97.9003i) q^{63} +(-64.8925 - 48.3107i) q^{65} +(-72.8296 + 77.1949i) q^{67} +(16.8510 - 60.5292i) q^{69} +(-63.7955 + 76.0285i) q^{71} +(-40.8467 + 34.2745i) q^{73} +(0.425101 + 21.9449i) q^{75} +(-32.1424 - 64.0007i) q^{77} +(70.7096 - 16.7585i) q^{79} +(26.2297 - 76.6355i) q^{81} +(20.3016 + 85.6592i) q^{83} +(109.787 - 55.1373i) q^{85} +(-9.85837 + 17.8656i) q^{87} +(-17.1945 - 20.4917i) q^{89} +(127.121 + 106.667i) q^{91} +(-26.0664 - 101.206i) q^{93} +(-145.445 - 137.220i) q^{95} +(25.5532 - 34.3239i) q^{97} +(-26.7029 - 48.3997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 324 q + O(q^{10}) \) \( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).

\(n\) \(163\) \(245\)
\(\chi(n)\) \(1\) \(e\left(\frac{23}{54}\right)\)

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
\(3\) −2.85677 + 0.915910i −0.952255 + 0.305303i
\(4\) 0 0
\(5\) −4.55987 + 3.39470i −0.911973 + 0.678939i −0.947270 0.320438i \(-0.896170\pi\)
0.0352962 + 0.999377i \(0.488763\pi\)
\(6\) 0 0
\(7\) 9.74231 6.40762i 1.39176 0.915374i 0.391770 0.920063i \(-0.371863\pi\)
0.999989 + 0.00468942i \(0.00149269\pi\)
\(8\) 0 0
\(9\) 7.32222 5.23308i 0.813580 0.581454i
\(10\) 0 0
\(11\) 0.713033 6.10039i 0.0648212 0.554581i −0.921336 0.388767i \(-0.872901\pi\)
0.986157 0.165813i \(-0.0530250\pi\)
\(12\) 0 0
\(13\) 4.08156 + 13.6334i 0.313966 + 1.04872i 0.958725 + 0.284334i \(0.0917725\pi\)
−0.644759 + 0.764386i \(0.723042\pi\)
\(14\) 0 0
\(15\) 9.91723 13.8743i 0.661149 0.924952i
\(16\) 0 0
\(17\) −21.2831 3.75278i −1.25194 0.220752i −0.491917 0.870642i \(-0.663704\pi\)
−0.760028 + 0.649891i \(0.774815\pi\)
\(18\) 0 0
\(19\) 6.10801 + 34.6402i 0.321474 + 1.82317i 0.533375 + 0.845879i \(0.320924\pi\)
−0.211901 + 0.977291i \(0.567965\pi\)
\(20\) 0 0
\(21\) −21.9627 + 27.2281i −1.04584 + 1.29658i
\(22\) 0 0
\(23\) −11.5087 + 17.4982i −0.500380 + 0.760791i −0.994058 0.108854i \(-0.965282\pi\)
0.493678 + 0.869645i \(0.335652\pi\)
\(24\) 0 0
\(25\) 2.09835 7.00898i 0.0839340 0.280359i
\(26\) 0 0
\(27\) −16.1248 + 21.6562i −0.597216 + 0.802081i
\(28\) 0 0
\(29\) 4.94737 4.66760i 0.170599 0.160952i −0.596207 0.802831i \(-0.703326\pi\)
0.766806 + 0.641879i \(0.221845\pi\)
\(30\) 0 0
\(31\) −2.02555 + 34.7774i −0.0653404 + 1.12185i 0.793152 + 0.609024i \(0.208439\pi\)
−0.858492 + 0.512827i \(0.828598\pi\)
\(32\) 0 0
\(33\) 3.55044 + 18.0805i 0.107589 + 0.547893i
\(34\) 0 0
\(35\) −22.6717 + 62.2901i −0.647764 + 1.77972i
\(36\) 0 0
\(37\) 14.3291 5.21535i 0.387272 0.140955i −0.141044 0.990003i \(-0.545046\pi\)
0.528316 + 0.849048i \(0.322824\pi\)
\(38\) 0 0
\(39\) −24.1470 35.2090i −0.619154 0.902794i
\(40\) 0 0
\(41\) −0.792837 + 3.34524i −0.0193375 + 0.0815913i −0.981858 0.189617i \(-0.939275\pi\)
0.962521 + 0.271209i \(0.0874234\pi\)
\(42\) 0 0
\(43\) −5.34616 12.3938i −0.124329 0.288228i 0.844672 0.535285i \(-0.179796\pi\)
−0.969001 + 0.247057i \(0.920536\pi\)
\(44\) 0 0
\(45\) −15.6236 + 48.7188i −0.347191 + 1.08264i
\(46\) 0 0
\(47\) 29.6405 1.72636i 0.630648 0.0367311i 0.260156 0.965567i \(-0.416226\pi\)
0.370492 + 0.928836i \(0.379189\pi\)
\(48\) 0 0
\(49\) 34.4471 79.8574i 0.703002 1.62974i
\(50\) 0 0
\(51\) 64.2379 8.77257i 1.25957 0.172011i
\(52\) 0 0
\(53\) 58.2609 + 33.6369i 1.09926 + 0.634659i 0.936027 0.351928i \(-0.114474\pi\)
0.163235 + 0.986587i \(0.447807\pi\)
\(54\) 0 0
\(55\) 17.4576 + 30.2375i 0.317411 + 0.549773i
\(56\) 0 0
\(57\) −49.1765 93.3646i −0.862746 1.63798i
\(58\) 0 0
\(59\) 5.87325 + 50.2489i 0.0995467 + 0.851676i 0.947094 + 0.320956i \(0.104004\pi\)
−0.847547 + 0.530720i \(0.821922\pi\)
\(60\) 0 0
\(61\) −19.7711 9.92944i −0.324117 0.162778i 0.279299 0.960204i \(-0.409898\pi\)
−0.603416 + 0.797426i \(0.706194\pi\)
\(62\) 0 0
\(63\) 37.8037 97.9003i 0.600059 1.55397i
\(64\) 0 0
\(65\) −64.8925 48.3107i −0.998346 0.743241i
\(66\) 0 0
\(67\) −72.8296 + 77.1949i −1.08701 + 1.15216i −0.0994298 + 0.995045i \(0.531702\pi\)
−0.987580 + 0.157118i \(0.949780\pi\)
\(68\) 0 0
\(69\) 16.8510 60.5292i 0.244217 0.877235i
\(70\) 0 0
\(71\) −63.7955 + 76.0285i −0.898528 + 1.07082i 0.0986029 + 0.995127i \(0.468563\pi\)
−0.997131 + 0.0756971i \(0.975882\pi\)
\(72\) 0 0
\(73\) −40.8467 + 34.2745i −0.559544 + 0.469514i −0.878158 0.478371i \(-0.841227\pi\)
0.318613 + 0.947885i \(0.396783\pi\)
\(74\) 0 0
\(75\) 0.425101 + 21.9449i 0.00566802 + 0.292599i
\(76\) 0 0
\(77\) −32.1424 64.0007i −0.417433 0.831178i
\(78\) 0 0
\(79\) 70.7096 16.7585i 0.895059 0.212133i 0.242752 0.970088i \(-0.421950\pi\)
0.652306 + 0.757955i \(0.273802\pi\)
\(80\) 0 0
\(81\) 26.2297 76.6355i 0.323823 0.946118i
\(82\) 0 0
\(83\) 20.3016 + 85.6592i 0.244598 + 1.03204i 0.947248 + 0.320503i \(0.103852\pi\)
−0.702650 + 0.711536i \(0.748000\pi\)
\(84\) 0 0
\(85\) 109.787 55.1373i 1.29162 0.648674i
\(86\) 0 0
\(87\) −9.85837 + 17.8656i −0.113315 + 0.205352i
\(88\) 0 0
\(89\) −17.1945 20.4917i −0.193197 0.230243i 0.660746 0.750609i \(-0.270240\pi\)
−0.853943 + 0.520366i \(0.825796\pi\)
\(90\) 0 0
\(91\) 127.121 + 106.667i 1.39694 + 1.17217i
\(92\) 0 0
\(93\) −26.0664 101.206i −0.280284 1.08824i
\(94\) 0 0
\(95\) −145.445 137.220i −1.53100 1.44442i
\(96\) 0 0
\(97\) 25.5532 34.3239i 0.263435 0.353855i −0.650650 0.759378i \(-0.725503\pi\)
0.914085 + 0.405523i \(0.132911\pi\)
\(98\) 0 0
\(99\) −26.7029 48.3997i −0.269726 0.488886i
\(100\) 0 0
\(101\) −62.6480 + 124.742i −0.620277 + 1.23507i 0.335793 + 0.941936i \(0.390996\pi\)
−0.956070 + 0.293138i \(0.905301\pi\)
\(102\) 0 0
\(103\) 65.2925 7.63160i 0.633908 0.0740932i 0.206931 0.978356i \(-0.433653\pi\)
0.426977 + 0.904262i \(0.359578\pi\)
\(104\) 0 0
\(105\) 7.71569 198.713i 0.0734828 1.89251i
\(106\) 0 0
\(107\) 181.287 104.666i 1.69427 0.978189i 0.743280 0.668981i \(-0.233269\pi\)
0.950994 0.309209i \(-0.100064\pi\)
\(108\) 0 0
\(109\) 20.8349 36.0872i 0.191146 0.331075i −0.754484 0.656318i \(-0.772113\pi\)
0.945630 + 0.325243i \(0.105446\pi\)
\(110\) 0 0
\(111\) −36.1580 + 28.0232i −0.325747 + 0.252461i
\(112\) 0 0
\(113\) −122.722 52.9372i −1.08604 0.468471i −0.223624 0.974676i \(-0.571789\pi\)
−0.862413 + 0.506205i \(0.831048\pi\)
\(114\) 0 0
\(115\) −6.92269 118.858i −0.0601973 1.03355i
\(116\) 0 0
\(117\) 101.231 + 78.4673i 0.865219 + 0.670661i
\(118\) 0 0
\(119\) −231.393 + 99.8130i −1.94447 + 0.838765i
\(120\) 0 0
\(121\) 81.0321 + 19.2050i 0.669687 + 0.158719i
\(122\) 0 0
\(123\) −0.798993 10.2827i −0.00649588 0.0835995i
\(124\) 0 0
\(125\) −34.3823 94.4646i −0.275058 0.755717i
\(126\) 0 0
\(127\) −94.9637 34.5640i −0.747746 0.272157i −0.0600888 0.998193i \(-0.519138\pi\)
−0.687657 + 0.726036i \(0.741361\pi\)
\(128\) 0 0
\(129\) 26.6243 + 30.5095i 0.206390 + 0.236508i
\(130\) 0 0
\(131\) 252.920 + 14.7309i 1.93068 + 0.112450i 0.980161 0.198204i \(-0.0635110\pi\)
0.950523 + 0.310654i \(0.100548\pi\)
\(132\) 0 0
\(133\) 281.467 + 298.338i 2.11630 + 2.24314i
\(134\) 0 0
\(135\) 0.0108963 153.488i 8.07134e−5 1.13695i
\(136\) 0 0
\(137\) 10.5100 + 3.14647i 0.0767150 + 0.0229670i 0.324931 0.945738i \(-0.394659\pi\)
−0.248216 + 0.968705i \(0.579844\pi\)
\(138\) 0 0
\(139\) −147.347 96.9117i −1.06005 0.697206i −0.105248 0.994446i \(-0.533564\pi\)
−0.954803 + 0.297240i \(0.903934\pi\)
\(140\) 0 0
\(141\) −83.0946 + 32.0798i −0.589324 + 0.227516i
\(142\) 0 0
\(143\) 86.0791 15.1781i 0.601952 0.106140i
\(144\) 0 0
\(145\) −6.71426 + 38.0785i −0.0463052 + 0.262610i
\(146\) 0 0
\(147\) −25.2651 + 259.684i −0.171872 + 1.76656i
\(148\) 0 0
\(149\) −145.353 + 43.5159i −0.975525 + 0.292053i −0.734607 0.678493i \(-0.762634\pi\)
−0.240918 + 0.970546i \(0.577448\pi\)
\(150\) 0 0
\(151\) 242.653 + 28.3621i 1.60697 + 0.187828i 0.871734 0.489980i \(-0.162996\pi\)
0.735239 + 0.677808i \(0.237070\pi\)
\(152\) 0 0
\(153\) −175.478 + 83.8973i −1.14691 + 0.548349i
\(154\) 0 0
\(155\) −108.822 165.456i −0.702080 1.06746i
\(156\) 0 0
\(157\) −169.034 227.051i −1.07665 1.44619i −0.885508 0.464625i \(-0.846189\pi\)
−0.191139 0.981563i \(-0.561218\pi\)
\(158\) 0 0
\(159\) −197.246 42.7311i −1.24054 0.268749i
\(160\) 0 0
\(161\) 244.216i 1.51687i
\(162\) 0 0
\(163\) −240.338 −1.47447 −0.737234 0.675637i \(-0.763869\pi\)
−0.737234 + 0.675637i \(0.763869\pi\)
\(164\) 0 0
\(165\) −77.5672 70.3918i −0.470104 0.426617i
\(166\) 0 0
\(167\) 217.785 162.135i 1.30410 0.970868i 0.304269 0.952586i \(-0.401588\pi\)
0.999833 0.0182817i \(-0.00581957\pi\)
\(168\) 0 0
\(169\) −28.0120 + 18.4238i −0.165751 + 0.109016i
\(170\) 0 0
\(171\) 225.999 + 221.680i 1.32163 + 1.29637i
\(172\) 0 0
\(173\) −32.6034 + 278.939i −0.188459 + 1.61237i 0.485935 + 0.873995i \(0.338479\pi\)
−0.674394 + 0.738372i \(0.735595\pi\)
\(174\) 0 0
\(175\) −24.4681 81.7290i −0.139818 0.467023i
\(176\) 0 0
\(177\) −62.8020 138.170i −0.354813 0.780621i
\(178\) 0 0
\(179\) 123.722 + 21.8155i 0.691183 + 0.121874i 0.508197 0.861241i \(-0.330312\pi\)
0.182987 + 0.983115i \(0.441423\pi\)
\(180\) 0 0
\(181\) −17.3397 98.3386i −0.0957997 0.543307i −0.994499 0.104743i \(-0.966598\pi\)
0.898700 0.438565i \(-0.144513\pi\)
\(182\) 0 0
\(183\) 65.5760 + 10.2575i 0.358339 + 0.0560518i
\(184\) 0 0
\(185\) −47.6341 + 72.4241i −0.257481 + 0.391481i
\(186\) 0 0
\(187\) −38.0689 + 127.159i −0.203577 + 0.679995i
\(188\) 0 0
\(189\) −18.3284 + 314.303i −0.0969759 + 1.66298i
\(190\) 0 0
\(191\) −2.52109 + 2.37852i −0.0131994 + 0.0124530i −0.692813 0.721117i \(-0.743629\pi\)
0.679614 + 0.733570i \(0.262147\pi\)
\(192\) 0 0
\(193\) 9.65273 165.731i 0.0500142 0.858710i −0.876255 0.481848i \(-0.839966\pi\)
0.926269 0.376862i \(-0.122997\pi\)
\(194\) 0 0
\(195\) 229.631 + 78.5765i 1.17759 + 0.402957i
\(196\) 0 0
\(197\) 35.0480 96.2936i 0.177909 0.488800i −0.818399 0.574650i \(-0.805138\pi\)
0.996308 + 0.0858498i \(0.0273605\pi\)
\(198\) 0 0
\(199\) 30.5394 11.1154i 0.153464 0.0558564i −0.264146 0.964483i \(-0.585090\pi\)
0.417610 + 0.908626i \(0.362868\pi\)
\(200\) 0 0
\(201\) 137.354 287.233i 0.683351 1.42902i
\(202\) 0 0
\(203\) 18.2906 77.1741i 0.0901014 0.380168i
\(204\) 0 0
\(205\) −7.74085 17.9453i −0.0377602 0.0875381i
\(206\) 0 0
\(207\) 7.29998 + 188.352i 0.0352656 + 0.909912i
\(208\) 0 0
\(209\) 215.674 12.5616i 1.03193 0.0601033i
\(210\) 0 0
\(211\) −77.0783 + 178.688i −0.365300 + 0.846861i 0.632106 + 0.774882i \(0.282191\pi\)
−0.997406 + 0.0719788i \(0.977069\pi\)
\(212\) 0 0
\(213\) 112.613 275.627i 0.528702 1.29402i
\(214\) 0 0
\(215\) 66.4509 + 38.3654i 0.309074 + 0.178444i
\(216\) 0 0
\(217\) 203.107 + 351.791i 0.935975 + 1.62116i
\(218\) 0 0
\(219\) 85.2972 135.326i 0.389485 0.617928i
\(220\) 0 0
\(221\) −35.7051 305.477i −0.161562 1.38225i
\(222\) 0 0
\(223\) −112.471 56.4849i −0.504353 0.253295i 0.178383 0.983961i \(-0.442914\pi\)
−0.682735 + 0.730666i \(0.739210\pi\)
\(224\) 0 0
\(225\) −21.3140 62.3021i −0.0947288 0.276898i
\(226\) 0 0
\(227\) −354.671 264.043i −1.56243 1.16319i −0.916671 0.399643i \(-0.869134\pi\)
−0.645758 0.763542i \(-0.723458\pi\)
\(228\) 0 0
\(229\) −69.5855 + 73.7563i −0.303867 + 0.322080i −0.861256 0.508171i \(-0.830322\pi\)
0.557389 + 0.830251i \(0.311803\pi\)
\(230\) 0 0
\(231\) 150.442 + 153.396i 0.651265 + 0.664050i
\(232\) 0 0
\(233\) −63.5879 + 75.7811i −0.272909 + 0.325241i −0.885039 0.465517i \(-0.845869\pi\)
0.612130 + 0.790757i \(0.290313\pi\)
\(234\) 0 0
\(235\) −129.296 + 108.492i −0.550196 + 0.461669i
\(236\) 0 0
\(237\) −186.652 + 112.639i −0.787559 + 0.475269i
\(238\) 0 0
\(239\) 6.13576 + 12.2173i 0.0256726 + 0.0511184i 0.906103 0.423056i \(-0.139043\pi\)
−0.880431 + 0.474175i \(0.842746\pi\)
\(240\) 0 0
\(241\) 96.4899 22.8685i 0.400373 0.0948902i −0.0254961 0.999675i \(-0.508117\pi\)
0.425869 + 0.904785i \(0.359968\pi\)
\(242\) 0 0
\(243\) −4.74084 + 242.954i −0.0195096 + 0.999810i
\(244\) 0 0
\(245\) 114.017 + 481.077i 0.465377 + 1.96358i
\(246\) 0 0
\(247\) −447.333 + 224.659i −1.81106 + 0.909550i
\(248\) 0 0
\(249\) −136.453 226.114i −0.548004 0.908087i
\(250\) 0 0
\(251\) 157.220 + 187.368i 0.626375 + 0.746485i 0.982153 0.188086i \(-0.0602283\pi\)
−0.355777 + 0.934571i \(0.615784\pi\)
\(252\) 0 0
\(253\) 98.5397 + 82.6846i 0.389485 + 0.326817i
\(254\) 0 0
\(255\) −263.136 + 258.070i −1.03191 + 1.01204i
\(256\) 0 0
\(257\) 256.249 + 241.758i 0.997076 + 0.940693i 0.998240 0.0593067i \(-0.0188890\pi\)
−0.00116387 + 0.999999i \(0.500370\pi\)
\(258\) 0 0
\(259\) 106.180 142.625i 0.409962 0.550674i
\(260\) 0 0
\(261\) 11.7998 60.0672i 0.0452098 0.230142i
\(262\) 0 0
\(263\) −196.319 + 390.904i −0.746461 + 1.48633i 0.123043 + 0.992401i \(0.460735\pi\)
−0.869504 + 0.493925i \(0.835562\pi\)
\(264\) 0 0
\(265\) −379.849 + 44.3980i −1.43339 + 0.167540i
\(266\) 0 0
\(267\) 67.8893 + 42.7912i 0.254267 + 0.160267i
\(268\) 0 0
\(269\) 166.520 96.1402i 0.619033 0.357399i −0.157460 0.987525i \(-0.550330\pi\)
0.776492 + 0.630127i \(0.216997\pi\)
\(270\) 0 0
\(271\) −60.1759 + 104.228i −0.222051 + 0.384604i −0.955431 0.295215i \(-0.904609\pi\)
0.733379 + 0.679820i \(0.237942\pi\)
\(272\) 0 0
\(273\) −460.853 188.292i −1.68811 0.689714i
\(274\) 0 0
\(275\) −41.2613 17.7984i −0.150041 0.0647214i
\(276\) 0 0
\(277\) −13.4243 230.487i −0.0484633 0.832082i −0.931717 0.363186i \(-0.881689\pi\)
0.883253 0.468896i \(-0.155348\pi\)
\(278\) 0 0
\(279\) 167.161 + 265.247i 0.599145 + 0.950707i
\(280\) 0 0
\(281\) 245.678 105.975i 0.874300 0.377136i 0.0888383 0.996046i \(-0.471685\pi\)
0.785462 + 0.618910i \(0.212425\pi\)
\(282\) 0 0
\(283\) −15.5619 3.68823i −0.0549889 0.0130326i 0.203029 0.979173i \(-0.434921\pi\)
−0.258018 + 0.966140i \(0.583069\pi\)
\(284\) 0 0
\(285\) 541.183 + 258.791i 1.89889 + 0.908039i
\(286\) 0 0
\(287\) 13.7110 + 37.6706i 0.0477734 + 0.131256i
\(288\) 0 0
\(289\) 167.314 + 60.8974i 0.578942 + 0.210717i
\(290\) 0 0
\(291\) −41.5619 + 121.460i −0.142824 + 0.417388i
\(292\) 0 0
\(293\) −509.342 29.6658i −1.73837 0.101248i −0.840584 0.541681i \(-0.817788\pi\)
−0.897786 + 0.440433i \(0.854825\pi\)
\(294\) 0 0
\(295\) −197.361 209.190i −0.669020 0.709120i
\(296\) 0 0
\(297\) 120.614 + 113.809i 0.406106 + 0.383196i
\(298\) 0 0
\(299\) −285.533 85.4829i −0.954959 0.285896i
\(300\) 0 0
\(301\) −131.499 86.4880i −0.436872 0.287335i
\(302\) 0 0
\(303\) 64.7177 413.740i 0.213590 1.36548i
\(304\) 0 0
\(305\) 123.861 21.8401i 0.406102 0.0716068i
\(306\) 0 0
\(307\) −11.0876 + 62.8808i −0.0361159 + 0.204823i −0.997526 0.0702950i \(-0.977606\pi\)
0.961410 + 0.275118i \(0.0887171\pi\)
\(308\) 0 0
\(309\) −179.535 + 81.6038i −0.581021 + 0.264090i
\(310\) 0 0
\(311\) 540.937 161.946i 1.73935 0.520726i 0.749393 0.662125i \(-0.230345\pi\)
0.989953 + 0.141399i \(0.0451600\pi\)
\(312\) 0 0
\(313\) −127.811 14.9390i −0.408343 0.0477285i −0.0905580 0.995891i \(-0.528865\pi\)
−0.317785 + 0.948163i \(0.602939\pi\)
\(314\) 0 0
\(315\) 159.962 + 574.744i 0.507815 + 1.82458i
\(316\) 0 0
\(317\) −170.224 258.812i −0.536983 0.816443i 0.460477 0.887672i \(-0.347678\pi\)
−0.997460 + 0.0712288i \(0.977308\pi\)
\(318\) 0 0
\(319\) −24.9466 33.5090i −0.0782024 0.105044i
\(320\) 0 0
\(321\) −422.030 + 465.050i −1.31474 + 1.44875i
\(322\) 0 0
\(323\) 760.172i 2.35347i
\(324\) 0 0
\(325\) 104.120 0.320371
\(326\) 0 0
\(327\) −26.4679 + 122.175i −0.0809416 + 0.373625i
\(328\) 0 0
\(329\) 277.705 206.743i 0.844087 0.628399i
\(330\) 0 0
\(331\) 208.163 136.911i 0.628891 0.413628i −0.194660 0.980871i \(-0.562360\pi\)
0.823551 + 0.567243i \(0.191990\pi\)
\(332\) 0 0
\(333\) 77.6281 113.173i 0.233117 0.339859i
\(334\) 0 0
\(335\) 70.0403 599.233i 0.209075 1.78876i
\(336\) 0 0
\(337\) −22.4371 74.9452i −0.0665790 0.222389i 0.918225 0.396059i \(-0.129623\pi\)
−0.984804 + 0.173670i \(0.944437\pi\)
\(338\) 0 0
\(339\) 399.074 + 38.8266i 1.17721 + 0.114533i
\(340\) 0 0
\(341\) 210.711 + 37.1541i 0.617922 + 0.108956i
\(342\) 0 0
\(343\) −76.8837 436.029i −0.224151 1.27122i
\(344\) 0 0
\(345\) 128.640 + 333.209i 0.372869 + 0.965823i
\(346\) 0 0
\(347\) 85.9382 130.663i 0.247660 0.376549i −0.690168 0.723649i \(-0.742463\pi\)
0.937828 + 0.347100i \(0.112834\pi\)
\(348\) 0 0
\(349\) 142.642 476.457i 0.408716 1.36521i −0.467800 0.883834i \(-0.654953\pi\)
0.876516 0.481372i \(-0.159861\pi\)
\(350\) 0 0
\(351\) −361.061 131.444i −1.02866 0.374486i
\(352\) 0 0
\(353\) 83.6354 78.9059i 0.236927 0.223529i −0.558615 0.829427i \(-0.688667\pi\)
0.795543 + 0.605897i \(0.207186\pi\)
\(354\) 0 0
\(355\) 32.8053 563.246i 0.0924094 1.58661i
\(356\) 0 0
\(357\) 569.614 497.077i 1.59556 1.39237i
\(358\) 0 0
\(359\) −40.0128 + 109.934i −0.111456 + 0.306224i −0.982863 0.184338i \(-0.940986\pi\)
0.871407 + 0.490561i \(0.163208\pi\)
\(360\) 0 0
\(361\) −823.409 + 299.696i −2.28091 + 0.830184i
\(362\) 0 0
\(363\) −249.080 + 19.3541i −0.686170 + 0.0533170i
\(364\) 0 0
\(365\) 69.9043 294.949i 0.191519 0.808080i
\(366\) 0 0
\(367\) −84.6431 196.225i −0.230635 0.534672i 0.763120 0.646257i \(-0.223667\pi\)
−0.993755 + 0.111585i \(0.964407\pi\)
\(368\) 0 0
\(369\) 11.7006 + 28.6436i 0.0317090 + 0.0776249i
\(370\) 0 0
\(371\) 783.128 45.6120i 2.11086 0.122943i
\(372\) 0 0
\(373\) 88.1077 204.257i 0.236214 0.547605i −0.758337 0.651863i \(-0.773988\pi\)
0.994550 + 0.104258i \(0.0332469\pi\)
\(374\) 0 0
\(375\) 184.743 + 238.372i 0.492649 + 0.635659i
\(376\) 0 0
\(377\) 83.8281 + 48.3982i 0.222356 + 0.128377i
\(378\) 0 0
\(379\) 289.707 + 501.788i 0.764399 + 1.32398i 0.940564 + 0.339618i \(0.110298\pi\)
−0.176164 + 0.984361i \(0.556369\pi\)
\(380\) 0 0
\(381\) 302.946 + 11.7629i 0.795135 + 0.0308737i
\(382\) 0 0
\(383\) −73.9675 632.833i −0.193127 1.65230i −0.647920 0.761708i \(-0.724361\pi\)
0.454794 0.890597i \(-0.349713\pi\)
\(384\) 0 0
\(385\) 363.828 + 182.721i 0.945008 + 0.474601i
\(386\) 0 0
\(387\) −104.003 62.7731i −0.268743 0.162204i
\(388\) 0 0
\(389\) −78.9710 58.7917i −0.203010 0.151136i 0.490853 0.871243i \(-0.336685\pi\)
−0.693863 + 0.720107i \(0.744093\pi\)
\(390\) 0 0
\(391\) 310.608 329.225i 0.794394 0.842008i
\(392\) 0 0
\(393\) −736.024 + 189.569i −1.87283 + 0.482364i
\(394\) 0 0
\(395\) −265.537 + 316.454i −0.672244 + 0.801150i
\(396\) 0 0
\(397\) −349.614 + 293.361i −0.880640 + 0.738945i −0.966311 0.257379i \(-0.917141\pi\)
0.0856707 + 0.996324i \(0.472697\pi\)
\(398\) 0 0
\(399\) −1077.34 594.483i −2.70009 1.48993i
\(400\) 0 0
\(401\) 69.8376 + 139.058i 0.174159 + 0.346778i 0.963729 0.266881i \(-0.0859931\pi\)
−0.789571 + 0.613659i \(0.789697\pi\)
\(402\) 0 0
\(403\) −482.400 + 114.331i −1.19702 + 0.283700i
\(404\) 0 0
\(405\) 140.550 + 438.490i 0.347038 + 1.08269i
\(406\) 0 0
\(407\) −21.5986 91.1315i −0.0530677 0.223910i
\(408\) 0 0
\(409\) 415.908 208.877i 1.01689 0.510701i 0.139370 0.990240i \(-0.455492\pi\)
0.877521 + 0.479539i \(0.159196\pi\)
\(410\) 0 0
\(411\) −32.9064 + 0.637439i −0.0800642 + 0.00155095i
\(412\) 0 0
\(413\) 379.195 + 451.907i 0.918147 + 1.09421i
\(414\) 0 0
\(415\) −383.359 321.677i −0.923758 0.775125i
\(416\) 0 0
\(417\) 509.698 + 141.897i 1.22230 + 0.340281i
\(418\) 0 0
\(419\) 188.971 + 178.285i 0.451005 + 0.425501i 0.877932 0.478785i \(-0.158922\pi\)
−0.426927 + 0.904286i \(0.640404\pi\)
\(420\) 0 0
\(421\) 102.618 137.840i 0.243748 0.327410i −0.663366 0.748295i \(-0.730873\pi\)
0.907114 + 0.420885i \(0.138280\pi\)
\(422\) 0 0
\(423\) 208.000 167.752i 0.491725 0.396576i
\(424\) 0 0
\(425\) −70.9624 + 141.298i −0.166970 + 0.332465i
\(426\) 0 0
\(427\) −256.241 + 29.9502i −0.600095 + 0.0701411i
\(428\) 0 0
\(429\) −232.006 + 122.201i −0.540807 + 0.284851i
\(430\) 0 0
\(431\) −85.6611 + 49.4564i −0.198750 + 0.114748i −0.596072 0.802931i \(-0.703273\pi\)
0.397323 + 0.917679i \(0.369939\pi\)
\(432\) 0 0
\(433\) 366.778 635.278i 0.847062 1.46715i −0.0367569 0.999324i \(-0.511703\pi\)
0.883819 0.467830i \(-0.154964\pi\)
\(434\) 0 0
\(435\) −15.6954 114.931i −0.0360814 0.264209i
\(436\) 0 0
\(437\) −676.437 291.786i −1.54791 0.667703i
\(438\) 0 0
\(439\) 17.3442 + 297.789i 0.0395085 + 0.678335i 0.958682 + 0.284481i \(0.0918214\pi\)
−0.919173 + 0.393854i \(0.871142\pi\)
\(440\) 0 0
\(441\) −165.671 764.998i −0.375671 1.73469i
\(442\) 0 0
\(443\) 246.735 106.431i 0.556964 0.240251i −0.0989420 0.995093i \(-0.531546\pi\)
0.655906 + 0.754842i \(0.272287\pi\)
\(444\) 0 0
\(445\) 147.968 + 35.0690i 0.332512 + 0.0788068i
\(446\) 0 0
\(447\) 375.383 257.445i 0.839784 0.575940i
\(448\) 0 0
\(449\) 116.174 + 319.185i 0.258739 + 0.710881i 0.999246 + 0.0388313i \(0.0123635\pi\)
−0.740506 + 0.672049i \(0.765414\pi\)
\(450\) 0 0
\(451\) 19.8420 + 7.22189i 0.0439955 + 0.0160131i
\(452\) 0 0
\(453\) −719.179 + 141.225i −1.58759 + 0.311754i
\(454\) 0 0
\(455\) −941.759 54.8512i −2.06980 0.120552i
\(456\) 0 0
\(457\) 230.720 + 244.549i 0.504858 + 0.535118i 0.928805 0.370569i \(-0.120837\pi\)
−0.423947 + 0.905687i \(0.639356\pi\)
\(458\) 0 0
\(459\) 424.456 400.397i 0.924741 0.872324i
\(460\) 0 0
\(461\) −547.795 163.999i −1.18827 0.355746i −0.369154 0.929368i \(-0.620353\pi\)
−0.819120 + 0.573622i \(0.805538\pi\)
\(462\) 0 0
\(463\) −468.978 308.451i −1.01291 0.666202i −0.0694153 0.997588i \(-0.522113\pi\)
−0.943495 + 0.331386i \(0.892484\pi\)
\(464\) 0 0
\(465\) 462.423 + 372.998i 0.994458 + 0.802147i
\(466\) 0 0
\(467\) 858.425 151.363i 1.83817 0.324119i 0.856711 0.515797i \(-0.172504\pi\)
0.981458 + 0.191678i \(0.0613930\pi\)
\(468\) 0 0
\(469\) −214.893 + 1218.72i −0.458195 + 2.59855i
\(470\) 0 0
\(471\) 690.848 + 493.813i 1.46677 + 1.04844i
\(472\) 0 0
\(473\) −79.4189 + 23.7765i −0.167905 + 0.0502674i
\(474\) 0 0
\(475\) 255.609 + 29.8764i 0.538125 + 0.0628978i
\(476\) 0 0
\(477\) 602.624 58.5871i 1.26336 0.122824i
\(478\) 0 0
\(479\) 22.1952 + 33.7461i 0.0463365 + 0.0704512i 0.857913 0.513795i \(-0.171761\pi\)
−0.811577 + 0.584246i \(0.801390\pi\)
\(480\) 0 0
\(481\) 129.588 + 174.066i 0.269413 + 0.361884i
\(482\) 0 0
\(483\) −223.680 697.669i −0.463106 1.44445i
\(484\) 0 0
\(485\) 243.258i 0.501562i
\(486\) 0 0
\(487\) −31.4352 −0.0645487 −0.0322743 0.999479i \(-0.510275\pi\)
−0.0322743 + 0.999479i \(0.510275\pi\)
\(488\) 0 0
\(489\) 686.590 220.128i 1.40407 0.450160i
\(490\) 0 0
\(491\) −331.401 + 246.719i −0.674951 + 0.502482i −0.879210 0.476434i \(-0.841929\pi\)
0.204259 + 0.978917i \(0.434522\pi\)
\(492\) 0 0
\(493\) −122.812 + 80.7745i −0.249111 + 0.163843i
\(494\) 0 0
\(495\) 286.064 + 130.048i 0.577907 + 0.262724i
\(496\) 0 0
\(497\) −134.354 + 1149.47i −0.270330 + 2.31282i
\(498\) 0 0
\(499\) 241.974 + 808.249i 0.484917 + 1.61974i 0.754178 + 0.656670i \(0.228035\pi\)
−0.269261 + 0.963067i \(0.586779\pi\)
\(500\) 0 0
\(501\) −473.660 + 662.653i −0.945428 + 1.32266i
\(502\) 0 0
\(503\) −253.898 44.7690i −0.504767 0.0890040i −0.0845346 0.996421i \(-0.526940\pi\)
−0.420232 + 0.907416i \(0.638051\pi\)
\(504\) 0 0
\(505\) −137.796 781.480i −0.272863 1.54748i
\(506\) 0 0
\(507\) 63.1491 78.2889i 0.124555 0.154416i
\(508\) 0 0
\(509\) −12.7762 + 19.4252i −0.0251005 + 0.0381634i −0.847820 0.530284i \(-0.822085\pi\)
0.822720 + 0.568447i \(0.192456\pi\)
\(510\) 0 0
\(511\) −178.324 + 595.643i −0.348970 + 1.16564i
\(512\) 0 0
\(513\) −848.666 426.291i −1.65432 0.830977i
\(514\) 0 0
\(515\) −271.818 + 256.447i −0.527802 + 0.497956i
\(516\) 0 0
\(517\) 10.6032 182.049i 0.0205090 0.352126i
\(518\) 0 0
\(519\) −162.343 826.726i −0.312800 1.59292i
\(520\) 0 0
\(521\) −62.8514 + 172.683i −0.120636 + 0.331445i −0.985282 0.170937i \(-0.945321\pi\)
0.864646 + 0.502382i \(0.167543\pi\)
\(522\) 0 0
\(523\) −671.395 + 244.368i −1.28374 + 0.467242i −0.891667 0.452693i \(-0.850463\pi\)
−0.392071 + 0.919935i \(0.628241\pi\)
\(524\) 0 0
\(525\) 144.756 + 211.070i 0.275726 + 0.402038i
\(526\) 0 0
\(527\) 173.622 732.568i 0.329453 1.39007i
\(528\) 0 0
\(529\) 35.7907 + 82.9721i 0.0676573 + 0.156847i
\(530\) 0 0
\(531\) 305.962 + 337.198i 0.576199 + 0.635025i
\(532\) 0 0
\(533\) −48.8429 + 2.84478i −0.0916378 + 0.00533729i
\(534\) 0 0
\(535\) −471.336 + 1092.68i −0.881002 + 2.04239i
\(536\) 0 0
\(537\) −373.425 + 50.9964i −0.695392 + 0.0949653i
\(538\) 0 0
\(539\) −462.599 267.082i −0.858255 0.495514i
\(540\) 0 0
\(541\) 225.360 + 390.335i 0.416561 + 0.721506i 0.995591 0.0938010i \(-0.0299017\pi\)
−0.579030 + 0.815307i \(0.696568\pi\)
\(542\) 0 0
\(543\) 139.605 + 265.049i 0.257099 + 0.488119i
\(544\) 0 0
\(545\) 27.5004 + 235.281i 0.0504594 + 0.431708i
\(546\) 0 0
\(547\) −733.120 368.187i −1.34026 0.673102i −0.373221 0.927743i \(-0.621747\pi\)
−0.967036 + 0.254640i \(0.918043\pi\)
\(548\) 0 0
\(549\) −196.730 + 30.7585i −0.358343 + 0.0560264i
\(550\) 0 0
\(551\) 191.905 + 142.868i 0.348286 + 0.259289i
\(552\) 0 0
\(553\) 581.493 616.347i 1.05152 1.11455i
\(554\) 0 0
\(555\) 69.7454 250.527i 0.125667 0.451400i
\(556\) 0 0
\(557\) 431.034 513.686i 0.773848 0.922237i −0.224790 0.974407i \(-0.572170\pi\)
0.998638 + 0.0521707i \(0.0166140\pi\)
\(558\) 0 0
\(559\) 147.148 123.472i 0.263235 0.220880i
\(560\) 0 0
\(561\) −7.71233 398.131i −0.0137475 0.709682i
\(562\) 0 0
\(563\) 322.900 + 642.947i 0.573535 + 1.14200i 0.974181 + 0.225769i \(0.0724896\pi\)
−0.400646 + 0.916233i \(0.631214\pi\)
\(564\) 0 0
\(565\) 739.303 175.218i 1.30850 0.310120i
\(566\) 0 0
\(567\) −235.513 914.677i −0.415367 1.61319i
\(568\) 0 0
\(569\) 180.519 + 761.670i 0.317257 + 1.33861i 0.864918 + 0.501912i \(0.167370\pi\)
−0.547661 + 0.836700i \(0.684482\pi\)
\(570\) 0 0
\(571\) 946.211 475.205i 1.65711 0.832233i 0.660426 0.750891i \(-0.270376\pi\)
0.996686 0.0813421i \(-0.0259206\pi\)
\(572\) 0 0
\(573\) 5.02364 9.10398i 0.00876726 0.0158883i
\(574\) 0 0
\(575\) 98.4950 + 117.382i 0.171296 + 0.204142i
\(576\) 0 0
\(577\) 636.586 + 534.159i 1.10327 + 0.925752i 0.997641 0.0686535i \(-0.0218703\pi\)
0.105628 + 0.994406i \(0.466315\pi\)
\(578\) 0 0
\(579\) 124.219 + 482.296i 0.214541 + 0.832981i
\(580\) 0 0
\(581\) 746.656 + 704.433i 1.28512 + 1.21245i
\(582\) 0 0
\(583\) 246.740 331.430i 0.423225 0.568490i
\(584\) 0 0
\(585\) −727.970 14.1534i −1.24439 0.0241939i
\(586\) 0 0
\(587\) −54.2594 + 108.039i −0.0924350 + 0.184053i −0.935099 0.354386i \(-0.884690\pi\)
0.842664 + 0.538440i \(0.180986\pi\)
\(588\) 0 0
\(589\) −1217.07 + 142.255i −2.06633 + 0.241519i
\(590\) 0 0
\(591\) −11.9276 + 307.189i −0.0201821 + 0.519778i
\(592\) 0 0
\(593\) 313.520 181.011i 0.528702 0.305246i −0.211786 0.977316i \(-0.567928\pi\)
0.740488 + 0.672070i \(0.234595\pi\)
\(594\) 0 0
\(595\) 716.284 1240.64i 1.20384 2.08511i
\(596\) 0 0
\(597\) −77.0631 + 59.7255i −0.129084 + 0.100043i
\(598\) 0 0
\(599\) −356.686 153.859i −0.595469 0.256860i 0.0769452 0.997035i \(-0.475483\pi\)
−0.672414 + 0.740175i \(0.734743\pi\)
\(600\) 0 0
\(601\) 15.2482 + 261.801i 0.0253714 + 0.435610i 0.986945 + 0.161061i \(0.0514915\pi\)
−0.961573 + 0.274549i \(0.911471\pi\)
\(602\) 0 0
\(603\) −129.307 + 946.361i −0.214440 + 1.56942i
\(604\) 0 0
\(605\) −434.690 + 187.507i −0.718497 + 0.309929i
\(606\) 0 0
\(607\) −83.7301 19.8444i −0.137941 0.0326926i 0.161065 0.986944i \(-0.448507\pi\)
−0.299006 + 0.954251i \(0.596655\pi\)
\(608\) 0 0
\(609\) 18.4326 + 237.221i 0.0302670 + 0.389525i
\(610\) 0 0
\(611\) 144.515 + 397.053i 0.236523 + 0.649841i
\(612\) 0 0
\(613\) 12.8212 + 4.66653i 0.0209155 + 0.00761261i 0.352457 0.935828i \(-0.385346\pi\)
−0.331541 + 0.943441i \(0.607569\pi\)
\(614\) 0 0
\(615\) 38.5501 + 44.1756i 0.0626831 + 0.0718302i
\(616\) 0 0
\(617\) −313.342 18.2501i −0.507847 0.0295787i −0.197691 0.980264i \(-0.563344\pi\)
−0.310156 + 0.950686i \(0.600381\pi\)
\(618\) 0 0
\(619\) −102.967 109.139i −0.166344 0.176314i 0.638840 0.769340i \(-0.279415\pi\)
−0.805184 + 0.593026i \(0.797933\pi\)
\(620\) 0 0
\(621\) −193.368 531.390i −0.311381 0.855701i
\(622\) 0 0
\(623\) −298.817 89.4600i −0.479643 0.143596i
\(624\) 0 0
\(625\) 630.275 + 414.538i 1.00844 + 0.663261i
\(626\) 0 0
\(627\) −604.625 + 233.424i −0.964315 + 0.372287i
\(628\) 0 0
\(629\) −324.538 + 57.2248i −0.515959 + 0.0909775i
\(630\) 0 0
\(631\) 147.025 833.822i 0.233004 1.32143i −0.613773 0.789482i \(-0.710349\pi\)
0.846777 0.531948i \(-0.178540\pi\)
\(632\) 0 0
\(633\) 56.5328 581.065i 0.0893093 0.917955i
\(634\) 0 0
\(635\) 550.356 164.766i 0.866702 0.259474i
\(636\) 0 0
\(637\) 1229.32 + 143.687i 1.92986 + 0.225569i
\(638\) 0 0
\(639\) −69.2610 + 890.544i −0.108390 + 1.39365i
\(640\) 0 0
\(641\) −433.403 658.957i −0.676136 1.02801i −0.996730 0.0807981i \(-0.974253\pi\)
0.320595 0.947216i \(-0.396117\pi\)
\(642\) 0 0
\(643\) 435.168 + 584.531i 0.676777 + 0.909069i 0.999297 0.0374936i \(-0.0119374\pi\)
−0.322520 + 0.946563i \(0.604530\pi\)
\(644\) 0 0
\(645\) −224.974 48.7380i −0.348797 0.0755628i
\(646\) 0 0
\(647\) 540.276i 0.835048i −0.908666 0.417524i \(-0.862898\pi\)
0.908666 0.417524i \(-0.137102\pi\)
\(648\) 0 0
\(649\) 310.726 0.478776
\(650\) 0 0
\(651\) −902.437 818.957i −1.38623 1.25800i
\(652\) 0 0
\(653\) 217.491 161.916i 0.333065 0.247958i −0.417614 0.908624i \(-0.637134\pi\)
0.750679 + 0.660667i \(0.229726\pi\)
\(654\) 0 0
\(655\) −1203.29 + 791.414i −1.83708 + 1.20827i
\(656\) 0 0
\(657\) −119.727 + 464.720i −0.182234 + 0.707336i
\(658\) 0 0
\(659\) 96.9441 829.409i 0.147108 1.25859i −0.694894 0.719113i \(-0.744549\pi\)
0.842001 0.539475i \(-0.181377\pi\)
\(660\) 0 0
\(661\) 138.086 + 461.240i 0.208905 + 0.697792i 0.996650 + 0.0817896i \(0.0260636\pi\)
−0.787744 + 0.616002i \(0.788751\pi\)
\(662\) 0 0
\(663\) 381.791 + 839.973i 0.575853 + 1.26693i
\(664\) 0 0
\(665\) −2296.22 404.886i −3.45296 0.608851i
\(666\) 0 0
\(667\) 24.7366 + 140.288i 0.0370863 + 0.210327i
\(668\) 0 0
\(669\) 373.037 + 58.3510i 0.557604 + 0.0872213i
\(670\) 0 0
\(671\) −74.6709 + 113.532i −0.111283 + 0.169198i
\(672\) 0 0
\(673\) −186.905 + 624.307i −0.277720 + 0.927648i 0.699359 + 0.714770i \(0.253469\pi\)
−0.977079 + 0.212878i \(0.931716\pi\)
\(674\) 0 0
\(675\) 117.952 + 158.461i 0.174744 + 0.234757i
\(676\) 0 0
\(677\) −745.201 + 703.061i −1.10074 + 1.03849i −0.101694 + 0.994816i \(0.532426\pi\)
−0.999046 + 0.0436787i \(0.986092\pi\)
\(678\) 0 0
\(679\) 29.0127 498.129i 0.0427286 0.733622i
\(680\) 0 0
\(681\) 1255.05 + 429.462i 1.84296 + 0.630634i
\(682\) 0 0
\(683\) −226.518 + 622.353i −0.331652 + 0.911205i 0.656031 + 0.754734i \(0.272234\pi\)
−0.987683 + 0.156471i \(0.949988\pi\)
\(684\) 0 0
\(685\) −58.6053 + 21.3306i −0.0855552 + 0.0311396i
\(686\) 0 0
\(687\) 131.235 274.439i 0.191027 0.399474i
\(688\) 0 0
\(689\) −220.789 + 931.583i −0.320449 + 1.35208i
\(690\) 0 0
\(691\) 207.987 + 482.167i 0.300994 + 0.697782i 0.999847 0.0174831i \(-0.00556532\pi\)
−0.698853 + 0.715265i \(0.746306\pi\)
\(692\) 0 0
\(693\) −570.275 300.424i −0.822907 0.433512i
\(694\) 0 0
\(695\) 1000.87 58.2940i 1.44010 0.0838762i
\(696\) 0 0
\(697\) 29.4280 68.2217i 0.0422209 0.0978790i
\(698\) 0 0
\(699\) 112.247 274.730i 0.160582 0.393032i
\(700\) 0 0
\(701\) −646.931 373.506i −0.922868 0.532818i −0.0383193 0.999266i \(-0.512200\pi\)
−0.884549 + 0.466447i \(0.845534\pi\)
\(702\) 0 0
\(703\) 268.183 + 464.506i 0.381484 + 0.660749i
\(704\) 0 0
\(705\) 269.999 428.361i 0.382978 0.607604i
\(706\) 0 0
\(707\) 188.966 + 1616.70i 0.267278 + 2.28671i
\(708\) 0 0
\(709\) −224.708 112.853i −0.316936 0.159171i 0.283218 0.959055i \(-0.408598\pi\)
−0.600154 + 0.799884i \(0.704894\pi\)
\(710\) 0 0
\(711\) 430.053 492.739i 0.604856 0.693022i
\(712\) 0 0
\(713\) −585.230 435.687i −0.820799 0.611062i
\(714\) 0 0
\(715\) −340.984 + 361.422i −0.476901 + 0.505486i
\(716\) 0 0
\(717\) −28.7184 29.2822i −0.0400535 0.0408398i
\(718\) 0 0
\(719\) 76.7779 91.5004i 0.106784 0.127261i −0.710005 0.704197i \(-0.751307\pi\)
0.816789 + 0.576936i \(0.195752\pi\)
\(720\) 0 0
\(721\) 587.199 492.719i 0.814423 0.683382i
\(722\) 0 0
\(723\) −254.704 + 153.706i −0.352287 + 0.212595i
\(724\) 0 0
\(725\) −22.3338 44.4703i −0.0308052 0.0613383i
\(726\) 0 0
\(727\) −3.58303 + 0.849193i −0.00492851 + 0.00116808i −0.233079 0.972458i \(-0.574880\pi\)
0.228151 + 0.973626i \(0.426732\pi\)
\(728\) 0 0
\(729\) −208.980 698.404i −0.286667 0.958030i
\(730\) 0 0
\(731\) 67.2715 + 283.841i 0.0920266 + 0.388291i
\(732\) 0 0
\(733\) −325.858 + 163.652i −0.444554 + 0.223263i −0.656971 0.753916i \(-0.728163\pi\)
0.212417 + 0.977179i \(0.431866\pi\)
\(734\) 0 0
\(735\) −766.344 1269.89i −1.04264 1.72775i
\(736\) 0 0
\(737\) 418.989 + 499.332i 0.568506 + 0.677519i
\(738\) 0 0
\(739\) 410.682 + 344.603i 0.555726 + 0.466310i 0.876875 0.480719i \(-0.159624\pi\)
−0.321148 + 0.947029i \(0.604069\pi\)
\(740\) 0 0
\(741\) 1072.16 1051.51i 1.44691 1.41905i
\(742\) 0 0
\(743\) 530.708 + 500.697i 0.714277 + 0.673886i 0.954966 0.296716i \(-0.0958916\pi\)
−0.240688 + 0.970603i \(0.577373\pi\)
\(744\) 0 0
\(745\) 515.068 691.857i 0.691367 0.928666i
\(746\) 0 0
\(747\) 596.914 + 520.975i 0.799082 + 0.697423i
\(748\) 0 0
\(749\) 1095.50 2181.31i 1.46261 2.91230i
\(750\) 0 0
\(751\) 572.563 66.9230i 0.762400 0.0891118i 0.273998 0.961730i \(-0.411654\pi\)
0.488402 + 0.872619i \(0.337580\pi\)
\(752\) 0 0
\(753\) −620.753 391.266i −0.824373 0.519610i
\(754\) 0 0
\(755\) −1202.75 + 694.405i −1.59304 + 0.919742i
\(756\) 0 0
\(757\) 76.0153 131.662i 0.100416 0.173926i −0.811440 0.584436i \(-0.801316\pi\)
0.911856 + 0.410510i \(0.134649\pi\)
\(758\) 0 0
\(759\) −357.236 145.957i −0.470667 0.192302i
\(760\) 0 0
\(761\) −18.5423 7.99837i −0.0243657 0.0105103i 0.383862 0.923390i \(-0.374594\pi\)
−0.408228 + 0.912880i \(0.633853\pi\)
\(762\) 0 0
\(763\) −28.2524 485.075i −0.0370280 0.635746i
\(764\) 0 0
\(765\) 515.349 978.254i 0.673659 1.27876i
\(766\) 0 0
\(767\) −661.089 + 285.166i −0.861916 + 0.371794i
\(768\) 0 0
\(769\) −30.1241 7.13955i −0.0391731 0.00928420i 0.210983 0.977490i \(-0.432334\pi\)
−0.250156 + 0.968206i \(0.580482\pi\)
\(770\) 0 0
\(771\) −953.471 455.945i −1.23667 0.591369i
\(772\) 0 0
\(773\) −400.057 1099.15i −0.517538 1.42192i −0.873225 0.487318i \(-0.837975\pi\)
0.355687 0.934605i \(-0.384247\pi\)
\(774\) 0 0
\(775\) 239.504 + 87.1721i 0.309037 + 0.112480i
\(776\) 0 0
\(777\) −172.700 + 504.697i −0.222266 + 0.649545i
\(778\) 0 0
\(779\) −120.723 7.03130i −0.154971 0.00902605i
\(780\) 0 0
\(781\) 418.315 + 443.388i 0.535615 + 0.567719i
\(782\) 0 0
\(783\) 21.3070 + 182.405i 0.0272120 + 0.232957i
\(784\) 0 0
\(785\) 1541.54 + 461.507i 1.96375 + 0.587907i
\(786\) 0 0
\(787\) 928.845 + 610.911i 1.18024 + 0.776253i 0.979114 0.203313i \(-0.0651710\pi\)
0.201122 + 0.979566i \(0.435541\pi\)
\(788\) 0 0
\(789\) 202.805 1296.53i 0.257041 1.64326i
\(790\) 0 0
\(791\) −1534.80 + 270.626i −1.94033 + 0.342132i
\(792\) 0 0
\(793\) 54.6745 310.075i 0.0689465 0.391015i
\(794\) 0 0
\(795\) 1044.47 474.742i 1.31380 0.597160i
\(796\) 0