Properties

Label 405.4.e.b.271.1
Level $405$
Weight $4$
Character 405.271
Analytic conductor $23.896$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.4.e.b.136.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.50000 - 4.33013i) q^{2} +(-8.50000 + 14.7224i) q^{4} +(2.50000 - 4.33013i) q^{5} +(15.0000 + 25.9808i) q^{7} +45.0000 q^{8} +O(q^{10})\) \(q+(-2.50000 - 4.33013i) q^{2} +(-8.50000 + 14.7224i) q^{4} +(2.50000 - 4.33013i) q^{5} +(15.0000 + 25.9808i) q^{7} +45.0000 q^{8} -25.0000 q^{10} +(-25.0000 - 43.3013i) q^{11} +(10.0000 - 17.3205i) q^{13} +(75.0000 - 129.904i) q^{14} +(-44.5000 - 77.0763i) q^{16} -10.0000 q^{17} -44.0000 q^{19} +(42.5000 + 73.6122i) q^{20} +(-125.000 + 216.506i) q^{22} +(-60.0000 + 103.923i) q^{23} +(-12.5000 - 21.6506i) q^{25} -100.000 q^{26} -510.000 q^{28} +(25.0000 + 43.3013i) q^{29} +(-54.0000 + 93.5307i) q^{31} +(-42.5000 + 73.6122i) q^{32} +(25.0000 + 43.3013i) q^{34} +150.000 q^{35} -40.0000 q^{37} +(110.000 + 190.526i) q^{38} +(112.500 - 194.856i) q^{40} +(-200.000 + 346.410i) q^{41} +(-140.000 - 242.487i) q^{43} +850.000 q^{44} +600.000 q^{46} +(140.000 + 242.487i) q^{47} +(-278.500 + 482.376i) q^{49} +(-62.5000 + 108.253i) q^{50} +(170.000 + 294.449i) q^{52} -610.000 q^{53} -250.000 q^{55} +(675.000 + 1169.13i) q^{56} +(125.000 - 216.506i) q^{58} +(-25.0000 + 43.3013i) q^{59} +(259.000 + 448.601i) q^{61} +540.000 q^{62} -287.000 q^{64} +(-50.0000 - 86.6025i) q^{65} +(90.0000 - 155.885i) q^{67} +(85.0000 - 147.224i) q^{68} +(-375.000 - 649.519i) q^{70} +700.000 q^{71} -410.000 q^{73} +(100.000 + 173.205i) q^{74} +(374.000 - 647.787i) q^{76} +(750.000 - 1299.04i) q^{77} +(258.000 + 446.869i) q^{79} -445.000 q^{80} +2000.00 q^{82} +(-330.000 - 571.577i) q^{83} +(-25.0000 + 43.3013i) q^{85} +(-700.000 + 1212.44i) q^{86} +(-1125.00 - 1948.56i) q^{88} -1500.00 q^{89} +600.000 q^{91} +(-1020.00 - 1766.69i) q^{92} +(700.000 - 1212.44i) q^{94} +(-110.000 + 190.526i) q^{95} +(815.000 + 1411.62i) q^{97} +2785.00 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 5 q^{2} - 17 q^{4} + 5 q^{5} + 30 q^{7} + 90 q^{8} + O(q^{10}) \) \( 2 q - 5 q^{2} - 17 q^{4} + 5 q^{5} + 30 q^{7} + 90 q^{8} - 50 q^{10} - 50 q^{11} + 20 q^{13} + 150 q^{14} - 89 q^{16} - 20 q^{17} - 88 q^{19} + 85 q^{20} - 250 q^{22} - 120 q^{23} - 25 q^{25} - 200 q^{26} - 1020 q^{28} + 50 q^{29} - 108 q^{31} - 85 q^{32} + 50 q^{34} + 300 q^{35} - 80 q^{37} + 220 q^{38} + 225 q^{40} - 400 q^{41} - 280 q^{43} + 1700 q^{44} + 1200 q^{46} + 280 q^{47} - 557 q^{49} - 125 q^{50} + 340 q^{52} - 1220 q^{53} - 500 q^{55} + 1350 q^{56} + 250 q^{58} - 50 q^{59} + 518 q^{61} + 1080 q^{62} - 574 q^{64} - 100 q^{65} + 180 q^{67} + 170 q^{68} - 750 q^{70} + 1400 q^{71} - 820 q^{73} + 200 q^{74} + 748 q^{76} + 1500 q^{77} + 516 q^{79} - 890 q^{80} + 4000 q^{82} - 660 q^{83} - 50 q^{85} - 1400 q^{86} - 2250 q^{88} - 3000 q^{89} + 1200 q^{91} - 2040 q^{92} + 1400 q^{94} - 220 q^{95} + 1630 q^{97} + 5570 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.50000 4.33013i −0.883883 1.53093i −0.846988 0.531612i \(-0.821586\pi\)
−0.0368954 0.999319i \(-0.511747\pi\)
\(3\) 0 0
\(4\) −8.50000 + 14.7224i −1.06250 + 1.84030i
\(5\) 2.50000 4.33013i 0.223607 0.387298i
\(6\) 0 0
\(7\) 15.0000 + 25.9808i 0.809924 + 1.40283i 0.912916 + 0.408147i \(0.133825\pi\)
−0.102992 + 0.994682i \(0.532842\pi\)
\(8\) 45.0000 1.98874
\(9\) 0 0
\(10\) −25.0000 −0.790569
\(11\) −25.0000 43.3013i −0.685253 1.18689i −0.973357 0.229294i \(-0.926358\pi\)
0.288104 0.957599i \(-0.406975\pi\)
\(12\) 0 0
\(13\) 10.0000 17.3205i 0.213346 0.369527i −0.739413 0.673252i \(-0.764897\pi\)
0.952760 + 0.303725i \(0.0982304\pi\)
\(14\) 75.0000 129.904i 1.43176 2.47988i
\(15\) 0 0
\(16\) −44.5000 77.0763i −0.695312 1.20432i
\(17\) −10.0000 −0.142668 −0.0713340 0.997452i \(-0.522726\pi\)
−0.0713340 + 0.997452i \(0.522726\pi\)
\(18\) 0 0
\(19\) −44.0000 −0.531279 −0.265639 0.964072i \(-0.585583\pi\)
−0.265639 + 0.964072i \(0.585583\pi\)
\(20\) 42.5000 + 73.6122i 0.475164 + 0.823009i
\(21\) 0 0
\(22\) −125.000 + 216.506i −1.21137 + 2.09815i
\(23\) −60.0000 + 103.923i −0.543951 + 0.942150i 0.454721 + 0.890634i \(0.349739\pi\)
−0.998672 + 0.0515165i \(0.983595\pi\)
\(24\) 0 0
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −100.000 −0.754293
\(27\) 0 0
\(28\) −510.000 −3.44218
\(29\) 25.0000 + 43.3013i 0.160082 + 0.277270i 0.934898 0.354917i \(-0.115491\pi\)
−0.774816 + 0.632187i \(0.782157\pi\)
\(30\) 0 0
\(31\) −54.0000 + 93.5307i −0.312861 + 0.541891i −0.978980 0.203954i \(-0.934621\pi\)
0.666120 + 0.745845i \(0.267954\pi\)
\(32\) −42.5000 + 73.6122i −0.234782 + 0.406654i
\(33\) 0 0
\(34\) 25.0000 + 43.3013i 0.126102 + 0.218415i
\(35\) 150.000 0.724418
\(36\) 0 0
\(37\) −40.0000 −0.177729 −0.0888643 0.996044i \(-0.528324\pi\)
−0.0888643 + 0.996044i \(0.528324\pi\)
\(38\) 110.000 + 190.526i 0.469588 + 0.813351i
\(39\) 0 0
\(40\) 112.500 194.856i 0.444695 0.770235i
\(41\) −200.000 + 346.410i −0.761823 + 1.31952i 0.180087 + 0.983651i \(0.442362\pi\)
−0.941910 + 0.335866i \(0.890971\pi\)
\(42\) 0 0
\(43\) −140.000 242.487i −0.496507 0.859975i 0.503485 0.864004i \(-0.332051\pi\)
−0.999992 + 0.00402871i \(0.998718\pi\)
\(44\) 850.000 2.91233
\(45\) 0 0
\(46\) 600.000 1.92316
\(47\) 140.000 + 242.487i 0.434491 + 0.752561i 0.997254 0.0740573i \(-0.0235948\pi\)
−0.562763 + 0.826619i \(0.690261\pi\)
\(48\) 0 0
\(49\) −278.500 + 482.376i −0.811953 + 1.40634i
\(50\) −62.5000 + 108.253i −0.176777 + 0.306186i
\(51\) 0 0
\(52\) 170.000 + 294.449i 0.453361 + 0.785244i
\(53\) −610.000 −1.58094 −0.790471 0.612499i \(-0.790164\pi\)
−0.790471 + 0.612499i \(0.790164\pi\)
\(54\) 0 0
\(55\) −250.000 −0.612909
\(56\) 675.000 + 1169.13i 1.61073 + 2.78986i
\(57\) 0 0
\(58\) 125.000 216.506i 0.282988 0.490150i
\(59\) −25.0000 + 43.3013i −0.0551648 + 0.0955482i −0.892289 0.451465i \(-0.850902\pi\)
0.837124 + 0.547013i \(0.184235\pi\)
\(60\) 0 0
\(61\) 259.000 + 448.601i 0.543632 + 0.941598i 0.998692 + 0.0511373i \(0.0162846\pi\)
−0.455060 + 0.890461i \(0.650382\pi\)
\(62\) 540.000 1.10613
\(63\) 0 0
\(64\) −287.000 −0.560547
\(65\) −50.0000 86.6025i −0.0954113 0.165257i
\(66\) 0 0
\(67\) 90.0000 155.885i 0.164108 0.284244i −0.772230 0.635343i \(-0.780859\pi\)
0.936338 + 0.351099i \(0.114192\pi\)
\(68\) 85.0000 147.224i 0.151585 0.262553i
\(69\) 0 0
\(70\) −375.000 649.519i −0.640301 1.10903i
\(71\) 700.000 1.17007 0.585033 0.811009i \(-0.301081\pi\)
0.585033 + 0.811009i \(0.301081\pi\)
\(72\) 0 0
\(73\) −410.000 −0.657354 −0.328677 0.944442i \(-0.606603\pi\)
−0.328677 + 0.944442i \(0.606603\pi\)
\(74\) 100.000 + 173.205i 0.157091 + 0.272090i
\(75\) 0 0
\(76\) 374.000 647.787i 0.564483 0.977714i
\(77\) 750.000 1299.04i 1.11001 1.92259i
\(78\) 0 0
\(79\) 258.000 + 446.869i 0.367434 + 0.636414i 0.989164 0.146818i \(-0.0469031\pi\)
−0.621730 + 0.783232i \(0.713570\pi\)
\(80\) −445.000 −0.621906
\(81\) 0 0
\(82\) 2000.00 2.69345
\(83\) −330.000 571.577i −0.436412 0.755888i 0.560998 0.827817i \(-0.310418\pi\)
−0.997410 + 0.0719295i \(0.977084\pi\)
\(84\) 0 0
\(85\) −25.0000 + 43.3013i −0.0319015 + 0.0552551i
\(86\) −700.000 + 1212.44i −0.877709 + 1.52024i
\(87\) 0 0
\(88\) −1125.00 1948.56i −1.36279 2.36042i
\(89\) −1500.00 −1.78651 −0.893257 0.449547i \(-0.851585\pi\)
−0.893257 + 0.449547i \(0.851585\pi\)
\(90\) 0 0
\(91\) 600.000 0.691177
\(92\) −1020.00 1766.69i −1.15590 2.00207i
\(93\) 0 0
\(94\) 700.000 1212.44i 0.768080 1.33035i
\(95\) −110.000 + 190.526i −0.118797 + 0.205763i
\(96\) 0 0
\(97\) 815.000 + 1411.62i 0.853100 + 1.47761i 0.878396 + 0.477933i \(0.158614\pi\)
−0.0252963 + 0.999680i \(0.508053\pi\)
\(98\) 2785.00 2.87069
\(99\) 0 0
\(100\) 425.000 0.425000
\(101\) 225.000 + 389.711i 0.221667 + 0.383938i 0.955314 0.295592i \(-0.0955170\pi\)
−0.733647 + 0.679530i \(0.762184\pi\)
\(102\) 0 0
\(103\) −385.000 + 666.840i −0.368303 + 0.637919i −0.989300 0.145893i \(-0.953394\pi\)
0.620998 + 0.783812i \(0.286728\pi\)
\(104\) 450.000 779.423i 0.424290 0.734891i
\(105\) 0 0
\(106\) 1525.00 + 2641.38i 1.39737 + 2.42031i
\(107\) 660.000 0.596305 0.298152 0.954518i \(-0.403630\pi\)
0.298152 + 0.954518i \(0.403630\pi\)
\(108\) 0 0
\(109\) 1754.00 1.54131 0.770655 0.637253i \(-0.219929\pi\)
0.770655 + 0.637253i \(0.219929\pi\)
\(110\) 625.000 + 1082.53i 0.541740 + 0.938321i
\(111\) 0 0
\(112\) 1335.00 2312.29i 1.12630 1.95081i
\(113\) 155.000 268.468i 0.129037 0.223499i −0.794267 0.607569i \(-0.792145\pi\)
0.923304 + 0.384071i \(0.125478\pi\)
\(114\) 0 0
\(115\) 300.000 + 519.615i 0.243262 + 0.421342i
\(116\) −850.000 −0.680349
\(117\) 0 0
\(118\) 250.000 0.195037
\(119\) −150.000 259.808i −0.115550 0.200139i
\(120\) 0 0
\(121\) −584.500 + 1012.38i −0.439144 + 0.760619i
\(122\) 1295.00 2243.01i 0.961015 1.66453i
\(123\) 0 0
\(124\) −918.000 1590.02i −0.664829 1.15152i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −1070.00 −0.747615 −0.373808 0.927506i \(-0.621948\pi\)
−0.373808 + 0.927506i \(0.621948\pi\)
\(128\) 1057.50 + 1831.64i 0.730240 + 1.26481i
\(129\) 0 0
\(130\) −250.000 + 433.013i −0.168665 + 0.292136i
\(131\) −975.000 + 1688.75i −0.650276 + 1.12631i 0.332780 + 0.943005i \(0.392013\pi\)
−0.983056 + 0.183306i \(0.941320\pi\)
\(132\) 0 0
\(133\) −660.000 1143.15i −0.430295 0.745293i
\(134\) −900.000 −0.580210
\(135\) 0 0
\(136\) −450.000 −0.283729
\(137\) −525.000 909.327i −0.327400 0.567073i 0.654595 0.755980i \(-0.272839\pi\)
−0.981995 + 0.188906i \(0.939506\pi\)
\(138\) 0 0
\(139\) −838.000 + 1451.46i −0.511354 + 0.885691i 0.488559 + 0.872531i \(0.337523\pi\)
−0.999913 + 0.0131607i \(0.995811\pi\)
\(140\) −1275.00 + 2208.36i −0.769694 + 1.33315i
\(141\) 0 0
\(142\) −1750.00 3031.09i −1.03420 1.79129i
\(143\) −1000.00 −0.584785
\(144\) 0 0
\(145\) 250.000 0.143182
\(146\) 1025.00 + 1775.35i 0.581025 + 1.00636i
\(147\) 0 0
\(148\) 340.000 588.897i 0.188837 0.327075i
\(149\) −1025.00 + 1775.35i −0.563566 + 0.976124i 0.433616 + 0.901098i \(0.357237\pi\)
−0.997182 + 0.0750264i \(0.976096\pi\)
\(150\) 0 0
\(151\) −224.000 387.979i −0.120721 0.209095i 0.799331 0.600891i \(-0.205187\pi\)
−0.920052 + 0.391796i \(0.871854\pi\)
\(152\) −1980.00 −1.05657
\(153\) 0 0
\(154\) −7500.00 −3.92446
\(155\) 270.000 + 467.654i 0.139916 + 0.242341i
\(156\) 0 0
\(157\) 50.0000 86.6025i 0.0254168 0.0440232i −0.853037 0.521850i \(-0.825242\pi\)
0.878454 + 0.477827i \(0.158575\pi\)
\(158\) 1290.00 2234.35i 0.649537 1.12503i
\(159\) 0 0
\(160\) 212.500 + 368.061i 0.104998 + 0.181861i
\(161\) −3600.00 −1.76223
\(162\) 0 0
\(163\) −1900.00 −0.913003 −0.456501 0.889723i \(-0.650898\pi\)
−0.456501 + 0.889723i \(0.650898\pi\)
\(164\) −3400.00 5888.97i −1.61887 2.80397i
\(165\) 0 0
\(166\) −1650.00 + 2857.88i −0.771475 + 1.33623i
\(167\) −960.000 + 1662.77i −0.444833 + 0.770473i −0.998041 0.0625706i \(-0.980070\pi\)
0.553208 + 0.833043i \(0.313403\pi\)
\(168\) 0 0
\(169\) 898.500 + 1556.25i 0.408967 + 0.708351i
\(170\) 250.000 0.112789
\(171\) 0 0
\(172\) 4760.00 2.11015
\(173\) −1275.00 2208.36i −0.560326 0.970514i −0.997468 0.0711209i \(-0.977342\pi\)
0.437141 0.899393i \(-0.355991\pi\)
\(174\) 0 0
\(175\) 375.000 649.519i 0.161985 0.280566i
\(176\) −2225.00 + 3853.81i −0.952930 + 1.65052i
\(177\) 0 0
\(178\) 3750.00 + 6495.19i 1.57907 + 2.73503i
\(179\) 3650.00 1.52410 0.762050 0.647518i \(-0.224193\pi\)
0.762050 + 0.647518i \(0.224193\pi\)
\(180\) 0 0
\(181\) −4342.00 −1.78308 −0.891542 0.452937i \(-0.850376\pi\)
−0.891542 + 0.452937i \(0.850376\pi\)
\(182\) −1500.00 2598.08i −0.610920 1.05814i
\(183\) 0 0
\(184\) −2700.00 + 4676.54i −1.08178 + 1.87369i
\(185\) −100.000 + 173.205i −0.0397413 + 0.0688340i
\(186\) 0 0
\(187\) 250.000 + 433.013i 0.0977637 + 0.169332i
\(188\) −4760.00 −1.84659
\(189\) 0 0
\(190\) 1100.00 0.420013
\(191\) 1750.00 + 3031.09i 0.662961 + 1.14828i 0.979834 + 0.199814i \(0.0640338\pi\)
−0.316873 + 0.948468i \(0.602633\pi\)
\(192\) 0 0
\(193\) −1675.00 + 2901.19i −0.624711 + 1.08203i 0.363886 + 0.931443i \(0.381450\pi\)
−0.988597 + 0.150587i \(0.951884\pi\)
\(194\) 4075.00 7058.11i 1.50808 2.61208i
\(195\) 0 0
\(196\) −4734.50 8200.39i −1.72540 2.98848i
\(197\) 90.0000 0.0325494 0.0162747 0.999868i \(-0.494819\pi\)
0.0162747 + 0.999868i \(0.494819\pi\)
\(198\) 0 0
\(199\) 3664.00 1.30520 0.652598 0.757704i \(-0.273679\pi\)
0.652598 + 0.757704i \(0.273679\pi\)
\(200\) −562.500 974.279i −0.198874 0.344459i
\(201\) 0 0
\(202\) 1125.00 1948.56i 0.391855 0.678713i
\(203\) −750.000 + 1299.04i −0.259309 + 0.449136i
\(204\) 0 0
\(205\) 1000.00 + 1732.05i 0.340698 + 0.590106i
\(206\) 3850.00 1.30215
\(207\) 0 0
\(208\) −1780.00 −0.593369
\(209\) 1100.00 + 1905.26i 0.364060 + 0.630571i
\(210\) 0 0
\(211\) 134.000 232.095i 0.0437201 0.0757254i −0.843337 0.537385i \(-0.819412\pi\)
0.887057 + 0.461659i \(0.152746\pi\)
\(212\) 5185.00 8980.68i 1.67975 2.90941i
\(213\) 0 0
\(214\) −1650.00 2857.88i −0.527064 0.912901i
\(215\) −1400.00 −0.444089
\(216\) 0 0
\(217\) −3240.00 −1.01357
\(218\) −4385.00 7595.04i −1.36234 2.35964i
\(219\) 0 0
\(220\) 2125.00 3680.61i 0.651216 1.12794i
\(221\) −100.000 + 173.205i −0.0304377 + 0.0527196i
\(222\) 0 0
\(223\) 1835.00 + 3178.31i 0.551034 + 0.954420i 0.998200 + 0.0599686i \(0.0191001\pi\)
−0.447166 + 0.894451i \(0.647567\pi\)
\(224\) −2550.00 −0.760621
\(225\) 0 0
\(226\) −1550.00 −0.456214
\(227\) −1880.00 3256.26i −0.549692 0.952094i −0.998295 0.0583630i \(-0.981412\pi\)
0.448604 0.893731i \(-0.351921\pi\)
\(228\) 0 0
\(229\) 717.000 1241.88i 0.206903 0.358366i −0.743835 0.668364i \(-0.766995\pi\)
0.950737 + 0.309998i \(0.100328\pi\)
\(230\) 1500.00 2598.08i 0.430031 0.744835i
\(231\) 0 0
\(232\) 1125.00 + 1948.56i 0.318362 + 0.551418i
\(233\) −3450.00 −0.970030 −0.485015 0.874506i \(-0.661186\pi\)
−0.485015 + 0.874506i \(0.661186\pi\)
\(234\) 0 0
\(235\) 1400.00 0.388621
\(236\) −425.000 736.122i −0.117225 0.203040i
\(237\) 0 0
\(238\) −750.000 + 1299.04i −0.204266 + 0.353799i
\(239\) 2450.00 4243.52i 0.663085 1.14850i −0.316716 0.948521i \(-0.602580\pi\)
0.979801 0.199976i \(-0.0640866\pi\)
\(240\) 0 0
\(241\) −2411.00 4175.97i −0.644424 1.11617i −0.984434 0.175753i \(-0.943764\pi\)
0.340010 0.940422i \(-0.389569\pi\)
\(242\) 5845.00 1.55261
\(243\) 0 0
\(244\) −8806.00 −2.31044
\(245\) 1392.50 + 2411.88i 0.363117 + 0.628936i
\(246\) 0 0
\(247\) −440.000 + 762.102i −0.113346 + 0.196322i
\(248\) −2430.00 + 4208.88i −0.622198 + 1.07768i
\(249\) 0 0
\(250\) 312.500 + 541.266i 0.0790569 + 0.136931i
\(251\) −4650.00 −1.16934 −0.584672 0.811270i \(-0.698777\pi\)
−0.584672 + 0.811270i \(0.698777\pi\)
\(252\) 0 0
\(253\) 6000.00 1.49098
\(254\) 2675.00 + 4633.24i 0.660805 + 1.14455i
\(255\) 0 0
\(256\) 4139.50 7169.82i 1.01062 1.75045i
\(257\) −2565.00 + 4442.71i −0.622569 + 1.07832i 0.366436 + 0.930443i \(0.380578\pi\)
−0.989006 + 0.147878i \(0.952756\pi\)
\(258\) 0 0
\(259\) −600.000 1039.23i −0.143947 0.249323i
\(260\) 1700.00 0.405498
\(261\) 0 0
\(262\) 9750.00 2.29907
\(263\) 640.000 + 1108.51i 0.150054 + 0.259900i 0.931247 0.364389i \(-0.118722\pi\)
−0.781193 + 0.624289i \(0.785389\pi\)
\(264\) 0 0
\(265\) −1525.00 + 2641.38i −0.353509 + 0.612296i
\(266\) −3300.00 + 5715.77i −0.760662 + 1.31750i
\(267\) 0 0
\(268\) 1530.00 + 2650.04i 0.348730 + 0.604018i
\(269\) 3350.00 0.759305 0.379653 0.925129i \(-0.376044\pi\)
0.379653 + 0.925129i \(0.376044\pi\)
\(270\) 0 0
\(271\) 5512.00 1.23554 0.617768 0.786361i \(-0.288037\pi\)
0.617768 + 0.786361i \(0.288037\pi\)
\(272\) 445.000 + 770.763i 0.0991989 + 0.171817i
\(273\) 0 0
\(274\) −2625.00 + 4546.63i −0.578767 + 1.00245i
\(275\) −625.000 + 1082.53i −0.137051 + 0.237379i
\(276\) 0 0
\(277\) −2460.00 4260.84i −0.533600 0.924222i −0.999230 0.0392421i \(-0.987506\pi\)
0.465630 0.884979i \(-0.345828\pi\)
\(278\) 8380.00 1.80791
\(279\) 0 0
\(280\) 6750.00 1.44068
\(281\) −2250.00 3897.11i −0.477665 0.827339i 0.522008 0.852941i \(-0.325183\pi\)
−0.999672 + 0.0256015i \(0.991850\pi\)
\(282\) 0 0
\(283\) 3450.00 5975.58i 0.724669 1.25516i −0.234442 0.972130i \(-0.575326\pi\)
0.959110 0.283033i \(-0.0913405\pi\)
\(284\) −5950.00 + 10305.7i −1.24320 + 2.15328i
\(285\) 0 0
\(286\) 2500.00 + 4330.13i 0.516881 + 0.895265i
\(287\) −12000.0 −2.46808
\(288\) 0 0
\(289\) −4813.00 −0.979646
\(290\) −625.000 1082.53i −0.126556 0.219202i
\(291\) 0 0
\(292\) 3485.00 6036.20i 0.698439 1.20973i
\(293\) −765.000 + 1325.02i −0.152532 + 0.264193i −0.932158 0.362053i \(-0.882076\pi\)
0.779626 + 0.626246i \(0.215409\pi\)
\(294\) 0 0
\(295\) 125.000 + 216.506i 0.0246704 + 0.0427305i
\(296\) −1800.00 −0.353456
\(297\) 0 0
\(298\) 10250.0 1.99251
\(299\) 1200.00 + 2078.46i 0.232100 + 0.402008i
\(300\) 0 0
\(301\) 4200.00 7274.61i 0.804266 1.39303i
\(302\) −1120.00 + 1939.90i −0.213406 + 0.369631i
\(303\) 0 0
\(304\) 1958.00 + 3391.36i 0.369405 + 0.639828i
\(305\) 2590.00 0.486239
\(306\) 0 0
\(307\) 3040.00 0.565153 0.282576 0.959245i \(-0.408811\pi\)
0.282576 + 0.959245i \(0.408811\pi\)
\(308\) 12750.0 + 22083.6i 2.35876 + 4.08550i
\(309\) 0 0
\(310\) 1350.00 2338.27i 0.247338 0.428402i
\(311\) 2850.00 4936.34i 0.519642 0.900046i −0.480097 0.877215i \(-0.659399\pi\)
0.999739 0.0228312i \(-0.00726802\pi\)
\(312\) 0 0
\(313\) −1555.00 2693.34i −0.280811 0.486379i 0.690774 0.723071i \(-0.257270\pi\)
−0.971585 + 0.236692i \(0.923937\pi\)
\(314\) −500.000 −0.0898619
\(315\) 0 0
\(316\) −8772.00 −1.56159
\(317\) 475.000 + 822.724i 0.0841598 + 0.145769i 0.905033 0.425342i \(-0.139846\pi\)
−0.820873 + 0.571111i \(0.806513\pi\)
\(318\) 0 0
\(319\) 1250.00 2165.06i 0.219394 0.380001i
\(320\) −717.500 + 1242.75i −0.125342 + 0.217099i
\(321\) 0 0
\(322\) 9000.00 + 15588.5i 1.55761 + 2.69786i
\(323\) 440.000 0.0757965
\(324\) 0 0
\(325\) −500.000 −0.0853385
\(326\) 4750.00 + 8227.24i 0.806988 + 1.39774i
\(327\) 0 0
\(328\) −9000.00 + 15588.5i −1.51507 + 2.62417i
\(329\) −4200.00 + 7274.61i −0.703810 + 1.21903i
\(330\) 0 0
\(331\) −1146.00 1984.93i −0.190302 0.329612i 0.755049 0.655669i \(-0.227613\pi\)
−0.945350 + 0.326057i \(0.894280\pi\)
\(332\) 11220.0 1.85475
\(333\) 0 0
\(334\) 9600.00 1.57272
\(335\) −450.000 779.423i −0.0733914 0.127118i
\(336\) 0 0
\(337\) 3865.00 6694.38i 0.624748 1.08209i −0.363842 0.931461i \(-0.618535\pi\)
0.988590 0.150634i \(-0.0481315\pi\)
\(338\) 4492.50 7781.24i 0.722958 1.25220i
\(339\) 0 0
\(340\) −425.000 736.122i −0.0677908 0.117417i
\(341\) 5400.00 0.857555
\(342\) 0 0
\(343\) −6420.00 −1.01063
\(344\) −6300.00 10911.9i −0.987422 1.71027i
\(345\) 0 0
\(346\) −6375.00 + 11041.8i −0.990526 + 1.71564i
\(347\) 560.000 969.948i 0.0866351 0.150056i −0.819452 0.573148i \(-0.805722\pi\)
0.906087 + 0.423092i \(0.139055\pi\)
\(348\) 0 0
\(349\) −593.000 1027.11i −0.0909529 0.157535i 0.816959 0.576695i \(-0.195658\pi\)
−0.907912 + 0.419160i \(0.862325\pi\)
\(350\) −3750.00 −0.572703
\(351\) 0 0
\(352\) 4250.00 0.643539
\(353\) −1815.00 3143.67i −0.273662 0.473997i 0.696135 0.717911i \(-0.254902\pi\)
−0.969797 + 0.243915i \(0.921568\pi\)
\(354\) 0 0
\(355\) 1750.00 3031.09i 0.261635 0.453165i
\(356\) 12750.0 22083.6i 1.89817 3.28773i
\(357\) 0 0
\(358\) −9125.00 15805.0i −1.34713 2.33329i
\(359\) −1800.00 −0.264625 −0.132312 0.991208i \(-0.542240\pi\)
−0.132312 + 0.991208i \(0.542240\pi\)
\(360\) 0 0
\(361\) −4923.00 −0.717743
\(362\) 10855.0 + 18801.4i 1.57604 + 2.72978i
\(363\) 0 0
\(364\) −5100.00 + 8833.46i −0.734375 + 1.27198i
\(365\) −1025.00 + 1775.35i −0.146989 + 0.254592i
\(366\) 0 0
\(367\) −4245.00 7352.56i −0.603780 1.04578i −0.992243 0.124313i \(-0.960327\pi\)
0.388463 0.921464i \(-0.373006\pi\)
\(368\) 10680.0 1.51286
\(369\) 0 0
\(370\) 1000.00 0.140507
\(371\) −9150.00 15848.3i −1.28044 2.21779i
\(372\) 0 0
\(373\) −50.0000 + 86.6025i −0.00694076 + 0.0120217i −0.869475 0.493977i \(-0.835543\pi\)
0.862534 + 0.505999i \(0.168876\pi\)
\(374\) 1250.00 2165.06i 0.172823 0.299339i
\(375\) 0 0
\(376\) 6300.00 + 10911.9i 0.864090 + 1.49665i
\(377\) 1000.00 0.136612
\(378\) 0 0
\(379\) −8084.00 −1.09564 −0.547820 0.836597i \(-0.684542\pi\)
−0.547820 + 0.836597i \(0.684542\pi\)
\(380\) −1870.00 3238.94i −0.252445 0.437247i
\(381\) 0 0
\(382\) 8750.00 15155.4i 1.17196 2.02990i
\(383\) 4740.00 8209.92i 0.632383 1.09532i −0.354680 0.934988i \(-0.615410\pi\)
0.987063 0.160332i \(-0.0512564\pi\)
\(384\) 0 0
\(385\) −3750.00 6495.19i −0.496410 0.859807i
\(386\) 16750.0 2.20869
\(387\) 0 0
\(388\) −27710.0 −3.62568
\(389\) 5475.00 + 9482.98i 0.713608 + 1.23601i 0.963494 + 0.267730i \(0.0862735\pi\)
−0.249886 + 0.968275i \(0.580393\pi\)
\(390\) 0 0
\(391\) 600.000 1039.23i 0.0776044 0.134415i
\(392\) −12532.5 + 21706.9i −1.61476 + 2.79685i
\(393\) 0 0
\(394\) −225.000 389.711i −0.0287699 0.0498309i
\(395\) 2580.00 0.328643
\(396\) 0 0
\(397\) 13840.0 1.74965 0.874823 0.484442i \(-0.160977\pi\)
0.874823 + 0.484442i \(0.160977\pi\)
\(398\) −9160.00 15865.6i −1.15364 1.99817i
\(399\) 0 0
\(400\) −1112.50 + 1926.91i −0.139063 + 0.240863i
\(401\) −4650.00 + 8054.04i −0.579077 + 1.00299i 0.416508 + 0.909132i \(0.363254\pi\)
−0.995585 + 0.0938591i \(0.970080\pi\)
\(402\) 0 0
\(403\) 1080.00 + 1870.61i 0.133495 + 0.231221i
\(404\) −7650.00 −0.942083
\(405\) 0 0
\(406\) 7500.00 0.916795
\(407\) 1000.00 + 1732.05i 0.121789 + 0.210945i
\(408\) 0 0
\(409\) 1427.00 2471.64i 0.172520 0.298813i −0.766780 0.641910i \(-0.778142\pi\)
0.939300 + 0.343096i \(0.111476\pi\)
\(410\) 5000.00 8660.25i 0.602274 1.04317i
\(411\) 0 0
\(412\) −6545.00 11336.3i −0.782643 1.35558i
\(413\) −1500.00 −0.178717
\(414\) 0 0
\(415\) −3300.00 −0.390339
\(416\) 850.000 + 1472.24i 0.100180 + 0.173516i
\(417\) 0 0
\(418\) 5500.00 9526.28i 0.643574 1.11470i
\(419\) −575.000 + 995.929i −0.0670420 + 0.116120i −0.897598 0.440815i \(-0.854689\pi\)
0.830556 + 0.556935i \(0.188023\pi\)
\(420\) 0 0
\(421\) 5581.00 + 9666.58i 0.646084 + 1.11905i 0.984050 + 0.177892i \(0.0569277\pi\)
−0.337966 + 0.941158i \(0.609739\pi\)
\(422\) −1340.00 −0.154574
\(423\) 0 0
\(424\) −27450.0 −3.14408
\(425\) 125.000 + 216.506i 0.0142668 + 0.0247108i
\(426\) 0 0
\(427\) −7770.00 + 13458.0i −0.880601 + 1.52525i
\(428\) −5610.00 + 9716.81i −0.633574 + 1.09738i
\(429\) 0 0
\(430\) 3500.00 + 6062.18i 0.392523 + 0.679870i
\(431\) −1200.00 −0.134111 −0.0670556 0.997749i \(-0.521361\pi\)
−0.0670556 + 0.997749i \(0.521361\pi\)
\(432\) 0 0
\(433\) 1510.00 0.167589 0.0837944 0.996483i \(-0.473296\pi\)
0.0837944 + 0.996483i \(0.473296\pi\)
\(434\) 8100.00 + 14029.6i 0.895881 + 1.55171i
\(435\) 0 0
\(436\) −14909.0 + 25823.1i −1.63764 + 2.83648i
\(437\) 2640.00 4572.61i 0.288989 0.500544i
\(438\) 0 0
\(439\) −212.000 367.195i −0.0230483 0.0399208i 0.854271 0.519828i \(-0.174004\pi\)
−0.877320 + 0.479907i \(0.840670\pi\)
\(440\) −11250.0 −1.21892
\(441\) 0 0
\(442\) 1000.00 0.107613
\(443\) −6180.00 10704.1i −0.662801 1.14800i −0.979877 0.199604i \(-0.936034\pi\)
0.317076 0.948400i \(-0.397299\pi\)
\(444\) 0 0
\(445\) −3750.00 + 6495.19i −0.399477 + 0.691914i
\(446\) 9175.00 15891.6i 0.974101 1.68719i
\(447\) 0 0
\(448\) −4305.00 7456.48i −0.454000 0.786352i
\(449\) −1300.00 −0.136639 −0.0683194 0.997664i \(-0.521764\pi\)
−0.0683194 + 0.997664i \(0.521764\pi\)
\(450\) 0 0
\(451\) 20000.0 2.08817
\(452\) 2635.00 + 4563.95i 0.274203 + 0.474934i
\(453\) 0 0
\(454\) −9400.00 + 16281.3i −0.971727 + 1.68308i
\(455\) 1500.00 2598.08i 0.154552 0.267692i
\(456\) 0 0
\(457\) 3595.00 + 6226.72i 0.367980 + 0.637361i 0.989250 0.146236i \(-0.0467160\pi\)
−0.621269 + 0.783597i \(0.713383\pi\)
\(458\) −7170.00 −0.731511
\(459\) 0 0
\(460\) −10200.0 −1.03386
\(461\) 75.0000 + 129.904i 0.00757722 + 0.0131241i 0.869789 0.493424i \(-0.164255\pi\)
−0.862212 + 0.506548i \(0.830921\pi\)
\(462\) 0 0
\(463\) −1335.00 + 2312.29i −0.134002 + 0.232097i −0.925216 0.379442i \(-0.876116\pi\)
0.791214 + 0.611539i \(0.209449\pi\)
\(464\) 2225.00 3853.81i 0.222614 0.385579i
\(465\) 0 0
\(466\) 8625.00 + 14938.9i 0.857394 + 1.48505i
\(467\) 1180.00 0.116925 0.0584624 0.998290i \(-0.481380\pi\)
0.0584624 + 0.998290i \(0.481380\pi\)
\(468\) 0 0
\(469\) 5400.00 0.531661
\(470\) −3500.00 6062.18i −0.343496 0.594952i
\(471\) 0 0
\(472\) −1125.00 + 1948.56i −0.109708 + 0.190020i
\(473\) −7000.00 + 12124.4i −0.680466 + 1.17860i
\(474\) 0 0
\(475\) 550.000 + 952.628i 0.0531279 + 0.0920201i
\(476\) 5100.00 0.491088
\(477\) 0 0
\(478\) −24500.0 −2.34436
\(479\) 7050.00 + 12211.0i 0.672490 + 1.16479i 0.977196 + 0.212340i \(0.0681085\pi\)
−0.304706 + 0.952447i \(0.598558\pi\)
\(480\) 0 0
\(481\) −400.000 + 692.820i −0.0379177 + 0.0656754i
\(482\) −12055.0 + 20879.9i −1.13919 + 1.97314i
\(483\) 0 0
\(484\) −9936.50 17210.5i −0.933180 1.61632i
\(485\) 8150.00 0.763036
\(486\) 0 0
\(487\) −9850.00 −0.916522 −0.458261 0.888818i \(-0.651527\pi\)
−0.458261 + 0.888818i \(0.651527\pi\)
\(488\) 11655.0 + 20187.1i 1.08114 + 1.87259i
\(489\) 0 0
\(490\) 6962.50 12059.4i 0.641905 1.11181i
\(491\) 1225.00 2121.76i 0.112594 0.195018i −0.804222 0.594330i \(-0.797418\pi\)
0.916815 + 0.399312i \(0.130751\pi\)
\(492\) 0 0
\(493\) −250.000 433.013i −0.0228386 0.0395576i
\(494\) 4400.00 0.400740
\(495\) 0 0
\(496\) 9612.00 0.870144
\(497\) 10500.0 + 18186.5i 0.947665 + 1.64140i
\(498\) 0 0
\(499\) 8518.00 14753.6i 0.764164 1.32357i −0.176523 0.984297i \(-0.556485\pi\)
0.940687 0.339275i \(-0.110182\pi\)
\(500\) 1062.50 1840.30i 0.0950329 0.164602i
\(501\) 0 0
\(502\) 11625.0 + 20135.1i 1.03356 + 1.79019i
\(503\) −20600.0 −1.82606 −0.913030 0.407891i \(-0.866264\pi\)
−0.913030 + 0.407891i \(0.866264\pi\)
\(504\) 0 0
\(505\) 2250.00 0.198265
\(506\) −15000.0 25980.8i −1.31785 2.28258i
\(507\) 0 0
\(508\) 9095.00 15753.0i 0.794341 1.37584i
\(509\) −2875.00 + 4979.65i −0.250358 + 0.433632i −0.963624 0.267260i \(-0.913882\pi\)
0.713267 + 0.700893i \(0.247215\pi\)
\(510\) 0 0
\(511\) −6150.00 10652.1i −0.532407 0.922156i
\(512\) −24475.0 −2.11260
\(513\) 0 0
\(514\) 25650.0 2.20111
\(515\) 1925.00 + 3334.20i 0.164710 + 0.285286i
\(516\) 0 0
\(517\) 7000.00 12124.4i 0.595473 1.03139i
\(518\) −3000.00 + 5196.15i −0.254464 + 0.440745i
\(519\) 0 0
\(520\) −2250.00 3897.11i −0.189748 0.328653i
\(521\) −15500.0 −1.30339 −0.651696 0.758480i \(-0.725942\pi\)
−0.651696 + 0.758480i \(0.725942\pi\)
\(522\) 0 0
\(523\) −13940.0 −1.16549 −0.582747 0.812653i \(-0.698022\pi\)
−0.582747 + 0.812653i \(0.698022\pi\)
\(524\) −16575.0 28708.7i −1.38184 2.39341i
\(525\) 0 0
\(526\) 3200.00 5542.56i 0.265260 0.459443i
\(527\) 540.000 935.307i 0.0446352 0.0773105i
\(528\) 0 0
\(529\) −1116.50 1933.83i −0.0917646 0.158941i
\(530\) 15250.0 1.24984
\(531\) 0 0
\(532\) 22440.0 1.82875
\(533\) 4000.00 + 6928.20i 0.325064 + 0.563028i
\(534\) 0 0
\(535\) 1650.00 2857.88i 0.133338 0.230948i
\(536\) 4050.00 7014.81i 0.326368 0.565286i
\(537\) 0 0
\(538\) −8375.00 14505.9i −0.671137 1.16244i
\(539\) 27850.0 2.22557
\(540\) 0 0
\(541\) −20478.0 −1.62739 −0.813695 0.581292i \(-0.802547\pi\)
−0.813695 + 0.581292i \(0.802547\pi\)
\(542\) −13780.0 23867.7i −1.09207 1.89152i
\(543\) 0 0
\(544\) 425.000 736.122i 0.0334958 0.0580165i
\(545\) 4385.00 7595.04i 0.344647 0.596947i
\(546\) 0 0
\(547\) −6020.00 10426.9i −0.470561 0.815035i 0.528873 0.848701i \(-0.322615\pi\)
−0.999433 + 0.0336665i \(0.989282\pi\)
\(548\) 17850.0 1.39145
\(549\) 0 0
\(550\) 6250.00 0.484547
\(551\) −1100.00 1905.26i −0.0850482 0.147308i
\(552\) 0 0
\(553\) −7740.00 + 13406.1i −0.595187 + 1.03089i
\(554\) −12300.0 + 21304.2i −0.943280 + 1.63381i
\(555\) 0 0
\(556\) −14246.0 24674.8i −1.08663 1.88209i
\(557\) 23550.0 1.79146 0.895732 0.444594i \(-0.146652\pi\)
0.895732 + 0.444594i \(0.146652\pi\)
\(558\) 0 0
\(559\) −5600.00 −0.423712
\(560\) −6675.00 11561.4i −0.503697 0.872429i
\(561\) 0 0
\(562\) −11250.0 + 19485.6i −0.844400 + 1.46254i
\(563\) 3060.00 5300.08i 0.229065 0.396752i −0.728466 0.685082i \(-0.759766\pi\)
0.957531 + 0.288329i \(0.0930998\pi\)
\(564\) 0 0
\(565\) −775.000 1342.34i −0.0577071 0.0999516i
\(566\) −34500.0 −2.56209
\(567\) 0 0
\(568\) 31500.0 2.32696
\(569\) 5850.00 + 10132.5i 0.431010 + 0.746531i 0.996961 0.0779078i \(-0.0248240\pi\)
−0.565950 + 0.824439i \(0.691491\pi\)
\(570\) 0 0
\(571\) 4094.00 7091.02i 0.300050 0.519702i −0.676097 0.736813i \(-0.736330\pi\)
0.976147 + 0.217111i \(0.0696633\pi\)
\(572\) 8500.00 14722.4i 0.621334 1.07618i
\(573\) 0 0
\(574\) 30000.0 + 51961.5i 2.18149 + 3.77845i
\(575\) 3000.00 0.217580
\(576\) 0 0
\(577\) 11690.0 0.843433 0.421717 0.906728i \(-0.361428\pi\)
0.421717 + 0.906728i \(0.361428\pi\)
\(578\) 12032.5 + 20840.9i 0.865893 + 1.49977i
\(579\) 0 0
\(580\) −2125.00 + 3680.61i −0.152131 + 0.263498i
\(581\) 9900.00 17147.3i 0.706921 1.22442i
\(582\) 0 0
\(583\) 15250.0 + 26413.8i 1.08335 + 1.87641i
\(584\) −18450.0 −1.30731
\(585\) 0 0
\(586\) 7650.00 0.539281
\(587\) −10530.0 18238.5i −0.740408 1.28242i −0.952310 0.305134i \(-0.901299\pi\)
0.211901 0.977291i \(-0.432034\pi\)
\(588\) 0 0
\(589\) 2376.00 4115.35i 0.166216 0.287895i
\(590\) 625.000 1082.53i 0.0436116 0.0755375i
\(591\) 0 0
\(592\) 1780.00 + 3083.05i 0.123577 + 0.214042i
\(593\) −22910.0 −1.58651 −0.793255 0.608889i \(-0.791615\pi\)
−0.793255 + 0.608889i \(0.791615\pi\)
\(594\) 0 0
\(595\) −1500.00 −0.103351
\(596\) −17425.0 30181.0i −1.19758 2.07426i
\(597\) 0 0
\(598\) 6000.00 10392.3i 0.410298 0.710657i
\(599\) 700.000 1212.44i 0.0477483 0.0827025i −0.841163 0.540781i \(-0.818129\pi\)
0.888912 + 0.458078i \(0.151462\pi\)
\(600\) 0 0
\(601\) 5501.00 + 9528.01i 0.373362 + 0.646682i 0.990080 0.140502i \(-0.0448717\pi\)
−0.616719 + 0.787184i \(0.711538\pi\)
\(602\) −42000.0 −2.84351
\(603\) 0 0
\(604\) 7616.00 0.513064
\(605\) 2922.50 + 5061.92i 0.196391 + 0.340159i
\(606\) 0 0
\(607\) −2315.00 + 4009.70i −0.154799 + 0.268120i −0.932986 0.359913i \(-0.882806\pi\)
0.778187 + 0.628033i \(0.216140\pi\)
\(608\) 1870.00 3238.94i 0.124734 0.216046i
\(609\) 0 0
\(610\) −6475.00 11215.0i −0.429779 0.744399i
\(611\) 5600.00 0.370788
\(612\) 0 0
\(613\) 24040.0 1.58396 0.791979 0.610548i \(-0.209051\pi\)
0.791979 + 0.610548i \(0.209051\pi\)
\(614\) −7600.00 13163.6i −0.499529 0.865210i
\(615\) 0 0
\(616\) 33750.0 58456.7i 2.20751 3.82352i
\(617\) 945.000 1636.79i 0.0616601 0.106798i −0.833547 0.552448i \(-0.813694\pi\)
0.895208 + 0.445649i \(0.147027\pi\)
\(618\) 0 0
\(619\) −9622.00 16665.8i −0.624783 1.08216i −0.988583 0.150679i \(-0.951854\pi\)
0.363799 0.931477i \(-0.381479\pi\)
\(620\) −9180.00 −0.594641
\(621\) 0 0
\(622\) −28500.0 −1.83721
\(623\) −22500.0 38971.1i −1.44694 2.50617i
\(624\) 0 0
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) −7775.00 + 13466.7i −0.496408 + 0.859804i
\(627\) 0 0
\(628\) 850.000 + 1472.24i 0.0540107 + 0.0935492i
\(629\) 400.000 0.0253562
\(630\) 0 0
\(631\) 15892.0 1.00262 0.501308 0.865269i \(-0.332852\pi\)
0.501308 + 0.865269i \(0.332852\pi\)
\(632\) 11610.0 + 20109.1i 0.730729 + 1.26566i
\(633\) 0 0
\(634\) 2375.00 4113.62i 0.148775 0.257686i
\(635\) −2675.00 + 4633.24i −0.167172 + 0.289550i
\(636\) 0 0
\(637\) 5570.00 + 9647.52i 0.346454 + 0.600077i
\(638\) −12500.0 −0.775674
\(639\) 0 0
\(640\) 10575.0 0.653146
\(641\) 6300.00 + 10911.9i 0.388198 + 0.672379i 0.992207 0.124598i \(-0.0397643\pi\)
−0.604009 + 0.796977i \(0.706431\pi\)
\(642\) 0 0
\(643\) −3630.00 + 6287.34i −0.222633 + 0.385612i −0.955607 0.294645i \(-0.904799\pi\)
0.732973 + 0.680257i \(0.238132\pi\)
\(644\) 30600.0 53000.8i 1.87237 3.24305i
\(645\) 0 0
\(646\) −1100.00 1905.26i −0.0669952 0.116039i
\(647\) 7400.00 0.449651 0.224825 0.974399i \(-0.427819\pi\)
0.224825 + 0.974399i \(0.427819\pi\)
\(648\) 0 0
\(649\) 2500.00 0.151207
\(650\) 1250.00 + 2165.06i 0.0754293 + 0.130647i
\(651\) 0 0
\(652\) 16150.0 27972.6i 0.970066 1.68020i
\(653\) 2395.00 4148.26i 0.143528 0.248597i −0.785295 0.619122i \(-0.787489\pi\)
0.928823 + 0.370525i \(0.120822\pi\)
\(654\) 0 0
\(655\) 4875.00 + 8443.75i 0.290812 + 0.503702i
\(656\) 35600.0 2.11882
\(657\) 0 0
\(658\) 42000.0 2.48834
\(659\) 725.000 + 1255.74i 0.0428558 + 0.0742285i 0.886658 0.462426i \(-0.153021\pi\)
−0.843802 + 0.536655i \(0.819688\pi\)
\(660\) 0 0
\(661\) −5909.00 + 10234.7i −0.347706 + 0.602244i −0.985841 0.167680i \(-0.946372\pi\)
0.638136 + 0.769924i \(0.279706\pi\)
\(662\) −5730.00 + 9924.65i −0.336409 + 0.582678i
\(663\) 0 0
\(664\) −14850.0 25721.0i −0.867909 1.50326i
\(665\) −6600.00 −0.384868
\(666\) 0 0
\(667\) −6000.00 −0.348307
\(668\) −16320.0 28267.1i −0.945269 1.63725i
\(669\) 0 0
\(670\) −2250.00 + 3897.11i −0.129739 + 0.224714i
\(671\) 12950.0 22430.1i 0.745051 1.29047i
\(672\) 0 0
\(673\) −2775.00 4806.44i −0.158943 0.275297i 0.775545 0.631292i \(-0.217475\pi\)
−0.934488 + 0.355996i \(0.884142\pi\)
\(674\) −38650.0 −2.20882
\(675\) 0 0
\(676\) −30549.0 −1.73811
\(677\) −6465.00 11197.7i −0.367016 0.635691i 0.622081 0.782953i \(-0.286287\pi\)
−0.989098 + 0.147262i \(0.952954\pi\)
\(678\) 0 0
\(679\) −24450.0 + 42348.6i −1.38189 + 2.39351i
\(680\) −1125.00 + 1948.56i −0.0634438 + 0.109888i
\(681\) 0 0
\(682\) −13500.0 23382.7i −0.757979 1.31286i
\(683\) 32580.0 1.82524 0.912620 0.408809i \(-0.134056\pi\)
0.912620 + 0.408809i \(0.134056\pi\)
\(684\) 0 0
\(685\) −5250.00 −0.292835
\(686\) 16050.0 + 27799.4i 0.893283 + 1.54721i
\(687\) 0 0
\(688\) −12460.0 + 21581.4i −0.690455 + 1.19590i
\(689\) −6100.00 + 10565.5i −0.337288 + 0.584200i
\(690\) 0 0
\(691\) −5114.00 8857.71i −0.281542 0.487646i 0.690223 0.723597i \(-0.257513\pi\)
−0.971765 + 0.235952i \(0.924179\pi\)
\(692\) 43350.0 2.38139
\(693\) 0 0
\(694\) −5600.00 −0.306301
\(695\) 4190.00 + 7257.29i 0.228685 + 0.396093i
\(696\) 0 0
\(697\) 2000.00 3464.10i 0.108688 0.188253i
\(698\) −2965.00 + 5135.53i −0.160784 + 0.278485i
\(699\) 0 0
\(700\) 6375.00 + 11041.8i 0.344218 + 0.596202i
\(701\) 8350.00 0.449893 0.224947 0.974371i \(-0.427779\pi\)
0.224947 + 0.974371i \(0.427779\pi\)
\(702\) 0 0
\(703\) 1760.00 0.0944234
\(704\) 7175.00 + 12427.5i 0.384116 + 0.665309i
\(705\) 0 0
\(706\) −9075.00 + 15718.4i −0.483771 + 0.837915i
\(707\) −6750.00 + 11691.3i −0.359066 + 0.621921i
\(708\) 0 0
\(709\) 7477.00 + 12950.5i 0.396057 + 0.685991i 0.993236 0.116117i \(-0.0370448\pi\)
−0.597178 + 0.802109i \(0.703711\pi\)
\(710\) −17500.0 −0.925019
\(711\) 0 0
\(712\) −67500.0 −3.55291
\(713\) −6480.00 11223.7i −0.340362 0.589524i
\(714\) 0 0
\(715\) −2500.00 + 4330.13i −0.130762 + 0.226486i
\(716\) −31025.0 + 53736.9i −1.61936 + 2.80481i
\(717\) 0 0
\(718\) 4500.00 + 7794.23i 0.233898 + 0.405123i
\(719\) 29400.0 1.52494 0.762472 0.647021i \(-0.223985\pi\)
0.762472 + 0.647021i \(0.223985\pi\)
\(720\) 0 0
\(721\) −23100.0 −1.19319
\(722\) 12307.5 + 21317.2i 0.634401 + 1.09882i
\(723\) 0 0
\(724\) 36907.0 63924.8i 1.89453 3.28142i
\(725\) 625.000 1082.53i 0.0320164 0.0554541i
\(726\) 0 0
\(727\) 8165.00 + 14142.2i 0.416538 + 0.721465i 0.995589 0.0938267i \(-0.0299100\pi\)
−0.579051 + 0.815292i \(0.696577\pi\)
\(728\) 27000.0 1.37457
\(729\) 0 0
\(730\) 10250.0 0.519684
\(731\) 1400.00 + 2424.87i 0.0708357 + 0.122691i
\(732\) 0 0
\(733\) −15400.0 + 26673.6i −0.776005 + 1.34408i 0.158222 + 0.987404i \(0.449424\pi\)
−0.934228 + 0.356677i \(0.883910\pi\)
\(734\) −21225.0 + 36762.8i −1.06734 + 1.84869i
\(735\) 0 0
\(736\) −5100.00 8833.46i −0.255419 0.442399i
\(737\) −9000.00 −0.449823
\(738\) 0 0
\(739\) −9524.00 −0.474081 −0.237041 0.971500i \(-0.576177\pi\)
−0.237041 + 0.971500i \(0.576177\pi\)
\(740\) −1700.00 2944.49i −0.0844503 0.146272i
\(741\) 0 0
\(742\) −45750.0 + 79241.3i −2.26352 + 3.92054i
\(743\) 14300.0 24768.3i 0.706078 1.22296i −0.260223 0.965549i \(-0.583796\pi\)
0.966301 0.257415i \(-0.0828707\pi\)
\(744\) 0 0
\(745\) 5125.00 + 8876.76i 0.252034 + 0.436536i
\(746\) 500.000 0.0245393
\(747\) 0 0
\(748\) −8500.00 −0.415496
\(749\) 9900.00 + 17147.3i 0.482961 + 0.836514i
\(750\) 0 0
\(751\) 4126.00 7146.44i 0.200479 0.347240i −0.748204 0.663469i \(-0.769083\pi\)
0.948683 + 0.316229i \(0.102417\pi\)
\(752\) 12460.0 21581.4i 0.604215 1.04653i
\(753\) 0 0
\(754\) −2500.00 4330.13i −0.120749 0.209143i
\(755\) −2240.00 −0.107976
\(756\) 0 0
\(757\) −24920.0 −1.19648 −0.598238 0.801318i \(-0.704132\pi\)
−0.598238 + 0.801318i \(0.704132\pi\)
\(758\) 20210.0 + 35004.7i 0.968417 + 1.67735i
\(759\) 0 0
\(760\) −4950.00 + 8573.65i −0.236257 + 0.409209i
\(761\) −13950.0 + 24162.1i −0.664503 + 1.15095i 0.314916 + 0.949119i \(0.398024\pi\)
−0.979420 + 0.201834i \(0.935310\pi\)
\(762\) 0 0
\(763\) 26310.0 + 45570.3i 1.24834 + 2.16219i
\(764\) −59500.0 −2.81758
\(765\) 0 0
\(766\) −47400.0 −2.23581
\(767\) 500.000 + 866.025i 0.0235384 + 0.0407697i
\(768\) 0 0
\(769\) 5753.00 9964.49i 0.269777 0.467267i −0.699027 0.715095i \(-0.746383\pi\)
0.968804 + 0.247828i \(0.0797167\pi\)
\(770\) −18750.0 + 32476.0i −0.877536 + 1.51994i
\(771\) 0 0
\(772\) −28475.0 49320.1i −1.32751 2.29931i
\(773\) −12510.0 −0.582087 −0.291044 0.956710i \(-0.594002\pi\)
−0.291044 + 0.956710i \(0.594002\pi\)
\(774\) 0 0
\(775\) 2700.00 0.125144
\(776\) 36675.0 + 63523.0i 1.69659 + 2.93858i
\(777\) 0 0
\(778\) 27375.0 47414.9i 1.26149 2.18497i
\(779\) 8800.00 15242.0i 0.404740 0.701031i
\(780\) 0 0
\(781\) −17500.0 30310.9i −0.801792 1.38874i
\(782\) −6000.00 −0.274373
\(783\) 0 0
\(784\) 49573.0 2.25825
\(785\) −250.000 433.013i −0.0113667 0.0196878i
\(786\) 0