Properties

Label 225.4.h.d.46.2
Level $225$
Weight $4$
Character 225.46
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 46.2
Character \(\chi\) \(=\) 225.46
Dual form 225.4.h.d.181.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.45629 + 4.48200i) q^{2} +(-11.4954 - 8.35189i) q^{4} +(10.8155 + 2.83289i) q^{5} +2.19013 q^{7} +(23.6729 - 17.1993i) q^{8} +O(q^{10})\) \(q+(-1.45629 + 4.48200i) q^{2} +(-11.4954 - 8.35189i) q^{4} +(10.8155 + 2.83289i) q^{5} +2.19013 q^{7} +(23.6729 - 17.1993i) q^{8} +(-28.4475 + 44.3495i) q^{10} +(21.5342 - 66.2756i) q^{11} +(-9.27380 - 28.5418i) q^{13} +(-3.18946 + 9.81615i) q^{14} +(7.48608 + 23.0398i) q^{16} +(94.9162 - 68.9607i) q^{17} +(43.6560 - 31.7180i) q^{19} +(-100.668 - 122.895i) q^{20} +(265.687 + 193.033i) q^{22} +(-28.0510 + 86.3320i) q^{23} +(108.949 + 61.2782i) q^{25} +141.430 q^{26} +(-25.1764 - 18.2917i) q^{28} +(-45.7488 - 33.2384i) q^{29} +(-106.404 + 77.3069i) q^{31} +119.924 q^{32} +(170.856 + 525.841i) q^{34} +(23.6873 + 6.20439i) q^{35} +(-22.9600 - 70.6638i) q^{37} +(78.5840 + 241.857i) q^{38} +(304.757 - 118.957i) q^{40} +(-125.118 - 385.073i) q^{41} -136.952 q^{43} +(-801.071 + 582.012i) q^{44} +(-346.089 - 251.449i) q^{46} +(336.129 + 244.212i) q^{47} -338.203 q^{49} +(-433.311 + 399.072i) q^{50} +(-131.772 + 405.553i) q^{52} +(315.053 + 228.899i) q^{53} +(420.655 - 655.798i) q^{55} +(51.8466 - 37.6687i) q^{56} +(215.598 - 156.641i) q^{58} +(41.2750 + 127.031i) q^{59} +(-136.341 + 419.614i) q^{61} +(-191.535 - 589.483i) q^{62} +(-234.533 + 721.817i) q^{64} +(-19.4448 - 334.965i) q^{65} +(-89.2870 + 64.8708i) q^{67} -1667.05 q^{68} +(-62.3036 + 97.1310i) q^{70} +(775.800 + 563.651i) q^{71} +(242.057 - 744.974i) q^{73} +350.151 q^{74} -766.748 q^{76} +(47.1627 - 145.152i) q^{77} +(113.095 + 82.1684i) q^{79} +(15.6964 + 270.394i) q^{80} +1908.10 q^{82} +(642.434 - 466.756i) q^{83} +(1221.92 - 476.956i) q^{85} +(199.442 - 613.818i) q^{86} +(-630.119 - 1939.31i) q^{88} +(-26.6981 + 82.1683i) q^{89} +(-20.3108 - 62.5102i) q^{91} +(1043.49 - 758.141i) q^{92} +(-1584.06 + 1150.89i) q^{94} +(562.015 - 219.372i) q^{95} +(694.708 + 504.735i) q^{97} +(492.522 - 1515.83i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7} + O(q^{10}) \) \( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.45629 + 4.48200i −0.514876 + 1.58463i 0.268631 + 0.963243i \(0.413429\pi\)
−0.783507 + 0.621383i \(0.786571\pi\)
\(3\) 0 0
\(4\) −11.4954 8.35189i −1.43692 1.04399i
\(5\) 10.8155 + 2.83289i 0.967366 + 0.253382i
\(6\) 0 0
\(7\) 2.19013 0.118256 0.0591279 0.998250i \(-0.481168\pi\)
0.0591279 + 0.998250i \(0.481168\pi\)
\(8\) 23.6729 17.1993i 1.04620 0.760111i
\(9\) 0 0
\(10\) −28.4475 + 44.3495i −0.899589 + 1.40245i
\(11\) 21.5342 66.2756i 0.590256 1.81662i 0.0132058 0.999913i \(-0.495796\pi\)
0.577050 0.816709i \(-0.304204\pi\)
\(12\) 0 0
\(13\) −9.27380 28.5418i −0.197853 0.608929i −0.999931 0.0117102i \(-0.996272\pi\)
0.802078 0.597219i \(-0.203728\pi\)
\(14\) −3.18946 + 9.81615i −0.0608871 + 0.187391i
\(15\) 0 0
\(16\) 7.48608 + 23.0398i 0.116970 + 0.359997i
\(17\) 94.9162 68.9607i 1.35415 0.983848i 0.355358 0.934730i \(-0.384359\pi\)
0.998793 0.0491177i \(-0.0156409\pi\)
\(18\) 0 0
\(19\) 43.6560 31.7180i 0.527125 0.382979i −0.292156 0.956371i \(-0.594373\pi\)
0.819281 + 0.573392i \(0.194373\pi\)
\(20\) −100.668 122.895i −1.12551 1.37401i
\(21\) 0 0
\(22\) 265.687 + 193.033i 2.57476 + 1.87067i
\(23\) −28.0510 + 86.3320i −0.254306 + 0.782672i 0.739660 + 0.672981i \(0.234986\pi\)
−0.993966 + 0.109692i \(0.965014\pi\)
\(24\) 0 0
\(25\) 108.949 + 61.2782i 0.871596 + 0.490226i
\(26\) 141.430 1.06679
\(27\) 0 0
\(28\) −25.1764 18.2917i −0.169925 0.123457i
\(29\) −45.7488 33.2384i −0.292943 0.212835i 0.431600 0.902065i \(-0.357949\pi\)
−0.724543 + 0.689230i \(0.757949\pi\)
\(30\) 0 0
\(31\) −106.404 + 77.3069i −0.616474 + 0.447895i −0.851688 0.524049i \(-0.824421\pi\)
0.235214 + 0.971944i \(0.424421\pi\)
\(32\) 119.924 0.662492
\(33\) 0 0
\(34\) 170.856 + 525.841i 0.861811 + 2.65238i
\(35\) 23.6873 + 6.20439i 0.114397 + 0.0299638i
\(36\) 0 0
\(37\) −22.9600 70.6638i −0.102016 0.313974i 0.887002 0.461765i \(-0.152784\pi\)
−0.989019 + 0.147791i \(0.952784\pi\)
\(38\) 78.5840 + 241.857i 0.335474 + 1.03248i
\(39\) 0 0
\(40\) 304.757 118.957i 1.20466 0.470217i
\(41\) −125.118 385.073i −0.476588 1.46679i −0.843804 0.536652i \(-0.819689\pi\)
0.367216 0.930136i \(-0.380311\pi\)
\(42\) 0 0
\(43\) −136.952 −0.485697 −0.242849 0.970064i \(-0.578082\pi\)
−0.242849 + 0.970064i \(0.578082\pi\)
\(44\) −801.071 + 582.012i −2.74468 + 1.99413i
\(45\) 0 0
\(46\) −346.089 251.449i −1.10931 0.805958i
\(47\) 336.129 + 244.212i 1.04318 + 0.757915i 0.970904 0.239470i \(-0.0769737\pi\)
0.0722762 + 0.997385i \(0.476974\pi\)
\(48\) 0 0
\(49\) −338.203 −0.986016
\(50\) −433.311 + 399.072i −1.22559 + 1.12875i
\(51\) 0 0
\(52\) −131.772 + 405.553i −0.351414 + 1.08154i
\(53\) 315.053 + 228.899i 0.816525 + 0.593240i 0.915715 0.401829i \(-0.131625\pi\)
−0.0991901 + 0.995068i \(0.531625\pi\)
\(54\) 0 0
\(55\) 420.655 655.798i 1.03129 1.60778i
\(56\) 51.8466 37.6687i 0.123719 0.0898875i
\(57\) 0 0
\(58\) 215.598 156.641i 0.488093 0.354621i
\(59\) 41.2750 + 127.031i 0.0910771 + 0.280306i 0.986211 0.165490i \(-0.0529206\pi\)
−0.895134 + 0.445796i \(0.852921\pi\)
\(60\) 0 0
\(61\) −136.341 + 419.614i −0.286175 + 0.880756i 0.699869 + 0.714271i \(0.253242\pi\)
−0.986044 + 0.166485i \(0.946758\pi\)
\(62\) −191.535 589.483i −0.392338 1.20749i
\(63\) 0 0
\(64\) −234.533 + 721.817i −0.458072 + 1.40980i
\(65\) −19.4448 334.965i −0.0371050 0.639190i
\(66\) 0 0
\(67\) −89.2870 + 64.8708i −0.162808 + 0.118287i −0.666206 0.745768i \(-0.732083\pi\)
0.503398 + 0.864055i \(0.332083\pi\)
\(68\) −1667.05 −2.97294
\(69\) 0 0
\(70\) −62.3036 + 97.1310i −0.106382 + 0.165848i
\(71\) 775.800 + 563.651i 1.29677 + 0.942156i 0.999918 0.0127681i \(-0.00406433\pi\)
0.296849 + 0.954925i \(0.404064\pi\)
\(72\) 0 0
\(73\) 242.057 744.974i 0.388090 1.19442i −0.546123 0.837705i \(-0.683897\pi\)
0.934213 0.356715i \(-0.116103\pi\)
\(74\) 350.151 0.550058
\(75\) 0 0
\(76\) −766.748 −1.15726
\(77\) 47.1627 145.152i 0.0698012 0.214826i
\(78\) 0 0
\(79\) 113.095 + 82.1684i 0.161066 + 0.117021i 0.665399 0.746488i \(-0.268262\pi\)
−0.504333 + 0.863509i \(0.668262\pi\)
\(80\) 15.6964 + 270.394i 0.0219364 + 0.377887i
\(81\) 0 0
\(82\) 1908.10 2.56969
\(83\) 642.434 466.756i 0.849594 0.617266i −0.0754401 0.997150i \(-0.524036\pi\)
0.925034 + 0.379884i \(0.124036\pi\)
\(84\) 0 0
\(85\) 1221.92 476.956i 1.55925 0.608625i
\(86\) 199.442 613.818i 0.250074 0.769648i
\(87\) 0 0
\(88\) −630.119 1939.31i −0.763306 2.34921i
\(89\) −26.6981 + 82.1683i −0.0317977 + 0.0978632i −0.965696 0.259676i \(-0.916384\pi\)
0.933898 + 0.357539i \(0.116384\pi\)
\(90\) 0 0
\(91\) −20.3108 62.5102i −0.0233973 0.0720093i
\(92\) 1043.49 758.141i 1.18252 0.859149i
\(93\) 0 0
\(94\) −1584.06 + 1150.89i −1.73812 + 1.26282i
\(95\) 562.015 219.372i 0.606963 0.236917i
\(96\) 0 0
\(97\) 694.708 + 504.735i 0.727184 + 0.528330i 0.888671 0.458544i \(-0.151629\pi\)
−0.161487 + 0.986875i \(0.551629\pi\)
\(98\) 492.522 1515.83i 0.507676 1.56247i
\(99\) 0 0
\(100\) −740.628 1614.35i −0.740628 1.61435i
\(101\) 949.841 0.935769 0.467885 0.883790i \(-0.345016\pi\)
0.467885 + 0.883790i \(0.345016\pi\)
\(102\) 0 0
\(103\) −1155.07 839.205i −1.10497 0.802809i −0.123108 0.992393i \(-0.539286\pi\)
−0.981864 + 0.189584i \(0.939286\pi\)
\(104\) −710.438 516.163i −0.669848 0.486673i
\(105\) 0 0
\(106\) −1484.73 + 1078.72i −1.36047 + 0.988441i
\(107\) −882.976 −0.797761 −0.398881 0.917003i \(-0.630601\pi\)
−0.398881 + 0.917003i \(0.630601\pi\)
\(108\) 0 0
\(109\) −338.398 1041.48i −0.297364 0.915192i −0.982417 0.186699i \(-0.940221\pi\)
0.685053 0.728493i \(-0.259779\pi\)
\(110\) 2326.69 + 2840.41i 2.01674 + 2.46202i
\(111\) 0 0
\(112\) 16.3955 + 50.4601i 0.0138324 + 0.0425717i
\(113\) −397.976 1224.84i −0.331314 1.01968i −0.968509 0.248977i \(-0.919906\pi\)
0.637196 0.770702i \(-0.280094\pi\)
\(114\) 0 0
\(115\) −547.954 + 854.257i −0.444321 + 0.692694i
\(116\) 248.296 + 764.178i 0.198739 + 0.611656i
\(117\) 0 0
\(118\) −629.463 −0.491074
\(119\) 207.879 151.033i 0.160136 0.116346i
\(120\) 0 0
\(121\) −2851.93 2072.05i −2.14269 1.55676i
\(122\) −1682.16 1222.16i −1.24832 0.906960i
\(123\) 0 0
\(124\) 1868.81 1.35342
\(125\) 1004.75 + 971.395i 0.718938 + 0.695074i
\(126\) 0 0
\(127\) 324.931 1000.03i 0.227031 0.698730i −0.771048 0.636777i \(-0.780267\pi\)
0.998079 0.0619531i \(-0.0197329\pi\)
\(128\) −2117.47 1538.43i −1.46219 1.06234i
\(129\) 0 0
\(130\) 1529.63 + 400.655i 1.03198 + 0.270306i
\(131\) −1593.57 + 1157.79i −1.06283 + 0.772191i −0.974610 0.223911i \(-0.928118\pi\)
−0.0882194 + 0.996101i \(0.528118\pi\)
\(132\) 0 0
\(133\) 95.6123 69.4664i 0.0623356 0.0452895i
\(134\) −160.723 494.655i −0.103615 0.318893i
\(135\) 0 0
\(136\) 1060.86 3264.99i 0.668883 2.05861i
\(137\) −420.629 1294.56i −0.262312 0.807313i −0.992301 0.123854i \(-0.960475\pi\)
0.729989 0.683459i \(-0.239525\pi\)
\(138\) 0 0
\(139\) −190.111 + 585.100i −0.116007 + 0.357033i −0.992156 0.125008i \(-0.960104\pi\)
0.876149 + 0.482041i \(0.160104\pi\)
\(140\) −220.476 269.156i −0.133097 0.162484i
\(141\) 0 0
\(142\) −3656.07 + 2656.29i −2.16064 + 1.56980i
\(143\) −2091.33 −1.22298
\(144\) 0 0
\(145\) −400.634 489.091i −0.229454 0.280116i
\(146\) 2986.47 + 2169.80i 1.69289 + 1.22996i
\(147\) 0 0
\(148\) −326.241 + 1004.07i −0.181195 + 0.557661i
\(149\) 1267.88 0.697104 0.348552 0.937289i \(-0.386673\pi\)
0.348552 + 0.937289i \(0.386673\pi\)
\(150\) 0 0
\(151\) 2731.39 1.47203 0.736017 0.676963i \(-0.236704\pi\)
0.736017 + 0.676963i \(0.236704\pi\)
\(152\) 487.935 1501.71i 0.260373 0.801347i
\(153\) 0 0
\(154\) 581.888 + 422.766i 0.304480 + 0.221217i
\(155\) −1369.81 + 534.681i −0.709844 + 0.277075i
\(156\) 0 0
\(157\) 2614.50 1.32904 0.664522 0.747269i \(-0.268635\pi\)
0.664522 + 0.747269i \(0.268635\pi\)
\(158\) −532.978 + 387.231i −0.268364 + 0.194978i
\(159\) 0 0
\(160\) 1297.04 + 339.732i 0.640873 + 0.167863i
\(161\) −61.4352 + 189.078i −0.0300731 + 0.0925555i
\(162\) 0 0
\(163\) 957.089 + 2945.62i 0.459908 + 1.41545i 0.865275 + 0.501298i \(0.167144\pi\)
−0.405367 + 0.914154i \(0.632856\pi\)
\(164\) −1777.81 + 5471.53i −0.846485 + 2.60521i
\(165\) 0 0
\(166\) 1156.43 + 3559.12i 0.540700 + 1.66410i
\(167\) −1095.49 + 795.921i −0.507614 + 0.368803i −0.811918 0.583772i \(-0.801576\pi\)
0.304303 + 0.952575i \(0.401576\pi\)
\(168\) 0 0
\(169\) 1048.78 761.982i 0.477368 0.346828i
\(170\) 358.241 + 6171.24i 0.161623 + 2.78419i
\(171\) 0 0
\(172\) 1574.32 + 1143.81i 0.697910 + 0.507061i
\(173\) −753.996 + 2320.56i −0.331360 + 1.01982i 0.637128 + 0.770758i \(0.280122\pi\)
−0.968487 + 0.249062i \(0.919878\pi\)
\(174\) 0 0
\(175\) 238.613 + 134.207i 0.103071 + 0.0579720i
\(176\) 1688.18 0.723020
\(177\) 0 0
\(178\) −329.398 239.322i −0.138705 0.100775i
\(179\) −2226.69 1617.78i −0.929778 0.675524i 0.0161602 0.999869i \(-0.494856\pi\)
−0.945939 + 0.324346i \(0.894856\pi\)
\(180\) 0 0
\(181\) −2380.05 + 1729.20i −0.977389 + 0.710115i −0.957124 0.289680i \(-0.906451\pi\)
−0.0202653 + 0.999795i \(0.506451\pi\)
\(182\) 309.749 0.126155
\(183\) 0 0
\(184\) 820.807 + 2526.18i 0.328862 + 1.01213i
\(185\) −48.1413 829.306i −0.0191320 0.329577i
\(186\) 0 0
\(187\) −2526.46 7775.64i −0.987984 3.04070i
\(188\) −1824.30 5614.63i −0.707718 2.17813i
\(189\) 0 0
\(190\) 164.771 + 2838.42i 0.0629143 + 1.08379i
\(191\) −284.218 874.733i −0.107672 0.331380i 0.882676 0.469981i \(-0.155739\pi\)
−0.990348 + 0.138602i \(0.955739\pi\)
\(192\) 0 0
\(193\) 4742.42 1.76874 0.884370 0.466787i \(-0.154588\pi\)
0.884370 + 0.466787i \(0.154588\pi\)
\(194\) −3273.92 + 2378.64i −1.21162 + 0.880290i
\(195\) 0 0
\(196\) 3887.78 + 2824.64i 1.41683 + 1.02939i
\(197\) 4008.20 + 2912.13i 1.44961 + 1.05320i 0.985923 + 0.167198i \(0.0534719\pi\)
0.463682 + 0.886002i \(0.346528\pi\)
\(198\) 0 0
\(199\) −3302.37 −1.17638 −0.588189 0.808724i \(-0.700159\pi\)
−0.588189 + 0.808724i \(0.700159\pi\)
\(200\) 3633.09 423.229i 1.28449 0.149634i
\(201\) 0 0
\(202\) −1383.24 + 4257.19i −0.481805 + 1.48284i
\(203\) −100.196 72.7964i −0.0346421 0.0251690i
\(204\) 0 0
\(205\) −262.340 4519.20i −0.0893785 1.53968i
\(206\) 5443.43 3954.88i 1.84108 1.33762i
\(207\) 0 0
\(208\) 588.173 427.333i 0.196070 0.142453i
\(209\) −1162.03 3576.35i −0.384589 1.18364i
\(210\) 0 0
\(211\) −168.471 + 518.500i −0.0549669 + 0.169171i −0.974771 0.223207i \(-0.928347\pi\)
0.919804 + 0.392378i \(0.128347\pi\)
\(212\) −1709.91 5262.57i −0.553950 1.70488i
\(213\) 0 0
\(214\) 1285.87 3957.50i 0.410748 1.26415i
\(215\) −1481.20 387.970i −0.469847 0.123067i
\(216\) 0 0
\(217\) −233.038 + 169.312i −0.0729016 + 0.0529661i
\(218\) 5160.73 1.60334
\(219\) 0 0
\(220\) −10312.7 + 4025.40i −3.16039 + 1.23360i
\(221\) −2848.50 2069.55i −0.867016 0.629924i
\(222\) 0 0
\(223\) −1325.36 + 4079.04i −0.397994 + 1.22490i 0.528611 + 0.848864i \(0.322713\pi\)
−0.926605 + 0.376036i \(0.877287\pi\)
\(224\) 262.649 0.0783435
\(225\) 0 0
\(226\) 6069.32 1.78639
\(227\) 142.138 437.457i 0.0415597 0.127908i −0.928124 0.372271i \(-0.878579\pi\)
0.969684 + 0.244364i \(0.0785791\pi\)
\(228\) 0 0
\(229\) −4727.25 3434.55i −1.36413 0.991097i −0.998170 0.0604658i \(-0.980741\pi\)
−0.365958 0.930631i \(-0.619259\pi\)
\(230\) −3030.80 3699.97i −0.868891 1.06073i
\(231\) 0 0
\(232\) −1654.68 −0.468256
\(233\) −3152.98 + 2290.77i −0.886516 + 0.644092i −0.934967 0.354734i \(-0.884571\pi\)
0.0484511 + 0.998826i \(0.484571\pi\)
\(234\) 0 0
\(235\) 2943.57 + 3593.49i 0.817096 + 0.997504i
\(236\) 586.480 1805.00i 0.161765 0.497862i
\(237\) 0 0
\(238\) 374.197 + 1151.66i 0.101914 + 0.313659i
\(239\) −1921.95 + 5915.15i −0.520169 + 1.60092i 0.253506 + 0.967334i \(0.418416\pi\)
−0.773675 + 0.633582i \(0.781584\pi\)
\(240\) 0 0
\(241\) 770.998 + 2372.89i 0.206076 + 0.634237i 0.999667 + 0.0257860i \(0.00820885\pi\)
−0.793591 + 0.608451i \(0.791791\pi\)
\(242\) 13440.1 9764.83i 3.57010 2.59383i
\(243\) 0 0
\(244\) 5071.87 3684.93i 1.33071 0.966816i
\(245\) −3657.83 958.093i −0.953838 0.249838i
\(246\) 0 0
\(247\) −1310.15 951.877i −0.337500 0.245208i
\(248\) −1189.26 + 3660.15i −0.304507 + 0.937177i
\(249\) 0 0
\(250\) −5816.99 + 3088.64i −1.47160 + 0.781371i
\(251\) 6788.45 1.70710 0.853552 0.521008i \(-0.174444\pi\)
0.853552 + 0.521008i \(0.174444\pi\)
\(252\) 0 0
\(253\) 5117.64 + 3718.19i 1.27171 + 0.923954i
\(254\) 4008.96 + 2912.68i 0.990333 + 0.719519i
\(255\) 0 0
\(256\) 5066.79 3681.24i 1.23701 0.898740i
\(257\) −2258.32 −0.548132 −0.274066 0.961711i \(-0.588369\pi\)
−0.274066 + 0.961711i \(0.588369\pi\)
\(258\) 0 0
\(259\) −50.2854 154.763i −0.0120640 0.0371293i
\(260\) −2574.07 + 4012.96i −0.613988 + 0.957204i
\(261\) 0 0
\(262\) −2868.54 8828.45i −0.676408 2.08177i
\(263\) 1041.31 + 3204.82i 0.244144 + 0.751398i 0.995776 + 0.0918153i \(0.0292669\pi\)
−0.751632 + 0.659583i \(0.770733\pi\)
\(264\) 0 0
\(265\) 2759.00 + 3368.17i 0.639563 + 0.780773i
\(266\) 172.109 + 529.697i 0.0396717 + 0.122097i
\(267\) 0 0
\(268\) 1568.18 0.357433
\(269\) −5885.65 + 4276.17i −1.33403 + 0.969230i −0.334390 + 0.942435i \(0.608530\pi\)
−0.999641 + 0.0267953i \(0.991470\pi\)
\(270\) 0 0
\(271\) −958.296 696.243i −0.214806 0.156066i 0.475180 0.879889i \(-0.342383\pi\)
−0.689985 + 0.723823i \(0.742383\pi\)
\(272\) 2299.39 + 1670.60i 0.512577 + 0.372409i
\(273\) 0 0
\(274\) 6414.78 1.41435
\(275\) 6407.39 5901.11i 1.40502 1.29400i
\(276\) 0 0
\(277\) 471.254 1450.37i 0.102220 0.314601i −0.886848 0.462061i \(-0.847110\pi\)
0.989068 + 0.147461i \(0.0471100\pi\)
\(278\) −2345.56 1704.15i −0.506034 0.367655i
\(279\) 0 0
\(280\) 667.457 260.530i 0.142458 0.0556059i
\(281\) 1904.06 1383.38i 0.404224 0.293686i −0.367035 0.930207i \(-0.619627\pi\)
0.771259 + 0.636521i \(0.219627\pi\)
\(282\) 0 0
\(283\) −6266.38 + 4552.79i −1.31625 + 0.956308i −0.316275 + 0.948668i \(0.602432\pi\)
−0.999971 + 0.00764053i \(0.997568\pi\)
\(284\) −4210.57 12958.8i −0.879757 2.70761i
\(285\) 0 0
\(286\) 3045.58 9373.33i 0.629682 1.93796i
\(287\) −274.024 843.359i −0.0563593 0.173456i
\(288\) 0 0
\(289\) 2735.31 8418.43i 0.556750 1.71350i
\(290\) 2775.55 1083.38i 0.562019 0.219374i
\(291\) 0 0
\(292\) −9004.48 + 6542.14i −1.80461 + 1.31113i
\(293\) 2728.74 0.544077 0.272039 0.962286i \(-0.412302\pi\)
0.272039 + 0.962286i \(0.412302\pi\)
\(294\) 0 0
\(295\) 86.5430 + 1490.83i 0.0170804 + 0.294236i
\(296\) −1758.90 1277.92i −0.345385 0.250937i
\(297\) 0 0
\(298\) −1846.40 + 5682.62i −0.358922 + 1.10465i
\(299\) 2724.21 0.526907
\(300\) 0 0
\(301\) −299.942 −0.0574365
\(302\) −3977.69 + 12242.1i −0.757915 + 2.33262i
\(303\) 0 0
\(304\) 1057.59 + 768.383i 0.199529 + 0.144966i
\(305\) −2663.31 + 4152.09i −0.500003 + 0.779502i
\(306\) 0 0
\(307\) 2511.50 0.466901 0.233450 0.972369i \(-0.424998\pi\)
0.233450 + 0.972369i \(0.424998\pi\)
\(308\) −1754.45 + 1274.68i −0.324574 + 0.235817i
\(309\) 0 0
\(310\) −401.599 6918.14i −0.0735783 1.26750i
\(311\) 898.070 2763.98i 0.163746 0.503957i −0.835196 0.549952i \(-0.814646\pi\)
0.998942 + 0.0459950i \(0.0146458\pi\)
\(312\) 0 0
\(313\) 116.152 + 357.478i 0.0209753 + 0.0645555i 0.960996 0.276561i \(-0.0891949\pi\)
−0.940021 + 0.341117i \(0.889195\pi\)
\(314\) −3807.47 + 11718.2i −0.684293 + 2.10604i
\(315\) 0 0
\(316\) −613.811 1889.12i −0.109271 0.336301i
\(317\) −2223.00 + 1615.10i −0.393867 + 0.286161i −0.767038 0.641601i \(-0.778270\pi\)
0.373171 + 0.927763i \(0.378270\pi\)
\(318\) 0 0
\(319\) −3188.06 + 2316.26i −0.559552 + 0.406539i
\(320\) −4581.41 + 7142.40i −0.800340 + 1.24773i
\(321\) 0 0
\(322\) −757.980 550.705i −0.131182 0.0953092i
\(323\) 1956.37 6021.10i 0.337014 1.03722i
\(324\) 0 0
\(325\) 738.616 3677.90i 0.126065 0.627732i
\(326\) −14596.1 −2.47976
\(327\) 0 0
\(328\) −9584.90 6963.83i −1.61353 1.17230i
\(329\) 736.165 + 534.855i 0.123362 + 0.0896278i
\(330\) 0 0
\(331\) −5147.60 + 3739.95i −0.854797 + 0.621046i −0.926464 0.376382i \(-0.877168\pi\)
0.0716677 + 0.997429i \(0.477168\pi\)
\(332\) −11283.3 −1.86522
\(333\) 0 0
\(334\) −1971.96 6069.08i −0.323057 0.994267i
\(335\) −1149.45 + 448.669i −0.187467 + 0.0731743i
\(336\) 0 0
\(337\) −1205.67 3710.68i −0.194888 0.599803i −0.999978 0.00665035i \(-0.997883\pi\)
0.805090 0.593153i \(-0.202117\pi\)
\(338\) 1887.88 + 5810.29i 0.303808 + 0.935024i
\(339\) 0 0
\(340\) −18030.0 4722.57i −2.87592 0.753287i
\(341\) 2832.23 + 8716.72i 0.449777 + 1.38427i
\(342\) 0 0
\(343\) −1491.92 −0.234858
\(344\) −3242.04 + 2355.48i −0.508138 + 0.369184i
\(345\) 0 0
\(346\) −9302.71 6758.82i −1.44542 1.05016i
\(347\) 8669.57 + 6298.81i 1.34123 + 0.974461i 0.999398 + 0.0347000i \(0.0110476\pi\)
0.341833 + 0.939761i \(0.388952\pi\)
\(348\) 0 0
\(349\) 2182.48 0.334743 0.167371 0.985894i \(-0.446472\pi\)
0.167371 + 0.985894i \(0.446472\pi\)
\(350\) −949.005 + 874.019i −0.144933 + 0.133481i
\(351\) 0 0
\(352\) 2582.47 7948.03i 0.391040 1.20350i
\(353\) −2719.98 1976.18i −0.410112 0.297964i 0.363535 0.931581i \(-0.381570\pi\)
−0.773647 + 0.633616i \(0.781570\pi\)
\(354\) 0 0
\(355\) 6793.89 + 8293.92i 1.01572 + 1.23999i
\(356\) 993.166 721.577i 0.147859 0.107426i
\(357\) 0 0
\(358\) 10493.6 7624.04i 1.54917 1.12554i
\(359\) −3406.35 10483.7i −0.500781 1.54125i −0.807749 0.589526i \(-0.799315\pi\)
0.306968 0.951720i \(-0.400685\pi\)
\(360\) 0 0
\(361\) −1219.73 + 3753.94i −0.177829 + 0.547301i
\(362\) −4284.25 13185.6i −0.622032 1.91442i
\(363\) 0 0
\(364\) −288.598 + 888.213i −0.0415567 + 0.127898i
\(365\) 4728.39 7371.54i 0.678070 1.05711i
\(366\) 0 0
\(367\) −1920.20 + 1395.11i −0.273116 + 0.198430i −0.715909 0.698193i \(-0.753988\pi\)
0.442793 + 0.896624i \(0.353988\pi\)
\(368\) −2199.06 −0.311506
\(369\) 0 0
\(370\) 3787.06 + 991.941i 0.532107 + 0.139374i
\(371\) 690.005 + 501.318i 0.0965588 + 0.0701540i
\(372\) 0 0
\(373\) −1219.82 + 3754.22i −0.169330 + 0.521143i −0.999329 0.0366209i \(-0.988341\pi\)
0.830000 + 0.557764i \(0.188341\pi\)
\(374\) 38529.7 5.32706
\(375\) 0 0
\(376\) 12157.4 1.66748
\(377\) −524.420 + 1614.00i −0.0716420 + 0.220491i
\(378\) 0 0
\(379\) −3593.67 2610.95i −0.487057 0.353867i 0.316995 0.948427i \(-0.397326\pi\)
−0.804051 + 0.594560i \(0.797326\pi\)
\(380\) −8292.76 2172.11i −1.11950 0.293229i
\(381\) 0 0
\(382\) 4334.46 0.580550
\(383\) −2258.25 + 1640.71i −0.301282 + 0.218895i −0.728147 0.685421i \(-0.759618\pi\)
0.426864 + 0.904316i \(0.359618\pi\)
\(384\) 0 0
\(385\) 921.287 1436.28i 0.121956 0.190129i
\(386\) −6906.33 + 21255.5i −0.910682 + 2.80279i
\(387\) 0 0
\(388\) −3770.45 11604.2i −0.493339 1.51834i
\(389\) 3117.28 9594.01i 0.406305 1.25048i −0.513496 0.858092i \(-0.671650\pi\)
0.919801 0.392386i \(-0.128350\pi\)
\(390\) 0 0
\(391\) 3291.02 + 10128.7i 0.425662 + 1.31005i
\(392\) −8006.24 + 5816.87i −1.03157 + 0.749481i
\(393\) 0 0
\(394\) −18889.2 + 13723.8i −2.41529 + 1.75481i
\(395\) 990.404 + 1209.08i 0.126159 + 0.154013i
\(396\) 0 0
\(397\) 52.6650 + 38.2634i 0.00665789 + 0.00483724i 0.591109 0.806592i \(-0.298690\pi\)
−0.584451 + 0.811429i \(0.698690\pi\)
\(398\) 4809.21 14801.2i 0.605689 1.86412i
\(399\) 0 0
\(400\) −596.232 + 2968.91i −0.0745290 + 0.371113i
\(401\) 343.841 0.0428194 0.0214097 0.999771i \(-0.493185\pi\)
0.0214097 + 0.999771i \(0.493185\pi\)
\(402\) 0 0
\(403\) 3193.25 + 2320.03i 0.394707 + 0.286772i
\(404\) −10918.8 7932.97i −1.34463 0.976931i
\(405\) 0 0
\(406\) 472.187 343.064i 0.0577198 0.0419359i
\(407\) −5177.71 −0.630588
\(408\) 0 0
\(409\) −797.299 2453.83i −0.0963909 0.296661i 0.891223 0.453566i \(-0.149848\pi\)
−0.987614 + 0.156905i \(0.949848\pi\)
\(410\) 20637.1 + 5405.45i 2.48583 + 0.651113i
\(411\) 0 0
\(412\) 6269.00 + 19294.0i 0.749639 + 2.30715i
\(413\) 90.3975 + 278.215i 0.0107704 + 0.0331478i
\(414\) 0 0
\(415\) 8270.50 3228.24i 0.978272 0.381851i
\(416\) −1112.15 3422.85i −0.131076 0.403411i
\(417\) 0 0
\(418\) 17721.4 2.07365
\(419\) 6475.44 4704.68i 0.755003 0.548541i −0.142371 0.989813i \(-0.545473\pi\)
0.897373 + 0.441272i \(0.145473\pi\)
\(420\) 0 0
\(421\) 6698.20 + 4866.53i 0.775416 + 0.563373i 0.903600 0.428378i \(-0.140915\pi\)
−0.128184 + 0.991750i \(0.540915\pi\)
\(422\) −2078.57 1510.17i −0.239771 0.174204i
\(423\) 0 0
\(424\) 11395.1 1.30518
\(425\) 14566.9 1696.93i 1.66258 0.193678i
\(426\) 0 0
\(427\) −298.604 + 919.008i −0.0338418 + 0.104154i
\(428\) 10150.2 + 7374.52i 1.14632 + 0.832852i
\(429\) 0 0
\(430\) 3895.94 6073.75i 0.436928 0.681168i
\(431\) −2123.78 + 1543.02i −0.237353 + 0.172447i −0.700103 0.714042i \(-0.746863\pi\)
0.462750 + 0.886489i \(0.346863\pi\)
\(432\) 0 0
\(433\) 3995.26 2902.73i 0.443418 0.322162i −0.343574 0.939126i \(-0.611638\pi\)
0.786992 + 0.616964i \(0.211638\pi\)
\(434\) −419.485 1291.04i −0.0463962 0.142793i
\(435\) 0 0
\(436\) −4808.33 + 14798.5i −0.528159 + 1.62551i
\(437\) 1513.68 + 4658.63i 0.165696 + 0.509960i
\(438\) 0 0
\(439\) −3507.87 + 10796.1i −0.381370 + 1.17374i 0.557709 + 0.830036i \(0.311680\pi\)
−0.939079 + 0.343700i \(0.888320\pi\)
\(440\) −1321.20 22759.6i −0.143149 2.46596i
\(441\) 0 0
\(442\) 13424.0 9753.09i 1.44460 1.04956i
\(443\) −5354.56 −0.574272 −0.287136 0.957890i \(-0.592703\pi\)
−0.287136 + 0.957890i \(0.592703\pi\)
\(444\) 0 0
\(445\) −521.527 + 813.057i −0.0555567 + 0.0866126i
\(446\) −16352.1 11880.5i −1.73609 1.26134i
\(447\) 0 0
\(448\) −513.656 + 1580.87i −0.0541696 + 0.166717i
\(449\) 10134.8 1.06524 0.532620 0.846354i \(-0.321207\pi\)
0.532620 + 0.846354i \(0.321207\pi\)
\(450\) 0 0
\(451\) −28215.2 −2.94591
\(452\) −5654.88 + 17403.9i −0.588458 + 1.81109i
\(453\) 0 0
\(454\) 1753.69 + 1274.13i 0.181288 + 0.131713i
\(455\) −42.5865 733.617i −0.00438788 0.0755879i
\(456\) 0 0
\(457\) −2257.95 −0.231121 −0.115561 0.993300i \(-0.536866\pi\)
−0.115561 + 0.993300i \(0.536866\pi\)
\(458\) 22277.9 16185.8i 2.27288 1.65134i
\(459\) 0 0
\(460\) 13433.6 5243.57i 1.36162 0.531484i
\(461\) 4601.16 14160.9i 0.464853 1.43067i −0.394313 0.918976i \(-0.629017\pi\)
0.859167 0.511696i \(-0.170983\pi\)
\(462\) 0 0
\(463\) 220.828 + 679.638i 0.0221657 + 0.0682191i 0.961528 0.274709i \(-0.0885814\pi\)
−0.939362 + 0.342928i \(0.888581\pi\)
\(464\) 423.327 1302.87i 0.0423545 0.130354i
\(465\) 0 0
\(466\) −5675.59 17467.7i −0.564198 1.73642i
\(467\) 11204.4 8140.46i 1.11023 0.806629i 0.127530 0.991835i \(-0.459295\pi\)
0.982700 + 0.185206i \(0.0592951\pi\)
\(468\) 0 0
\(469\) −195.550 + 142.075i −0.0192530 + 0.0139881i
\(470\) −20392.7 + 7959.93i −2.00137 + 0.781200i
\(471\) 0 0
\(472\) 3161.95 + 2297.29i 0.308349 + 0.224029i
\(473\) −2949.16 + 9076.57i −0.286686 + 0.882328i
\(474\) 0 0
\(475\) 6699.92 780.492i 0.647186 0.0753925i
\(476\) −3651.05 −0.351567
\(477\) 0 0
\(478\) −23712.8 17228.3i −2.26903 1.64855i
\(479\) −7721.46 5609.97i −0.736540 0.535128i 0.155086 0.987901i \(-0.450435\pi\)
−0.891626 + 0.452773i \(0.850435\pi\)
\(480\) 0 0
\(481\) −1803.95 + 1310.64i −0.171004 + 0.124242i
\(482\) −11758.1 −1.11113
\(483\) 0 0
\(484\) 15478.5 + 47638.0i 1.45365 + 4.47389i
\(485\) 6083.74 + 7426.98i 0.569585 + 0.695344i
\(486\) 0 0
\(487\) 4971.26 + 15300.0i 0.462566 + 1.42363i 0.862019 + 0.506877i \(0.169200\pi\)
−0.399453 + 0.916754i \(0.630800\pi\)
\(488\) 3989.51 + 12278.4i 0.370075 + 1.13897i
\(489\) 0 0
\(490\) 9621.04 14999.1i 0.887008 1.38284i
\(491\) 1377.21 + 4238.63i 0.126584 + 0.389585i 0.994186 0.107673i \(-0.0343400\pi\)
−0.867602 + 0.497259i \(0.834340\pi\)
\(492\) 0 0
\(493\) −6634.45 −0.606086
\(494\) 6174.26 4485.86i 0.562334 0.408560i
\(495\) 0 0
\(496\) −2577.68 1872.80i −0.233350 0.169538i
\(497\) 1699.10 + 1234.47i 0.153350 + 0.111415i
\(498\) 0 0
\(499\) −15914.9 −1.42776 −0.713878 0.700270i \(-0.753063\pi\)
−0.713878 + 0.700270i \(0.753063\pi\)
\(500\) −3436.97 19558.1i −0.307412 1.74933i
\(501\) 0 0
\(502\) −9885.95 + 30425.8i −0.878947 + 2.70512i
\(503\) −3391.75 2464.25i −0.300658 0.218441i 0.427220 0.904148i \(-0.359493\pi\)
−0.727877 + 0.685707i \(0.759493\pi\)
\(504\) 0 0
\(505\) 10273.0 + 2690.80i 0.905232 + 0.237107i
\(506\) −24117.7 + 17522.5i −2.11890 + 1.53947i
\(507\) 0 0
\(508\) −12087.4 + 8782.01i −1.05569 + 0.767005i
\(509\) −1242.10 3822.80i −0.108163 0.332893i 0.882296 0.470694i \(-0.155996\pi\)
−0.990460 + 0.137801i \(0.955996\pi\)
\(510\) 0 0
\(511\) 530.135 1631.59i 0.0458939 0.141247i
\(512\) 2650.18 + 8156.41i 0.228755 + 0.704035i
\(513\) 0 0
\(514\) 3288.76 10121.8i 0.282220 0.868584i
\(515\) −10115.2 12348.6i −0.865496 1.05659i
\(516\) 0 0
\(517\) 23423.6 17018.2i 1.99259 1.44770i
\(518\) 766.876 0.0650475
\(519\) 0 0
\(520\) −6221.50 7595.15i −0.524674 0.640518i
\(521\) 16843.1 + 12237.2i 1.41633 + 1.02903i 0.992363 + 0.123348i \(0.0393631\pi\)
0.423968 + 0.905677i \(0.360637\pi\)
\(522\) 0 0
\(523\) −4858.36 + 14952.5i −0.406197 + 1.25015i 0.513694 + 0.857974i \(0.328277\pi\)
−0.919891 + 0.392174i \(0.871723\pi\)
\(524\) 27988.5 2.33336
\(525\) 0 0
\(526\) −15880.4 −1.31639
\(527\) −4768.31 + 14675.4i −0.394138 + 1.21303i
\(528\) 0 0
\(529\) 3176.96 + 2308.19i 0.261113 + 0.189709i
\(530\) −19114.0 + 7460.81i −1.56653 + 0.611466i
\(531\) 0 0
\(532\) −1679.28 −0.136853
\(533\) −9830.36 + 7142.18i −0.798875 + 0.580417i
\(534\) 0 0
\(535\) −9549.81 2501.37i −0.771728 0.202138i
\(536\) −997.944 + 3071.36i −0.0804190 + 0.247504i
\(537\) 0 0
\(538\) −10594.6 32606.8i −0.849006 2.61297i
\(539\) −7282.95 + 22414.6i −0.582002 + 1.79122i
\(540\) 0 0
\(541\) −3747.64 11534.1i −0.297826 0.916613i −0.982258 0.187537i \(-0.939950\pi\)
0.684432 0.729077i \(-0.260050\pi\)
\(542\) 4516.12 3281.15i 0.357904 0.260032i
\(543\) 0 0
\(544\) 11382.7 8270.03i 0.897115 0.651792i
\(545\) −709.534 12222.8i −0.0557672 0.960673i
\(546\) 0 0
\(547\) 7149.70 + 5194.56i 0.558865 + 0.406039i 0.831043 0.556208i \(-0.187744\pi\)
−0.272178 + 0.962247i \(0.587744\pi\)
\(548\) −5976.75 + 18394.5i −0.465901 + 1.43390i
\(549\) 0 0
\(550\) 17117.7 + 37311.6i 1.32710 + 2.89268i
\(551\) −3051.47 −0.235929
\(552\) 0 0
\(553\) 247.693 + 179.959i 0.0190470 + 0.0138384i
\(554\) 5814.28 + 4224.32i 0.445893 + 0.323961i
\(555\) 0 0
\(556\) 7072.09 5138.17i 0.539431 0.391919i
\(557\) −3059.58 −0.232744 −0.116372 0.993206i \(-0.537127\pi\)
−0.116372 + 0.993206i \(0.537127\pi\)
\(558\) 0 0
\(559\) 1270.06 + 3908.86i 0.0960966 + 0.295755i
\(560\) 34.3771 + 592.197i 0.00259410 + 0.0446873i
\(561\) 0 0
\(562\) 3427.45 + 10548.6i 0.257257 + 0.791756i
\(563\) 5711.65 + 17578.7i 0.427562 + 1.31590i 0.900519 + 0.434816i \(0.143187\pi\)
−0.472957 + 0.881085i \(0.656813\pi\)
\(564\) 0 0
\(565\) −834.453 14374.7i −0.0621340 1.07035i
\(566\) −11279.9 34716.1i −0.837687 2.57814i
\(567\) 0 0
\(568\) 28059.8 2.07282
\(569\) −21450.9 + 15585.0i −1.58044 + 1.14826i −0.664251 + 0.747509i \(0.731249\pi\)
−0.916189 + 0.400747i \(0.868751\pi\)
\(570\) 0 0
\(571\) 469.169 + 340.871i 0.0343855 + 0.0249825i 0.604845 0.796343i \(-0.293235\pi\)
−0.570460 + 0.821326i \(0.693235\pi\)
\(572\) 24040.7 + 17466.6i 1.75733 + 1.27677i
\(573\) 0 0
\(574\) 4178.99 0.303881
\(575\) −8346.40 + 7686.91i −0.605338 + 0.557507i
\(576\) 0 0
\(577\) 4891.04 15053.1i 0.352889 1.08608i −0.604335 0.796731i \(-0.706561\pi\)
0.957224 0.289350i \(-0.0934390\pi\)
\(578\) 33748.0 + 24519.3i 2.42860 + 1.76448i
\(579\) 0 0
\(580\) 520.614 + 8968.35i 0.0372712 + 0.642053i
\(581\) 1407.01 1022.25i 0.100469 0.0729953i
\(582\) 0 0
\(583\) 21954.8 15951.1i 1.55965 1.13315i
\(584\) −7082.89 21798.9i −0.501870 1.54460i
\(585\) 0 0
\(586\) −3973.83 + 12230.2i −0.280132 + 0.862159i
\(587\) 1033.54 + 3180.90i 0.0726722 + 0.223662i 0.980795 0.195042i \(-0.0624844\pi\)
−0.908123 + 0.418704i \(0.862484\pi\)
\(588\) 0 0
\(589\) −2193.15 + 6749.83i −0.153425 + 0.472193i
\(590\) −6807.94 1783.20i −0.475049 0.124429i
\(591\) 0 0
\(592\) 1456.20 1057.99i 0.101097 0.0734512i
\(593\) 3265.57 0.226140 0.113070 0.993587i \(-0.463932\pi\)
0.113070 + 0.993587i \(0.463932\pi\)
\(594\) 0 0
\(595\) 2676.17 1044.59i 0.184390 0.0719734i
\(596\) −14574.7 10589.2i −1.00169 0.727767i
\(597\) 0 0
\(598\) −3967.24 + 12209.9i −0.271292 + 0.834950i
\(599\) −14508.4 −0.989645 −0.494822 0.868994i \(-0.664767\pi\)
−0.494822 + 0.868994i \(0.664767\pi\)
\(600\) 0 0
\(601\) 1098.44 0.0745530 0.0372765 0.999305i \(-0.488132\pi\)
0.0372765 + 0.999305i \(0.488132\pi\)
\(602\) 436.803 1344.34i 0.0295727 0.0910153i
\(603\) 0 0
\(604\) −31398.4 22812.2i −2.11520 1.53678i
\(605\) −24975.1 30489.4i −1.67832 2.04887i
\(606\) 0 0
\(607\) −17611.8 −1.17766 −0.588829 0.808257i \(-0.700411\pi\)
−0.588829 + 0.808257i \(0.700411\pi\)
\(608\) 5235.40 3803.74i 0.349217 0.253721i
\(609\) 0 0
\(610\) −14731.1 17983.6i −0.977779 1.19366i
\(611\) 3853.06 11858.5i 0.255120 0.785178i
\(612\) 0 0
\(613\) 4303.56 + 13245.0i 0.283555 + 0.872692i 0.986828 + 0.161772i \(0.0517210\pi\)
−0.703273 + 0.710919i \(0.748279\pi\)
\(614\) −3657.46 + 11256.5i −0.240396 + 0.739863i
\(615\) 0 0
\(616\) −1380.04 4247.33i −0.0902653 0.277808i
\(617\) −12667.0 + 9203.14i −0.826508 + 0.600493i −0.918569 0.395260i \(-0.870654\pi\)
0.0920612 + 0.995753i \(0.470654\pi\)
\(618\) 0 0
\(619\) −9733.13 + 7071.54i −0.632000 + 0.459175i −0.857092 0.515163i \(-0.827731\pi\)
0.225093 + 0.974337i \(0.427731\pi\)
\(620\) 20212.1 + 5294.14i 1.30926 + 0.342932i
\(621\) 0 0
\(622\) 11080.3 + 8050.30i 0.714275 + 0.518951i
\(623\) −58.4722 + 179.959i −0.00376026 + 0.0115729i
\(624\) 0 0
\(625\) 8114.97 + 13352.5i 0.519358 + 0.854557i
\(626\) −1771.37 −0.113096
\(627\) 0 0
\(628\) −30054.7 21836.0i −1.90973 1.38750i
\(629\) −7052.30 5123.80i −0.447049 0.324800i
\(630\) 0 0
\(631\) −5492.97 + 3990.88i −0.346548 + 0.251782i −0.747419 0.664353i \(-0.768707\pi\)
0.400872 + 0.916134i \(0.368707\pi\)
\(632\) 4090.53 0.257456
\(633\) 0 0
\(634\) −4001.55 12315.5i −0.250666 0.771470i
\(635\) 6347.28 9895.37i 0.396668 0.618403i
\(636\) 0 0
\(637\) 3136.43 + 9652.94i 0.195086 + 0.600413i
\(638\) −5738.74 17662.0i −0.356111 1.09600i
\(639\) 0 0
\(640\) −18543.3 22637.5i −1.14529 1.39816i
\(641\) −4738.38 14583.2i −0.291973 0.898600i −0.984221 0.176941i \(-0.943380\pi\)
0.692249 0.721659i \(-0.256620\pi\)
\(642\) 0 0
\(643\) −6133.45 −0.376173 −0.188087 0.982152i \(-0.560229\pi\)
−0.188087 + 0.982152i \(0.560229\pi\)
\(644\) 2285.38 1660.43i 0.139839 0.101599i
\(645\) 0 0
\(646\) 24137.5 + 17536.9i 1.47009 + 1.06808i
\(647\) 15511.8 + 11270.0i 0.942554 + 0.684805i 0.949034 0.315174i \(-0.102063\pi\)
−0.00648045 + 0.999979i \(0.502063\pi\)
\(648\) 0 0
\(649\) 9307.90 0.562969
\(650\) 15408.7 + 8666.56i 0.929813 + 0.522970i
\(651\) 0 0
\(652\) 13599.4 41854.5i 0.816859 2.51403i
\(653\) 26.1050 + 18.9664i 0.00156442 + 0.00113662i 0.588567 0.808448i \(-0.299692\pi\)
−0.587003 + 0.809585i \(0.699692\pi\)
\(654\) 0 0
\(655\) −20515.1 + 8007.70i −1.22380 + 0.477690i
\(656\) 7935.36 5765.37i 0.472292 0.343140i
\(657\) 0 0
\(658\) −3469.29 + 2520.59i −0.205543 + 0.149335i
\(659\) −7750.36 23853.2i −0.458136 1.41000i −0.867414 0.497587i \(-0.834220\pi\)
0.409279 0.912409i \(-0.365780\pi\)
\(660\) 0 0
\(661\) 2323.83 7152.00i 0.136742 0.420848i −0.859115 0.511782i \(-0.828985\pi\)
0.995857 + 0.0909345i \(0.0289854\pi\)
\(662\) −9266.06 28518.0i −0.544011 1.67429i
\(663\) 0 0
\(664\) 7180.36 22098.9i 0.419657 1.29157i
\(665\) 1230.88 480.453i 0.0717769 0.0280168i
\(666\) 0 0
\(667\) 4152.84 3017.21i 0.241077 0.175153i
\(668\) 19240.5 1.11443
\(669\) 0 0
\(670\) −336.995 5805.24i −0.0194317 0.334740i
\(671\) 24874.2 + 18072.1i 1.43108 + 1.03974i
\(672\) 0 0
\(673\) 7958.41 24493.5i 0.455831 1.40290i −0.414326 0.910129i \(-0.635983\pi\)
0.870157 0.492775i \(-0.164017\pi\)
\(674\) 18387.1 1.05081
\(675\) 0 0
\(676\) −18420.1 −1.04803
\(677\) −583.981 + 1797.31i −0.0331525 + 0.102033i −0.966263 0.257556i \(-0.917083\pi\)
0.933111 + 0.359588i \(0.117083\pi\)
\(678\) 0 0
\(679\) 1521.50 + 1105.43i 0.0859937 + 0.0624781i
\(680\) 20723.1 32307.2i 1.16867 1.82195i
\(681\) 0 0
\(682\) −43192.9 −2.42513
\(683\) −10288.0 + 7474.69i −0.576369 + 0.418757i −0.837413 0.546570i \(-0.815933\pi\)
0.261044 + 0.965327i \(0.415933\pi\)
\(684\) 0 0
\(685\) −881.950 15192.9i −0.0491935 0.847432i
\(686\) 2172.67 6686.79i 0.120923 0.372162i
\(687\) 0 0
\(688\) −1025.23 3155.34i −0.0568120 0.174849i
\(689\) 3611.46 11114.9i 0.199689 0.614580i
\(690\) 0 0
\(691\) −251.500 774.039i −0.0138459 0.0426133i 0.943895 0.330246i \(-0.107132\pi\)
−0.957741 + 0.287633i \(0.907132\pi\)
\(692\) 28048.6 20378.5i 1.54082 1.11947i
\(693\) 0 0
\(694\) −40856.7 + 29684.1i −2.23472 + 1.62362i
\(695\) −3713.66 + 5789.58i −0.202687 + 0.315987i
\(696\) 0 0
\(697\) −38430.6 27921.5i −2.08847 1.51736i
\(698\) −3178.32 + 9781.85i −0.172351 + 0.530442i
\(699\) 0 0
\(700\) −1622.07 3535.63i −0.0875835 0.190906i
\(701\) −12443.3 −0.670437 −0.335219 0.942140i \(-0.608810\pi\)
−0.335219 + 0.942140i \(0.608810\pi\)
\(702\) 0 0
\(703\) −3243.66 2356.65i −0.174021 0.126434i
\(704\) 42788.4 + 31087.6i 2.29069 + 1.66429i
\(705\) 0 0
\(706\) 12818.3 9313.04i 0.683319 0.496460i
\(707\) 2080.27 0.110660
\(708\) 0 0
\(709\) −1995.93 6142.85i −0.105725 0.325387i 0.884175 0.467156i \(-0.154721\pi\)
−0.989900 + 0.141768i \(0.954721\pi\)
\(710\) −47067.2 + 18371.8i −2.48789 + 0.971102i
\(711\) 0 0
\(712\) 781.220 + 2404.35i 0.0411200 + 0.126554i
\(713\) −3689.33 11354.6i −0.193782 0.596399i
\(714\) 0 0
\(715\) −22618.7 5924.51i −1.18307 0.309880i
\(716\) 12085.1 + 37194.1i 0.630784 + 1.94135i
\(717\) 0 0
\(718\) 51948.5 2.70014
\(719\) 10070.8 7316.89i 0.522363 0.379519i −0.295130 0.955457i \(-0.595363\pi\)
0.817493 + 0.575938i \(0.195363\pi\)
\(720\) 0 0
\(721\) −2529.74 1837.97i −0.130669 0.0949368i
\(722\) −15048.9 10933.6i −0.775707 0.563584i
\(723\) 0 0
\(724\) 41801.7 2.14578
\(725\) −2947.51 6424.71i −0.150990 0.329114i
\(726\) 0 0
\(727\) −2165.86 + 6665.83i −0.110491 + 0.340058i −0.990980 0.134010i \(-0.957215\pi\)
0.880489 + 0.474067i \(0.157215\pi\)
\(728\) −1555.95 1130.46i −0.0792133 0.0575519i
\(729\) 0 0
\(730\) 26153.3 + 31927.7i 1.32600 + 1.61877i
\(731\) −12999.0 + 9444.30i −0.657707 + 0.477852i
\(732\) 0 0
\(733\) −18335.1 + 13321.2i −0.923906 + 0.671257i −0.944493 0.328531i \(-0.893446\pi\)
0.0205872 + 0.999788i \(0.493446\pi\)
\(734\) −3456.50 10638.0i −0.173817 0.534954i
\(735\) 0 0
\(736\) −3363.98 + 10353.3i −0.168476 + 0.518514i
\(737\) 2376.62 + 7314.49i 0.118784 + 0.365580i
\(738\) 0 0
\(739\) 9762.50 30045.9i 0.485953 1.49561i −0.344642 0.938734i \(-0.612000\pi\)
0.830595 0.556876i \(-0.188000\pi\)
\(740\) −6372.87 + 9935.27i −0.316583 + 0.493551i
\(741\) 0 0
\(742\) −3251.76 + 2362.54i −0.160884 + 0.116889i
\(743\) −3878.19 −0.191490 −0.0957449 0.995406i \(-0.530523\pi\)
−0.0957449 + 0.995406i \(0.530523\pi\)
\(744\) 0 0
\(745\) 13712.7 + 3591.76i 0.674355 + 0.176633i
\(746\) −15050.0 10934.5i −0.738633 0.536648i
\(747\) 0 0
\(748\) −35898.7 + 110485.i −1.75479 + 5.40070i
\(749\) −1933.83 −0.0943399
\(750\) 0 0
\(751\) 26124.2 1.26935 0.634677 0.772778i \(-0.281133\pi\)
0.634677 + 0.772778i \(0.281133\pi\)
\(752\) −3110.30 + 9572.53i −0.150826 + 0.464195i
\(753\) 0 0
\(754\) −6470.24 4700.90i −0.312509 0.227051i
\(755\) 29541.3 + 7737.72i 1.42400 + 0.372986i
\(756\) 0 0
\(757\) 8989.00 0.431586 0.215793 0.976439i \(-0.430766\pi\)
0.215793 + 0.976439i \(0.430766\pi\)
\(758\) 16935.7 12304.5i 0.811521 0.589605i
\(759\) 0 0
\(760\) 9531.44 14859.5i 0.454923 0.709223i
\(761\) 2883.92 8875.79i 0.137374 0.422795i −0.858577 0.512684i \(-0.828651\pi\)
0.995952 + 0.0898889i \(0.0286512\pi\)
\(762\) 0 0
\(763\) −741.135 2280.98i −0.0351650 0.108227i
\(764\) −4038.48 + 12429.2i −0.191240 + 0.588575i
\(765\) 0 0
\(766\) −4065.01 12510.8i −0.191743 0.590123i
\(767\) 3242.93 2356.13i 0.152667 0.110919i
\(768\) 0 0
\(769\) 10026.5 7284.68i 0.470175 0.341602i −0.327334 0.944909i \(-0.606150\pi\)
0.797510 + 0.603306i \(0.206150\pi\)
\(770\) 5095.75 + 6220.85i 0.238491 + 0.291148i
\(771\) 0 0
\(772\) −54516.0 39608.2i −2.54154 1.84654i
\(773\) −1319.96 + 4062.43i −0.0614176 + 0.189024i −0.977058 0.212975i \(-0.931685\pi\)
0.915640 + 0.401999i \(0.131685\pi\)
\(774\) 0 0
\(775\) −16329.9 + 1902.31i −0.756885 + 0.0881717i
\(776\) 25126.8 1.16237
\(777\) 0 0
\(778\) 38460.7 + 27943.3i 1.77234 + 1.28768i
\(779\) −17675.9 12842.3i −0.812970 0.590658i
\(780\) 0 0
\(781\) 54062.6 39278.8i 2.47697 1.79962i
\(782\) −50189.6 −2.29511
\(783\) 0 0
\(784\) −2531.82 7792.13i −0.115334 0.354962i
\(785\) 28277.1 + 7406.59i 1.28567 + 0.336755i
\(786\) 0 0
\(787\) 10262.1 + 31583.6i 0.464809 + 1.43054i 0.859222 + 0.511603i \(0.170948\pi\)
−0.394412 + 0.918934i \(0.629052\pi\)
\(788\) −21754.0