Properties

Label 225.4.h.d.46.15
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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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,4,Mod(46,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.46");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
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 46.15
Character \(\chi\) \(=\) 225.46
Dual form 225.4.h.d.181.15

$q$-expansion

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

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 \(-0.586571\pi\)
0.783507 0.621383i \(-0.213429\pi\)
\(3\) 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 \(0.504204\pi\)
−0.577050 + 0.816709i \(0.695796\pi\)
\(12\) 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 \(0.615641\pi\)
−0.998793 + 0.0491177i \(0.984359\pi\)
\(18\) 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 \(-0.765014\pi\)
0.993966 0.109692i \(-0.0349863\pi\)
\(24\) 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 0.724543 0.689230i \(-0.242051\pi\)
−0.431600 + 0.902065i \(0.642051\pi\)
\(30\) 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 \(0.180311\pi\)
−0.367216 + 0.930136i \(0.619689\pi\)
\(42\) 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 −0.0722762 0.997385i \(-0.523026\pi\)
−0.970904 + 0.239470i \(0.923026\pi\)
\(48\) 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 0.0991901 0.995068i \(-0.468375\pi\)
−0.915715 + 0.401829i \(0.868375\pi\)
\(54\) 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 0.895134 0.445796i \(-0.147079\pi\)
−0.986211 + 0.165490i \(0.947079\pi\)
\(60\) 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 −0.296849 0.954925i \(-0.595936\pi\)
−0.999918 + 0.0127681i \(0.995936\pi\)
\(72\) 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 −0.925034 0.379884i \(-0.875964\pi\)
0.0754401 + 0.997150i \(0.475964\pi\)
\(84\) 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 −0.933898 0.357539i \(-0.883616\pi\)
0.965696 + 0.259676i \(0.0836158\pi\)
\(90\) 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 \(-0.654984\pi\)
−0.467885 + 0.883790i \(0.654984\pi\)
\(102\) 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 \(-0.369399\pi\)
0.398881 + 0.917003i \(0.369399\pi\)
\(108\) 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 \(0.0800943\pi\)
−0.637196 + 0.770702i \(0.719906\pi\)
\(114\) 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 0.0882194 0.996101i \(-0.471882\pi\)
0.974610 + 0.223911i \(0.0718824\pi\)
\(132\) 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 \(0.0395253\pi\)
−0.729989 + 0.683459i \(0.760475\pi\)
\(138\) 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 \(-0.613327\pi\)
−0.348552 + 0.937289i \(0.613327\pi\)
\(150\) 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 −0.304303 0.952575i \(-0.598424\pi\)
0.811918 + 0.583772i \(0.198424\pi\)
\(168\) 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 \(-0.719878\pi\)
0.968487 0.249062i \(-0.0801224\pi\)
\(174\) 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 0.945939 0.324346i \(-0.105144\pi\)
−0.0161602 + 0.999869i \(0.505144\pi\)
\(180\) 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 0.990348 0.138602i \(-0.0442607\pi\)
−0.882676 + 0.469981i \(0.844261\pi\)
\(192\) 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 \(-0.946528\pi\)
−0.463682 0.886002i \(-0.653472\pi\)
\(198\) 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 −0.969684 0.244364i \(-0.921421\pi\)
0.928124 + 0.372271i \(0.121421\pi\)
\(228\) 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 −0.0484511 0.998826i \(-0.515429\pi\)
0.934967 + 0.354734i \(0.115429\pi\)
\(234\) 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 \(-0.581584\pi\)
0.773675 0.633582i \(-0.218416\pi\)
\(240\) 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 \(-0.825556\pi\)
−0.853552 + 0.521008i \(0.825556\pi\)
\(252\) 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 \(-0.411631\pi\)
0.274066 + 0.961711i \(0.411631\pi\)
\(258\) 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 \(-0.970733\pi\)
0.751632 0.659583i \(-0.229267\pi\)
\(264\) 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 \(-0.391470\pi\)
0.999641 0.0267953i \(-0.00853023\pi\)
\(270\) 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 −0.771259 0.636521i \(-0.780373\pi\)
0.367035 + 0.930207i \(0.380373\pi\)
\(282\) 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 \(-0.587698\pi\)
−0.272039 + 0.962286i \(0.587698\pi\)
\(294\) 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 −0.998942 0.0459950i \(-0.985354\pi\)
0.835196 + 0.549952i \(0.185354\pi\)
\(312\) 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 −0.373171 0.927763i \(-0.621730\pi\)
0.767038 + 0.641601i \(0.221730\pi\)
\(318\) 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 \(-0.988952\pi\)
−0.341833 0.939761i \(-0.611048\pi\)
\(348\) 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 0.773647 0.633616i \(-0.218430\pi\)
−0.363535 + 0.931581i \(0.618430\pi\)
\(354\) 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 \(0.200685\pi\)
−0.306968 + 0.951720i \(0.599315\pi\)
\(360\) 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 −0.426864 0.904316i \(-0.640382\pi\)
0.728147 + 0.685421i \(0.240382\pi\)
\(384\) 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 \(0.328350\pi\)
−0.919801 + 0.392386i \(0.871650\pi\)
\(390\) 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 \(-0.506815\pi\)
−0.0214097 + 0.999771i \(0.506815\pi\)
\(402\) 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 −0.897373 0.441272i \(-0.854527\pi\)
0.142371 + 0.989813i \(0.454527\pi\)
\(420\) 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 −0.462750 0.886489i \(-0.653137\pi\)
0.700103 + 0.714042i \(0.253137\pi\)
\(432\) 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 \(-0.407297\pi\)
0.287136 + 0.957890i \(0.407297\pi\)
\(444\) 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 \(-0.678793\pi\)
−0.532620 + 0.846354i \(0.678793\pi\)
\(450\) 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 \(0.370983\pi\)
−0.859167 + 0.511696i \(0.829017\pi\)
\(462\) 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 −0.982700 0.185206i \(-0.940705\pi\)
−0.127530 + 0.991835i \(0.540705\pi\)
\(468\) 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 0.891626 0.452773i \(-0.149565\pi\)
−0.155086 + 0.987901i \(0.549565\pi\)
\(480\) 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 0.867602 0.497259i \(-0.165660\pi\)
−0.994186 + 0.107673i \(0.965660\pi\)
\(492\) 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 0.727877 0.685707i \(-0.240507\pi\)
−0.427220 + 0.904148i \(0.640507\pi\)
\(504\) 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 0.990460 0.137801i \(-0.0440035\pi\)
−0.882296 + 0.470694i \(0.844004\pi\)
\(510\) 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 \(-0.960637\pi\)
−0.423968 0.905677i \(-0.639363\pi\)
\(522\) 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 \(-0.462873\pi\)
0.116372 + 0.993206i \(0.462873\pi\)
\(558\) 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 \(-0.856813\pi\)
0.472957 0.881085i \(-0.343187\pi\)
\(564\) 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 \(-0.268751\pi\)
0.916189 0.400747i \(-0.131249\pi\)
\(570\) 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 0.908123 0.418704i \(-0.137516\pi\)
−0.980795 + 0.195042i \(0.937516\pi\)
\(588\) 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 \(-0.536068\pi\)
−0.113070 + 0.993587i \(0.536068\pi\)
\(594\) 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 \(-0.335233\pi\)
0.494822 + 0.868994i \(0.335233\pi\)
\(600\) 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 −0.0920612 0.995753i \(-0.529346\pi\)
0.918569 + 0.395260i \(0.129346\pi\)
\(618\) 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 \(0.0566202\pi\)
−0.692249 + 0.721659i \(0.743380\pi\)
\(642\) 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 0.00648045 0.999979i \(-0.497937\pi\)
−0.949034 + 0.315174i \(0.897937\pi\)
\(648\) 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 0.587003 0.809585i \(-0.300308\pi\)
−0.588567 + 0.808448i \(0.700308\pi\)
\(654\) 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 \(0.165780\pi\)
−0.409279 + 0.912409i \(0.634220\pi\)
\(660\) 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 −0.933111 0.359588i \(-0.882917\pi\)
0.966263 + 0.257556i \(0.0829171\pi\)
\(678\) 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 −0.261044 0.965327i \(-0.584067\pi\)
0.837413 + 0.546570i \(0.184067\pi\)
\(684\) 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 \(-0.391190\pi\)
0.335219 + 0.942140i \(0.391190\pi\)
\(702\) 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 −0.817493 0.575938i \(-0.804637\pi\)
0.295130 + 0.955457i \(0.404637\pi\)
\(720\) 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 \(-0.469477\pi\)
0.0957449 + 0.995406i \(0.469477\pi\)
\(744\) 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 −0.995952 0.0898889i \(-0.971349\pi\)
0.858577 + 0.512684i \(0.171349\pi\)
\(762\) 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 −0.915640 0.401999i \(-0.868315\pi\)
0.977058 + 0.212975i \(0.0683154\pi\)
\(774\) 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