Properties

Label 252.4.be.a.179.23
Level $252$
Weight $4$
Character 252.179
Analytic conductor $14.868$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [252,4,Mod(107,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.107");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.be (of order \(6\), degree \(2\), 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: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(48\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 179.23
Character \(\chi\) \(=\) 252.179
Dual form 252.4.be.a.107.23

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.151648 - 2.82436i) q^{2} +(-7.95401 + 0.856618i) q^{4} +(14.8202 - 8.55643i) q^{5} +(-11.3319 + 14.6489i) q^{7} +(3.62561 + 22.3351i) q^{8} +O(q^{10})\) \(q+(-0.151648 - 2.82436i) q^{2} +(-7.95401 + 0.856618i) q^{4} +(14.8202 - 8.55643i) q^{5} +(-11.3319 + 14.6489i) q^{7} +(3.62561 + 22.3351i) q^{8} +(-26.4139 - 40.5599i) q^{10} +(-29.5475 + 51.1777i) q^{11} -42.9268 q^{13} +(43.0921 + 29.7838i) q^{14} +(62.5324 - 13.6271i) q^{16} +(-81.2955 - 46.9360i) q^{17} +(-75.1664 + 43.3973i) q^{19} +(-110.550 + 80.7532i) q^{20} +(149.025 + 75.6916i) q^{22} +(-50.9747 - 88.2909i) q^{23} +(83.9251 - 145.363i) q^{25} +(6.50977 + 121.241i) q^{26} +(77.5852 - 126.224i) q^{28} +302.226i q^{29} +(37.3298 + 21.5524i) q^{31} +(-47.9707 - 174.547i) q^{32} +(-120.236 + 236.726i) q^{34} +(-42.5982 + 314.059i) q^{35} +(43.7307 + 75.7438i) q^{37} +(133.968 + 205.716i) q^{38} +(244.841 + 299.987i) q^{40} +423.830i q^{41} -214.086i q^{43} +(191.181 - 432.379i) q^{44} +(-241.635 + 157.360i) q^{46} +(-51.0341 - 88.3937i) q^{47} +(-86.1780 - 331.998i) q^{49} +(-423.283 - 214.991i) q^{50} +(341.440 - 36.7719i) q^{52} +(224.794 + 129.785i) q^{53} +1011.28i q^{55} +(-368.268 - 199.987i) q^{56} +(853.594 - 45.8320i) q^{58} +(185.741 - 321.714i) q^{59} +(-226.821 - 392.865i) q^{61} +(55.2106 - 108.701i) q^{62} +(-485.710 + 161.956i) q^{64} +(-636.183 + 367.300i) q^{65} +(-159.170 - 91.8966i) q^{67} +(686.831 + 303.690i) q^{68} +(893.475 + 72.6860i) q^{70} +1002.00 q^{71} +(216.995 - 375.846i) q^{73} +(207.296 - 134.998i) q^{74} +(560.699 - 409.571i) q^{76} +(-414.867 - 1012.78i) q^{77} +(-111.598 + 64.4311i) q^{79} +(810.142 - 737.010i) q^{80} +(1197.05 - 64.2731i) q^{82} -802.817 q^{83} -1606.42 q^{85} +(-604.656 + 32.4658i) q^{86} +(-1250.18 - 474.394i) q^{88} +(-401.231 + 231.651i) q^{89} +(486.440 - 628.828i) q^{91} +(481.085 + 658.600i) q^{92} +(-241.916 + 157.544i) q^{94} +(-742.653 + 1286.31i) q^{95} -652.945 q^{97} +(-924.611 + 293.745i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 144 q^{13} - 60 q^{16} + 480 q^{22} + 1032 q^{25} + 900 q^{28} - 1008 q^{34} + 504 q^{37} + 492 q^{40} + 120 q^{46} + 1488 q^{49} - 708 q^{52} + 1932 q^{58} - 2160 q^{61} - 2376 q^{64} - 588 q^{70} + 1320 q^{73} - 1368 q^{76} - 996 q^{82} + 2592 q^{85} - 1524 q^{88} - 3852 q^{94} - 2064 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.151648 2.82436i −0.0536158 0.998562i
\(3\) 0 0
\(4\) −7.95401 + 0.856618i −0.994251 + 0.107077i
\(5\) 14.8202 8.55643i 1.32556 0.765311i 0.340948 0.940082i \(-0.389252\pi\)
0.984609 + 0.174771i \(0.0559186\pi\)
\(6\) 0 0
\(7\) −11.3319 + 14.6489i −0.611863 + 0.790964i
\(8\) 3.62561 + 22.3351i 0.160231 + 0.987080i
\(9\) 0 0
\(10\) −26.4139 40.5599i −0.835281 1.28262i
\(11\) −29.5475 + 51.1777i −0.809900 + 1.40279i 0.103033 + 0.994678i \(0.467145\pi\)
−0.912933 + 0.408110i \(0.866188\pi\)
\(12\) 0 0
\(13\) −42.9268 −0.915827 −0.457913 0.888997i \(-0.651403\pi\)
−0.457913 + 0.888997i \(0.651403\pi\)
\(14\) 43.0921 + 29.7838i 0.822632 + 0.568575i
\(15\) 0 0
\(16\) 62.5324 13.6271i 0.977069 0.212923i
\(17\) −81.2955 46.9360i −1.15983 0.669627i −0.208565 0.978009i \(-0.566879\pi\)
−0.951263 + 0.308382i \(0.900212\pi\)
\(18\) 0 0
\(19\) −75.1664 + 43.3973i −0.907597 + 0.524002i −0.879657 0.475608i \(-0.842228\pi\)
−0.0279400 + 0.999610i \(0.508895\pi\)
\(20\) −110.550 + 80.7532i −1.23599 + 0.902848i
\(21\) 0 0
\(22\) 149.025 + 75.6916i 1.44419 + 0.733523i
\(23\) −50.9747 88.2909i −0.462129 0.800431i 0.536938 0.843622i \(-0.319581\pi\)
−0.999067 + 0.0431908i \(0.986248\pi\)
\(24\) 0 0
\(25\) 83.9251 145.363i 0.671401 1.16290i
\(26\) 6.50977 + 121.241i 0.0491028 + 0.914510i
\(27\) 0 0
\(28\) 77.5852 126.224i 0.523651 0.851933i
\(29\) 302.226i 1.93524i 0.252415 + 0.967619i \(0.418775\pi\)
−0.252415 + 0.967619i \(0.581225\pi\)
\(30\) 0 0
\(31\) 37.3298 + 21.5524i 0.216278 + 0.124868i 0.604226 0.796813i \(-0.293482\pi\)
−0.387947 + 0.921681i \(0.626816\pi\)
\(32\) −47.9707 174.547i −0.265003 0.964247i
\(33\) 0 0
\(34\) −120.236 + 236.726i −0.606478 + 1.19406i
\(35\) −42.5982 + 314.059i −0.205726 + 1.51673i
\(36\) 0 0
\(37\) 43.7307 + 75.7438i 0.194305 + 0.336546i 0.946672 0.322198i \(-0.104422\pi\)
−0.752368 + 0.658744i \(0.771088\pi\)
\(38\) 133.968 + 205.716i 0.571909 + 0.878197i
\(39\) 0 0
\(40\) 244.841 + 299.987i 0.967818 + 1.18580i
\(41\) 423.830i 1.61442i 0.590266 + 0.807209i \(0.299023\pi\)
−0.590266 + 0.807209i \(0.700977\pi\)
\(42\) 0 0
\(43\) 214.086i 0.759252i −0.925140 0.379626i \(-0.876053\pi\)
0.925140 0.379626i \(-0.123947\pi\)
\(44\) 191.181 432.379i 0.655037 1.48144i
\(45\) 0 0
\(46\) −241.635 + 157.360i −0.774502 + 0.504380i
\(47\) −51.0341 88.3937i −0.158385 0.274331i 0.775901 0.630854i \(-0.217295\pi\)
−0.934286 + 0.356523i \(0.883962\pi\)
\(48\) 0 0
\(49\) −86.1780 331.998i −0.251248 0.967923i
\(50\) −423.283 214.991i −1.19723 0.608086i
\(51\) 0 0
\(52\) 341.440 36.7719i 0.910561 0.0980643i
\(53\) 224.794 + 129.785i 0.582602 + 0.336365i 0.762167 0.647381i \(-0.224136\pi\)
−0.179565 + 0.983746i \(0.557469\pi\)
\(54\) 0 0
\(55\) 1011.28i 2.47930i
\(56\) −368.268 199.987i −0.878784 0.477220i
\(57\) 0 0
\(58\) 853.594 45.8320i 1.93245 0.103759i
\(59\) 185.741 321.714i 0.409855 0.709890i −0.585018 0.811020i \(-0.698912\pi\)
0.994873 + 0.101130i \(0.0322458\pi\)
\(60\) 0 0
\(61\) −226.821 392.865i −0.476089 0.824610i 0.523536 0.852004i \(-0.324613\pi\)
−0.999625 + 0.0273937i \(0.991279\pi\)
\(62\) 55.2106 108.701i 0.113093 0.222662i
\(63\) 0 0
\(64\) −485.710 + 161.956i −0.948652 + 0.316321i
\(65\) −636.183 + 367.300i −1.21398 + 0.700892i
\(66\) 0 0
\(67\) −159.170 91.8966i −0.290234 0.167566i 0.347814 0.937564i \(-0.386924\pi\)
−0.638047 + 0.769997i \(0.720258\pi\)
\(68\) 686.831 + 303.690i 1.22486 + 0.541585i
\(69\) 0 0
\(70\) 893.475 + 72.6860i 1.52558 + 0.124109i
\(71\) 1002.00 1.67486 0.837432 0.546542i \(-0.184056\pi\)
0.837432 + 0.546542i \(0.184056\pi\)
\(72\) 0 0
\(73\) 216.995 375.846i 0.347909 0.602595i −0.637969 0.770062i \(-0.720225\pi\)
0.985878 + 0.167467i \(0.0535586\pi\)
\(74\) 207.296 134.998i 0.325644 0.212070i
\(75\) 0 0
\(76\) 560.699 409.571i 0.846271 0.618172i
\(77\) −414.867 1012.78i −0.614007 1.49891i
\(78\) 0 0
\(79\) −111.598 + 64.4311i −0.158934 + 0.0917604i −0.577357 0.816492i \(-0.695916\pi\)
0.418424 + 0.908252i \(0.362583\pi\)
\(80\) 810.142 737.010i 1.13221 1.03000i
\(81\) 0 0
\(82\) 1197.05 64.2731i 1.61210 0.0865583i
\(83\) −802.817 −1.06169 −0.530847 0.847468i \(-0.678126\pi\)
−0.530847 + 0.847468i \(0.678126\pi\)
\(84\) 0 0
\(85\) −1606.42 −2.04989
\(86\) −604.656 + 32.4658i −0.758159 + 0.0407079i
\(87\) 0 0
\(88\) −1250.18 474.394i −1.51443 0.574666i
\(89\) −401.231 + 231.651i −0.477869 + 0.275898i −0.719528 0.694463i \(-0.755642\pi\)
0.241659 + 0.970361i \(0.422309\pi\)
\(90\) 0 0
\(91\) 486.440 628.828i 0.560360 0.724386i
\(92\) 481.085 + 658.600i 0.545180 + 0.746346i
\(93\) 0 0
\(94\) −241.916 + 157.544i −0.265444 + 0.172866i
\(95\) −742.653 + 1286.31i −0.802048 + 1.38919i
\(96\) 0 0
\(97\) −652.945 −0.683469 −0.341734 0.939797i \(-0.611014\pi\)
−0.341734 + 0.939797i \(0.611014\pi\)
\(98\) −924.611 + 293.745i −0.953060 + 0.302782i
\(99\) 0 0
\(100\) −543.021 + 1228.11i −0.543021 + 1.22811i
\(101\) −229.378 132.432i −0.225980 0.130470i 0.382736 0.923858i \(-0.374982\pi\)
−0.608716 + 0.793388i \(0.708315\pi\)
\(102\) 0 0
\(103\) −1250.99 + 722.261i −1.19674 + 0.690937i −0.959826 0.280594i \(-0.909468\pi\)
−0.236911 + 0.971531i \(0.576135\pi\)
\(104\) −155.636 958.772i −0.146744 0.903994i
\(105\) 0 0
\(106\) 332.470 654.582i 0.304645 0.599798i
\(107\) 534.555 + 925.876i 0.482966 + 0.836521i 0.999809 0.0195590i \(-0.00622622\pi\)
−0.516843 + 0.856080i \(0.672893\pi\)
\(108\) 0 0
\(109\) −344.726 + 597.083i −0.302924 + 0.524680i −0.976797 0.214167i \(-0.931296\pi\)
0.673873 + 0.738847i \(0.264630\pi\)
\(110\) 2856.23 153.359i 2.47573 0.132930i
\(111\) 0 0
\(112\) −508.987 + 1070.45i −0.429417 + 0.903106i
\(113\) 189.378i 0.157656i −0.996888 0.0788282i \(-0.974882\pi\)
0.996888 0.0788282i \(-0.0251179\pi\)
\(114\) 0 0
\(115\) −1510.91 872.324i −1.22516 0.707345i
\(116\) −258.892 2403.90i −0.207220 1.92411i
\(117\) 0 0
\(118\) −936.802 475.813i −0.730844 0.371205i
\(119\) 1608.79 659.015i 1.23931 0.507662i
\(120\) 0 0
\(121\) −1080.61 1871.66i −0.811875 1.40621i
\(122\) −1075.19 + 700.200i −0.797898 + 0.519616i
\(123\) 0 0
\(124\) −315.384 139.450i −0.228405 0.100992i
\(125\) 733.291i 0.524700i
\(126\) 0 0
\(127\) 1180.84i 0.825058i −0.910944 0.412529i \(-0.864646\pi\)
0.910944 0.412529i \(-0.135354\pi\)
\(128\) 531.080 + 1347.26i 0.366729 + 0.930328i
\(129\) 0 0
\(130\) 1133.86 + 1741.11i 0.764972 + 1.17466i
\(131\) −230.038 398.438i −0.153424 0.265738i 0.779060 0.626949i \(-0.215697\pi\)
−0.932484 + 0.361211i \(0.882363\pi\)
\(132\) 0 0
\(133\) 216.053 1592.87i 0.140859 1.03849i
\(134\) −235.411 + 463.488i −0.151764 + 0.298800i
\(135\) 0 0
\(136\) 753.572 1985.91i 0.475135 1.25214i
\(137\) 191.954 + 110.825i 0.119706 + 0.0691125i 0.558658 0.829398i \(-0.311317\pi\)
−0.438951 + 0.898511i \(0.644650\pi\)
\(138\) 0 0
\(139\) 330.244i 0.201518i −0.994911 0.100759i \(-0.967873\pi\)
0.994911 0.100759i \(-0.0321270\pi\)
\(140\) 69.7973 2534.52i 0.0421354 1.53004i
\(141\) 0 0
\(142\) −151.951 2830.00i −0.0897991 1.67245i
\(143\) 1268.38 2196.89i 0.741728 1.28471i
\(144\) 0 0
\(145\) 2585.97 + 4479.04i 1.48106 + 2.56527i
\(146\) −1094.43 555.875i −0.620382 0.315100i
\(147\) 0 0
\(148\) −412.718 565.006i −0.229224 0.313805i
\(149\) −750.128 + 433.087i −0.412435 + 0.238120i −0.691836 0.722055i \(-0.743198\pi\)
0.279400 + 0.960175i \(0.409864\pi\)
\(150\) 0 0
\(151\) 1988.27 + 1147.93i 1.07154 + 0.618656i 0.928603 0.371075i \(-0.121011\pi\)
0.142941 + 0.989731i \(0.454344\pi\)
\(152\) −1241.81 1521.50i −0.662656 0.811910i
\(153\) 0 0
\(154\) −2797.53 + 1325.32i −1.46384 + 0.693489i
\(155\) 737.646 0.382252
\(156\) 0 0
\(157\) 1068.94 1851.46i 0.543381 0.941163i −0.455326 0.890325i \(-0.650477\pi\)
0.998707 0.0508385i \(-0.0161894\pi\)
\(158\) 198.900 + 305.422i 0.100150 + 0.153785i
\(159\) 0 0
\(160\) −2204.44 2176.37i −1.08923 1.07536i
\(161\) 1871.00 + 253.778i 0.915872 + 0.124227i
\(162\) 0 0
\(163\) −330.930 + 191.063i −0.159021 + 0.0918110i −0.577399 0.816462i \(-0.695932\pi\)
0.418378 + 0.908273i \(0.362599\pi\)
\(164\) −363.061 3371.15i −0.172868 1.60514i
\(165\) 0 0
\(166\) 121.746 + 2267.44i 0.0569235 + 1.06017i
\(167\) −794.247 −0.368028 −0.184014 0.982924i \(-0.558909\pi\)
−0.184014 + 0.982924i \(0.558909\pi\)
\(168\) 0 0
\(169\) −354.291 −0.161261
\(170\) 243.611 + 4537.10i 0.109906 + 2.04694i
\(171\) 0 0
\(172\) 183.390 + 1702.84i 0.0812986 + 0.754886i
\(173\) −26.6193 + 15.3687i −0.0116984 + 0.00675409i −0.505838 0.862629i \(-0.668817\pi\)
0.494139 + 0.869383i \(0.335483\pi\)
\(174\) 0 0
\(175\) 1178.37 + 2876.64i 0.509007 + 1.24259i
\(176\) −1150.27 + 3602.91i −0.492642 + 1.54307i
\(177\) 0 0
\(178\) 715.111 + 1098.09i 0.301122 + 0.462390i
\(179\) −1473.69 + 2552.50i −0.615355 + 1.06583i 0.374967 + 0.927038i \(0.377654\pi\)
−0.990322 + 0.138788i \(0.955679\pi\)
\(180\) 0 0
\(181\) 1320.02 0.542080 0.271040 0.962568i \(-0.412632\pi\)
0.271040 + 0.962568i \(0.412632\pi\)
\(182\) −1849.80 1278.52i −0.753388 0.520716i
\(183\) 0 0
\(184\) 1787.17 1458.63i 0.716042 0.584412i
\(185\) 1296.19 + 748.358i 0.515125 + 0.297407i
\(186\) 0 0
\(187\) 4804.15 2773.68i 1.87869 1.08466i
\(188\) 481.646 + 659.367i 0.186849 + 0.255794i
\(189\) 0 0
\(190\) 3745.63 + 1902.45i 1.43019 + 0.726412i
\(191\) 565.044 + 978.684i 0.214058 + 0.370760i 0.952981 0.303031i \(-0.0979984\pi\)
−0.738923 + 0.673790i \(0.764665\pi\)
\(192\) 0 0
\(193\) −1278.39 + 2214.23i −0.476789 + 0.825823i −0.999646 0.0265973i \(-0.991533\pi\)
0.522857 + 0.852420i \(0.324866\pi\)
\(194\) 99.0179 + 1844.15i 0.0366447 + 0.682486i
\(195\) 0 0
\(196\) 969.856 + 2566.89i 0.353446 + 0.935455i
\(197\) 1494.38i 0.540456i 0.962796 + 0.270228i \(0.0870992\pi\)
−0.962796 + 0.270228i \(0.912901\pi\)
\(198\) 0 0
\(199\) −1996.88 1152.90i −0.711331 0.410687i 0.100223 0.994965i \(-0.468044\pi\)
−0.811554 + 0.584278i \(0.801378\pi\)
\(200\) 3550.96 + 1347.44i 1.25545 + 0.476394i
\(201\) 0 0
\(202\) −339.250 + 667.930i −0.118166 + 0.232650i
\(203\) −4427.26 3424.78i −1.53070 1.18410i
\(204\) 0 0
\(205\) 3626.47 + 6281.24i 1.23553 + 2.14000i
\(206\) 2229.64 + 3423.72i 0.754107 + 1.15797i
\(207\) 0 0
\(208\) −2684.32 + 584.967i −0.894826 + 0.195001i
\(209\) 5129.12i 1.69755i
\(210\) 0 0
\(211\) 1353.94i 0.441749i −0.975302 0.220875i \(-0.929109\pi\)
0.975302 0.220875i \(-0.0708911\pi\)
\(212\) −1899.19 839.749i −0.615269 0.272048i
\(213\) 0 0
\(214\) 2533.94 1650.18i 0.809423 0.527122i
\(215\) −1831.81 3172.79i −0.581063 1.00643i
\(216\) 0 0
\(217\) −738.733 + 302.610i −0.231099 + 0.0946661i
\(218\) 1738.65 + 883.083i 0.540167 + 0.274357i
\(219\) 0 0
\(220\) −866.284 8043.76i −0.265477 2.46505i
\(221\) 3489.76 + 2014.81i 1.06220 + 0.613262i
\(222\) 0 0
\(223\) 4101.54i 1.23166i 0.787881 + 0.615828i \(0.211178\pi\)
−0.787881 + 0.615828i \(0.788822\pi\)
\(224\) 3100.52 + 1275.23i 0.924831 + 0.380379i
\(225\) 0 0
\(226\) −534.871 + 28.7188i −0.157430 + 0.00845287i
\(227\) −216.589 + 375.143i −0.0633282 + 0.109688i −0.895951 0.444153i \(-0.853505\pi\)
0.832623 + 0.553840i \(0.186838\pi\)
\(228\) 0 0
\(229\) −1354.84 2346.66i −0.390963 0.677169i 0.601613 0.798787i \(-0.294525\pi\)
−0.992577 + 0.121619i \(0.961191\pi\)
\(230\) −2234.63 + 4399.64i −0.640640 + 1.26132i
\(231\) 0 0
\(232\) −6750.23 + 1095.75i −1.91023 + 0.310085i
\(233\) 235.372 135.892i 0.0661792 0.0382086i −0.466545 0.884497i \(-0.654502\pi\)
0.532724 + 0.846289i \(0.321168\pi\)
\(234\) 0 0
\(235\) −1512.67 873.341i −0.419897 0.242428i
\(236\) −1201.80 + 2718.02i −0.331486 + 0.749695i
\(237\) 0 0
\(238\) −2105.26 4443.86i −0.573378 1.21030i
\(239\) −6354.33 −1.71978 −0.859890 0.510479i \(-0.829468\pi\)
−0.859890 + 0.510479i \(0.829468\pi\)
\(240\) 0 0
\(241\) 1169.63 2025.85i 0.312623 0.541479i −0.666306 0.745678i \(-0.732126\pi\)
0.978929 + 0.204199i \(0.0654590\pi\)
\(242\) −5122.38 + 3335.85i −1.36066 + 0.886102i
\(243\) 0 0
\(244\) 2140.67 + 2930.55i 0.561649 + 0.768891i
\(245\) −4117.89 4182.89i −1.07381 1.09075i
\(246\) 0 0
\(247\) 3226.65 1862.91i 0.831202 0.479895i
\(248\) −346.030 + 911.904i −0.0886006 + 0.233492i
\(249\) 0 0
\(250\) −2071.08 + 111.202i −0.523945 + 0.0281322i
\(251\) 5180.74 1.30281 0.651406 0.758730i \(-0.274180\pi\)
0.651406 + 0.758730i \(0.274180\pi\)
\(252\) 0 0
\(253\) 6024.70 1.49711
\(254\) −3335.11 + 179.072i −0.823872 + 0.0442361i
\(255\) 0 0
\(256\) 3724.60 1704.27i 0.909327 0.416082i
\(257\) 3138.15 1811.81i 0.761683 0.439758i −0.0682169 0.997671i \(-0.521731\pi\)
0.829900 + 0.557913i \(0.188398\pi\)
\(258\) 0 0
\(259\) −1605.11 217.713i −0.385084 0.0522318i
\(260\) 4745.56 3466.47i 1.13195 0.826852i
\(261\) 0 0
\(262\) −1090.45 + 710.132i −0.257130 + 0.167451i
\(263\) −683.315 + 1183.54i −0.160209 + 0.277490i −0.934944 0.354796i \(-0.884550\pi\)
0.774735 + 0.632287i \(0.217884\pi\)
\(264\) 0 0
\(265\) 4441.99 1.02970
\(266\) −4531.61 368.656i −1.04455 0.0849764i
\(267\) 0 0
\(268\) 1344.76 + 594.598i 0.306508 + 0.135526i
\(269\) 6423.13 + 3708.39i 1.45585 + 0.840538i 0.998804 0.0489025i \(-0.0155724\pi\)
0.457051 + 0.889440i \(0.348906\pi\)
\(270\) 0 0
\(271\) −1610.08 + 929.582i −0.360906 + 0.208369i −0.669478 0.742832i \(-0.733482\pi\)
0.308572 + 0.951201i \(0.400149\pi\)
\(272\) −5723.21 1827.20i −1.27581 0.407317i
\(273\) 0 0
\(274\) 283.900 558.955i 0.0625949 0.123240i
\(275\) 4959.55 + 8590.19i 1.08754 + 1.88367i
\(276\) 0 0
\(277\) −1280.47 + 2217.83i −0.277746 + 0.481071i −0.970824 0.239792i \(-0.922921\pi\)
0.693078 + 0.720863i \(0.256254\pi\)
\(278\) −932.728 + 50.0810i −0.201228 + 0.0108045i
\(279\) 0 0
\(280\) −7168.97 + 187.223i −1.53010 + 0.0399596i
\(281\) 6441.96i 1.36760i 0.729670 + 0.683799i \(0.239674\pi\)
−0.729670 + 0.683799i \(0.760326\pi\)
\(282\) 0 0
\(283\) 2799.87 + 1616.51i 0.588110 + 0.339545i 0.764350 0.644802i \(-0.223060\pi\)
−0.176240 + 0.984347i \(0.556393\pi\)
\(284\) −7969.90 + 858.330i −1.66523 + 0.179340i
\(285\) 0 0
\(286\) −6397.17 3249.20i −1.32263 0.671780i
\(287\) −6208.63 4802.78i −1.27695 0.987802i
\(288\) 0 0
\(289\) 1949.48 + 3376.59i 0.396799 + 0.687277i
\(290\) 12258.3 7982.96i 2.48217 1.61647i
\(291\) 0 0
\(292\) −1404.02 + 3175.36i −0.281384 + 0.636384i
\(293\) 1715.41i 0.342033i 0.985268 + 0.171016i \(0.0547051\pi\)
−0.985268 + 0.171016i \(0.945295\pi\)
\(294\) 0 0
\(295\) 6357.14i 1.25467i
\(296\) −1533.19 + 1251.35i −0.301064 + 0.245719i
\(297\) 0 0
\(298\) 1336.95 + 2052.95i 0.259890 + 0.399075i
\(299\) 2188.18 + 3790.04i 0.423230 + 0.733056i
\(300\) 0 0
\(301\) 3136.12 + 2425.99i 0.600541 + 0.464558i
\(302\) 2940.64 5789.67i 0.560314 1.10317i
\(303\) 0 0
\(304\) −4108.96 + 3738.04i −0.775213 + 0.705234i
\(305\) −6723.05 3881.55i −1.26217 0.728712i
\(306\) 0 0
\(307\) 7776.45i 1.44569i 0.691012 + 0.722843i \(0.257165\pi\)
−0.691012 + 0.722843i \(0.742835\pi\)
\(308\) 4167.42 + 7700.24i 0.770976 + 1.42455i
\(309\) 0 0
\(310\) −111.863 2083.38i −0.0204948 0.381703i
\(311\) 2639.63 4571.97i 0.481285 0.833610i −0.518484 0.855087i \(-0.673504\pi\)
0.999769 + 0.0214770i \(0.00683688\pi\)
\(312\) 0 0
\(313\) −3791.20 6566.56i −0.684637 1.18583i −0.973551 0.228472i \(-0.926627\pi\)
0.288913 0.957355i \(-0.406706\pi\)
\(314\) −5391.29 2738.30i −0.968943 0.492138i
\(315\) 0 0
\(316\) 832.458 608.082i 0.148194 0.108251i
\(317\) 865.378 499.626i 0.153326 0.0885230i −0.421374 0.906887i \(-0.638452\pi\)
0.574700 + 0.818364i \(0.305119\pi\)
\(318\) 0 0
\(319\) −15467.2 8930.00i −2.71473 1.56735i
\(320\) −5812.54 + 6556.17i −1.01541 + 1.14532i
\(321\) 0 0
\(322\) 433.025 5322.86i 0.0749427 0.921215i
\(323\) 8147.59 1.40354
\(324\) 0 0
\(325\) −3602.64 + 6239.95i −0.614887 + 1.06502i
\(326\) 589.815 + 905.692i 0.100205 + 0.153870i
\(327\) 0 0
\(328\) −9466.27 + 1536.64i −1.59356 + 0.258680i
\(329\) 1873.18 + 254.073i 0.313896 + 0.0425760i
\(330\) 0 0
\(331\) 4142.90 2391.90i 0.687959 0.397193i −0.114888 0.993378i \(-0.536651\pi\)
0.802847 + 0.596185i \(0.203318\pi\)
\(332\) 6385.61 687.708i 1.05559 0.113683i
\(333\) 0 0
\(334\) 120.446 + 2243.24i 0.0197321 + 0.367499i
\(335\) −3145.23 −0.512962
\(336\) 0 0
\(337\) 582.478 0.0941532 0.0470766 0.998891i \(-0.485010\pi\)
0.0470766 + 0.998891i \(0.485010\pi\)
\(338\) 53.7276 + 1000.64i 0.00864615 + 0.161029i
\(339\) 0 0
\(340\) 12777.5 1376.09i 2.03810 0.219497i
\(341\) −2206.00 + 1273.64i −0.350328 + 0.202262i
\(342\) 0 0
\(343\) 5839.94 + 2499.74i 0.919321 + 0.393508i
\(344\) 4781.62 776.192i 0.749442 0.121655i
\(345\) 0 0
\(346\) 47.4434 + 72.8518i 0.00737159 + 0.0113195i
\(347\) 4960.07 8591.09i 0.767350 1.32909i −0.171646 0.985159i \(-0.554908\pi\)
0.938995 0.343930i \(-0.111758\pi\)
\(348\) 0 0
\(349\) −9238.72 −1.41701 −0.708506 0.705705i \(-0.750631\pi\)
−0.708506 + 0.705705i \(0.750631\pi\)
\(350\) 7945.95 3764.37i 1.21351 0.574897i
\(351\) 0 0
\(352\) 10350.4 + 2702.40i 1.56726 + 0.409200i
\(353\) −1995.34 1152.01i −0.300853 0.173698i 0.341973 0.939710i \(-0.388905\pi\)
−0.642826 + 0.766012i \(0.722238\pi\)
\(354\) 0 0
\(355\) 14849.8 8573.53i 2.22013 1.28179i
\(356\) 2992.96 2186.25i 0.445580 0.325481i
\(357\) 0 0
\(358\) 7432.66 + 3775.14i 1.09729 + 0.557325i
\(359\) −3076.29 5328.29i −0.452257 0.783333i 0.546269 0.837610i \(-0.316048\pi\)
−0.998526 + 0.0542774i \(0.982714\pi\)
\(360\) 0 0
\(361\) 337.156 583.971i 0.0491553 0.0851394i
\(362\) −200.179 3728.22i −0.0290640 0.541300i
\(363\) 0 0
\(364\) −3330.48 + 5418.40i −0.479573 + 0.780223i
\(365\) 7426.81i 1.06503i
\(366\) 0 0
\(367\) −4297.82 2481.35i −0.611293 0.352930i 0.162178 0.986761i \(-0.448148\pi\)
−0.773471 + 0.633831i \(0.781481\pi\)
\(368\) −4390.72 4826.40i −0.621962 0.683678i
\(369\) 0 0
\(370\) 1917.06 3774.40i 0.269361 0.530329i
\(371\) −4448.54 + 1822.28i −0.622525 + 0.255008i
\(372\) 0 0
\(373\) −1427.95 2473.29i −0.198222 0.343330i 0.749730 0.661743i \(-0.230183\pi\)
−0.947952 + 0.318414i \(0.896850\pi\)
\(374\) −8562.41 13148.0i −1.18383 1.81783i
\(375\) 0 0
\(376\) 1789.25 1460.33i 0.245408 0.200295i
\(377\) 12973.6i 1.77234i
\(378\) 0 0
\(379\) 13658.0i 1.85109i 0.378637 + 0.925545i \(0.376393\pi\)
−0.378637 + 0.925545i \(0.623607\pi\)
\(380\) 4805.19 10867.5i 0.648686 1.46708i
\(381\) 0 0
\(382\) 2678.47 1744.30i 0.358749 0.233629i
\(383\) 3411.17 + 5908.33i 0.455099 + 0.788254i 0.998694 0.0510933i \(-0.0162706\pi\)
−0.543595 + 0.839348i \(0.682937\pi\)
\(384\) 0 0
\(385\) −14814.2 11459.7i −1.96104 1.51699i
\(386\) 6447.65 + 3274.84i 0.850199 + 0.431826i
\(387\) 0 0
\(388\) 5193.52 559.324i 0.679539 0.0731840i
\(389\) −8474.16 4892.56i −1.10452 0.637693i −0.167113 0.985938i \(-0.553445\pi\)
−0.937404 + 0.348244i \(0.886778\pi\)
\(390\) 0 0
\(391\) 9570.20i 1.23782i
\(392\) 7102.74 3128.48i 0.915159 0.403093i
\(393\) 0 0
\(394\) 4220.66 226.620i 0.539679 0.0289770i
\(395\) −1102.60 + 1909.76i −0.140450 + 0.243267i
\(396\) 0 0
\(397\) −6754.48 11699.1i −0.853898 1.47899i −0.877664 0.479277i \(-0.840899\pi\)
0.0237661 0.999718i \(-0.492434\pi\)
\(398\) −2953.37 + 5814.73i −0.371958 + 0.732327i
\(399\) 0 0
\(400\) 3267.17 10233.5i 0.408396 1.27919i
\(401\) 857.321 494.974i 0.106764 0.0616405i −0.445667 0.895199i \(-0.647033\pi\)
0.552431 + 0.833558i \(0.313700\pi\)
\(402\) 0 0
\(403\) −1602.45 925.174i −0.198074 0.114358i
\(404\) 1937.92 + 856.872i 0.238651 + 0.105522i
\(405\) 0 0
\(406\) −9001.42 + 13023.5i −1.10033 + 1.59199i
\(407\) −5168.53 −0.629470
\(408\) 0 0
\(409\) −2964.96 + 5135.45i −0.358454 + 0.620860i −0.987703 0.156344i \(-0.950029\pi\)
0.629249 + 0.777204i \(0.283363\pi\)
\(410\) 17190.5 11195.0i 2.07068 1.34849i
\(411\) 0 0
\(412\) 9331.70 6816.49i 1.11587 0.815108i
\(413\) 2607.94 + 6366.51i 0.310722 + 0.758536i
\(414\) 0 0
\(415\) −11897.9 + 6869.25i −1.40734 + 0.812526i
\(416\) 2059.23 + 7492.76i 0.242697 + 0.883084i
\(417\) 0 0
\(418\) −14486.5 + 777.823i −1.69511 + 0.0910157i
\(419\) 16065.6 1.87316 0.936581 0.350452i \(-0.113972\pi\)
0.936581 + 0.350452i \(0.113972\pi\)
\(420\) 0 0
\(421\) −2720.79 −0.314972 −0.157486 0.987521i \(-0.550339\pi\)
−0.157486 + 0.987521i \(0.550339\pi\)
\(422\) −3824.01 + 205.323i −0.441114 + 0.0236847i
\(423\) 0 0
\(424\) −2083.74 + 5491.35i −0.238669 + 0.628970i
\(425\) −13645.5 + 7878.22i −1.55742 + 0.899176i
\(426\) 0 0
\(427\) 8325.32 + 1129.23i 0.943538 + 0.127979i
\(428\) −5044.97 6906.51i −0.569761 0.779997i
\(429\) 0 0
\(430\) −8683.32 + 5654.85i −0.973829 + 0.634188i
\(431\) −6131.45 + 10620.0i −0.685247 + 1.18688i 0.288112 + 0.957597i \(0.406972\pi\)
−0.973359 + 0.229286i \(0.926361\pi\)
\(432\) 0 0
\(433\) 11603.6 1.28783 0.643916 0.765096i \(-0.277309\pi\)
0.643916 + 0.765096i \(0.277309\pi\)
\(434\) 966.708 + 2040.56i 0.106920 + 0.225691i
\(435\) 0 0
\(436\) 2230.48 5044.50i 0.245001 0.554100i
\(437\) 7663.17 + 4424.34i 0.838854 + 0.484313i
\(438\) 0 0
\(439\) 1082.48 624.968i 0.117685 0.0679455i −0.440002 0.897997i \(-0.645022\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(440\) −22587.1 + 3666.52i −2.44727 + 0.397260i
\(441\) 0 0
\(442\) 5161.33 10161.9i 0.555429 1.09355i
\(443\) 8070.42 + 13978.4i 0.865547 + 1.49917i 0.866503 + 0.499171i \(0.166362\pi\)
−0.000956502 1.00000i \(0.500304\pi\)
\(444\) 0 0
\(445\) −3964.21 + 6866.21i −0.422295 + 0.731437i
\(446\) 11584.2 621.991i 1.22988 0.0660362i
\(447\) 0 0
\(448\) 3131.52 8950.36i 0.330246 0.943895i
\(449\) 7440.67i 0.782065i 0.920377 + 0.391032i \(0.127882\pi\)
−0.920377 + 0.391032i \(0.872118\pi\)
\(450\) 0 0
\(451\) −21690.7 12523.1i −2.26469 1.30752i
\(452\) 162.225 + 1506.31i 0.0168814 + 0.156750i
\(453\) 0 0
\(454\) 1092.38 + 554.835i 0.112925 + 0.0573561i
\(455\) 1828.60 13481.5i 0.188409 1.38906i
\(456\) 0 0
\(457\) 1959.56 + 3394.06i 0.200578 + 0.347412i 0.948715 0.316133i \(-0.102385\pi\)
−0.748136 + 0.663545i \(0.769051\pi\)
\(458\) −6422.35 + 4182.43i −0.655233 + 0.426708i
\(459\) 0 0
\(460\) 12765.0 + 5644.20i 1.29385 + 0.572091i
\(461\) 149.785i 0.0151328i −0.999971 0.00756638i \(-0.997592\pi\)
0.999971 0.00756638i \(-0.00240848\pi\)
\(462\) 0 0
\(463\) 12047.3i 1.20925i −0.796509 0.604627i \(-0.793322\pi\)
0.796509 0.604627i \(-0.206678\pi\)
\(464\) 4118.46 + 18898.9i 0.412057 + 1.89086i
\(465\) 0 0
\(466\) −419.502 644.168i −0.0417019 0.0640354i
\(467\) −2768.05 4794.40i −0.274283 0.475071i 0.695671 0.718360i \(-0.255107\pi\)
−0.969954 + 0.243289i \(0.921774\pi\)
\(468\) 0 0
\(469\) 3149.87 1290.29i 0.310122 0.127037i
\(470\) −2237.23 + 4404.76i −0.219566 + 0.432291i
\(471\) 0 0
\(472\) 7858.92 + 2982.14i 0.766390 + 0.290814i
\(473\) 10956.4 + 6325.70i 1.06507 + 0.614918i
\(474\) 0 0
\(475\) 14568.5i 1.40726i
\(476\) −12231.8 + 6619.92i −1.17782 + 0.637445i
\(477\) 0 0
\(478\) 963.624 + 17946.9i 0.0922074 + 1.71731i
\(479\) −458.120 + 793.487i −0.0436995 + 0.0756897i −0.887048 0.461678i \(-0.847248\pi\)
0.843348 + 0.537367i \(0.180581\pi\)
\(480\) 0 0
\(481\) −1877.22 3251.44i −0.177950 0.308218i
\(482\) −5899.10 2996.22i −0.557462 0.283142i
\(483\) 0 0
\(484\) 10198.4 + 13961.6i 0.957780 + 1.31119i
\(485\) −9676.76 + 5586.88i −0.905977 + 0.523066i
\(486\) 0 0
\(487\) −3979.10 2297.33i −0.370246 0.213762i 0.303320 0.952889i \(-0.401905\pi\)
−0.673566 + 0.739127i \(0.735238\pi\)
\(488\) 7952.30 6490.43i 0.737671 0.602065i
\(489\) 0 0
\(490\) −11189.5 + 12264.7i −1.03161 + 1.13074i
\(491\) −225.794 −0.0207535 −0.0103767 0.999946i \(-0.503303\pi\)
−0.0103767 + 0.999946i \(0.503303\pi\)
\(492\) 0 0
\(493\) 14185.3 24569.6i 1.29589 2.24454i
\(494\) −5750.84 8830.71i −0.523770 0.804276i
\(495\) 0 0
\(496\) 2628.02 + 839.025i 0.237906 + 0.0759543i
\(497\) −11354.5 + 14678.1i −1.02479 + 1.32476i
\(498\) 0 0
\(499\) −14898.0 + 8601.36i −1.33653 + 0.771643i −0.986290 0.165019i \(-0.947232\pi\)
−0.350235 + 0.936662i \(0.613898\pi\)
\(500\) 628.150 + 5832.60i 0.0561835 + 0.521684i
\(501\) 0 0
\(502\) −785.651 14632.3i −0.0698512 1.30094i
\(503\) −3932.26 −0.348570 −0.174285 0.984695i \(-0.555761\pi\)
−0.174285 + 0.984695i \(0.555761\pi\)
\(504\) 0 0
\(505\) −4532.57 −0.399400
\(506\) −913.635 17015.9i −0.0802689 1.49496i
\(507\) 0 0
\(508\) 1011.53 + 9392.39i 0.0883450 + 0.820315i
\(509\) −18643.2 + 10763.6i −1.62346 + 0.937308i −0.637480 + 0.770467i \(0.720023\pi\)
−0.985984 + 0.166841i \(0.946643\pi\)
\(510\) 0 0
\(511\) 3046.76 + 7437.76i 0.263759 + 0.643889i
\(512\) −5378.30 10261.2i −0.464237 0.885711i
\(513\) 0 0
\(514\) −5593.10 8588.50i −0.479963 0.737009i
\(515\) −12360.0 + 21408.1i −1.05756 + 1.83175i
\(516\) 0 0
\(517\) 6031.72 0.513104
\(518\) −371.488 + 4566.42i −0.0315101 + 0.387330i
\(519\) 0 0
\(520\) −10510.2 12877.5i −0.886353 1.08599i
\(521\) 9708.07 + 5604.96i 0.816350 + 0.471320i 0.849156 0.528142i \(-0.177111\pi\)
−0.0328062 + 0.999462i \(0.510444\pi\)
\(522\) 0 0
\(523\) 8559.92 4942.07i 0.715677 0.413197i −0.0974822 0.995237i \(-0.531079\pi\)
0.813160 + 0.582041i \(0.197746\pi\)
\(524\) 2171.03 + 2972.12i 0.180996 + 0.247782i
\(525\) 0 0
\(526\) 3446.35 + 1750.44i 0.285681 + 0.145101i
\(527\) −2023.16 3504.22i −0.167230 0.289651i
\(528\) 0 0
\(529\) 886.650 1535.72i 0.0728734 0.126220i
\(530\) −673.621 12545.8i −0.0552079 1.02821i
\(531\) 0 0
\(532\) −354.005 + 12854.8i −0.0288497 + 1.04761i
\(533\) 18193.7i 1.47853i
\(534\) 0 0
\(535\) 15844.4 + 9147.76i 1.28040 + 0.739238i
\(536\) 1475.43 3888.24i 0.118897 0.313333i
\(537\) 0 0
\(538\) 9499.78 18703.6i 0.761272 1.49883i
\(539\) 19537.2 + 5399.29i 1.56128 + 0.431473i
\(540\) 0 0
\(541\) −5817.56 10076.3i −0.462323 0.800767i 0.536753 0.843739i \(-0.319651\pi\)
−0.999076 + 0.0429726i \(0.986317\pi\)
\(542\) 2869.64 + 4406.48i 0.227420 + 0.349215i
\(543\) 0 0
\(544\) −4292.75 + 16441.5i −0.338328 + 1.29581i
\(545\) 11798.5i 0.927325i
\(546\) 0 0
\(547\) 22662.9i 1.77147i −0.464187 0.885737i \(-0.653653\pi\)
0.464187 0.885737i \(-0.346347\pi\)
\(548\) −1621.74 717.070i −0.126419 0.0558973i
\(549\) 0 0
\(550\) 23509.7 15310.2i 1.82265 1.18696i
\(551\) −13115.8 22717.2i −1.01407 1.75642i
\(552\) 0 0
\(553\) 320.770 2364.91i 0.0246664 0.181856i
\(554\) 6458.13 + 3280.16i 0.495270 + 0.251554i
\(555\) 0 0
\(556\) 282.893 + 2626.76i 0.0215780 + 0.200359i
\(557\) 21756.9 + 12561.3i 1.65506 + 0.955548i 0.974946 + 0.222440i \(0.0714020\pi\)
0.680112 + 0.733109i \(0.261931\pi\)
\(558\) 0 0
\(559\) 9190.03i 0.695343i
\(560\) 1615.95 + 20219.4i 0.121940 + 1.52576i
\(561\) 0 0
\(562\) 18194.4 976.912i 1.36563 0.0733248i
\(563\) −6462.85 + 11194.0i −0.483795 + 0.837958i −0.999827 0.0186119i \(-0.994075\pi\)
0.516032 + 0.856569i \(0.327409\pi\)
\(564\) 0 0
\(565\) −1620.40 2806.62i −0.120656 0.208983i
\(566\) 4141.00 8152.98i 0.307525 0.605469i
\(567\) 0 0
\(568\) 3632.85 + 22379.7i 0.268365 + 1.65322i
\(569\) 5077.65 2931.58i 0.374106 0.215990i −0.301145 0.953578i \(-0.597369\pi\)
0.675251 + 0.737588i \(0.264035\pi\)
\(570\) 0 0
\(571\) 9167.78 + 5293.02i 0.671908 + 0.387926i 0.796799 0.604244i \(-0.206525\pi\)
−0.124891 + 0.992170i \(0.539858\pi\)
\(572\) −8206.78 + 18560.6i −0.599900 + 1.35675i
\(573\) 0 0
\(574\) −12623.3 + 18263.7i −0.917917 + 1.32807i
\(575\) −17112.2 −1.24110
\(576\) 0 0
\(577\) −12153.9 + 21051.1i −0.876901 + 1.51884i −0.0221772 + 0.999754i \(0.507060\pi\)
−0.854724 + 0.519083i \(0.826274\pi\)
\(578\) 9241.07 6018.07i 0.665013 0.433077i
\(579\) 0 0
\(580\) −24405.7 33411.1i −1.74723 2.39193i
\(581\) 9097.41 11760.4i 0.649611 0.839762i
\(582\) 0 0
\(583\) −13284.2 + 7669.65i −0.943698 + 0.544844i
\(584\) 9181.29 + 3483.92i 0.650555 + 0.246859i
\(585\) 0 0
\(586\) 4844.95 260.140i 0.341541 0.0183383i
\(587\) 1958.28 0.137695 0.0688474 0.997627i \(-0.478068\pi\)
0.0688474 + 0.997627i \(0.478068\pi\)
\(588\) 0 0
\(589\) −3741.26 −0.261725
\(590\) −17954.8 + 964.049i −1.25286 + 0.0672699i
\(591\) 0 0
\(592\) 3766.75 + 4140.52i 0.261508 + 0.287457i
\(593\) 20986.1 12116.3i 1.45328 0.839051i 0.454614 0.890689i \(-0.349777\pi\)
0.998666 + 0.0516373i \(0.0164440\pi\)
\(594\) 0 0
\(595\) 18203.7 23532.2i 1.25425 1.62139i
\(596\) 5595.53 4087.35i 0.384567 0.280913i
\(597\) 0 0
\(598\) 10372.6 6754.97i 0.709310 0.461925i
\(599\) 3792.08 6568.08i 0.258665 0.448020i −0.707220 0.706994i \(-0.750051\pi\)
0.965884 + 0.258973i \(0.0833842\pi\)
\(600\) 0 0
\(601\) 21603.1 1.46624 0.733120 0.680099i \(-0.238063\pi\)
0.733120 + 0.680099i \(0.238063\pi\)
\(602\) 6376.29 9225.41i 0.431691 0.624584i
\(603\) 0 0
\(604\) −16798.0 7427.44i −1.13163 0.500361i
\(605\) −32029.5 18492.3i −2.15237 1.24267i
\(606\) 0 0
\(607\) −20178.7 + 11650.2i −1.34931 + 0.779022i −0.988151 0.153484i \(-0.950951\pi\)
−0.361155 + 0.932506i \(0.617617\pi\)
\(608\) 11180.7 + 11038.3i 0.745784 + 0.736286i
\(609\) 0 0
\(610\) −9943.36 + 19576.9i −0.659991 + 1.29942i
\(611\) 2190.73 + 3794.46i 0.145053 + 0.251240i
\(612\) 0 0
\(613\) −5466.30 + 9467.90i −0.360166 + 0.623825i −0.987988 0.154531i \(-0.950613\pi\)
0.627822 + 0.778357i \(0.283947\pi\)
\(614\) 21963.5 1179.29i 1.44361 0.0775116i
\(615\) 0 0
\(616\) 21116.2 12938.0i 1.38117 0.846246i
\(617\) 16801.8i 1.09630i 0.836381 + 0.548148i \(0.184667\pi\)
−0.836381 + 0.548148i \(0.815333\pi\)
\(618\) 0 0
\(619\) 14271.0 + 8239.36i 0.926655 + 0.535004i 0.885752 0.464159i \(-0.153643\pi\)
0.0409028 + 0.999163i \(0.486977\pi\)
\(620\) −5867.24 + 631.881i −0.380055 + 0.0409306i
\(621\) 0 0
\(622\) −13313.2 6761.93i −0.858216 0.435898i
\(623\) 1153.27 8502.60i 0.0741651 0.546789i
\(624\) 0 0
\(625\) 4216.29 + 7302.82i 0.269842 + 0.467381i
\(626\) −17971.4 + 11703.5i −1.14741 + 0.747232i
\(627\) 0 0
\(628\) −6916.37 + 15642.2i −0.439480 + 0.993936i
\(629\) 8210.17i 0.520447i
\(630\) 0 0
\(631\) 27965.1i 1.76430i 0.470967 + 0.882151i \(0.343905\pi\)
−0.470967 + 0.882151i \(0.656095\pi\)
\(632\) −1843.68 2258.95i −0.116041 0.142177i
\(633\) 0 0
\(634\) −1542.36 2368.37i −0.0966164 0.148360i
\(635\) −10103.8 17500.2i −0.631426 1.09366i
\(636\) 0 0
\(637\) 3699.35 + 14251.6i 0.230100 + 0.886450i
\(638\) −22876.0 + 45039.2i −1.41954 + 2.79486i
\(639\) 0 0
\(640\) 19398.4 + 15422.5i 1.19811 + 0.952541i
\(641\) −13378.0 7723.82i −0.824338 0.475932i 0.0275718 0.999620i \(-0.491222\pi\)
−0.851910 + 0.523688i \(0.824556\pi\)
\(642\) 0 0
\(643\) 750.600i 0.0460354i 0.999735 + 0.0230177i \(0.00732741\pi\)
−0.999735 + 0.0230177i \(0.992673\pi\)
\(644\) −15099.3 415.816i −0.923908 0.0254432i
\(645\) 0 0
\(646\) −1235.57 23011.7i −0.0752520 1.40152i
\(647\) 3864.07 6692.77i 0.234795 0.406677i −0.724418 0.689361i \(-0.757891\pi\)
0.959213 + 0.282684i \(0.0912248\pi\)
\(648\) 0 0
\(649\) 10976.4 + 19011.6i 0.663884 + 1.14988i
\(650\) 18170.2 + 9228.86i 1.09645 + 0.556901i
\(651\) 0 0
\(652\) 2468.55 1803.20i 0.148276 0.108311i
\(653\) 23229.0 13411.3i 1.39207 0.803711i 0.398523 0.917158i \(-0.369523\pi\)
0.993544 + 0.113448i \(0.0361894\pi\)
\(654\) 0 0
\(655\) −6818.41 3936.61i −0.406744 0.234834i
\(656\) 5775.57 + 26503.1i 0.343747 + 1.57740i
\(657\) 0 0
\(658\) 433.530 5329.06i 0.0256850 0.315727i
\(659\) 17914.2 1.05893 0.529467 0.848331i \(-0.322392\pi\)
0.529467 + 0.848331i \(0.322392\pi\)
\(660\) 0 0
\(661\) −9620.57 + 16663.3i −0.566107 + 0.980527i 0.430838 + 0.902429i \(0.358218\pi\)
−0.996946 + 0.0780975i \(0.975115\pi\)
\(662\) −7383.86 11338.3i −0.433507 0.665674i
\(663\) 0 0
\(664\) −2910.70 17931.0i −0.170116 1.04798i
\(665\) −10427.4 25455.3i −0.608054 1.48438i
\(666\) 0 0
\(667\) 26683.8 15405.9i 1.54902 0.894330i
\(668\) 6317.45 680.367i 0.365912 0.0394075i
\(669\) 0 0
\(670\) 476.968 + 8883.25i 0.0275028 + 0.512224i
\(671\) 26807.9 1.54234
\(672\) 0 0
\(673\) −11564.3 −0.662363 −0.331181 0.943567i \(-0.607447\pi\)
−0.331181 + 0.943567i \(0.607447\pi\)
\(674\) −88.3318 1645.13i −0.00504809 0.0940177i
\(675\) 0 0
\(676\) 2818.03 303.492i 0.160334 0.0172674i
\(677\) −2193.88 + 1266.64i −0.124546 + 0.0719067i −0.560979 0.827830i \(-0.689575\pi\)
0.436433 + 0.899737i \(0.356242\pi\)
\(678\) 0 0
\(679\) 7399.07 9564.89i 0.418189 0.540599i
\(680\) −5824.25 35879.5i −0.328455 2.02340i
\(681\) 0 0
\(682\) 3931.74 + 6037.40i 0.220754 + 0.338979i
\(683\) −14481.5 + 25082.7i −0.811303 + 1.40522i 0.100650 + 0.994922i \(0.467908\pi\)
−0.911953 + 0.410295i \(0.865426\pi\)
\(684\) 0 0
\(685\) 3793.06 0.211570
\(686\) 6174.54 16873.2i 0.343652 0.939097i
\(687\) 0 0
\(688\) −2917.37 13387.3i −0.161662 0.741841i
\(689\) −9649.71 5571.26i −0.533562 0.308052i
\(690\) 0 0
\(691\) 15172.3 8759.75i 0.835286 0.482253i −0.0203730 0.999792i \(-0.506485\pi\)
0.855659 + 0.517540i \(0.173152\pi\)
\(692\) 198.565 145.045i 0.0109080 0.00796789i
\(693\) 0 0
\(694\) −25016.5 12706.2i −1.36832 0.694986i
\(695\) −2825.71 4894.28i −0.154224 0.267123i
\(696\) 0 0
\(697\) 19892.9 34455.5i 1.08106 1.87245i
\(698\) 1401.04 + 26093.5i 0.0759742 + 1.41497i
\(699\) 0 0
\(700\) −11836.9 21871.4i −0.639134 1.18094i
\(701\) 18033.4i 0.971630i 0.874062 + 0.485815i \(0.161477\pi\)
−0.874062 + 0.485815i \(0.838523\pi\)
\(702\) 0 0
\(703\) −6574.16 3795.59i −0.352701 0.203632i
\(704\) 6062.94 29642.9i 0.324582 1.58695i
\(705\) 0 0
\(706\) −2951.10 + 5810.25i −0.157317 + 0.309733i
\(707\) 4539.26 1859.43i 0.241466 0.0989126i
\(708\) 0 0
\(709\) 6073.89 + 10520.3i 0.321734 + 0.557260i 0.980846 0.194785i \(-0.0624009\pi\)
−0.659112 + 0.752045i \(0.729068\pi\)
\(710\) −26466.7 40641.0i −1.39898 2.14821i
\(711\) 0 0
\(712\) −6628.64 8121.64i −0.348903 0.427488i
\(713\) 4394.51i 0.230821i
\(714\) 0 0
\(715\) 43411.2i 2.27061i
\(716\) 9535.20 21565.0i 0.497692 1.12559i
\(717\) 0 0
\(718\) −14582.5 + 9496.57i −0.757958 + 0.493606i
\(719\) −16020.2 27747.8i −0.830949 1.43925i −0.897287 0.441449i \(-0.854465\pi\)
0.0663375 0.997797i \(-0.478869\pi\)
\(720\) 0 0
\(721\) 3595.77 26510.2i 0.185733 1.36933i
\(722\) −1700.47 863.691i −0.0876525 0.0445198i
\(723\) 0 0
\(724\) −10499.5 + 1130.76i −0.538963 + 0.0580445i
\(725\) 43932.3 + 25364.3i 2.25049 + 1.29932i
\(726\) 0 0
\(727\) 5922.68i 0.302146i 0.988523 + 0.151073i \(0.0482729\pi\)
−0.988523 + 0.151073i \(0.951727\pi\)
\(728\) 15808.6 + 8584.79i 0.804814 + 0.437051i
\(729\) 0 0
\(730\) −20976.0 + 1126.26i −1.06350 + 0.0571026i
\(731\) −10048.3 + 17404.2i −0.508415 + 0.880601i
\(732\) 0 0
\(733\) 3318.01 + 5746.96i 0.167194 + 0.289589i 0.937432 0.348167i \(-0.113196\pi\)
−0.770238 + 0.637757i \(0.779863\pi\)
\(734\) −6356.46 + 12514.9i −0.319648 + 0.629336i
\(735\) 0 0
\(736\) −12965.6 + 13132.9i −0.649348 + 0.657724i
\(737\) 9406.11 5430.62i 0.470120 0.271424i
\(738\) 0 0
\(739\) −27402.8 15821.0i −1.36405 0.787532i −0.373886 0.927475i \(-0.621975\pi\)
−0.990160 + 0.139942i \(0.955308\pi\)
\(740\) −10951.0 4842.10i −0.544008 0.240539i
\(741\) 0 0
\(742\) 5821.37 + 12287.9i 0.288018 + 0.607957i
\(743\) −1062.56 −0.0524650 −0.0262325 0.999656i \(-0.508351\pi\)
−0.0262325 + 0.999656i \(0.508351\pi\)
\(744\) 0 0
\(745\) −7411.35 + 12836.8i −0.364471 + 0.631283i
\(746\) −6768.91 + 4408.12i −0.332208 + 0.216344i
\(747\) 0 0
\(748\) −35836.3 + 26177.2i −1.75174 + 1.27959i
\(749\) −19620.5 2661.28i −0.957167 0.129828i
\(750\) 0 0
\(751\) −13065.1 + 7543.11i −0.634821 + 0.366514i −0.782617 0.622504i \(-0.786116\pi\)
0.147796 + 0.989018i \(0.452782\pi\)
\(752\) −4395.84 4832.03i −0.213165 0.234316i
\(753\) 0 0
\(754\) −36642.0 + 1967.42i −1.76979 + 0.0950255i
\(755\) 39288.7 1.89386
\(756\) 0 0
\(757\) 21390.4 1.02701 0.513504 0.858087i \(-0.328347\pi\)
0.513504 + 0.858087i \(0.328347\pi\)
\(758\) 38575.0 2071.21i 1.84843 0.0992476i
\(759\) 0 0
\(760\) −31422.4 11923.5i −1.49975 0.569095i
\(761\) 32800.0 18937.1i 1.56242 0.902061i 0.565403 0.824815i \(-0.308721\pi\)
0.997012 0.0772461i \(-0.0246127\pi\)
\(762\) 0 0
\(763\) −4840.20 11815.9i −0.229655 0.560635i
\(764\) −5332.72 7300.43i −0.252527 0.345707i
\(765\) 0 0
\(766\) 16169.9 10530.4i 0.762720 0.496707i
\(767\) −7973.28 + 13810.1i −0.375357 + 0.650137i
\(768\) 0 0
\(769\) −8846.40 −0.414836 −0.207418 0.978252i \(-0.566506\pi\)
−0.207418 + 0.978252i \(0.566506\pi\)
\(770\) −30119.8 + 43578.3i −1.40967 + 2.03955i
\(771\) 0 0
\(772\) 8271.55 18707.1i 0.385621 0.872129i
\(773\) 8387.68 + 4842.63i 0.390277 + 0.225326i 0.682280 0.731091i \(-0.260989\pi\)
−0.292003 + 0.956417i \(0.594322\pi\)
\(774\) 0 0
\(775\) 6265.82 3617.57i 0.290419 0.167674i
\(776\) −2367.32 14583.6i −0.109513 0.674638i
\(777\) 0 0
\(778\) −12533.3 + 24676.0i −0.577556 + 1.13712i
\(779\) −18393.1 31857.8i −0.845958 1.46524i
\(780\) 0 0
\(781\) −29606.5 + 51280.0i −1.35647 + 2.34948i
\(782\) 27029.7 1451.30i 1.23604 0.0663664i
\(783\) 0 0
\(784\) −9913.08 19586.2i −0.451580 0.892231i
\(785\) 36585.3i 1.66342i
\(786\) 0 0
\(787\) 4876.52 + 2815.46i 0.220876 + 0.127523i 0.606356 0.795194i \(-0.292631\pi\)
−0.385480 + 0.922716i \(0.625964\pi\)
\(788\) −1280.11 11886.3i −0.0578706 0.537349i
\(789\) 0 0
\(790\) 5561.06 + 2824.53i 0.250448 + 0.127205i
\(791\) 2774.17 + 2146.00i 0.124701 + 0.0964641i
\(792\) 0 0
\(793\) 9736.68 + 16864.4i 0.436015 + 0.755200i
\(794\) −32018.1 + 20851.2i −1.43108 + 0.931967i
\(795\) 0 0
\(796\) 16870.8 + 7459.59i 0.751216 + 0.332158i
\(797\) 14199.7i 0.631091i −0.948910 0.315545i \(-0.897813\pi\)
0.948910 0.315545i \(-0.102187\pi\)
\(798\) 0 0
\(799\) 9581.35i 0.424235i
\(800\) −29398.6 7675.77i −1.29925 0.339224i
\(801\) 0 0
\(802\) −1528.00 2346.32i −0.0672761 0.103306i
\(803\) 12823.3 + 22210.6i 0.563542 + 0.976084i
\(804\) 0 0
\(805\) 29900.0 12248.0i 1.30911 0.536257i
\(806\) −2370.01 + 4666.19i −0.103573 + 0.203920i
\(807\) 0 0
\(808\) 2126.23 5603.33i 0.0925750 0.243966i
\(809\) −21567.0 12451.7i −0.937276 0.541137i −0.0481708 0.998839i \(-0.515339\pi\)
−0.889105 + 0.457702i \(0.848673\pi\)
\(810\) 0 0
\(811\) 18557.0i 0.803482i −0.915753 0.401741i \(-0.868405\pi\)
0.915753 0.401741i \(-0.131595\pi\)
\(812\) 38148.2 + 23448.2i 1.64869 + 1.01339i
\(813\) 0 0
\(814\) 783.798 + 14597.8i 0.0337495 + 0.628565i
\(815\) −3269.63 + 5663.17i −0.140528 + 0.243401i
\(816\) 0 0
\(817\) 9290.76 + 16092.1i 0.397849 + 0.689095i
\(818\) 14954.0 + 7595.32i 0.639186 + 0.324650i
\(819\) 0 0
\(820\) −34225.6 46854.5i −1.45757 1.99540i
\(821\) −5318.09 + 3070.40i −0.226069 + 0.130521i −0.608757 0.793357i \(-0.708332\pi\)
0.382688 + 0.923878i \(0.374998\pi\)
\(822\) 0 0
\(823\) −17282.2 9977.86i −0.731978 0.422608i 0.0871672 0.996194i \(-0.472219\pi\)
−0.819145 + 0.573586i \(0.805552\pi\)
\(824\) −20667.4 25322.4i −0.873764 1.07057i
\(825\) 0 0
\(826\) 17585.8 8331.23i 0.740786 0.350945i
\(827\) −10464.3 −0.439998 −0.219999 0.975500i \(-0.570605\pi\)
−0.219999 + 0.975500i \(0.570605\pi\)
\(828\) 0 0
\(829\) 6805.40 11787.3i 0.285116 0.493835i −0.687521 0.726164i \(-0.741301\pi\)
0.972637 + 0.232329i \(0.0746345\pi\)
\(830\) 21205.5 + 32562.2i 0.886813 + 1.36175i
\(831\) 0 0
\(832\) 20850.0 6952.27i 0.868801 0.289695i
\(833\) −8576.74 + 31034.8i −0.356743 + 1.29087i
\(834\) 0 0
\(835\) −11770.9 + 6795.92i −0.487842 + 0.281656i
\(836\) 4393.70 + 40797.1i 0.181770 + 1.68780i
\(837\) 0 0
\(838\) −2436.32 45374.9i −0.100431 1.87047i
\(839\) 7552.99 0.310797 0.155398 0.987852i \(-0.450334\pi\)
0.155398 + 0.987852i \(0.450334\pi\)
\(840\) 0 0
\(841\) −66951.4 −2.74515
\(842\) 412.603 + 7684.48i 0.0168875 + 0.314519i
\(843\) 0 0
\(844\) 1159.81 + 10769.2i 0.0473013 + 0.439209i
\(845\) −5250.66 + 3031.47i −0.213761 + 0.123415i
\(846\) 0 0
\(847\) 39663.0 + 5379.79i 1.60902 + 0.218243i
\(848\) 15825.5 + 5052.48i 0.640862 + 0.204603i
\(849\) 0 0
\(850\) 24320.2 + 37345.0i 0.981385 + 1.50697i
\(851\) 4458.32 7722.04i 0.179588 0.311055i
\(852\) 0 0
\(853\) 29075.2 1.16707 0.583537 0.812086i \(-0.301668\pi\)
0.583537 + 0.812086i \(0.301668\pi\)
\(854\) 1926.82 23684.9i 0.0772065 0.949042i
\(855\) 0 0
\(856\) −18741.4 + 15296.2i −0.748327 + 0.610762i
\(857\) −18567.6 10720.0i −0.740091 0.427292i 0.0820116 0.996631i \(-0.473866\pi\)
−0.822102 + 0.569340i \(0.807199\pi\)
\(858\) 0 0
\(859\) −12966.8 + 7486.41i −0.515044 + 0.297361i −0.734905 0.678170i \(-0.762773\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(860\) 17288.1 + 23667.3i 0.685489 + 0.938426i
\(861\) 0 0
\(862\) 30924.4 + 15706.9i 1.22192 + 0.620626i
\(863\) −19006.1 32919.6i −0.749683 1.29849i −0.947975 0.318346i \(-0.896873\pi\)
0.198291 0.980143i \(-0.436461\pi\)
\(864\) 0 0
\(865\) −263.002 + 455.532i −0.0103380 + 0.0179059i
\(866\) −1759.66 32772.6i −0.0690481 1.28598i
\(867\) 0 0
\(868\) 5616.67 3039.78i 0.219634 0.118867i
\(869\) 7615.11i 0.297267i
\(870\) 0 0
\(871\) 6832.64 + 3944.82i 0.265804 + 0.153462i
\(872\) −14585.7 5534.68i −0.566439 0.214940i
\(873\) 0 0
\(874\) 11333.8 22314.5i 0.438640 0.863615i
\(875\) 10741.9 + 8309.55i 0.415019 + 0.321045i
\(876\) 0 0
\(877\) −12119.5 20991.7i −0.466645 0.808253i 0.532629 0.846349i \(-0.321204\pi\)
−0.999274 + 0.0380957i \(0.987871\pi\)
\(878\) −1929.29 2962.53i −0.0741576 0.113873i
\(879\) 0 0
\(880\) 13780.9 + 63238.0i 0.527901 + 2.42245i
\(881\) 27664.5i 1.05793i 0.848642 + 0.528967i \(0.177421\pi\)
−0.848642 + 0.528967i \(0.822579\pi\)
\(882\) 0 0
\(883\) 25947.6i 0.988909i 0.869204 + 0.494454i \(0.164632\pi\)
−0.869204 + 0.494454i \(0.835368\pi\)
\(884\) −29483.5 13036.4i −1.12176 0.495998i
\(885\) 0 0
\(886\) 38256.1 24913.6i 1.45061 0.944681i
\(887\) 17565.5 + 30424.3i 0.664928 + 1.15169i 0.979305 + 0.202391i \(0.0648711\pi\)
−0.314377 + 0.949298i \(0.601796\pi\)
\(888\) 0 0
\(889\) 17297.9 + 13381.1i 0.652591 + 0.504822i
\(890\) 19993.8 + 10155.1i 0.753027 + 0.382471i
\(891\) 0 0
\(892\) −3513.45 32623.7i −0.131882 1.22457i
\(893\) 7672.10 + 4429.49i 0.287500 + 0.165988i
\(894\) 0 0
\(895\) 50438.1i 1.88375i
\(896\) −25753.9 7487.23i −0.960244 0.279164i
\(897\) 0 0
\(898\) 21015.1 1128.37i 0.780940 0.0419310i
\(899\) −6513.68 + 11282.0i −0.241650 + 0.418550i
\(900\) 0 0
\(901\) −12183.2 21101.9i −0.450478 0.780251i
\(902\) −32080.4 + 63161.3i −1.18421 + 2.33153i
\(903\) 0 0
\(904\) 4229.77 686.611i 0.155619 0.0252614i
\(905\) 19563.0 11294.7i 0.718558 0.414860i
\(906\) 0 0
\(907\) 10367.0 + 5985.40i 0.379527 + 0.219120i 0.677613 0.735419i \(-0.263015\pi\)
−0.298085 + 0.954539i \(0.596348\pi\)
\(908\) 1401.39 3169.42i 0.0512190 0.115838i
\(909\) 0 0
\(910\) −38354.0 3120.18i −1.39717 0.113662i
\(911\) −39587.4 −1.43973 −0.719863 0.694116i \(-0.755795\pi\)
−0.719863 + 0.694116i \(0.755795\pi\)
\(912\) 0 0
\(913\) 23721.2 41086.3i 0.859866 1.48933i
\(914\) 9288.87 6049.20i 0.336158 0.218917i
\(915\) 0 0
\(916\) 12786.6 + 17504.8i 0.461225 + 0.631412i
\(917\) 8443.41 + 1145.24i 0.304063 + 0.0412424i
\(918\) 0 0
\(919\) 1701.62 982.433i 0.0610788 0.0352639i −0.469150 0.883119i \(-0.655440\pi\)
0.530228 + 0.847855i \(0.322106\pi\)
\(920\) 14005.4 36909.0i 0.501898 1.32267i
\(921\) 0 0
\(922\) −423.048 + 22.7147i −0.0151110 + 0.000811355i
\(923\) −43012.6 −1.53389
\(924\) 0 0
\(925\) 14680.4 0.521826
\(926\) −34025.9 + 1826.95i −1.20752 + 0.0648351i
\(927\) 0 0
\(928\) 52752.7 14498.0i 1.86605 0.512845i
\(929\) 1300.11 750.617i 0.0459151 0.0265091i −0.476867 0.878976i \(-0.658228\pi\)
0.522782 + 0.852467i \(0.324894\pi\)
\(930\) 0 0
\(931\) 20885.5 + 21215.2i 0.735225 + 0.746830i
\(932\) −1755.75 + 1282.51i −0.0617075 + 0.0450752i
\(933\) 0 0
\(934\) −13121.3 + 8545.02i −0.459682 + 0.299359i
\(935\) 47465.6 82212.9i 1.66020 2.87556i
\(936\) 0 0
\(937\) −23460.4 −0.817949 −0.408975 0.912546i \(-0.634114\pi\)
−0.408975 + 0.912546i \(0.634114\pi\)
\(938\) −4121.92 8700.68i −0.143481 0.302865i
\(939\) 0 0
\(940\) 12779.9 + 5650.78i 0.443441 + 0.196072i
\(941\) −18966.8 10950.5i −0.657068 0.379358i 0.134091 0.990969i \(-0.457189\pi\)
−0.791159 + 0.611611i \(0.790522\pi\)
\(942\) 0 0
\(943\) 37420.3 21604.6i 1.29223 0.746070i
\(944\) 7230.84 22648.6i 0.249305 0.780880i
\(945\) 0 0
\(946\) 16204.5 31904.2i 0.556929 1.09651i
\(947\) 13504.2 + 23390.0i 0.463388 + 0.802611i 0.999127 0.0417720i \(-0.0133003\pi\)
−0.535739 + 0.844383i \(0.679967\pi\)
\(948\) 0 0
\(949\) −9314.89 + 16133.9i −0.318624 + 0.551873i
\(950\) 41146.7 2209.29i 1.40524 0.0754514i
\(951\) 0 0
\(952\) 20552.0 + 33543.0i 0.699678 + 1.14195i
\(953\) 8447.65i 0.287142i 0.989640 + 0.143571i \(0.0458585\pi\)
−0.989640 + 0.143571i \(0.954141\pi\)
\(954\) 0 0
\(955\) 16748.1 + 9669.52i 0.567493 + 0.327642i
\(956\) 50542.4 5443.24i 1.70989 0.184149i
\(957\) 0 0
\(958\) 2310.57 + 1173.56i 0.0779238 + 0.0395785i
\(959\) −3798.66 + 1556.06i −0.127909 + 0.0523960i
\(960\) 0 0
\(961\) −13966.5 24190.7i −0.468816 0.812013i
\(962\) −8898.55 + 5795.01i −0.298234 + 0.194219i
\(963\) 0 0
\(964\) −7567.83 + 17115.5i −0.252846 + 0.571841i
\(965\) 43753.7i 1.45957i
\(966\) 0 0
\(967\) 6959.11i 0.231427i 0.993283 + 0.115714i \(0.0369155\pi\)
−0.993283 + 0.115714i \(0.963085\pi\)
\(968\) 37885.9 30921.3i 1.25795 1.02670i
\(969\) 0 0
\(970\) 17246.8 + 26483.4i 0.570888 + 0.876629i
\(971\) 18808.0 + 32576.4i 0.621604 + 1.07665i 0.989187 + 0.146659i \(0.0468521\pi\)
−0.367583 + 0.929991i \(0.619815\pi\)
\(972\) 0 0
\(973\) 4837.70 + 3742.28i 0.159393 + 0.123301i
\(974\) −5885.07 + 11586.8i −0.193603 + 0.381175i
\(975\) 0 0
\(976\) −19537.3 21475.9i −0.640750 0.704330i
\(977\) −24837.9 14340.2i −0.813343 0.469584i 0.0347724 0.999395i \(-0.488929\pi\)
−0.848116 + 0.529811i \(0.822263\pi\)
\(978\) 0 0
\(979\) 27378.8i 0.893799i
\(980\) 36336.8 + 29743.2i 1.18443 + 0.969503i
\(981\) 0 0
\(982\) 34.2413 + 637.724i 0.00111271 + 0.0207236i
\(983\) −24634.8 + 42668.7i −0.799316 + 1.38446i 0.120747 + 0.992683i \(0.461471\pi\)
−0.920062 + 0.391772i \(0.871862\pi\)
\(984\) 0 0
\(985\) 12786.5 + 22146.9i 0.413617 + 0.716406i
\(986\) −71544.5 36338.3i −2.31079 1.17368i
\(987\) 0 0
\(988\) −24069.0 + 17581.6i −0.775037 + 0.566138i
\(989\) −18901.8 + 10913.0i −0.607729 + 0.350872i
\(990\) 0 0
\(991\) −6061.31 3499.50i −0.194293 0.112175i 0.399698 0.916647i \(-0.369115\pi\)
−0.593991 + 0.804472i \(0.702448\pi\)
\(992\) 1971.17 7549.70i 0.0630895 0.241636i
\(993\) 0 0
\(994\) 43178.2 + 29843.3i 1.37780 + 0.952285i
\(995\) −39458.8 −1.25721
\(996\) 0 0
\(997\) −9573.57 + 16581.9i −0.304110 + 0.526735i −0.977063 0.212951i \(-0.931693\pi\)
0.672952 + 0.739686i \(0.265026\pi\)
\(998\) 26552.6 + 40772.9i 0.842192 + 1.29323i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 252.4.be.a.179.23 yes 96
3.2 odd 2 inner 252.4.be.a.179.26 yes 96
4.3 odd 2 inner 252.4.be.a.179.40 yes 96
7.2 even 3 inner 252.4.be.a.107.9 96
12.11 even 2 inner 252.4.be.a.179.9 yes 96
21.2 odd 6 inner 252.4.be.a.107.40 yes 96
28.23 odd 6 inner 252.4.be.a.107.26 yes 96
84.23 even 6 inner 252.4.be.a.107.23 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.4.be.a.107.9 96 7.2 even 3 inner
252.4.be.a.107.23 yes 96 84.23 even 6 inner
252.4.be.a.107.26 yes 96 28.23 odd 6 inner
252.4.be.a.107.40 yes 96 21.2 odd 6 inner
252.4.be.a.179.9 yes 96 12.11 even 2 inner
252.4.be.a.179.23 yes 96 1.1 even 1 trivial
252.4.be.a.179.26 yes 96 3.2 odd 2 inner
252.4.be.a.179.40 yes 96 4.3 odd 2 inner