Properties

Label 572.2.b.c.571.14
Level $572$
Weight $2$
Character 572.571
Analytic conductor $4.567$
Analytic rank $0$
Dimension $56$
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] = [572,2,Mod(571,572)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(572, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("572.571");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 572.b (of order \(2\), degree \(1\), 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: \(4.56744299562\)
Analytic rank: \(0\)
Dimension: \(56\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 571.14
Character \(\chi\) \(=\) 572.571
Dual form 572.2.b.c.571.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.913620 - 1.07949i) q^{2} +1.67751i q^{3} +(-0.330598 + 1.97249i) q^{4} +1.10479i q^{5} +(1.81085 - 1.53260i) q^{6} -1.27047i q^{7} +(2.43132 - 1.44523i) q^{8} +0.185967 q^{9} +O(q^{10})\) \(q+(-0.913620 - 1.07949i) q^{2} +1.67751i q^{3} +(-0.330598 + 1.97249i) q^{4} +1.10479i q^{5} +(1.81085 - 1.53260i) q^{6} -1.27047i q^{7} +(2.43132 - 1.44523i) q^{8} +0.185967 q^{9} +(1.19260 - 1.00935i) q^{10} +(2.94635 - 1.52284i) q^{11} +(-3.30886 - 0.554581i) q^{12} +(1.61864 + 3.22180i) q^{13} +(-1.37146 + 1.16073i) q^{14} -1.85329 q^{15} +(-3.78141 - 1.30420i) q^{16} -1.40862i q^{17} +(-0.169903 - 0.200750i) q^{18} +0.947603i q^{19} +(-2.17917 - 0.365240i) q^{20} +2.13123 q^{21} +(-4.33573 - 1.78926i) q^{22} -2.58512i q^{23} +(2.42438 + 4.07856i) q^{24} +3.77945 q^{25} +(1.99908 - 4.69081i) q^{26} +5.34449i q^{27} +(2.50599 + 0.420015i) q^{28} +9.78308i q^{29} +(1.69320 + 2.00060i) q^{30} -5.63936 q^{31} +(2.04690 + 5.27354i) q^{32} +(2.55457 + 4.94252i) q^{33} +(-1.52059 + 1.28694i) q^{34} +1.40360 q^{35} +(-0.0614803 + 0.366818i) q^{36} +7.85601i q^{37} +(1.02293 - 0.865749i) q^{38} +(-5.40460 + 2.71529i) q^{39} +(1.59666 + 2.68609i) q^{40} +1.57573 q^{41} +(-1.94713 - 2.30064i) q^{42} -4.24023 q^{43} +(2.02972 + 6.31508i) q^{44} +0.205454i q^{45} +(-2.79062 + 2.36182i) q^{46} -0.265145 q^{47} +(2.18781 - 6.34335i) q^{48} +5.38590 q^{49} +(-3.45298 - 4.07988i) q^{50} +2.36297 q^{51} +(-6.89008 + 2.12763i) q^{52} +5.33730 q^{53} +(5.76932 - 4.88283i) q^{54} +(1.68241 + 3.25508i) q^{55} +(-1.83612 - 3.08892i) q^{56} -1.58961 q^{57} +(10.5607 - 8.93802i) q^{58} -0.801256 q^{59} +(0.612692 - 3.65558i) q^{60} -4.22552i q^{61} +(5.15224 + 6.08764i) q^{62} -0.236266i q^{63} +(3.82264 - 7.02762i) q^{64} +(-3.55940 + 1.78825i) q^{65} +(3.00150 - 7.27322i) q^{66} -10.3107 q^{67} +(2.77848 + 0.465686i) q^{68} +4.33657 q^{69} +(-1.28236 - 1.51517i) q^{70} +11.1238 q^{71} +(0.452146 - 0.268764i) q^{72} -10.0124 q^{73} +(8.48048 - 7.17740i) q^{74} +6.34006i q^{75} +(-1.86913 - 0.313276i) q^{76} +(-1.93472 - 3.74325i) q^{77} +(7.86887 + 3.35347i) q^{78} +7.91992 q^{79} +(1.44086 - 4.17765i) q^{80} -8.40751 q^{81} +(-1.43961 - 1.70098i) q^{82} -12.5969i q^{83} +(-0.704579 + 4.20382i) q^{84} +1.55622 q^{85} +(3.87396 + 4.57728i) q^{86} -16.4112 q^{87} +(4.96268 - 7.96064i) q^{88} +5.03112i q^{89} +(0.221785 - 0.187707i) q^{90} +(4.09321 - 2.05644i) q^{91} +(5.09913 + 0.854637i) q^{92} -9.46008i q^{93} +(0.242241 + 0.286221i) q^{94} -1.04690 q^{95} +(-8.84640 + 3.43369i) q^{96} -15.8353i q^{97} +(-4.92067 - 5.81403i) q^{98} +(0.547924 - 0.283197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q + 4 q^{4} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q + 4 q^{4} - 32 q^{9} - 12 q^{14} - 4 q^{16} - 4 q^{22} - 192 q^{25} + 4 q^{26} + 28 q^{36} + 24 q^{38} + 88 q^{42} + 56 q^{48} + 40 q^{49} - 8 q^{53} - 68 q^{56} + 28 q^{64} - 76 q^{66} - 16 q^{69} + 32 q^{77} + 108 q^{78} - 152 q^{81} - 60 q^{82} + 52 q^{88} + 132 q^{92}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(353\) \(365\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.913620 1.07949i −0.646027 0.763315i
\(3\) 1.67751i 0.968510i 0.874927 + 0.484255i \(0.160909\pi\)
−0.874927 + 0.484255i \(0.839091\pi\)
\(4\) −0.330598 + 1.97249i −0.165299 + 0.986244i
\(5\) 1.10479i 0.494075i 0.969006 + 0.247038i \(0.0794571\pi\)
−0.969006 + 0.247038i \(0.920543\pi\)
\(6\) 1.81085 1.53260i 0.739278 0.625683i
\(7\) 1.27047i 0.480193i −0.970749 0.240097i \(-0.922821\pi\)
0.970749 0.240097i \(-0.0771791\pi\)
\(8\) 2.43132 1.44523i 0.859602 0.510965i
\(9\) 0.185967 0.0619890
\(10\) 1.19260 1.00935i 0.377135 0.319186i
\(11\) 2.94635 1.52284i 0.888358 0.459152i
\(12\) −3.30886 0.554581i −0.955186 0.160094i
\(13\) 1.61864 + 3.22180i 0.448931 + 0.893567i
\(14\) −1.37146 + 1.16073i −0.366538 + 0.310218i
\(15\) −1.85329 −0.478516
\(16\) −3.78141 1.30420i −0.945353 0.326050i
\(17\) 1.40862i 0.341640i −0.985302 0.170820i \(-0.945358\pi\)
0.985302 0.170820i \(-0.0546416\pi\)
\(18\) −0.169903 0.200750i −0.0400466 0.0473171i
\(19\) 0.947603i 0.217395i 0.994075 + 0.108698i \(0.0346680\pi\)
−0.994075 + 0.108698i \(0.965332\pi\)
\(20\) −2.17917 0.365240i −0.487278 0.0816701i
\(21\) 2.13123 0.465072
\(22\) −4.33573 1.78926i −0.924381 0.381472i
\(23\) 2.58512i 0.539036i −0.962995 0.269518i \(-0.913136\pi\)
0.962995 0.269518i \(-0.0868643\pi\)
\(24\) 2.42438 + 4.07856i 0.494874 + 0.832533i
\(25\) 3.77945 0.755890
\(26\) 1.99908 4.69081i 0.392051 0.919943i
\(27\) 5.34449i 1.02855i
\(28\) 2.50599 + 0.420015i 0.473587 + 0.0793754i
\(29\) 9.78308i 1.81667i 0.418241 + 0.908336i \(0.362647\pi\)
−0.418241 + 0.908336i \(0.637353\pi\)
\(30\) 1.69320 + 2.00060i 0.309134 + 0.365259i
\(31\) −5.63936 −1.01286 −0.506430 0.862281i \(-0.669035\pi\)
−0.506430 + 0.862281i \(0.669035\pi\)
\(32\) 2.04690 + 5.27354i 0.361844 + 0.932239i
\(33\) 2.55457 + 4.94252i 0.444694 + 0.860383i
\(34\) −1.52059 + 1.28694i −0.260779 + 0.220708i
\(35\) 1.40360 0.237251
\(36\) −0.0614803 + 0.366818i −0.0102467 + 0.0611363i
\(37\) 7.85601i 1.29152i 0.763541 + 0.645760i \(0.223459\pi\)
−0.763541 + 0.645760i \(0.776541\pi\)
\(38\) 1.02293 0.865749i 0.165941 0.140443i
\(39\) −5.40460 + 2.71529i −0.865428 + 0.434794i
\(40\) 1.59666 + 2.68609i 0.252455 + 0.424708i
\(41\) 1.57573 0.246087 0.123044 0.992401i \(-0.460735\pi\)
0.123044 + 0.992401i \(0.460735\pi\)
\(42\) −1.94713 2.30064i −0.300449 0.354996i
\(43\) −4.24023 −0.646629 −0.323314 0.946292i \(-0.604797\pi\)
−0.323314 + 0.946292i \(0.604797\pi\)
\(44\) 2.02972 + 6.31508i 0.305992 + 0.952034i
\(45\) 0.205454i 0.0306272i
\(46\) −2.79062 + 2.36182i −0.411454 + 0.348232i
\(47\) −0.265145 −0.0386753 −0.0193377 0.999813i \(-0.506156\pi\)
−0.0193377 + 0.999813i \(0.506156\pi\)
\(48\) 2.18781 6.34335i 0.315783 0.915583i
\(49\) 5.38590 0.769415
\(50\) −3.45298 4.07988i −0.488325 0.576982i
\(51\) 2.36297 0.330881
\(52\) −6.89008 + 2.12763i −0.955482 + 0.295049i
\(53\) 5.33730 0.733135 0.366568 0.930391i \(-0.380533\pi\)
0.366568 + 0.930391i \(0.380533\pi\)
\(54\) 5.76932 4.88283i 0.785105 0.664469i
\(55\) 1.68241 + 3.25508i 0.226856 + 0.438915i
\(56\) −1.83612 3.08892i −0.245362 0.412775i
\(57\) −1.58961 −0.210549
\(58\) 10.5607 8.93802i 1.38669 1.17362i
\(59\) −0.801256 −0.104315 −0.0521573 0.998639i \(-0.516610\pi\)
−0.0521573 + 0.998639i \(0.516610\pi\)
\(60\) 0.612692 3.65558i 0.0790983 0.471934i
\(61\) 4.22552i 0.541022i −0.962717 0.270511i \(-0.912807\pi\)
0.962717 0.270511i \(-0.0871926\pi\)
\(62\) 5.15224 + 6.08764i 0.654335 + 0.773131i
\(63\) 0.236266i 0.0297667i
\(64\) 3.82264 7.02762i 0.477830 0.878452i
\(65\) −3.55940 + 1.78825i −0.441489 + 0.221805i
\(66\) 3.00150 7.27322i 0.369459 0.895271i
\(67\) −10.3107 −1.25965 −0.629826 0.776736i \(-0.716874\pi\)
−0.629826 + 0.776736i \(0.716874\pi\)
\(68\) 2.77848 + 0.465686i 0.336940 + 0.0564727i
\(69\) 4.33657 0.522061
\(70\) −1.28236 1.51517i −0.153271 0.181098i
\(71\) 11.1238 1.32015 0.660074 0.751201i \(-0.270525\pi\)
0.660074 + 0.751201i \(0.270525\pi\)
\(72\) 0.452146 0.268764i 0.0532859 0.0316742i
\(73\) −10.0124 −1.17186 −0.585932 0.810360i \(-0.699271\pi\)
−0.585932 + 0.810360i \(0.699271\pi\)
\(74\) 8.48048 7.17740i 0.985836 0.834356i
\(75\) 6.34006i 0.732087i
\(76\) −1.86913 0.313276i −0.214404 0.0359352i
\(77\) −1.93472 3.74325i −0.220482 0.426583i
\(78\) 7.86887 + 3.35347i 0.890974 + 0.379705i
\(79\) 7.91992 0.891061 0.445530 0.895267i \(-0.353015\pi\)
0.445530 + 0.895267i \(0.353015\pi\)
\(80\) 1.44086 4.17765i 0.161093 0.467075i
\(81\) −8.40751 −0.934168
\(82\) −1.43961 1.70098i −0.158979 0.187842i
\(83\) 12.5969i 1.38269i −0.722525 0.691345i \(-0.757019\pi\)
0.722525 0.691345i \(-0.242981\pi\)
\(84\) −0.704579 + 4.20382i −0.0768758 + 0.458674i
\(85\) 1.55622 0.168796
\(86\) 3.87396 + 4.57728i 0.417739 + 0.493581i
\(87\) −16.4112 −1.75946
\(88\) 4.96268 7.96064i 0.529023 0.848607i
\(89\) 5.03112i 0.533298i 0.963794 + 0.266649i \(0.0859164\pi\)
−0.963794 + 0.266649i \(0.914084\pi\)
\(90\) 0.221785 0.187707i 0.0233782 0.0197860i
\(91\) 4.09321 2.05644i 0.429084 0.215573i
\(92\) 5.09913 + 0.854637i 0.531621 + 0.0891020i
\(93\) 9.46008i 0.980964i
\(94\) 0.242241 + 0.286221i 0.0249853 + 0.0295214i
\(95\) −1.04690 −0.107409
\(96\) −8.84640 + 3.43369i −0.902882 + 0.350450i
\(97\) 15.8353i 1.60783i −0.594743 0.803916i \(-0.702746\pi\)
0.594743 0.803916i \(-0.297254\pi\)
\(98\) −4.92067 5.81403i −0.497062 0.587306i
\(99\) 0.547924 0.283197i 0.0550684 0.0284624i
\(100\) −1.24948 + 7.45491i −0.124948 + 0.745491i
\(101\) 2.96407i 0.294936i 0.989067 + 0.147468i \(0.0471123\pi\)
−0.989067 + 0.147468i \(0.952888\pi\)
\(102\) −2.15885 2.55080i −0.213758 0.252567i
\(103\) 8.90842i 0.877772i 0.898543 + 0.438886i \(0.144627\pi\)
−0.898543 + 0.438886i \(0.855373\pi\)
\(104\) 8.59167 + 5.49393i 0.842483 + 0.538724i
\(105\) 2.35455i 0.229780i
\(106\) −4.87627 5.76157i −0.473625 0.559613i
\(107\) 13.6915 1.32361 0.661805 0.749676i \(-0.269791\pi\)
0.661805 + 0.749676i \(0.269791\pi\)
\(108\) −10.5419 1.76688i −1.01440 0.170018i
\(109\) −7.99559 −0.765839 −0.382919 0.923782i \(-0.625081\pi\)
−0.382919 + 0.923782i \(0.625081\pi\)
\(110\) 1.97675 4.79005i 0.188476 0.456713i
\(111\) −13.1785 −1.25085
\(112\) −1.65695 + 4.80417i −0.156567 + 0.453952i
\(113\) 4.48064 0.421503 0.210751 0.977540i \(-0.432409\pi\)
0.210751 + 0.977540i \(0.432409\pi\)
\(114\) 1.45230 + 1.71597i 0.136020 + 0.160715i
\(115\) 2.85601 0.266324
\(116\) −19.2970 3.23427i −1.79168 0.300294i
\(117\) 0.301014 + 0.599149i 0.0278288 + 0.0553913i
\(118\) 0.732044 + 0.864948i 0.0673901 + 0.0796249i
\(119\) −1.78961 −0.164053
\(120\) −4.50593 + 2.67842i −0.411334 + 0.244505i
\(121\) 6.36194 8.97361i 0.578358 0.815783i
\(122\) −4.56140 + 3.86051i −0.412970 + 0.349515i
\(123\) 2.64329i 0.238338i
\(124\) 1.86436 11.1236i 0.167425 0.998926i
\(125\) 9.69941i 0.867541i
\(126\) −0.255047 + 0.215857i −0.0227214 + 0.0192301i
\(127\) −17.4581 −1.54916 −0.774578 0.632479i \(-0.782038\pi\)
−0.774578 + 0.632479i \(0.782038\pi\)
\(128\) −11.0787 + 2.29406i −0.979227 + 0.202768i
\(129\) 7.11301i 0.626266i
\(130\) 5.18234 + 2.20855i 0.454521 + 0.193703i
\(131\) 7.08768 0.619253 0.309627 0.950858i \(-0.399796\pi\)
0.309627 + 0.950858i \(0.399796\pi\)
\(132\) −10.5936 + 3.40487i −0.922054 + 0.296356i
\(133\) 1.20390 0.104392
\(134\) 9.42005 + 11.1303i 0.813769 + 0.961511i
\(135\) −5.90451 −0.508179
\(136\) −2.03577 3.42480i −0.174566 0.293674i
\(137\) 14.1974i 1.21296i −0.795098 0.606481i \(-0.792580\pi\)
0.795098 0.606481i \(-0.207420\pi\)
\(138\) −3.96197 4.68128i −0.337266 0.398497i
\(139\) −9.45130 −0.801649 −0.400824 0.916155i \(-0.631276\pi\)
−0.400824 + 0.916155i \(0.631276\pi\)
\(140\) −0.464027 + 2.76858i −0.0392174 + 0.233988i
\(141\) 0.444782i 0.0374574i
\(142\) −10.1629 12.0080i −0.852851 1.00769i
\(143\) 9.67536 + 7.02762i 0.809094 + 0.587679i
\(144\) −0.703218 0.242538i −0.0586015 0.0202115i
\(145\) −10.8082 −0.897573
\(146\) 9.14754 + 10.8083i 0.757056 + 0.894501i
\(147\) 9.03489i 0.745185i
\(148\) −15.4959 2.59718i −1.27375 0.213487i
\(149\) 11.5223 0.943943 0.471972 0.881614i \(-0.343543\pi\)
0.471972 + 0.881614i \(0.343543\pi\)
\(150\) 6.84403 5.79240i 0.558813 0.472948i
\(151\) 4.94593i 0.402494i 0.979541 + 0.201247i \(0.0644994\pi\)
−0.979541 + 0.201247i \(0.935501\pi\)
\(152\) 1.36950 + 2.30393i 0.111081 + 0.186873i
\(153\) 0.261956i 0.0211779i
\(154\) −2.27321 + 5.50842i −0.183180 + 0.443881i
\(155\) 6.23029i 0.500429i
\(156\) −3.56912 11.5582i −0.285758 0.925394i
\(157\) −14.3545 −1.14562 −0.572808 0.819690i \(-0.694146\pi\)
−0.572808 + 0.819690i \(0.694146\pi\)
\(158\) −7.23580 8.54948i −0.575649 0.680160i
\(159\) 8.95337i 0.710049i
\(160\) −5.82613 + 2.26139i −0.460596 + 0.178778i
\(161\) −3.28433 −0.258841
\(162\) 7.68127 + 9.07583i 0.603498 + 0.713064i
\(163\) 9.26462 0.725661 0.362831 0.931855i \(-0.381810\pi\)
0.362831 + 0.931855i \(0.381810\pi\)
\(164\) −0.520932 + 3.10810i −0.0406779 + 0.242702i
\(165\) −5.46043 + 2.82225i −0.425094 + 0.219712i
\(166\) −13.5982 + 11.5088i −1.05543 + 0.893254i
\(167\) 18.2430i 1.41168i 0.708370 + 0.705841i \(0.249431\pi\)
−0.708370 + 0.705841i \(0.750569\pi\)
\(168\) 5.18169 3.08010i 0.399776 0.237635i
\(169\) −7.75999 + 10.4299i −0.596922 + 0.802299i
\(170\) −1.42179 1.67992i −0.109047 0.128844i
\(171\) 0.176223i 0.0134761i
\(172\) 1.40181 8.36379i 0.106887 0.637733i
\(173\) 13.9837i 1.06316i −0.847009 0.531579i \(-0.821599\pi\)
0.847009 0.531579i \(-0.178401\pi\)
\(174\) 14.9936 + 17.7157i 1.13666 + 1.34303i
\(175\) 4.80168i 0.362973i
\(176\) −13.1274 + 1.91584i −0.989518 + 0.144412i
\(177\) 1.34411i 0.101030i
\(178\) 5.43104 4.59653i 0.407074 0.344525i
\(179\) 13.8697i 1.03667i −0.855178 0.518334i \(-0.826552\pi\)
0.855178 0.518334i \(-0.173448\pi\)
\(180\) −0.405255 0.0679226i −0.0302059 0.00506265i
\(181\) 10.5358 0.783123 0.391561 0.920152i \(-0.371935\pi\)
0.391561 + 0.920152i \(0.371935\pi\)
\(182\) −5.95954 2.53977i −0.441750 0.188260i
\(183\) 7.08834 0.523985
\(184\) −3.73609 6.28527i −0.275428 0.463356i
\(185\) −8.67920 −0.638108
\(186\) −10.2121 + 8.64292i −0.748785 + 0.633729i
\(187\) −2.14509 4.15028i −0.156865 0.303498i
\(188\) 0.0876562 0.522994i 0.00639299 0.0381433i
\(189\) 6.79002 0.493901
\(190\) 0.956467 + 1.13012i 0.0693894 + 0.0819872i
\(191\) 26.4504i 1.91388i −0.290283 0.956941i \(-0.593750\pi\)
0.290283 0.956941i \(-0.406250\pi\)
\(192\) 11.7889 + 6.41251i 0.850789 + 0.462783i
\(193\) −23.3881 −1.68351 −0.841755 0.539860i \(-0.818477\pi\)
−0.841755 + 0.539860i \(0.818477\pi\)
\(194\) −17.0941 + 14.4675i −1.22728 + 1.03870i
\(195\) −2.99981 5.97092i −0.214821 0.427586i
\(196\) −1.78057 + 10.6236i −0.127183 + 0.758830i
\(197\) 18.4367 1.31356 0.656782 0.754081i \(-0.271917\pi\)
0.656782 + 0.754081i \(0.271917\pi\)
\(198\) −0.806303 0.332744i −0.0573015 0.0236471i
\(199\) 16.5580i 1.17377i −0.809671 0.586884i \(-0.800354\pi\)
0.809671 0.586884i \(-0.199646\pi\)
\(200\) 9.18905 5.46216i 0.649764 0.386233i
\(201\) 17.2963i 1.21998i
\(202\) 3.19968 2.70803i 0.225129 0.190536i
\(203\) 12.4291 0.872354
\(204\) −0.781191 + 4.66092i −0.0546943 + 0.326330i
\(205\) 1.74084i 0.121585i
\(206\) 9.61655 8.13890i 0.670017 0.567064i
\(207\) 0.480748i 0.0334143i
\(208\) −1.91888 14.2940i −0.133050 0.991109i
\(209\) 1.44304 + 2.79197i 0.0998175 + 0.193125i
\(210\) 2.54171 2.15116i 0.175395 0.148444i
\(211\) 21.6526 1.49063 0.745314 0.666714i \(-0.232300\pi\)
0.745314 + 0.666714i \(0.232300\pi\)
\(212\) −1.76450 + 10.5278i −0.121186 + 0.723050i
\(213\) 18.6602i 1.27858i
\(214\) −12.5089 14.7799i −0.855087 1.01033i
\(215\) 4.68454i 0.319483i
\(216\) 7.72399 + 12.9942i 0.525551 + 0.884141i
\(217\) 7.16465i 0.486368i
\(218\) 7.30493 + 8.63116i 0.494752 + 0.584576i
\(219\) 16.7959i 1.13496i
\(220\) −6.97681 + 2.24240i −0.470376 + 0.151183i
\(221\) 4.53828 2.28005i 0.305278 0.153373i
\(222\) 12.0402 + 14.2261i 0.808082 + 0.954792i
\(223\) 4.27837 0.286501 0.143251 0.989686i \(-0.454245\pi\)
0.143251 + 0.989686i \(0.454245\pi\)
\(224\) 6.69988 2.60053i 0.447655 0.173755i
\(225\) 0.702853 0.0468569
\(226\) −4.09360 4.83680i −0.272302 0.321739i
\(227\) 1.22344i 0.0812028i −0.999175 0.0406014i \(-0.987073\pi\)
0.999175 0.0406014i \(-0.0129274\pi\)
\(228\) 0.525522 3.13549i 0.0348036 0.207653i
\(229\) 11.1604i 0.737498i −0.929529 0.368749i \(-0.879786\pi\)
0.929529 0.368749i \(-0.120214\pi\)
\(230\) −2.60931 3.08303i −0.172053 0.203289i
\(231\) 6.27933 3.24551i 0.413150 0.213539i
\(232\) 14.1388 + 23.7858i 0.928255 + 1.56161i
\(233\) 9.25724i 0.606462i −0.952917 0.303231i \(-0.901935\pi\)
0.952917 0.303231i \(-0.0980654\pi\)
\(234\) 0.371763 0.872336i 0.0243029 0.0570264i
\(235\) 0.292928i 0.0191085i
\(236\) 0.264894 1.58047i 0.0172431 0.102880i
\(237\) 13.2857i 0.863001i
\(238\) 1.63502 + 1.93186i 0.105983 + 0.125224i
\(239\) 20.7938i 1.34504i 0.740079 + 0.672520i \(0.234788\pi\)
−0.740079 + 0.672520i \(0.765212\pi\)
\(240\) 7.00804 + 2.41706i 0.452367 + 0.156020i
\(241\) −0.892259 −0.0574755 −0.0287377 0.999587i \(-0.509149\pi\)
−0.0287377 + 0.999587i \(0.509149\pi\)
\(242\) −15.4993 + 1.33082i −0.996334 + 0.0855483i
\(243\) 1.92978i 0.123796i
\(244\) 8.33478 + 1.39695i 0.533579 + 0.0894303i
\(245\) 5.95027i 0.380149i
\(246\) 2.85341 2.41496i 0.181927 0.153973i
\(247\) −3.05299 + 1.53383i −0.194257 + 0.0975953i
\(248\) −13.7111 + 8.15016i −0.870656 + 0.517535i
\(249\) 21.1314 1.33915
\(250\) 10.4704 8.86157i 0.662207 0.560455i
\(251\) 16.1974i 1.02237i −0.859471 0.511185i \(-0.829207\pi\)
0.859471 0.511185i \(-0.170793\pi\)
\(252\) 0.466031 + 0.0781090i 0.0293572 + 0.00492040i
\(253\) −3.93672 7.61668i −0.247500 0.478856i
\(254\) 15.9501 + 18.8458i 1.00080 + 1.18249i
\(255\) 2.61057i 0.163480i
\(256\) 12.5981 + 9.86343i 0.787383 + 0.616464i
\(257\) −24.6407 −1.53705 −0.768523 0.639822i \(-0.779008\pi\)
−0.768523 + 0.639822i \(0.779008\pi\)
\(258\) −7.67843 + 6.49859i −0.478038 + 0.404585i
\(259\) 9.98083 0.620179
\(260\) −2.35058 7.61206i −0.145777 0.472080i
\(261\) 1.81933i 0.112614i
\(262\) −6.47544 7.65108i −0.400054 0.472685i
\(263\) 7.39174 0.455794 0.227897 0.973685i \(-0.426815\pi\)
0.227897 + 0.973685i \(0.426815\pi\)
\(264\) 13.3540 + 8.32493i 0.821884 + 0.512364i
\(265\) 5.89658i 0.362224i
\(266\) −1.09991 1.29960i −0.0674398 0.0796836i
\(267\) −8.43974 −0.516504
\(268\) 3.40869 20.3377i 0.208219 1.24232i
\(269\) −17.0000 −1.03651 −0.518254 0.855227i \(-0.673418\pi\)
−0.518254 + 0.855227i \(0.673418\pi\)
\(270\) 5.39448 + 6.37386i 0.328297 + 0.387901i
\(271\) 7.36919i 0.447647i 0.974630 + 0.223823i \(0.0718539\pi\)
−0.974630 + 0.223823i \(0.928146\pi\)
\(272\) −1.83712 + 5.32656i −0.111392 + 0.322970i
\(273\) 3.44969 + 6.86638i 0.208785 + 0.415572i
\(274\) −15.3259 + 12.9710i −0.925872 + 0.783606i
\(275\) 11.1356 5.75548i 0.671500 0.347069i
\(276\) −1.43366 + 8.55382i −0.0862962 + 0.514880i
\(277\) 17.7070i 1.06391i −0.846772 0.531955i \(-0.821457\pi\)
0.846772 0.531955i \(-0.178543\pi\)
\(278\) 8.63490 + 10.2026i 0.517887 + 0.611910i
\(279\) −1.04874 −0.0627862
\(280\) 3.41260 2.02852i 0.203942 0.121227i
\(281\) 13.3348 0.795485 0.397743 0.917497i \(-0.369794\pi\)
0.397743 + 0.917497i \(0.369794\pi\)
\(282\) −0.480138 + 0.406362i −0.0285918 + 0.0241985i
\(283\) −0.959367 −0.0570284 −0.0285142 0.999593i \(-0.509078\pi\)
−0.0285142 + 0.999593i \(0.509078\pi\)
\(284\) −3.67749 + 21.9415i −0.218219 + 1.30199i
\(285\) 1.75618i 0.104027i
\(286\) −1.25336 16.8650i −0.0741125 0.997250i
\(287\) 2.00191i 0.118169i
\(288\) 0.380656 + 0.980704i 0.0224304 + 0.0577886i
\(289\) 15.0158 0.883282
\(290\) 9.87459 + 11.6674i 0.579856 + 0.685130i
\(291\) 26.5639 1.55720
\(292\) 3.31008 19.7494i 0.193708 1.15574i
\(293\) 6.63138 0.387409 0.193705 0.981060i \(-0.437950\pi\)
0.193705 + 0.981060i \(0.437950\pi\)
\(294\) 9.75308 8.25446i 0.568811 0.481410i
\(295\) 0.885216i 0.0515393i
\(296\) 11.3537 + 19.1005i 0.659921 + 1.11019i
\(297\) 8.13878 + 15.7467i 0.472260 + 0.913717i
\(298\) −10.5270 12.4382i −0.609812 0.720526i
\(299\) 8.32876 4.18439i 0.481664 0.241990i
\(300\) −12.5057 2.09601i −0.722016 0.121013i
\(301\) 5.38709i 0.310507i
\(302\) 5.33908 4.51870i 0.307230 0.260022i
\(303\) −4.97225 −0.285648
\(304\) 1.23586 3.58328i 0.0708816 0.205515i
\(305\) 4.66829 0.267305
\(306\) −0.282779 + 0.239328i −0.0161654 + 0.0136815i
\(307\) 7.55650i 0.431272i −0.976474 0.215636i \(-0.930818\pi\)
0.976474 0.215636i \(-0.0691825\pi\)
\(308\) 8.02313 2.57870i 0.457160 0.146935i
\(309\) −14.9439 −0.850131
\(310\) −6.72553 + 5.69211i −0.381985 + 0.323290i
\(311\) 5.99168i 0.339757i −0.985465 0.169879i \(-0.945662\pi\)
0.985465 0.169879i \(-0.0543376\pi\)
\(312\) −9.21610 + 14.4126i −0.521759 + 0.815952i
\(313\) −3.35058 −0.189386 −0.0946931 0.995507i \(-0.530187\pi\)
−0.0946931 + 0.995507i \(0.530187\pi\)
\(314\) 13.1146 + 15.4956i 0.740098 + 0.874466i
\(315\) 0.261023 0.0147070
\(316\) −2.61831 + 15.6219i −0.147291 + 0.878803i
\(317\) 13.8147i 0.775912i −0.921678 0.387956i \(-0.873181\pi\)
0.921678 0.387956i \(-0.126819\pi\)
\(318\) 9.66508 8.17998i 0.541991 0.458710i
\(319\) 14.8980 + 28.8244i 0.834129 + 1.61385i
\(320\) 7.76401 + 4.22320i 0.434021 + 0.236084i
\(321\) 22.9676i 1.28193i
\(322\) 3.00063 + 3.54540i 0.167218 + 0.197577i
\(323\) 1.33481 0.0742708
\(324\) 2.77951 16.5837i 0.154417 0.921317i
\(325\) 6.11758 + 12.1766i 0.339342 + 0.675438i
\(326\) −8.46434 10.0011i −0.468797 0.553908i
\(327\) 13.4127i 0.741722i
\(328\) 3.83110 2.27728i 0.211537 0.125742i
\(329\) 0.336859i 0.0185716i
\(330\) 8.03535 + 3.31601i 0.442331 + 0.182540i
\(331\) −5.70350 −0.313493 −0.156746 0.987639i \(-0.550100\pi\)
−0.156746 + 0.987639i \(0.550100\pi\)
\(332\) 24.8472 + 4.16451i 1.36367 + 0.228557i
\(333\) 1.46096i 0.0800600i
\(334\) 19.6931 16.6671i 1.07756 0.911984i
\(335\) 11.3911i 0.622363i
\(336\) −8.05904 2.77954i −0.439657 0.151637i
\(337\) 21.1705i 1.15323i −0.817015 0.576616i \(-0.804373\pi\)
0.817015 0.576616i \(-0.195627\pi\)
\(338\) 18.3486 1.15212i 0.998034 0.0626669i
\(339\) 7.51630i 0.408230i
\(340\) −0.514483 + 3.06962i −0.0279017 + 0.166474i
\(341\) −16.6155 + 8.58783i −0.899782 + 0.465057i
\(342\) 0.190231 0.161001i 0.0102865 0.00870593i
\(343\) 15.7359i 0.849661i
\(344\) −10.3094 + 6.12809i −0.555843 + 0.330404i
\(345\) 4.79098i 0.257937i
\(346\) −15.0952 + 12.7758i −0.811525 + 0.686829i
\(347\) −26.1754 −1.40517 −0.702584 0.711601i \(-0.747970\pi\)
−0.702584 + 0.711601i \(0.747970\pi\)
\(348\) 5.42551 32.3709i 0.290838 1.73526i
\(349\) 0.953092 0.0510179 0.0255089 0.999675i \(-0.491879\pi\)
0.0255089 + 0.999675i \(0.491879\pi\)
\(350\) −5.18337 + 4.38691i −0.277063 + 0.234490i
\(351\) −17.2189 + 8.65081i −0.919075 + 0.461746i
\(352\) 14.0616 + 12.4206i 0.749487 + 0.662020i
\(353\) 34.4757i 1.83496i −0.397786 0.917478i \(-0.630221\pi\)
0.397786 0.917478i \(-0.369779\pi\)
\(354\) −1.45096 + 1.22801i −0.0771175 + 0.0652679i
\(355\) 12.2894i 0.652252i
\(356\) −9.92382 1.66328i −0.525961 0.0881535i
\(357\) 3.00208i 0.158887i
\(358\) −14.9722 + 12.6716i −0.791304 + 0.669716i
\(359\) 3.10906i 0.164090i −0.996629 0.0820450i \(-0.973855\pi\)
0.996629 0.0820450i \(-0.0261451\pi\)
\(360\) 0.296927 + 0.499524i 0.0156494 + 0.0263272i
\(361\) 18.1020 0.952739
\(362\) −9.62575 11.3733i −0.505918 0.597769i
\(363\) 15.0533 + 10.6722i 0.790094 + 0.560145i
\(364\) 2.70310 + 8.75365i 0.141681 + 0.458816i
\(365\) 11.0616i 0.578989i
\(366\) −6.47604 7.65179i −0.338508 0.399965i
\(367\) 15.9489i 0.832526i 0.909244 + 0.416263i \(0.136660\pi\)
−0.909244 + 0.416263i \(0.863340\pi\)
\(368\) −3.37152 + 9.77542i −0.175753 + 0.509579i
\(369\) 0.293033 0.0152547
\(370\) 7.92949 + 9.36911i 0.412235 + 0.487077i
\(371\) 6.78089i 0.352046i
\(372\) 18.6599 + 3.12748i 0.967470 + 0.162152i
\(373\) 12.2599i 0.634792i 0.948293 + 0.317396i \(0.102808\pi\)
−0.948293 + 0.317396i \(0.897192\pi\)
\(374\) −2.52038 + 6.10738i −0.130326 + 0.315805i
\(375\) −16.2708 −0.840222
\(376\) −0.644652 + 0.383194i −0.0332454 + 0.0197617i
\(377\) −31.5191 + 15.8353i −1.62332 + 0.815560i
\(378\) −6.20349 7.32976i −0.319073 0.377002i
\(379\) −8.20078 −0.421246 −0.210623 0.977567i \(-0.567549\pi\)
−0.210623 + 0.977567i \(0.567549\pi\)
\(380\) 0.346102 2.06499i 0.0177547 0.105932i
\(381\) 29.2861i 1.50037i
\(382\) −28.5529 + 24.1656i −1.46089 + 1.23642i
\(383\) −37.2973 −1.90581 −0.952903 0.303276i \(-0.901920\pi\)
−0.952903 + 0.303276i \(0.901920\pi\)
\(384\) −3.84831 18.5846i −0.196383 0.948391i
\(385\) 4.13549 2.13745i 0.210764 0.108935i
\(386\) 21.3678 + 25.2472i 1.08759 + 1.28505i
\(387\) −0.788543 −0.0400839
\(388\) 31.2349 + 5.23512i 1.58571 + 0.265773i
\(389\) −8.68887 −0.440543 −0.220272 0.975439i \(-0.570694\pi\)
−0.220272 + 0.975439i \(0.570694\pi\)
\(390\) −3.70486 + 8.69341i −0.187603 + 0.440208i
\(391\) −3.64145 −0.184156
\(392\) 13.0949 7.78385i 0.661390 0.393144i
\(393\) 11.8896i 0.599753i
\(394\) −16.8442 19.9023i −0.848597 1.00266i
\(395\) 8.74981i 0.440251i
\(396\) 0.377461 + 1.17440i 0.0189681 + 0.0590157i
\(397\) 21.4029i 1.07418i −0.843524 0.537091i \(-0.819523\pi\)
0.843524 0.537091i \(-0.180477\pi\)
\(398\) −17.8742 + 15.1278i −0.895955 + 0.758286i
\(399\) 2.01956i 0.101104i
\(400\) −14.2916 4.92916i −0.714582 0.246458i
\(401\) 13.9031i 0.694288i 0.937812 + 0.347144i \(0.112848\pi\)
−0.937812 + 0.347144i \(0.887152\pi\)
\(402\) −18.6712 + 15.8022i −0.931233 + 0.788143i
\(403\) −9.12812 18.1689i −0.454704 0.905058i
\(404\) −5.84658 0.979914i −0.290878 0.0487526i
\(405\) 9.28850i 0.461549i
\(406\) −11.3555 13.4171i −0.563564 0.665880i
\(407\) 11.9634 + 23.1465i 0.593004 + 1.14733i
\(408\) 5.74513 3.41502i 0.284426 0.169069i
\(409\) 35.8638 1.77335 0.886676 0.462391i \(-0.153008\pi\)
0.886676 + 0.462391i \(0.153008\pi\)
\(410\) 1.87922 1.59046i 0.0928080 0.0785475i
\(411\) 23.8162 1.17477
\(412\) −17.5717 2.94510i −0.865697 0.145095i
\(413\) 1.01797i 0.0500912i
\(414\) −0.518963 + 0.439221i −0.0255056 + 0.0215865i
\(415\) 13.9169 0.683152
\(416\) −13.6771 + 15.1307i −0.670574 + 0.741842i
\(417\) 15.8546i 0.776405i
\(418\) 1.69551 4.10855i 0.0829301 0.200956i
\(419\) 1.60374i 0.0783479i −0.999232 0.0391740i \(-0.987527\pi\)
0.999232 0.0391740i \(-0.0124726\pi\)
\(420\) −4.64431 0.778408i −0.226619 0.0379824i
\(421\) 6.30644i 0.307357i 0.988121 + 0.153679i \(0.0491120\pi\)
−0.988121 + 0.153679i \(0.950888\pi\)
\(422\) −19.7823 23.3738i −0.962985 1.13782i
\(423\) −0.0493082 −0.00239745
\(424\) 12.9767 7.71361i 0.630204 0.374606i
\(425\) 5.32379i 0.258242i
\(426\) 20.1435 17.0483i 0.975956 0.825994i
\(427\) −5.36840 −0.259795
\(428\) −4.52639 + 27.0064i −0.218791 + 1.30540i
\(429\) −11.7889 + 16.2305i −0.569173 + 0.783616i
\(430\) −5.05692 + 4.27989i −0.243866 + 0.206395i
\(431\) 16.3244i 0.786317i 0.919471 + 0.393158i \(0.128618\pi\)
−0.919471 + 0.393158i \(0.871382\pi\)
\(432\) 6.97028 20.2097i 0.335358 0.972339i
\(433\) 19.7915 0.951118 0.475559 0.879684i \(-0.342246\pi\)
0.475559 + 0.879684i \(0.342246\pi\)
\(434\) 7.73417 6.54577i 0.371252 0.314207i
\(435\) 18.1308i 0.869308i
\(436\) 2.64332 15.7712i 0.126592 0.755303i
\(437\) 2.44967 0.117184
\(438\) −18.1310 + 15.3451i −0.866333 + 0.733216i
\(439\) −30.0570 −1.43454 −0.717272 0.696794i \(-0.754609\pi\)
−0.717272 + 0.696794i \(0.754609\pi\)
\(440\) 8.79480 + 5.48269i 0.419276 + 0.261377i
\(441\) 1.00160 0.0476953
\(442\) −6.60755 2.81593i −0.314289 0.133940i
\(443\) 10.8198i 0.514065i 0.966403 + 0.257032i \(0.0827447\pi\)
−0.966403 + 0.257032i \(0.917255\pi\)
\(444\) 4.35679 25.9944i 0.206764 1.23364i
\(445\) −5.55831 −0.263489
\(446\) −3.90881 4.61846i −0.185087 0.218690i
\(447\) 19.3287i 0.914218i
\(448\) −8.92839 4.85656i −0.421827 0.229451i
\(449\) 9.35084i 0.441293i −0.975354 0.220647i \(-0.929183\pi\)
0.975354 0.220647i \(-0.0708168\pi\)
\(450\) −0.642141 0.758723i −0.0302708 0.0357665i
\(451\) 4.64264 2.39957i 0.218613 0.112991i
\(452\) −1.48129 + 8.83800i −0.0696740 + 0.415704i
\(453\) −8.29683 −0.389819
\(454\) −1.32070 + 1.11776i −0.0619833 + 0.0524592i
\(455\) 2.27192 + 4.52211i 0.106509 + 0.212000i
\(456\) −3.86486 + 2.29735i −0.180988 + 0.107583i
\(457\) −8.51503 −0.398316 −0.199158 0.979967i \(-0.563821\pi\)
−0.199158 + 0.979967i \(0.563821\pi\)
\(458\) −12.0475 + 10.1963i −0.562943 + 0.476443i
\(459\) 7.52833 0.351392
\(460\) −0.944190 + 5.63344i −0.0440231 + 0.262660i
\(461\) −23.3707 −1.08848 −0.544241 0.838929i \(-0.683182\pi\)
−0.544241 + 0.838929i \(0.683182\pi\)
\(462\) −9.24042 3.81332i −0.429903 0.177412i
\(463\) −23.0963 −1.07337 −0.536687 0.843781i \(-0.680324\pi\)
−0.536687 + 0.843781i \(0.680324\pi\)
\(464\) 12.7591 36.9938i 0.592326 1.71740i
\(465\) 10.4514 0.484670
\(466\) −9.99310 + 8.45760i −0.462922 + 0.391791i
\(467\) 25.7065i 1.18956i 0.803890 + 0.594778i \(0.202760\pi\)
−0.803890 + 0.594778i \(0.797240\pi\)
\(468\) −1.28133 + 0.395669i −0.0592294 + 0.0182898i
\(469\) 13.0994i 0.604876i
\(470\) −0.316213 + 0.267625i −0.0145858 + 0.0123446i
\(471\) 24.0798i 1.10954i
\(472\) −1.94811 + 1.15800i −0.0896691 + 0.0533011i
\(473\) −12.4932 + 6.45717i −0.574437 + 0.296901i
\(474\) 14.3418 12.1381i 0.658741 0.557522i
\(475\) 3.58142i 0.164327i
\(476\) 0.591640 3.52998i 0.0271178 0.161796i
\(477\) 0.992563 0.0454463
\(478\) 22.4467 18.9976i 1.02669 0.868932i
\(479\) 6.79360i 0.310408i −0.987882 0.155204i \(-0.950397\pi\)
0.987882 0.155204i \(-0.0496034\pi\)
\(480\) −3.79349 9.77338i −0.173148 0.446092i
\(481\) −25.3105 + 12.7161i −1.15406 + 0.579803i
\(482\) 0.815186 + 0.963185i 0.0371307 + 0.0438719i
\(483\) 5.50949i 0.250690i
\(484\) 15.5971 + 15.5155i 0.708959 + 0.705250i
\(485\) 17.4946 0.794390
\(486\) 2.08318 1.76309i 0.0944950 0.0799753i
\(487\) −11.9308 −0.540638 −0.270319 0.962771i \(-0.587129\pi\)
−0.270319 + 0.962771i \(0.587129\pi\)
\(488\) −6.10683 10.2736i −0.276443 0.465063i
\(489\) 15.5415i 0.702810i
\(490\) 6.42325 5.43628i 0.290173 0.245586i
\(491\) −20.2617 −0.914398 −0.457199 0.889364i \(-0.651147\pi\)
−0.457199 + 0.889364i \(0.651147\pi\)
\(492\) −5.21386 0.873867i −0.235059 0.0393970i
\(493\) 13.7806 0.620647
\(494\) 4.44502 + 1.89433i 0.199991 + 0.0852300i
\(495\) 0.312872 + 0.605338i 0.0140626 + 0.0272079i
\(496\) 21.3248 + 7.35486i 0.957510 + 0.330243i
\(497\) 14.1324i 0.633926i
\(498\) −19.3061 22.8111i −0.865125 1.02219i
\(499\) 25.9523 1.16178 0.580891 0.813981i \(-0.302704\pi\)
0.580891 + 0.813981i \(0.302704\pi\)
\(500\) −19.1320 3.20660i −0.855607 0.143404i
\(501\) −30.6027 −1.36723
\(502\) −17.4849 + 14.7983i −0.780391 + 0.660479i
\(503\) −21.2219 −0.946236 −0.473118 0.880999i \(-0.656872\pi\)
−0.473118 + 0.880999i \(0.656872\pi\)
\(504\) −0.341458 0.574438i −0.0152097 0.0255875i
\(505\) −3.27466 −0.145720
\(506\) −4.62546 + 11.2084i −0.205627 + 0.498274i
\(507\) −17.4962 13.0174i −0.777034 0.578125i
\(508\) 5.77161 34.4359i 0.256074 1.52784i
\(509\) 3.90141i 0.172927i −0.996255 0.0864635i \(-0.972443\pi\)
0.996255 0.0864635i \(-0.0275566\pi\)
\(510\) 2.81808 2.38507i 0.124787 0.105613i
\(511\) 12.7205i 0.562721i
\(512\) −0.862421 22.6110i −0.0381140 0.999273i
\(513\) −5.06445 −0.223601
\(514\) 22.5123 + 26.5994i 0.992973 + 1.17325i
\(515\) −9.84189 −0.433685
\(516\) 14.0303 + 2.35155i 0.617651 + 0.103521i
\(517\) −0.781208 + 0.403772i −0.0343575 + 0.0177579i
\(518\) −9.11869 10.7742i −0.400652 0.473392i
\(519\) 23.4577 1.02968
\(520\) −6.06961 + 9.49195i −0.266170 + 0.416250i
\(521\) 1.17608 0.0515252 0.0257626 0.999668i \(-0.491799\pi\)
0.0257626 + 0.999668i \(0.491799\pi\)
\(522\) 1.96395 1.66218i 0.0859597 0.0727515i
\(523\) −37.3218 −1.63197 −0.815983 0.578076i \(-0.803804\pi\)
−0.815983 + 0.578076i \(0.803804\pi\)
\(524\) −2.34317 + 13.9803i −0.102362 + 0.610734i
\(525\) 8.05486 0.351543
\(526\) −6.75324 7.97931i −0.294455 0.347914i
\(527\) 7.94370i 0.346033i
\(528\) −3.21384 22.0214i −0.139864 0.958357i
\(529\) 16.3171 0.709440
\(530\) 6.36530 5.38723i 0.276491 0.234006i
\(531\) −0.149007 −0.00646637
\(532\) −0.398008 + 2.37468i −0.0172558 + 0.102956i
\(533\) 2.55054 + 5.07667i 0.110476 + 0.219895i
\(534\) 7.71072 + 9.11062i 0.333675 + 0.394255i
\(535\) 15.1262i 0.653963i
\(536\) −25.0686 + 14.9013i −1.08280 + 0.643637i
\(537\) 23.2665 1.00402
\(538\) 15.5315 + 18.3513i 0.669612 + 0.791181i
\(539\) 15.8687 8.20185i 0.683515 0.353279i
\(540\) 1.95202 11.6466i 0.0840015 0.501188i
\(541\) −18.2148 −0.783113 −0.391557 0.920154i \(-0.628063\pi\)
−0.391557 + 0.920154i \(0.628063\pi\)
\(542\) 7.95497 6.73264i 0.341695 0.289192i
\(543\) 17.6739i 0.758462i
\(544\) 7.42839 2.88330i 0.318490 0.123620i
\(545\) 8.83341i 0.378382i
\(546\) 4.26049 9.99717i 0.182332 0.427840i
\(547\) 22.5434 0.963886 0.481943 0.876203i \(-0.339931\pi\)
0.481943 + 0.876203i \(0.339931\pi\)
\(548\) 28.0041 + 4.69362i 1.19628 + 0.200501i
\(549\) 0.785807i 0.0335374i
\(550\) −16.3867 6.76242i −0.698730 0.288351i
\(551\) −9.27048 −0.394936
\(552\) 10.5436 6.26732i 0.448765 0.266755i
\(553\) 10.0620i 0.427881i
\(554\) −19.1145 + 16.1775i −0.812099 + 0.687315i
\(555\) 14.5594i 0.618013i
\(556\) 3.12458 18.6426i 0.132512 0.790621i
\(557\) −8.53866 −0.361795 −0.180897 0.983502i \(-0.557900\pi\)
−0.180897 + 0.983502i \(0.557900\pi\)
\(558\) 0.958146 + 1.13210i 0.0405616 + 0.0479256i
\(559\) −6.86341 13.6612i −0.290291 0.577806i
\(560\) −5.30758 1.83057i −0.224286 0.0773558i
\(561\) 6.96212 3.59841i 0.293941 0.151925i
\(562\) −12.1829 14.3947i −0.513905 0.607206i
\(563\) 27.5197 1.15982 0.579908 0.814682i \(-0.303089\pi\)
0.579908 + 0.814682i \(0.303089\pi\)
\(564\) 0.877327 + 0.147044i 0.0369421 + 0.00619167i
\(565\) 4.95014i 0.208254i
\(566\) 0.876497 + 1.03563i 0.0368419 + 0.0435307i
\(567\) 10.6815i 0.448581i
\(568\) 27.0454 16.0764i 1.13480 0.674549i
\(569\) 18.7923i 0.787815i 0.919150 + 0.393908i \(0.128877\pi\)
−0.919150 + 0.393908i \(0.871123\pi\)
\(570\) −1.89578 + 1.60448i −0.0794054 + 0.0672043i
\(571\) 19.1261 0.800401 0.400200 0.916428i \(-0.368941\pi\)
0.400200 + 0.916428i \(0.368941\pi\)
\(572\) −17.0605 + 16.7612i −0.713337 + 0.700821i
\(573\) 44.3707 1.85361
\(574\) −2.16105 + 1.82899i −0.0902004 + 0.0763405i
\(575\) 9.77035i 0.407452i
\(576\) 0.710886 1.30691i 0.0296202 0.0544544i
\(577\) 39.2228i 1.63287i 0.577440 + 0.816433i \(0.304052\pi\)
−0.577440 + 0.816433i \(0.695948\pi\)
\(578\) −13.7187 16.2094i −0.570624 0.674222i
\(579\) 39.2337i 1.63049i
\(580\) 3.57317 21.3190i 0.148368 0.885225i
\(581\) −16.0040 −0.663958
\(582\) −24.2693 28.6754i −1.00599 1.18863i
\(583\) 15.7256 8.12784i 0.651286 0.336621i
\(584\) −24.3434 + 14.4702i −1.00734 + 0.598781i
\(585\) −0.661931 + 0.332556i −0.0273675 + 0.0137495i
\(586\) −6.05856 7.15851i −0.250277 0.295715i
\(587\) 30.2126 1.24701 0.623504 0.781820i \(-0.285709\pi\)
0.623504 + 0.781820i \(0.285709\pi\)
\(588\) −17.8212 2.98692i −0.734934 0.123178i
\(589\) 5.34388i 0.220191i
\(590\) −0.955582 + 0.808751i −0.0393407 + 0.0332958i
\(591\) 30.9278i 1.27220i
\(592\) 10.2458 29.7068i 0.421100 1.22094i
\(593\) −13.8113 −0.567164 −0.283582 0.958948i \(-0.591523\pi\)
−0.283582 + 0.958948i \(0.591523\pi\)
\(594\) 9.56268 23.1722i 0.392361 0.950768i
\(595\) 1.97713i 0.0810545i
\(596\) −3.80925 + 22.7276i −0.156033 + 0.930958i
\(597\) 27.7762 1.13681
\(598\) −12.1263 5.16786i −0.495882 0.211330i
\(599\) 5.16630i 0.211089i −0.994415 0.105545i \(-0.966341\pi\)
0.994415 0.105545i \(-0.0336586\pi\)
\(600\) 9.16281 + 15.4147i 0.374070 + 0.629303i
\(601\) 5.45833i 0.222650i 0.993784 + 0.111325i \(0.0355094\pi\)
−0.993784 + 0.111325i \(0.964491\pi\)
\(602\) 5.81531 4.92175i 0.237014 0.200596i
\(603\) −1.91745 −0.0780846
\(604\) −9.75578 1.63511i −0.396957 0.0665318i
\(605\) 9.91392 + 7.02858i 0.403058 + 0.285752i
\(606\) 4.54274 + 5.36749i 0.184536 + 0.218039i
\(607\) −22.9795 −0.932709 −0.466355 0.884598i \(-0.654433\pi\)
−0.466355 + 0.884598i \(0.654433\pi\)
\(608\) −4.99722 + 1.93965i −0.202664 + 0.0786631i
\(609\) 20.8500i 0.844883i
\(610\) −4.26504 5.03937i −0.172686 0.204038i
\(611\) −0.429174 0.854243i −0.0173625 0.0345590i
\(612\) 0.516705 + 0.0866022i 0.0208866 + 0.00350069i
\(613\) −15.8032 −0.638287 −0.319143 0.947706i \(-0.603395\pi\)
−0.319143 + 0.947706i \(0.603395\pi\)
\(614\) −8.15717 + 6.90377i −0.329196 + 0.278613i
\(615\) −2.92027 −0.117757
\(616\) −10.1138 6.30494i −0.407495 0.254033i
\(617\) 39.9111i 1.60676i −0.595467 0.803380i \(-0.703033\pi\)
0.595467 0.803380i \(-0.296967\pi\)
\(618\) 13.6531 + 16.1318i 0.549207 + 0.648917i
\(619\) −30.1748 −1.21283 −0.606413 0.795150i \(-0.707392\pi\)
−0.606413 + 0.795150i \(0.707392\pi\)
\(620\) 12.2892 + 2.05972i 0.493545 + 0.0827203i
\(621\) 13.8162 0.554423
\(622\) −6.46796 + 5.47412i −0.259342 + 0.219492i
\(623\) 6.39189 0.256086
\(624\) 23.9783 3.21894i 0.959899 0.128861i
\(625\) 8.18148 0.327259
\(626\) 3.06116 + 3.61692i 0.122349 + 0.144561i
\(627\) −4.68355 + 2.42072i −0.187043 + 0.0966742i
\(628\) 4.74558 28.3141i 0.189369 1.12986i
\(629\) 11.0661 0.441234
\(630\) −0.238476 0.281772i −0.00950111 0.0112261i
\(631\) 31.8586 1.26827 0.634136 0.773222i \(-0.281356\pi\)
0.634136 + 0.773222i \(0.281356\pi\)
\(632\) 19.2559 11.4461i 0.765957 0.455300i
\(633\) 36.3224i 1.44369i
\(634\) −14.9129 + 12.6214i −0.592265 + 0.501260i
\(635\) 19.2874i 0.765399i
\(636\) −17.6604 2.95997i −0.700281 0.117370i
\(637\) 8.71785 + 17.3523i 0.345414 + 0.687523i
\(638\) 17.5045 42.4168i 0.693009 1.67930i
\(639\) 2.06865 0.0818347
\(640\) −2.53445 12.2396i −0.100183 0.483811i
\(641\) −16.9700 −0.670275 −0.335137 0.942169i \(-0.608783\pi\)
−0.335137 + 0.942169i \(0.608783\pi\)
\(642\) 24.7933 20.9837i 0.978515 0.828160i
\(643\) −16.2635 −0.641370 −0.320685 0.947186i \(-0.603913\pi\)
−0.320685 + 0.947186i \(0.603913\pi\)
\(644\) 1.08579 6.47829i 0.0427862 0.255281i
\(645\) 7.85836 0.309422
\(646\) −1.21951 1.44091i −0.0479809 0.0566920i
\(647\) 17.5307i 0.689205i −0.938749 0.344602i \(-0.888014\pi\)
0.938749 0.344602i \(-0.111986\pi\)
\(648\) −20.4414 + 12.1508i −0.803013 + 0.477327i
\(649\) −2.36078 + 1.22018i −0.0926687 + 0.0478963i
\(650\) 7.55541 17.7287i 0.296348 0.695376i
\(651\) −12.0188 −0.471052
\(652\) −3.06286 + 18.2743i −0.119951 + 0.715679i
\(653\) 39.6406 1.55126 0.775628 0.631190i \(-0.217433\pi\)
0.775628 + 0.631190i \(0.217433\pi\)
\(654\) −14.4788 + 12.2541i −0.566167 + 0.479172i
\(655\) 7.83036i 0.305958i
\(656\) −5.95847 2.05506i −0.232639 0.0802367i
\(657\) −1.86198 −0.0726427
\(658\) 0.363636 0.307761i 0.0141760 0.0119978i
\(659\) 15.2238 0.593036 0.296518 0.955027i \(-0.404175\pi\)
0.296518 + 0.955027i \(0.404175\pi\)
\(660\) −3.76165 11.7037i −0.146422 0.455564i
\(661\) 25.4504i 0.989906i −0.868920 0.494953i \(-0.835185\pi\)
0.868920 0.494953i \(-0.164815\pi\)
\(662\) 5.21083 + 6.15687i 0.202525 + 0.239294i
\(663\) 3.82480 + 7.61300i 0.148543 + 0.295665i
\(664\) −18.2054 30.6271i −0.706505 1.18856i
\(665\) 1.33005i 0.0515773i
\(666\) 1.57709 1.33476i 0.0611110 0.0517209i
\(667\) 25.2905 0.979251
\(668\) −35.9840 6.03108i −1.39226 0.233350i
\(669\) 7.17700i 0.277479i
\(670\) −12.2966 + 10.4071i −0.475059 + 0.402063i
\(671\) −6.43477 12.4498i −0.248411 0.480621i
\(672\) 4.36241 + 11.2391i 0.168283 + 0.433558i
\(673\) 2.38318i 0.0918648i 0.998945 + 0.0459324i \(0.0146259\pi\)
−0.998945 + 0.0459324i \(0.985374\pi\)
\(674\) −22.8534 + 19.3418i −0.880279 + 0.745019i
\(675\) 20.1992i 0.777468i
\(676\) −18.0074 18.7546i −0.692592 0.721330i
\(677\) 45.9970i 1.76781i −0.467668 0.883904i \(-0.654906\pi\)
0.467668 0.883904i \(-0.345094\pi\)
\(678\) 8.11378 6.86704i 0.311608 0.263727i
\(679\) −20.1183 −0.772070
\(680\) 3.78367 2.24909i 0.145097 0.0862486i
\(681\) 2.05234 0.0786457
\(682\) 24.4508 + 10.0903i 0.936268 + 0.386377i
\(683\) −11.4042 −0.436371 −0.218186 0.975907i \(-0.570014\pi\)
−0.218186 + 0.975907i \(0.570014\pi\)
\(684\) −0.347598 0.0582589i −0.0132907 0.00222759i
\(685\) 15.6850 0.599295
\(686\) −16.9868 + 14.3767i −0.648559 + 0.548904i
\(687\) 18.7216 0.714274
\(688\) 16.0340 + 5.53010i 0.611292 + 0.210833i
\(689\) 8.63919 + 17.1957i 0.329127 + 0.655105i
\(690\) 5.17181 4.37713i 0.196888 0.166635i
\(691\) −13.8920 −0.528478 −0.264239 0.964457i \(-0.585121\pi\)
−0.264239 + 0.964457i \(0.585121\pi\)
\(692\) 27.5826 + 4.62297i 1.04853 + 0.175739i
\(693\) −0.359794 0.696122i −0.0136675 0.0264435i
\(694\) 23.9143 + 28.2561i 0.907776 + 1.07259i
\(695\) 10.4417i 0.396075i
\(696\) −39.9009 + 23.7179i −1.51244 + 0.899024i
\(697\) 2.21959i 0.0840731i
\(698\) −0.870764 1.02885i −0.0329589 0.0389427i
\(699\) 15.5291 0.587364
\(700\) 9.47126 + 1.58743i 0.357980 + 0.0599991i
\(701\) 21.5113i 0.812471i −0.913768 0.406236i \(-0.866841\pi\)
0.913768 0.406236i \(-0.133159\pi\)
\(702\) 25.0700 + 10.6840i 0.946205 + 0.403243i
\(703\) −7.44438 −0.280770
\(704\) 0.560931 26.5271i 0.0211409 0.999777i
\(705\) 0.491389 0.0185068
\(706\) −37.2162 + 31.4977i −1.40065 + 1.18543i
\(707\) 3.76576 0.141626
\(708\) 2.65125 + 0.444361i 0.0996400 + 0.0167001i
\(709\) 43.6867i 1.64069i 0.571871 + 0.820344i \(0.306218\pi\)
−0.571871 + 0.820344i \(0.693782\pi\)
\(710\) 13.2663 11.2278i 0.497874 0.421372i
\(711\) 1.47284 0.0552360
\(712\) 7.27110 + 12.2323i 0.272496 + 0.458424i
\(713\) 14.5785i 0.545968i
\(714\) −3.24072 + 2.74276i −0.121281 + 0.102645i
\(715\) −7.76401 + 10.6892i −0.290358 + 0.399753i
\(716\) 27.3578 + 4.58529i 1.02241 + 0.171360i
\(717\) −34.8818 −1.30268
\(718\) −3.35620 + 2.84050i −0.125252 + 0.106007i
\(719\) 30.3223i 1.13083i 0.824806 + 0.565416i \(0.191284\pi\)
−0.824806 + 0.565416i \(0.808716\pi\)
\(720\) 0.267953 0.776905i 0.00998601 0.0289535i
\(721\) 11.3179 0.421500
\(722\) −16.5384 19.5410i −0.615495 0.727240i
\(723\) 1.49677i 0.0556656i
\(724\) −3.48312 + 20.7818i −0.129449 + 0.772349i
\(725\) 36.9747i 1.37320i
\(726\) −2.23246 26.0002i −0.0828543 0.964959i
\(727\) 31.9183i 1.18379i 0.806017 + 0.591893i \(0.201619\pi\)
−0.806017 + 0.591893i \(0.798381\pi\)
\(728\) 6.97988 10.9155i 0.258691 0.404554i
\(729\) −28.4598 −1.05407
\(730\) −11.9409 + 10.1061i −0.441951 + 0.374042i
\(731\) 5.97285i 0.220914i
\(732\) −2.34339 + 13.9817i −0.0866141 + 0.516777i
\(733\) −17.4514 −0.644582 −0.322291 0.946641i \(-0.604453\pi\)
−0.322291 + 0.946641i \(0.604453\pi\)
\(734\) 17.2167 14.5712i 0.635480 0.537834i
\(735\) −9.98162 −0.368178
\(736\) 13.6328 5.29149i 0.502510 0.195047i
\(737\) −30.3789 + 15.7015i −1.11902 + 0.578372i
\(738\) −0.267721 0.316326i −0.00985494 0.0116441i
\(739\) 28.6608i 1.05431i 0.849770 + 0.527153i \(0.176740\pi\)
−0.849770 + 0.527153i \(0.823260\pi\)
\(740\) 2.86933 17.1196i 0.105479 0.629330i
\(741\) −2.57301 5.12141i −0.0945220 0.188140i
\(742\) −7.31991 + 6.19516i −0.268722 + 0.227431i
\(743\) 26.5050i 0.972373i 0.873855 + 0.486186i \(0.161612\pi\)
−0.873855 + 0.486186i \(0.838388\pi\)
\(744\) −13.6720 23.0005i −0.501238 0.843239i
\(745\) 12.7297i 0.466379i
\(746\) 13.2344 11.2009i 0.484546 0.410092i
\(747\) 2.34261i 0.0857116i
\(748\) 8.89553 2.85909i 0.325253 0.104539i
\(749\) 17.3947i 0.635588i
\(750\) 14.8654 + 17.5642i 0.542806 + 0.641354i
\(751\) 0.329262i 0.0120149i −0.999982 0.00600746i \(-0.998088\pi\)
0.999982 0.00600746i \(-0.00191225\pi\)
\(752\) 1.00262 + 0.345802i 0.0365618 + 0.0126101i
\(753\) 27.1713 0.990176
\(754\) 45.8906 + 19.5571i 1.67124 + 0.712229i
\(755\) −5.46419 −0.198862
\(756\) −2.24476 + 13.3932i −0.0816413 + 0.487107i
\(757\) −6.45006 −0.234431 −0.117216 0.993106i \(-0.537397\pi\)
−0.117216 + 0.993106i \(0.537397\pi\)
\(758\) 7.49240 + 8.85266i 0.272136 + 0.321543i
\(759\) 12.7770 6.60388i 0.463777 0.239706i
\(760\) −2.54535 + 1.51300i −0.0923294 + 0.0548824i
\(761\) 29.8226 1.08107 0.540535 0.841322i \(-0.318222\pi\)
0.540535 + 0.841322i \(0.318222\pi\)
\(762\) −31.6140 + 26.7564i −1.14526 + 0.969280i
\(763\) 10.1582i 0.367750i
\(764\) 52.1730 + 8.74443i 1.88755 + 0.316363i
\(765\) 0.289406 0.0104635
\(766\) 34.0756 + 40.2621i 1.23120 + 1.45473i
\(767\) −1.29695 2.58149i −0.0468301 0.0932121i
\(768\) −16.5460 + 21.1335i −0.597052 + 0.762588i
\(769\) 49.1057 1.77080 0.885399 0.464832i \(-0.153885\pi\)
0.885399 + 0.464832i \(0.153885\pi\)
\(770\) −6.08562 2.51140i −0.219311 0.0905047i
\(771\) 41.3350i 1.48864i
\(772\) 7.73204 46.1326i 0.278282 1.66035i
\(773\) 21.3112i 0.766511i 0.923642 + 0.383256i \(0.125197\pi\)
−0.923642 + 0.383256i \(0.874803\pi\)
\(774\) 0.720428 + 0.851224i 0.0258953 + 0.0305966i
\(775\) −21.3137 −0.765610
\(776\) −22.8856 38.5007i −0.821545 1.38210i
\(777\) 16.7429i 0.600649i
\(778\) 7.93832 + 9.37955i 0.284603 + 0.336273i
\(779\) 1.49316i 0.0534981i
\(780\) 12.7693 3.94311i 0.457214 0.141186i
\(781\) 32.7745 16.9397i 1.17276 0.606149i
\(782\) 3.32690 + 3.93091i 0.118970 + 0.140569i
\(783\) −52.2855 −1.86853
\(784\) −20.3663 7.02429i −0.727368 0.250868i
\(785\) 15.8587i 0.566020i
\(786\) 12.8347 10.8626i 0.457800 0.387456i
\(787\) 32.9070i 1.17301i −0.809946 0.586504i \(-0.800504\pi\)
0.809946 0.586504i \(-0.199496\pi\)
\(788\) −6.09515 + 36.3662i −0.217131 + 1.29549i
\(789\) 12.3997i 0.441441i
\(790\) 9.44534 7.99400i 0.336050 0.284414i
\(791\) 5.69252i 0.202403i
\(792\) 0.922895 1.48042i 0.0327936 0.0526043i
\(793\) 13.6138 6.83960i 0.483439 0.242881i
\(794\) −23.1043 + 19.5541i −0.819939 + 0.693951i
\(795\) −9.89155 −0.350817
\(796\) 32.6605 + 5.47405i 1.15762 + 0.194023i
\(797\) −51.0946 −1.80986 −0.904931 0.425558i \(-0.860078\pi\)
−0.904931 + 0.425558i \(0.860078\pi\)
\(798\) 2.18009 1.84511i 0.0771744 0.0653161i
\(799\) 0.373487i 0.0132130i
\(800\) 7.73615 + 19.9311i 0.273514 + 0.704670i
\(801\) 0.935623i 0.0330586i
\(802\) 15.0083 12.7021i 0.529960 0.448528i
\(803\) −29.5001 + 15.2473i −1.04103 + 0.538064i
\(804\) 34.1167 + 5.71811i 1.20320 + 0.201662i
\(805\) 3.62848i 0.127887i
\(806\) −11.2735 + 26.4532i −0.397093 + 0.931774i
\(807\) 28.5176i 1.00387i
\(808\) 4.28375 + 7.20660i 0.150702 + 0.253527i
\(809\) 29.9457i 1.05283i −0.850227 0.526417i \(-0.823535\pi\)
0.850227 0.526417i \(-0.176465\pi\)
\(810\) −10.0268 + 8.48616i −0.352307 + 0.298173i
\(811\) 33.3267i 1.17026i 0.810940 + 0.585130i \(0.198957\pi\)
−0.810940 + 0.585130i \(0.801043\pi\)
\(812\) −4.10904 + 24.5163i −0.144199 + 0.860353i
\(813\) −12.3619 −0.433550
\(814\) 14.0564 34.0615i 0.492678 1.19386i
\(815\) 10.2354i 0.358531i
\(816\) −8.93534 3.08178i −0.312800 0.107884i
\(817\) 4.01805i 0.140574i
\(818\) −32.7659 38.7146i −1.14563 1.35363i
\(819\) 0.761201 0.382430i 0.0265985 0.0133632i
\(820\) −3.43378 0.575518i −0.119913 0.0200979i
\(821\) −24.6890 −0.861652 −0.430826 0.902435i \(-0.641778\pi\)
−0.430826 + 0.902435i \(0.641778\pi\)
\(822\) −21.7589 25.7093i −0.758930 0.896716i
\(823\) 16.3287i 0.569183i 0.958649 + 0.284592i \(0.0918580\pi\)
−0.958649 + 0.284592i \(0.908142\pi\)
\(824\) 12.8747 + 21.6592i 0.448511 + 0.754535i
\(825\) 9.65487 + 18.6800i 0.336139 + 0.650355i
\(826\) 1.09889 0.930041i 0.0382354 0.0323603i
\(827\) 15.4227i 0.536299i −0.963377 0.268150i \(-0.913588\pi\)
0.963377 0.268150i \(-0.0864122\pi\)
\(828\) 0.948269 + 0.158934i 0.0329546 + 0.00552335i
\(829\) −48.9319 −1.69947 −0.849737 0.527207i \(-0.823239\pi\)
−0.849737 + 0.527207i \(0.823239\pi\)
\(830\) −12.7147 15.0231i −0.441335 0.521460i
\(831\) 29.7036 1.03041
\(832\) 28.8291 + 0.940592i 0.999468 + 0.0326092i
\(833\) 7.58667i 0.262863i
\(834\) −17.1149 + 14.4851i −0.592641 + 0.501578i
\(835\) −20.1546 −0.697477
\(836\) −5.98419 + 1.92337i −0.206968 + 0.0665210i
\(837\) 30.1395i 1.04177i
\(838\) −1.73122 + 1.46521i −0.0598041 + 0.0506148i
\(839\) −4.51783 −0.155973 −0.0779865 0.996954i \(-0.524849\pi\)
−0.0779865 + 0.996954i \(0.524849\pi\)
\(840\) 3.40285 + 5.72466i 0.117410 + 0.197520i
\(841\) −66.7087 −2.30030
\(842\) 6.80774 5.76169i 0.234610 0.198561i
\(843\) 22.3692i 0.770435i
\(844\) −7.15831 + 42.7095i −0.246399 + 1.47012i
\(845\) −11.5228 8.57312i −0.396396 0.294924i
\(846\) 0.0450489 + 0.0532277i 0.00154881 + 0.00183001i
\(847\) −11.4007 8.08266i −0.391733 0.277724i
\(848\) −20.1825 6.96091i −0.693071 0.239039i
\(849\) 1.60935i 0.0552326i
\(850\) −5.74698 + 4.86392i −0.197120 + 0.166831i
\(851\) 20.3088 0.696175
\(852\) −36.8070 6.16902i −1.26099 0.211347i
\(853\) 37.0817 1.26965 0.634826 0.772655i \(-0.281072\pi\)
0.634826 + 0.772655i \(0.281072\pi\)
\(854\) 4.90467 + 5.79513i 0.167834 + 0.198305i
\(855\) −0.194689 −0.00665821
\(856\) 33.2885 19.7874i 1.13778 0.676318i
\(857\) 51.0814i 1.74491i −0.488698 0.872453i \(-0.662528\pi\)
0.488698 0.872453i \(-0.337472\pi\)
\(858\) 28.2912 2.10251i 0.965846 0.0717786i
\(859\) 36.8343i 1.25677i 0.777903 + 0.628385i \(0.216284\pi\)
−0.777903 + 0.628385i \(0.783716\pi\)
\(860\) 9.24020 + 1.54870i 0.315088 + 0.0528102i
\(861\) 3.35823 0.114448
\(862\) 17.6220 14.9143i 0.600207 0.507981i
\(863\) −47.1911 −1.60640 −0.803202 0.595707i \(-0.796872\pi\)
−0.803202 + 0.595707i \(0.796872\pi\)
\(864\) −28.1843 + 10.9396i −0.958851 + 0.372174i
\(865\) 15.4489 0.525280
\(866\) −18.0819 21.3647i −0.614448 0.726002i
\(867\) 25.1891i 0.855467i
\(868\) −14.1322 2.36862i −0.479678 0.0803962i
\(869\) 23.3348 12.0607i 0.791581 0.409133i
\(870\) −19.5721 + 16.5647i −0.663555 + 0.561596i
\(871\) −16.6893 33.2190i −0.565496 1.12558i
\(872\) −19.4398 + 11.5554i −0.658316 + 0.391316i
\(873\) 2.94485i 0.0996680i
\(874\) −2.23807 2.64440i −0.0757038 0.0894481i
\(875\) 12.3228 0.416587
\(876\) 33.1297 + 5.55269i 1.11935 + 0.187608i
\(877\) 30.8744 1.04255 0.521277 0.853388i \(-0.325456\pi\)
0.521277 + 0.853388i \(0.325456\pi\)
\(878\) 27.4607 + 32.4462i 0.926753 + 1.09501i
\(879\) 11.1242i 0.375210i
\(880\) −2.11659 14.5030i −0.0713503 0.488896i
\(881\) −23.1218 −0.778994 −0.389497 0.921028i \(-0.627351\pi\)
−0.389497 + 0.921028i \(0.627351\pi\)
\(882\) −0.915082 1.08122i −0.0308124 0.0364065i
\(883\) 2.56715i 0.0863915i −0.999067 0.0431958i \(-0.986246\pi\)
0.999067 0.0431958i \(-0.0137539\pi\)
\(884\) 2.99702 + 9.70548i 0.100801 + 0.326431i
\(885\) 1.48496 0.0499163
\(886\) 11.6799 9.88520i 0.392393 0.332100i
\(887\) 15.8965 0.533752 0.266876 0.963731i \(-0.414009\pi\)
0.266876 + 0.963731i \(0.414009\pi\)
\(888\) −32.0412 + 19.0459i −1.07523 + 0.639140i
\(889\) 22.1800i 0.743894i
\(890\) 5.07818 + 6.00014i 0.170221 + 0.201125i
\(891\) −24.7715 + 12.8033i −0.829875 + 0.428926i
\(892\) −1.41442 + 8.43903i −0.0473583 + 0.282560i
\(893\) 0.251252i 0.00840782i
\(894\) 20.8652 17.6591i 0.697836 0.590609i
\(895\) 15.3230 0.512192
\(896\) 2.91454 + 14.0752i 0.0973680 + 0.470218i
\(897\) 7.01935 + 13.9716i 0.234369 + 0.466497i
\(898\) −10.0941 + 8.54311i −0.336846 + 0.285087i
\(899\) 55.1704i 1.84003i
\(900\) −0.232362 + 1.38637i −0.00774539 + 0.0462123i
\(901\) 7.51822i 0.250468i
\(902\) −6.83192 2.81938i −0.227478 0.0938752i
\(903\) −9.03688 −0.300729
\(904\) 10.8939 6.47553i 0.362325 0.215373i
\(905\) 11.6398i 0.386921i
\(906\) 7.58015 + 8.95635i 0.251834 + 0.297555i
\(907\) 29.8657i 0.991674i −0.868416 0.495837i \(-0.834861\pi\)
0.868416 0.495837i \(-0.165139\pi\)
\(908\) 2.41323 + 0.404468i 0.0800858 + 0.0134227i
\(909\) 0.551219i 0.0182828i
\(910\) 2.80590 6.58401i 0.0930147 0.218258i
\(911\) 8.02735i 0.265958i −0.991119 0.132979i \(-0.957546\pi\)
0.991119 0.132979i \(-0.0424543\pi\)
\(912\) 6.01097 + 2.07317i 0.199043 + 0.0686496i
\(913\) −19.1830 37.1149i −0.634865 1.22832i
\(914\) 7.77950 + 9.19189i 0.257323 + 0.304041i
\(915\) 7.83109i 0.258888i
\(916\) 22.0137 + 3.68959i 0.727352 + 0.121908i
\(917\) 9.00469i 0.297361i
\(918\) −6.87803 8.12676i −0.227009 0.268223i
\(919\) 51.9419 1.71340 0.856702 0.515811i \(-0.172509\pi\)
0.856702 + 0.515811i \(0.172509\pi\)
\(920\) 6.94387 4.12758i 0.228933 0.136082i
\(921\) 12.6761 0.417691
\(922\) 21.3519 + 25.2284i 0.703189 + 0.830855i
\(923\) 18.0054 + 35.8385i 0.592655 + 1.17964i
\(924\) 4.32579 + 13.4589i 0.142308 + 0.442764i
\(925\) 29.6914i 0.976247i
\(926\) 21.1012 + 24.9322i 0.693428 + 0.819322i
\(927\) 1.65667i 0.0544122i
\(928\) −51.5914 + 20.0250i −1.69357 + 0.657352i
\(929\) 12.3727i 0.405936i 0.979185 + 0.202968i \(0.0650588\pi\)
−0.979185 + 0.202968i \(0.934941\pi\)
\(930\) −9.54857 11.2821i −0.313110 0.369956i
\(931\) 5.10370i 0.167267i
\(932\) 18.2598 + 3.06042i 0.598119 + 0.100248i
\(933\) 10.0511 0.329058
\(934\) 27.7499 23.4860i 0.908006 0.768485i
\(935\) 4.58516 2.36987i 0.149951 0.0775029i
\(936\) 1.59777 + 1.02169i 0.0522247 + 0.0333950i
\(937\) 23.1504i 0.756292i 0.925746 + 0.378146i \(0.123438\pi\)
−0.925746 + 0.378146i \(0.876562\pi\)
\(938\) 14.1407 11.9679i 0.461711 0.390766i
\(939\) 5.62063i 0.183422i
\(940\) 0.577796 + 0.0968413i 0.0188456 + 0.00315862i
\(941\) 45.1728 1.47259 0.736296 0.676660i \(-0.236573\pi\)
0.736296 + 0.676660i \(0.236573\pi\)
\(942\) −25.9939 + 21.9998i −0.846928 + 0.716793i
\(943\) 4.07345i 0.132650i
\(944\) 3.02988 + 1.04500i 0.0986142 + 0.0340118i
\(945\) 7.50151i 0.244024i
\(946\) 18.3845 + 7.58687i 0.597731 + 0.246671i
\(947\) 22.7811 0.740286 0.370143 0.928975i \(-0.379309\pi\)
0.370143 + 0.928975i \(0.379309\pi\)
\(948\) −26.2059 4.39223i −0.851129 0.142653i
\(949\) −16.2065 32.2580i −0.526086 1.04714i
\(950\) 3.86610 3.27205i 0.125433 0.106159i
\(951\) 23.1743 0.751478
\(952\) −4.35111 + 2.58639i −0.141020 + 0.0838253i
\(953\) 32.8772i 1.06500i 0.846431 + 0.532498i \(0.178747\pi\)
−0.846431 + 0.532498i \(0.821253\pi\)
\(954\) −0.906825 1.07146i −0.0293595 0.0346899i
\(955\) 29.2220 0.945601
\(956\) −41.0155 6.87439i −1.32654 0.222334i
\(957\) −48.3531 + 24.9916i −1.56303 + 0.807862i
\(958\) −7.33362 + 6.20677i −0.236939 + 0.200532i
\(959\) −18.0373 −0.582456
\(960\) −7.08445 + 13.0242i −0.228650 + 0.420354i
\(961\) 0.802434 0.0258850
\(962\) 36.8510 + 15.7048i 1.18812 + 0.506342i
\(963\) 2.54617 0.0820493
\(964\) 0.294979 1.75997i 0.00950063 0.0566848i
\(965\) 25.8388i 0.831780i
\(966\) −5.94743 + 5.03357i −0.191356 + 0.161953i
\(967\) 58.8056i 1.89106i −0.325535 0.945530i \(-0.605544\pi\)
0.325535 0.945530i \(-0.394456\pi\)
\(968\) 2.49902 31.0122i 0.0803215 0.996769i
\(969\) 2.23915i 0.0719320i
\(970\) −15.9834 18.8853i −0.513197 0.606370i
\(971\) 12.7843i 0.410268i −0.978734 0.205134i \(-0.934237\pi\)
0.978734 0.205134i \(-0.0657630\pi\)
\(972\) −3.80647 0.637982i −0.122093 0.0204633i
\(973\) 12.0076i 0.384946i
\(974\) 10.9003 + 12.8792i 0.349267 + 0.412677i
\(975\) −20.4264 + 10.2623i −0.654168 + 0.328656i
\(976\) −5.51092 + 15.9784i −0.176400 + 0.511456i
\(977\) 35.1203i 1.12360i −0.827274 0.561799i \(-0.810109\pi\)
0.827274 0.561799i \(-0.189891\pi\)
\(978\) 16.7769 14.1990i 0.536465 0.454034i
\(979\) 7.66157 + 14.8234i 0.244865 + 0.473759i
\(980\) −11.7368 1.96715i −0.374919 0.0628381i
\(981\) −1.48692 −0.0474736
\(982\) 18.5115 + 21.8723i 0.590726 + 0.697974i
\(983\) 11.3212 0.361090 0.180545 0.983567i \(-0.442214\pi\)
0.180545 + 0.983567i \(0.442214\pi\)
\(984\) 3.82016 + 6.42669i 0.121782 + 0.204875i
\(985\) 20.3686i 0.648999i
\(986\) −12.5902 14.8760i −0.400955 0.473749i
\(987\) −0.565083 −0.0179868
\(988\) −2.01615 6.52906i −0.0641423 0.207717i
\(989\) 10.9615i 0.348556i
\(990\) 0.367610 0.890792i 0.0116834 0.0283112i
\(991\) 48.1334i 1.52901i −0.644618 0.764505i \(-0.722984\pi\)
0.644618 0.764505i \(-0.277016\pi\)
\(992\) −11.5432 29.7394i −0.366497 0.944227i
\(993\) 9.56766i 0.303621i
\(994\) −15.2558 + 12.9117i −0.483885 + 0.409533i
\(995\) 18.2931 0.579930
\(996\) −6.98599 + 41.6814i −0.221360 + 1.32073i
\(997\) 54.8576i 1.73736i 0.495375 + 0.868679i \(0.335031\pi\)
−0.495375 + 0.868679i \(0.664969\pi\)
\(998\) −23.7105 28.0152i −0.750543 0.886806i
\(999\) −41.9863 −1.32839
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 572.2.b.c.571.14 yes 56
4.3 odd 2 inner 572.2.b.c.571.16 yes 56
11.10 odd 2 inner 572.2.b.c.571.44 yes 56
13.12 even 2 inner 572.2.b.c.571.43 yes 56
44.43 even 2 inner 572.2.b.c.571.42 yes 56
52.51 odd 2 inner 572.2.b.c.571.41 yes 56
143.142 odd 2 inner 572.2.b.c.571.13 56
572.571 even 2 inner 572.2.b.c.571.15 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.b.c.571.13 56 143.142 odd 2 inner
572.2.b.c.571.14 yes 56 1.1 even 1 trivial
572.2.b.c.571.15 yes 56 572.571 even 2 inner
572.2.b.c.571.16 yes 56 4.3 odd 2 inner
572.2.b.c.571.41 yes 56 52.51 odd 2 inner
572.2.b.c.571.42 yes 56 44.43 even 2 inner
572.2.b.c.571.43 yes 56 13.12 even 2 inner
572.2.b.c.571.44 yes 56 11.10 odd 2 inner