Properties

Label 572.2.b.c.571.18
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 571.18
Character \(\chi\) \(=\) 572.571
Dual form 572.2.b.c.571.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.883550 - 1.10424i) q^{2} -2.47596i q^{3} +(-0.438678 + 1.95130i) q^{4} +2.76928i q^{5} +(-2.73405 + 2.18764i) q^{6} +0.534510i q^{7} +(2.54229 - 1.23966i) q^{8} -3.13038 q^{9} +O(q^{10})\) \(q+(-0.883550 - 1.10424i) q^{2} -2.47596i q^{3} +(-0.438678 + 1.95130i) q^{4} +2.76928i q^{5} +(-2.73405 + 2.18764i) q^{6} +0.534510i q^{7} +(2.54229 - 1.23966i) q^{8} -3.13038 q^{9} +(3.05794 - 2.44680i) q^{10} +(3.29596 + 0.369696i) q^{11} +(4.83134 + 1.08615i) q^{12} +(-3.35334 - 1.32481i) q^{13} +(0.590226 - 0.472267i) q^{14} +6.85664 q^{15} +(-3.61512 - 1.71198i) q^{16} -5.90649i q^{17} +(2.76585 + 3.45669i) q^{18} -5.54527i q^{19} +(-5.40369 - 1.21482i) q^{20} +1.32343 q^{21} +(-2.50391 - 3.96616i) q^{22} -4.48555i q^{23} +(-3.06936 - 6.29461i) q^{24} -2.66893 q^{25} +(1.49994 + 4.87341i) q^{26} +0.322828i q^{27} +(-1.04299 - 0.234478i) q^{28} -0.677674i q^{29} +(-6.05818 - 7.57135i) q^{30} +9.20526 q^{31} +(1.30371 + 5.50458i) q^{32} +(0.915354 - 8.16066i) q^{33} +(-6.52216 + 5.21868i) q^{34} -1.48021 q^{35} +(1.37323 - 6.10831i) q^{36} -1.55230i q^{37} +(-6.12329 + 4.89953i) q^{38} +(-3.28017 + 8.30274i) q^{39} +(3.43298 + 7.04032i) q^{40} +2.50658 q^{41} +(-1.16931 - 1.46138i) q^{42} +8.49046 q^{43} +(-2.16725 + 6.26921i) q^{44} -8.66892i q^{45} +(-4.95311 + 3.96321i) q^{46} -10.0993 q^{47} +(-4.23881 + 8.95090i) q^{48} +6.71430 q^{49} +(2.35813 + 2.94713i) q^{50} -14.6242 q^{51} +(4.05613 - 5.96220i) q^{52} +4.38869 q^{53} +(0.356479 - 0.285235i) q^{54} +(-1.02379 + 9.12743i) q^{55} +(0.662613 + 1.35888i) q^{56} -13.7299 q^{57} +(-0.748313 + 0.598759i) q^{58} -5.47956 q^{59} +(-3.00786 + 13.3793i) q^{60} +10.3154i q^{61} +(-8.13331 - 10.1648i) q^{62} -1.67322i q^{63} +(4.92647 - 6.30317i) q^{64} +(3.66876 - 9.28634i) q^{65} +(-9.82006 + 6.19958i) q^{66} +2.88040 q^{67} +(11.5253 + 2.59105i) q^{68} -11.1060 q^{69} +(1.30784 + 1.63450i) q^{70} -3.09875 q^{71} +(-7.95834 + 3.88063i) q^{72} -9.44310 q^{73} +(-1.71411 + 1.37154i) q^{74} +6.60816i q^{75} +(10.8205 + 2.43259i) q^{76} +(-0.197607 + 1.76172i) q^{77} +(12.0664 - 3.71380i) q^{78} +8.42639 q^{79} +(4.74097 - 10.0113i) q^{80} -8.59184 q^{81} +(-2.21469 - 2.76786i) q^{82} -2.83221i q^{83} +(-0.580559 + 2.58240i) q^{84} +16.3567 q^{85} +(-7.50175 - 9.37548i) q^{86} -1.67789 q^{87} +(8.83757 - 3.14600i) q^{88} -6.95222i q^{89} +(-9.57254 + 7.65943i) q^{90} +(0.708123 - 1.79239i) q^{91} +(8.75264 + 1.96771i) q^{92} -22.7919i q^{93} +(8.92321 + 11.1520i) q^{94} +15.3564 q^{95} +(13.6291 - 3.22792i) q^{96} -2.27247i q^{97} +(-5.93242 - 7.41418i) q^{98} +(-10.3176 - 1.15729i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.883550 1.10424i −0.624764 0.780813i
\(3\) 2.47596i 1.42950i −0.699382 0.714748i \(-0.746541\pi\)
0.699382 0.714748i \(-0.253459\pi\)
\(4\) −0.438678 + 1.95130i −0.219339 + 0.975649i
\(5\) 2.76928i 1.23846i 0.785209 + 0.619230i \(0.212555\pi\)
−0.785209 + 0.619230i \(0.787445\pi\)
\(6\) −2.73405 + 2.18764i −1.11617 + 0.893099i
\(7\) 0.534510i 0.202026i 0.994885 + 0.101013i \(0.0322083\pi\)
−0.994885 + 0.101013i \(0.967792\pi\)
\(8\) 2.54229 1.23966i 0.898835 0.438287i
\(9\) −3.13038 −1.04346
\(10\) 3.05794 2.44680i 0.967007 0.773746i
\(11\) 3.29596 + 0.369696i 0.993768 + 0.111468i
\(12\) 4.83134 + 1.08615i 1.39469 + 0.313545i
\(13\) −3.35334 1.32481i −0.930049 0.367435i
\(14\) 0.590226 0.472267i 0.157745 0.126219i
\(15\) 6.85664 1.77038
\(16\) −3.61512 1.71198i −0.903781 0.427996i
\(17\) 5.90649i 1.43253i −0.697827 0.716267i \(-0.745849\pi\)
0.697827 0.716267i \(-0.254151\pi\)
\(18\) 2.76585 + 3.45669i 0.651918 + 0.814749i
\(19\) 5.54527i 1.27217i −0.771618 0.636086i \(-0.780552\pi\)
0.771618 0.636086i \(-0.219448\pi\)
\(20\) −5.40369 1.21482i −1.20830 0.271643i
\(21\) 1.32343 0.288795
\(22\) −2.50391 3.96616i −0.533835 0.845588i
\(23\) 4.48555i 0.935301i −0.883913 0.467651i \(-0.845101\pi\)
0.883913 0.467651i \(-0.154899\pi\)
\(24\) −3.06936 6.29461i −0.626531 1.28488i
\(25\) −2.66893 −0.533785
\(26\) 1.49994 + 4.87341i 0.294163 + 0.955755i
\(27\) 0.322828i 0.0621283i
\(28\) −1.04299 0.234478i −0.197106 0.0443122i
\(29\) 0.677674i 0.125841i −0.998019 0.0629204i \(-0.979959\pi\)
0.998019 0.0629204i \(-0.0200414\pi\)
\(30\) −6.05818 7.57135i −1.10607 1.38233i
\(31\) 9.20526 1.65331 0.826657 0.562706i \(-0.190240\pi\)
0.826657 + 0.562706i \(0.190240\pi\)
\(32\) 1.30371 + 5.50458i 0.230465 + 0.973081i
\(33\) 0.915354 8.16066i 0.159343 1.42059i
\(34\) −6.52216 + 5.21868i −1.11854 + 0.894996i
\(35\) −1.48021 −0.250201
\(36\) 1.37323 6.10831i 0.228872 1.01805i
\(37\) 1.55230i 0.255197i −0.991826 0.127598i \(-0.959273\pi\)
0.991826 0.127598i \(-0.0407268\pi\)
\(38\) −6.12329 + 4.89953i −0.993329 + 0.794808i
\(39\) −3.28017 + 8.30274i −0.525248 + 1.32950i
\(40\) 3.43298 + 7.04032i 0.542802 + 1.11317i
\(41\) 2.50658 0.391462 0.195731 0.980658i \(-0.437292\pi\)
0.195731 + 0.980658i \(0.437292\pi\)
\(42\) −1.16931 1.46138i −0.180429 0.225495i
\(43\) 8.49046 1.29478 0.647392 0.762157i \(-0.275860\pi\)
0.647392 + 0.762157i \(0.275860\pi\)
\(44\) −2.16725 + 6.26921i −0.326726 + 0.945119i
\(45\) 8.66892i 1.29229i
\(46\) −4.95311 + 3.96321i −0.730296 + 0.584343i
\(47\) −10.0993 −1.47313 −0.736565 0.676367i \(-0.763553\pi\)
−0.736565 + 0.676367i \(0.763553\pi\)
\(48\) −4.23881 + 8.95090i −0.611819 + 1.29195i
\(49\) 6.71430 0.959186
\(50\) 2.35813 + 2.94713i 0.333490 + 0.416787i
\(51\) −14.6242 −2.04780
\(52\) 4.05613 5.96220i 0.562484 0.826808i
\(53\) 4.38869 0.602834 0.301417 0.953492i \(-0.402540\pi\)
0.301417 + 0.953492i \(0.402540\pi\)
\(54\) 0.356479 0.285235i 0.0485106 0.0388156i
\(55\) −1.02379 + 9.12743i −0.138048 + 1.23074i
\(56\) 0.662613 + 1.35888i 0.0885454 + 0.181588i
\(57\) −13.7299 −1.81857
\(58\) −0.748313 + 0.598759i −0.0982583 + 0.0786209i
\(59\) −5.47956 −0.713378 −0.356689 0.934223i \(-0.616094\pi\)
−0.356689 + 0.934223i \(0.616094\pi\)
\(60\) −3.00786 + 13.3793i −0.388313 + 1.72726i
\(61\) 10.3154i 1.32076i 0.750933 + 0.660378i \(0.229604\pi\)
−0.750933 + 0.660378i \(0.770396\pi\)
\(62\) −8.13331 10.1648i −1.03293 1.29093i
\(63\) 1.67322i 0.210806i
\(64\) 4.92647 6.30317i 0.615808 0.787896i
\(65\) 3.66876 9.28634i 0.455054 1.15183i
\(66\) −9.82006 + 6.19958i −1.20877 + 0.763116i
\(67\) 2.88040 0.351897 0.175949 0.984399i \(-0.443701\pi\)
0.175949 + 0.984399i \(0.443701\pi\)
\(68\) 11.5253 + 2.59105i 1.39765 + 0.314211i
\(69\) −11.1060 −1.33701
\(70\) 1.30784 + 1.63450i 0.156317 + 0.195360i
\(71\) −3.09875 −0.367754 −0.183877 0.982949i \(-0.558865\pi\)
−0.183877 + 0.982949i \(0.558865\pi\)
\(72\) −7.95834 + 3.88063i −0.937900 + 0.457336i
\(73\) −9.44310 −1.10523 −0.552616 0.833436i \(-0.686370\pi\)
−0.552616 + 0.833436i \(0.686370\pi\)
\(74\) −1.71411 + 1.37154i −0.199261 + 0.159438i
\(75\) 6.60816i 0.763044i
\(76\) 10.8205 + 2.43259i 1.24119 + 0.279037i
\(77\) −0.197607 + 1.76172i −0.0225194 + 0.200767i
\(78\) 12.0664 3.71380i 1.36625 0.420505i
\(79\) 8.42639 0.948043 0.474021 0.880513i \(-0.342802\pi\)
0.474021 + 0.880513i \(0.342802\pi\)
\(80\) 4.74097 10.0113i 0.530056 1.11930i
\(81\) −8.59184 −0.954649
\(82\) −2.21469 2.76786i −0.244572 0.305659i
\(83\) 2.83221i 0.310875i −0.987846 0.155438i \(-0.950321\pi\)
0.987846 0.155438i \(-0.0496788\pi\)
\(84\) −0.580559 + 2.58240i −0.0633442 + 0.281763i
\(85\) 16.3567 1.77414
\(86\) −7.50175 9.37548i −0.808935 1.01098i
\(87\) −1.67789 −0.179889
\(88\) 8.83757 3.14600i 0.942088 0.335365i
\(89\) 6.95222i 0.736933i −0.929641 0.368467i \(-0.879883\pi\)
0.929641 0.368467i \(-0.120117\pi\)
\(90\) −9.57254 + 7.65943i −1.00903 + 0.807374i
\(91\) 0.708123 1.79239i 0.0742314 0.187894i
\(92\) 8.75264 + 1.96771i 0.912526 + 0.205148i
\(93\) 22.7919i 2.36341i
\(94\) 8.92321 + 11.1520i 0.920358 + 1.15024i
\(95\) 15.3564 1.57554
\(96\) 13.6291 3.22792i 1.39102 0.329449i
\(97\) 2.27247i 0.230734i −0.993323 0.115367i \(-0.963196\pi\)
0.993323 0.115367i \(-0.0368045\pi\)
\(98\) −5.93242 7.41418i −0.599265 0.748945i
\(99\) −10.3176 1.15729i −1.03696 0.116312i
\(100\) 1.17080 5.20787i 0.117080 0.520787i
\(101\) 17.2908i 1.72050i 0.509874 + 0.860249i \(0.329692\pi\)
−0.509874 + 0.860249i \(0.670308\pi\)
\(102\) 12.9212 + 16.1486i 1.27939 + 1.59895i
\(103\) 16.1107i 1.58744i −0.608285 0.793718i \(-0.708142\pi\)
0.608285 0.793718i \(-0.291858\pi\)
\(104\) −10.1675 + 0.788973i −0.997003 + 0.0773652i
\(105\) 3.66494i 0.357662i
\(106\) −3.87763 4.84616i −0.376629 0.470701i
\(107\) 2.42591 0.234522 0.117261 0.993101i \(-0.462589\pi\)
0.117261 + 0.993101i \(0.462589\pi\)
\(108\) −0.629934 0.141618i −0.0606154 0.0136272i
\(109\) 3.59775 0.344602 0.172301 0.985044i \(-0.444880\pi\)
0.172301 + 0.985044i \(0.444880\pi\)
\(110\) 10.9834 6.93403i 1.04723 0.661134i
\(111\) −3.84344 −0.364803
\(112\) 0.915073 1.93232i 0.0864663 0.182587i
\(113\) −16.3185 −1.53511 −0.767556 0.640982i \(-0.778527\pi\)
−0.767556 + 0.640982i \(0.778527\pi\)
\(114\) 12.1310 + 15.1610i 1.13618 + 1.41996i
\(115\) 12.4217 1.15833
\(116\) 1.32234 + 0.297281i 0.122776 + 0.0276018i
\(117\) 10.4972 + 4.14715i 0.970471 + 0.383405i
\(118\) 4.84147 + 6.05074i 0.445693 + 0.557015i
\(119\) 3.15708 0.289409
\(120\) 17.4316 8.49993i 1.59128 0.775933i
\(121\) 10.7266 + 2.43701i 0.975150 + 0.221546i
\(122\) 11.3907 9.11420i 1.03126 0.825161i
\(123\) 6.20620i 0.559594i
\(124\) −4.03815 + 17.9622i −0.362637 + 1.61305i
\(125\) 6.45540i 0.577389i
\(126\) −1.84763 + 1.47838i −0.164600 + 0.131704i
\(127\) 13.6785 1.21377 0.606887 0.794788i \(-0.292418\pi\)
0.606887 + 0.794788i \(0.292418\pi\)
\(128\) −11.3130 + 0.129179i −0.999935 + 0.0114179i
\(129\) 21.0221i 1.85089i
\(130\) −13.4959 + 4.15377i −1.18367 + 0.364309i
\(131\) −5.26829 −0.460292 −0.230146 0.973156i \(-0.573920\pi\)
−0.230146 + 0.973156i \(0.573920\pi\)
\(132\) 15.5223 + 5.36603i 1.35105 + 0.467053i
\(133\) 2.96400 0.257012
\(134\) −2.54498 3.18065i −0.219853 0.274766i
\(135\) −0.894002 −0.0769435
\(136\) −7.32206 15.0160i −0.627861 1.28761i
\(137\) 14.4042i 1.23063i 0.788281 + 0.615315i \(0.210971\pi\)
−0.788281 + 0.615315i \(0.789029\pi\)
\(138\) 9.81275 + 12.2637i 0.835316 + 1.04396i
\(139\) −10.9164 −0.925915 −0.462958 0.886380i \(-0.653212\pi\)
−0.462958 + 0.886380i \(0.653212\pi\)
\(140\) 0.649336 2.88833i 0.0548789 0.244108i
\(141\) 25.0054i 2.10583i
\(142\) 2.73790 + 3.42175i 0.229760 + 0.287147i
\(143\) −10.5627 5.60622i −0.883296 0.468816i
\(144\) 11.3167 + 5.35917i 0.943060 + 0.446597i
\(145\) 1.87667 0.155849
\(146\) 8.34345 + 10.4274i 0.690509 + 0.862980i
\(147\) 16.6243i 1.37115i
\(148\) 3.02900 + 0.680961i 0.248982 + 0.0559746i
\(149\) −17.4380 −1.42857 −0.714287 0.699853i \(-0.753249\pi\)
−0.714287 + 0.699853i \(0.753249\pi\)
\(150\) 7.29697 5.83864i 0.595795 0.476723i
\(151\) 11.6811i 0.950595i 0.879825 + 0.475298i \(0.157660\pi\)
−0.879825 + 0.475298i \(0.842340\pi\)
\(152\) −6.87427 14.0977i −0.557577 1.14347i
\(153\) 18.4896i 1.49479i
\(154\) 2.11995 1.33837i 0.170831 0.107849i
\(155\) 25.4920i 2.04756i
\(156\) −14.7622 10.0428i −1.18192 0.804069i
\(157\) −8.98086 −0.716750 −0.358375 0.933578i \(-0.616669\pi\)
−0.358375 + 0.933578i \(0.616669\pi\)
\(158\) −7.44514 9.30473i −0.592303 0.740245i
\(159\) 10.8662i 0.861749i
\(160\) −15.2437 + 3.61033i −1.20512 + 0.285422i
\(161\) 2.39757 0.188955
\(162\) 7.59133 + 9.48743i 0.596431 + 0.745403i
\(163\) 11.2972 0.884862 0.442431 0.896803i \(-0.354116\pi\)
0.442431 + 0.896803i \(0.354116\pi\)
\(164\) −1.09958 + 4.89108i −0.0858630 + 0.381929i
\(165\) 22.5992 + 2.53487i 1.75934 + 0.197340i
\(166\) −3.12743 + 2.50240i −0.242736 + 0.194224i
\(167\) 8.52950i 0.660032i −0.943975 0.330016i \(-0.892946\pi\)
0.943975 0.330016i \(-0.107054\pi\)
\(168\) 3.36453 1.64060i 0.259579 0.126575i
\(169\) 9.48977 + 8.88505i 0.729983 + 0.683466i
\(170\) −14.4520 18.0617i −1.10842 1.38527i
\(171\) 17.3588i 1.32746i
\(172\) −3.72458 + 16.5674i −0.283997 + 1.26325i
\(173\) 13.0482i 0.992033i 0.868313 + 0.496017i \(0.165204\pi\)
−0.868313 + 0.496017i \(0.834796\pi\)
\(174\) 1.48250 + 1.85279i 0.112388 + 0.140460i
\(175\) 1.42657i 0.107838i
\(176\) −11.2824 6.97912i −0.850441 0.526071i
\(177\) 13.5672i 1.01977i
\(178\) −7.67689 + 6.14263i −0.575408 + 0.460410i
\(179\) 7.19411i 0.537713i −0.963180 0.268857i \(-0.913354\pi\)
0.963180 0.268857i \(-0.0866458\pi\)
\(180\) 16.9156 + 3.80287i 1.26082 + 0.283449i
\(181\) 6.78219 0.504116 0.252058 0.967712i \(-0.418893\pi\)
0.252058 + 0.967712i \(0.418893\pi\)
\(182\) −2.60489 + 0.801735i −0.193087 + 0.0594286i
\(183\) 25.5406 1.88802
\(184\) −5.56057 11.4036i −0.409931 0.840682i
\(185\) 4.29876 0.316051
\(186\) −25.1676 + 20.1378i −1.84538 + 1.47657i
\(187\) 2.18361 19.4675i 0.159681 1.42361i
\(188\) 4.43033 19.7067i 0.323115 1.43726i
\(189\) −0.172555 −0.0125515
\(190\) −13.5682 16.9571i −0.984338 1.23020i
\(191\) 2.12348i 0.153650i −0.997045 0.0768248i \(-0.975522\pi\)
0.997045 0.0768248i \(-0.0244782\pi\)
\(192\) −15.6064 12.1977i −1.12629 0.880296i
\(193\) 13.1530 0.946770 0.473385 0.880856i \(-0.343032\pi\)
0.473385 + 0.880856i \(0.343032\pi\)
\(194\) −2.50935 + 2.00784i −0.180161 + 0.144155i
\(195\) −22.9926 9.08372i −1.64654 0.650499i
\(196\) −2.94542 + 13.1016i −0.210387 + 0.935828i
\(197\) 2.47118 0.176064 0.0880321 0.996118i \(-0.471942\pi\)
0.0880321 + 0.996118i \(0.471942\pi\)
\(198\) 7.83820 + 12.4156i 0.557037 + 0.882339i
\(199\) 17.6493i 1.25113i 0.780174 + 0.625563i \(0.215131\pi\)
−0.780174 + 0.625563i \(0.784869\pi\)
\(200\) −6.78518 + 3.30857i −0.479785 + 0.233951i
\(201\) 7.13177i 0.503036i
\(202\) 19.0931 15.2773i 1.34339 1.07491i
\(203\) 0.362224 0.0254231
\(204\) 6.41534 28.5362i 0.449163 1.99794i
\(205\) 6.94143i 0.484810i
\(206\) −17.7901 + 14.2346i −1.23949 + 0.991774i
\(207\) 14.0415i 0.975951i
\(208\) 9.85469 + 10.5302i 0.683300 + 0.730138i
\(209\) 2.05007 18.2770i 0.141806 1.26424i
\(210\) 4.04696 3.23816i 0.279267 0.223454i
\(211\) −25.0448 −1.72416 −0.862078 0.506775i \(-0.830837\pi\)
−0.862078 + 0.506775i \(0.830837\pi\)
\(212\) −1.92523 + 8.56365i −0.132225 + 0.588154i
\(213\) 7.67239i 0.525703i
\(214\) −2.14342 2.67878i −0.146521 0.183118i
\(215\) 23.5125i 1.60354i
\(216\) 0.400199 + 0.820723i 0.0272301 + 0.0558431i
\(217\) 4.92031i 0.334012i
\(218\) −3.17879 3.97276i −0.215295 0.269070i
\(219\) 23.3808i 1.57993i
\(220\) −17.3612 6.00173i −1.17049 0.404637i
\(221\) −7.82495 + 19.8065i −0.526363 + 1.33233i
\(222\) 3.39587 + 4.24406i 0.227916 + 0.284843i
\(223\) 1.33070 0.0891100 0.0445550 0.999007i \(-0.485813\pi\)
0.0445550 + 0.999007i \(0.485813\pi\)
\(224\) −2.94225 + 0.696844i −0.196587 + 0.0465598i
\(225\) 8.35476 0.556984
\(226\) 14.4182 + 18.0195i 0.959083 + 1.19864i
\(227\) 18.9517i 1.25787i 0.777458 + 0.628935i \(0.216509\pi\)
−0.777458 + 0.628935i \(0.783491\pi\)
\(228\) 6.02300 26.7911i 0.398883 1.77428i
\(229\) 11.3147i 0.747697i −0.927490 0.373848i \(-0.878038\pi\)
0.927490 0.373848i \(-0.121962\pi\)
\(230\) −10.9752 13.7166i −0.723686 0.904443i
\(231\) 4.36196 + 0.489266i 0.286996 + 0.0321913i
\(232\) −0.840088 1.72284i −0.0551545 0.113110i
\(233\) 27.0748i 1.77373i −0.462028 0.886865i \(-0.652878\pi\)
0.462028 0.886865i \(-0.347122\pi\)
\(234\) −4.69540 15.2557i −0.306948 0.997294i
\(235\) 27.9677i 1.82441i
\(236\) 2.40377 10.6923i 0.156472 0.696007i
\(237\) 20.8634i 1.35522i
\(238\) −2.78944 3.48616i −0.180812 0.225974i
\(239\) 14.6552i 0.947969i −0.880533 0.473984i \(-0.842815\pi\)
0.880533 0.473984i \(-0.157185\pi\)
\(240\) −24.7876 11.7385i −1.60003 0.757714i
\(241\) −7.37547 −0.475096 −0.237548 0.971376i \(-0.576344\pi\)
−0.237548 + 0.971376i \(0.576344\pi\)
\(242\) −6.78650 13.9980i −0.436253 0.899824i
\(243\) 22.2416i 1.42680i
\(244\) −20.1285 4.52516i −1.28859 0.289694i
\(245\) 18.5938i 1.18791i
\(246\) −6.85311 + 5.48349i −0.436938 + 0.349614i
\(247\) −7.34641 + 18.5952i −0.467441 + 1.18318i
\(248\) 23.4024 11.4114i 1.48606 0.724627i
\(249\) −7.01244 −0.444395
\(250\) 7.12830 5.70367i 0.450833 0.360732i
\(251\) 2.77747i 0.175312i 0.996151 + 0.0876562i \(0.0279377\pi\)
−0.996151 + 0.0876562i \(0.972062\pi\)
\(252\) 3.26496 + 0.734007i 0.205673 + 0.0462381i
\(253\) 1.65829 14.7842i 0.104256 0.929473i
\(254\) −12.0857 15.1043i −0.758322 0.947730i
\(255\) 40.4986i 2.53612i
\(256\) 10.1382 + 12.3781i 0.633639 + 0.773629i
\(257\) 15.1479 0.944903 0.472452 0.881357i \(-0.343369\pi\)
0.472452 + 0.881357i \(0.343369\pi\)
\(258\) −23.2133 + 18.5740i −1.44520 + 1.15637i
\(259\) 0.829720 0.0515563
\(260\) 16.5110 + 11.2326i 1.02397 + 0.696614i
\(261\) 2.12138i 0.131310i
\(262\) 4.65479 + 5.81744i 0.287574 + 0.359402i
\(263\) 3.46372 0.213582 0.106791 0.994281i \(-0.465942\pi\)
0.106791 + 0.994281i \(0.465942\pi\)
\(264\) −7.78938 21.8815i −0.479403 1.34671i
\(265\) 12.1535i 0.746586i
\(266\) −2.61885 3.27296i −0.160572 0.200678i
\(267\) −17.2134 −1.05344
\(268\) −1.26357 + 5.62052i −0.0771849 + 0.343328i
\(269\) 20.6283 1.25773 0.628863 0.777516i \(-0.283520\pi\)
0.628863 + 0.777516i \(0.283520\pi\)
\(270\) 0.789896 + 0.987191i 0.0480715 + 0.0600785i
\(271\) 14.0761i 0.855065i −0.904000 0.427532i \(-0.859383\pi\)
0.904000 0.427532i \(-0.140617\pi\)
\(272\) −10.1118 + 21.3527i −0.613119 + 1.29470i
\(273\) −4.43790 1.75328i −0.268594 0.106114i
\(274\) 15.9056 12.7268i 0.960892 0.768854i
\(275\) −8.79666 0.986692i −0.530459 0.0594998i
\(276\) 4.87198 21.6712i 0.293259 1.30445i
\(277\) 26.1430i 1.57078i 0.619000 + 0.785391i \(0.287538\pi\)
−0.619000 + 0.785391i \(0.712462\pi\)
\(278\) 9.64517 + 12.0543i 0.578479 + 0.722967i
\(279\) −28.8160 −1.72517
\(280\) −3.76312 + 1.83496i −0.224889 + 0.109660i
\(281\) 22.8496 1.36309 0.681545 0.731776i \(-0.261308\pi\)
0.681545 + 0.731776i \(0.261308\pi\)
\(282\) 27.6119 22.0935i 1.64426 1.31565i
\(283\) 13.1440 0.781331 0.390666 0.920533i \(-0.372245\pi\)
0.390666 + 0.920533i \(0.372245\pi\)
\(284\) 1.35936 6.04658i 0.0806629 0.358799i
\(285\) 38.0219i 2.25222i
\(286\) 3.14206 + 16.6171i 0.185794 + 0.982589i
\(287\) 1.33979i 0.0790855i
\(288\) −4.08110 17.2314i −0.240481 1.01537i
\(289\) −17.8866 −1.05215
\(290\) −1.65813 2.07229i −0.0973689 0.121689i
\(291\) −5.62655 −0.329834
\(292\) 4.14249 18.4263i 0.242421 1.07832i
\(293\) −11.1419 −0.650917 −0.325459 0.945556i \(-0.605519\pi\)
−0.325459 + 0.945556i \(0.605519\pi\)
\(294\) −18.3572 + 14.6884i −1.07061 + 0.856647i
\(295\) 15.1745i 0.883491i
\(296\) −1.92433 3.94640i −0.111849 0.229380i
\(297\) −0.119348 + 1.06403i −0.00692530 + 0.0617411i
\(298\) 15.4073 + 19.2556i 0.892521 + 1.11545i
\(299\) −5.94248 + 15.0416i −0.343663 + 0.869876i
\(300\) −12.8945 2.89886i −0.744463 0.167366i
\(301\) 4.53824i 0.261580i
\(302\) 12.8987 10.3208i 0.742238 0.593898i
\(303\) 42.8113 2.45945
\(304\) −9.49342 + 20.0468i −0.544485 + 1.14976i
\(305\) −28.5663 −1.63570
\(306\) 20.4169 16.3365i 1.16716 0.933894i
\(307\) 28.8175i 1.64470i 0.568980 + 0.822351i \(0.307338\pi\)
−0.568980 + 0.822351i \(0.692662\pi\)
\(308\) −3.35096 1.15842i −0.190939 0.0660070i
\(309\) −39.8895 −2.26924
\(310\) 28.1492 22.5234i 1.59877 1.27924i
\(311\) 14.7627i 0.837114i −0.908190 0.418557i \(-0.862536\pi\)
0.908190 0.418557i \(-0.137464\pi\)
\(312\) 1.95347 + 25.1743i 0.110593 + 1.42521i
\(313\) −12.4148 −0.701726 −0.350863 0.936427i \(-0.614112\pi\)
−0.350863 + 0.936427i \(0.614112\pi\)
\(314\) 7.93504 + 9.91699i 0.447800 + 0.559648i
\(315\) 4.63363 0.261075
\(316\) −3.69648 + 16.4424i −0.207943 + 0.924957i
\(317\) 8.15212i 0.457869i 0.973442 + 0.228934i \(0.0735241\pi\)
−0.973442 + 0.228934i \(0.926476\pi\)
\(318\) −11.9989 + 9.60087i −0.672865 + 0.538390i
\(319\) 0.250534 2.23358i 0.0140272 0.125057i
\(320\) 17.4553 + 13.6428i 0.975778 + 0.762654i
\(321\) 6.00647i 0.335248i
\(322\) −2.11837 2.64749i −0.118052 0.147539i
\(323\) −32.7531 −1.82243
\(324\) 3.76906 16.7652i 0.209392 0.931402i
\(325\) 8.94981 + 3.53581i 0.496446 + 0.196131i
\(326\) −9.98161 12.4747i −0.552830 0.690912i
\(327\) 8.90788i 0.492607i
\(328\) 6.37245 3.10732i 0.351860 0.171573i
\(329\) 5.39816i 0.297610i
\(330\) −17.1684 27.1945i −0.945089 1.49701i
\(331\) 10.6108 0.583223 0.291611 0.956537i \(-0.405809\pi\)
0.291611 + 0.956537i \(0.405809\pi\)
\(332\) 5.52648 + 1.24243i 0.303305 + 0.0681871i
\(333\) 4.85930i 0.266288i
\(334\) −9.41859 + 7.53624i −0.515362 + 0.412365i
\(335\) 7.97665i 0.435811i
\(336\) −4.78435 2.26569i −0.261008 0.123603i
\(337\) 9.58696i 0.522235i −0.965307 0.261117i \(-0.915909\pi\)
0.965307 0.261117i \(-0.0840910\pi\)
\(338\) 1.42651 18.3293i 0.0775921 0.996985i
\(339\) 40.4039i 2.19444i
\(340\) −7.17534 + 31.9168i −0.389138 + 1.73093i
\(341\) 30.3401 + 3.40315i 1.64301 + 0.184291i
\(342\) 19.1683 15.3374i 1.03650 0.829352i
\(343\) 7.33043i 0.395806i
\(344\) 21.5852 10.5253i 1.16380 0.567487i
\(345\) 30.7558i 1.65584i
\(346\) 14.4083 11.5287i 0.774593 0.619787i
\(347\) −15.7991 −0.848142 −0.424071 0.905629i \(-0.639399\pi\)
−0.424071 + 0.905629i \(0.639399\pi\)
\(348\) 0.736056 3.27407i 0.0394568 0.175509i
\(349\) −18.7254 −1.00235 −0.501174 0.865346i \(-0.667098\pi\)
−0.501174 + 0.865346i \(0.667098\pi\)
\(350\) −1.57527 + 1.26044i −0.0842017 + 0.0673736i
\(351\) 0.427685 1.08255i 0.0228281 0.0577824i
\(352\) 2.26193 + 18.6248i 0.120562 + 0.992706i
\(353\) 4.16295i 0.221571i 0.993844 + 0.110786i \(0.0353367\pi\)
−0.993844 + 0.110786i \(0.964663\pi\)
\(354\) 14.9814 11.9873i 0.796252 0.637117i
\(355\) 8.58132i 0.455449i
\(356\) 13.5658 + 3.04979i 0.718988 + 0.161638i
\(357\) 7.81680i 0.413709i
\(358\) −7.94401 + 6.35636i −0.419854 + 0.335944i
\(359\) 9.90104i 0.522557i −0.965264 0.261278i \(-0.915856\pi\)
0.965264 0.261278i \(-0.0841440\pi\)
\(360\) −10.7465 22.0389i −0.566393 1.16155i
\(361\) −11.7500 −0.618423
\(362\) −5.99240 7.48914i −0.314954 0.393621i
\(363\) 6.03393 26.5588i 0.316699 1.39397i
\(364\) 3.18686 + 2.16804i 0.167037 + 0.113636i
\(365\) 26.1506i 1.36879i
\(366\) −22.5664 28.2029i −1.17957 1.47419i
\(367\) 4.13130i 0.215652i −0.994170 0.107826i \(-0.965611\pi\)
0.994170 0.107826i \(-0.0343890\pi\)
\(368\) −7.67919 + 16.2158i −0.400305 + 0.845307i
\(369\) −7.84656 −0.408476
\(370\) −3.79817 4.74685i −0.197457 0.246777i
\(371\) 2.34580i 0.121788i
\(372\) 44.4737 + 9.99830i 2.30585 + 0.518388i
\(373\) 34.4449i 1.78349i 0.452538 + 0.891745i \(0.350519\pi\)
−0.452538 + 0.891745i \(0.649481\pi\)
\(374\) −23.4261 + 14.7893i −1.21133 + 0.764737i
\(375\) 15.9833 0.825376
\(376\) −25.6752 + 12.5197i −1.32410 + 0.645654i
\(377\) −0.897787 + 2.27247i −0.0462384 + 0.117038i
\(378\) 0.152461 + 0.190542i 0.00784175 + 0.00980040i
\(379\) −29.3313 −1.50665 −0.753323 0.657651i \(-0.771550\pi\)
−0.753323 + 0.657651i \(0.771550\pi\)
\(380\) −6.73653 + 29.9649i −0.345577 + 1.53717i
\(381\) 33.8675i 1.73509i
\(382\) −2.34482 + 1.87620i −0.119972 + 0.0959948i
\(383\) −23.6902 −1.21051 −0.605255 0.796032i \(-0.706929\pi\)
−0.605255 + 0.796032i \(0.706929\pi\)
\(384\) 0.319842 + 28.0105i 0.0163218 + 1.42940i
\(385\) −4.87871 0.547228i −0.248642 0.0278893i
\(386\) −11.6213 14.5240i −0.591508 0.739251i
\(387\) −26.5784 −1.35106
\(388\) 4.43427 + 0.996884i 0.225116 + 0.0506091i
\(389\) −18.0886 −0.917130 −0.458565 0.888661i \(-0.651636\pi\)
−0.458565 + 0.888661i \(0.651636\pi\)
\(390\) 10.2846 + 33.4152i 0.520779 + 1.69205i
\(391\) −26.4938 −1.33985
\(392\) 17.0697 8.32347i 0.862149 0.420399i
\(393\) 13.0441i 0.657986i
\(394\) −2.18341 2.72877i −0.109999 0.137473i
\(395\) 23.3351i 1.17411i
\(396\) 6.78433 19.6250i 0.340926 0.986196i
\(397\) 27.1183i 1.36103i −0.732735 0.680514i \(-0.761757\pi\)
0.732735 0.680514i \(-0.238243\pi\)
\(398\) 19.4890 15.5940i 0.976896 0.781659i
\(399\) 7.33876i 0.367398i
\(400\) 9.64849 + 4.56916i 0.482425 + 0.228458i
\(401\) 30.7606i 1.53611i 0.640383 + 0.768056i \(0.278776\pi\)
−0.640383 + 0.768056i \(0.721224\pi\)
\(402\) −7.87516 + 6.30128i −0.392777 + 0.314279i
\(403\) −30.8684 12.1952i −1.53766 0.607486i
\(404\) −33.7395 7.58510i −1.67860 0.377373i
\(405\) 23.7932i 1.18230i
\(406\) −0.320043 0.399981i −0.0158835 0.0198507i
\(407\) 0.573880 5.11631i 0.0284462 0.253606i
\(408\) −37.1790 + 18.1291i −1.84064 + 0.897526i
\(409\) 30.4703 1.50666 0.753331 0.657642i \(-0.228446\pi\)
0.753331 + 0.657642i \(0.228446\pi\)
\(410\) 7.66498 6.13310i 0.378546 0.302892i
\(411\) 35.6641 1.75918
\(412\) 31.4368 + 7.06743i 1.54878 + 0.348187i
\(413\) 2.92888i 0.144121i
\(414\) 15.5051 12.4064i 0.762036 0.609739i
\(415\) 7.84318 0.385007
\(416\) 2.92073 20.1859i 0.143201 0.989694i
\(417\) 27.0285i 1.32359i
\(418\) −21.9934 + 13.8849i −1.07573 + 0.679131i
\(419\) 3.97053i 0.193973i 0.995286 + 0.0969866i \(0.0309204\pi\)
−0.995286 + 0.0969866i \(0.969080\pi\)
\(420\) −7.15139 1.60773i −0.348952 0.0784493i
\(421\) 20.6838i 1.00807i 0.863684 + 0.504033i \(0.168151\pi\)
−0.863684 + 0.504033i \(0.831849\pi\)
\(422\) 22.1284 + 27.6554i 1.07719 + 1.34624i
\(423\) 31.6146 1.53715
\(424\) 11.1573 5.44051i 0.541848 0.264214i
\(425\) 15.7640i 0.764665i
\(426\) 8.47213 6.77894i 0.410476 0.328441i
\(427\) −5.51370 −0.266827
\(428\) −1.06420 + 4.73368i −0.0514399 + 0.228811i
\(429\) −13.8808 + 26.1528i −0.670171 + 1.26267i
\(430\) 25.9634 20.7745i 1.25206 1.00183i
\(431\) 28.8707i 1.39065i −0.718693 0.695327i \(-0.755260\pi\)
0.718693 0.695327i \(-0.244740\pi\)
\(432\) 0.552677 1.16706i 0.0265907 0.0561504i
\(433\) 0.958185 0.0460474 0.0230237 0.999735i \(-0.492671\pi\)
0.0230237 + 0.999735i \(0.492671\pi\)
\(434\) 5.43318 4.34734i 0.260801 0.208679i
\(435\) 4.64656i 0.222786i
\(436\) −1.57825 + 7.02027i −0.0755846 + 0.336210i
\(437\) −24.8736 −1.18986
\(438\) 25.8179 20.6581i 1.23363 0.987081i
\(439\) −1.22798 −0.0586083 −0.0293042 0.999571i \(-0.509329\pi\)
−0.0293042 + 0.999571i \(0.509329\pi\)
\(440\) 8.71217 + 24.4737i 0.415336 + 1.16674i
\(441\) −21.0183 −1.00087
\(442\) 28.7848 8.85939i 1.36915 0.421398i
\(443\) 31.4487i 1.49417i 0.664727 + 0.747086i \(0.268548\pi\)
−0.664727 + 0.747086i \(0.731452\pi\)
\(444\) 1.68603 7.49969i 0.0800156 0.355919i
\(445\) 19.2526 0.912663
\(446\) −1.17574 1.46940i −0.0556727 0.0695783i
\(447\) 43.1757i 2.04214i
\(448\) 3.36911 + 2.63325i 0.159175 + 0.124409i
\(449\) 4.36055i 0.205787i 0.994692 + 0.102894i \(0.0328101\pi\)
−0.994692 + 0.102894i \(0.967190\pi\)
\(450\) −7.38185 9.22564i −0.347984 0.434901i
\(451\) 8.26158 + 0.926674i 0.389023 + 0.0436354i
\(452\) 7.15856 31.8422i 0.336710 1.49773i
\(453\) 28.9220 1.35887
\(454\) 20.9272 16.7448i 0.982161 0.785872i
\(455\) 4.96365 + 1.96099i 0.232699 + 0.0919327i
\(456\) −34.9053 + 17.0204i −1.63459 + 0.797055i
\(457\) 30.1840 1.41195 0.705974 0.708237i \(-0.250509\pi\)
0.705974 + 0.708237i \(0.250509\pi\)
\(458\) −12.4941 + 9.99711i −0.583812 + 0.467134i
\(459\) 1.90678 0.0890009
\(460\) −5.44915 + 24.2385i −0.254068 + 1.13013i
\(461\) 32.5822 1.51751 0.758753 0.651378i \(-0.225809\pi\)
0.758753 + 0.651378i \(0.225809\pi\)
\(462\) −3.31374 5.24892i −0.154169 0.244202i
\(463\) 4.03113 0.187343 0.0936713 0.995603i \(-0.470140\pi\)
0.0936713 + 0.995603i \(0.470140\pi\)
\(464\) −1.16017 + 2.44987i −0.0538594 + 0.113733i
\(465\) 63.1171 2.92699
\(466\) −29.8970 + 23.9220i −1.38495 + 1.10816i
\(467\) 3.41015i 0.157803i 0.996882 + 0.0789014i \(0.0251412\pi\)
−0.996882 + 0.0789014i \(0.974859\pi\)
\(468\) −12.6972 + 18.6640i −0.586930 + 0.862743i
\(469\) 1.53961i 0.0710924i
\(470\) −30.8830 + 24.7109i −1.42453 + 1.13983i
\(471\) 22.2363i 1.02459i
\(472\) −13.9306 + 6.79282i −0.641209 + 0.312665i
\(473\) 27.9842 + 3.13889i 1.28671 + 0.144326i
\(474\) −23.0382 + 18.4339i −1.05818 + 0.846696i
\(475\) 14.7999i 0.679067i
\(476\) −1.38494 + 6.16040i −0.0634787 + 0.282361i
\(477\) −13.7383 −0.629034
\(478\) −16.1829 + 12.9486i −0.740187 + 0.592257i
\(479\) 7.23882i 0.330750i −0.986231 0.165375i \(-0.947117\pi\)
0.986231 0.165375i \(-0.0528834\pi\)
\(480\) 8.93904 + 37.7429i 0.408009 + 1.72272i
\(481\) −2.05650 + 5.20539i −0.0937682 + 0.237345i
\(482\) 6.51660 + 8.14427i 0.296823 + 0.370961i
\(483\) 5.93629i 0.270111i
\(484\) −9.46087 + 19.8618i −0.430040 + 0.902810i
\(485\) 6.29311 0.285756
\(486\) 24.5600 19.6515i 1.11406 0.891412i
\(487\) 22.4374 1.01674 0.508368 0.861140i \(-0.330249\pi\)
0.508368 + 0.861140i \(0.330249\pi\)
\(488\) 12.7877 + 26.2248i 0.578871 + 1.18714i
\(489\) 27.9713i 1.26491i
\(490\) 20.5319 16.4285i 0.927539 0.742166i
\(491\) 21.1277 0.953480 0.476740 0.879044i \(-0.341818\pi\)
0.476740 + 0.879044i \(0.341818\pi\)
\(492\) 12.1101 + 2.72252i 0.545967 + 0.122741i
\(493\) −4.00267 −0.180271
\(494\) 27.0244 8.31759i 1.21589 0.374226i
\(495\) 3.20487 28.5724i 0.144048 1.28423i
\(496\) −33.2781 15.7593i −1.49423 0.707612i
\(497\) 1.65631i 0.0742958i
\(498\) 6.19584 + 7.74339i 0.277642 + 0.346990i
\(499\) 8.39062 0.375616 0.187808 0.982206i \(-0.439862\pi\)
0.187808 + 0.982206i \(0.439862\pi\)
\(500\) −12.5964 2.83185i −0.563329 0.126644i
\(501\) −21.1187 −0.943514
\(502\) 3.06699 2.45403i 0.136886 0.109529i
\(503\) −20.0923 −0.895870 −0.447935 0.894066i \(-0.647840\pi\)
−0.447935 + 0.894066i \(0.647840\pi\)
\(504\) −2.07423 4.25382i −0.0923937 0.189480i
\(505\) −47.8831 −2.13077
\(506\) −17.7904 + 11.2314i −0.790880 + 0.499297i
\(507\) 21.9990 23.4963i 0.977012 1.04351i
\(508\) −6.00048 + 26.6909i −0.266228 + 1.18422i
\(509\) 19.2550i 0.853463i −0.904378 0.426732i \(-0.859665\pi\)
0.904378 0.426732i \(-0.140335\pi\)
\(510\) −44.7201 + 35.7826i −1.98024 + 1.58448i
\(511\) 5.04743i 0.223285i
\(512\) 4.71069 22.1316i 0.208185 0.978089i
\(513\) 1.79017 0.0790379
\(514\) −13.3840 16.7269i −0.590342 0.737793i
\(515\) 44.6151 1.96598
\(516\) 41.0203 + 9.22193i 1.80582 + 0.405973i
\(517\) −33.2867 3.73366i −1.46395 0.164206i
\(518\) −0.733100 0.916208i −0.0322105 0.0402559i
\(519\) 32.3067 1.41811
\(520\) −2.18489 28.1566i −0.0958137 1.23475i
\(521\) 37.4309 1.63988 0.819939 0.572451i \(-0.194007\pi\)
0.819939 + 0.572451i \(0.194007\pi\)
\(522\) 2.34251 1.87435i 0.102529 0.0820379i
\(523\) −7.29447 −0.318965 −0.159482 0.987201i \(-0.550983\pi\)
−0.159482 + 0.987201i \(0.550983\pi\)
\(524\) 2.31108 10.2800i 0.100960 0.449084i
\(525\) −3.53213 −0.154155
\(526\) −3.06037 3.82477i −0.133439 0.166768i
\(527\) 54.3708i 2.36843i
\(528\) −17.2800 + 27.9347i −0.752017 + 1.21570i
\(529\) 2.87986 0.125211
\(530\) 13.4204 10.7383i 0.582944 0.466440i
\(531\) 17.1531 0.744383
\(532\) −1.30024 + 5.78365i −0.0563728 + 0.250753i
\(533\) −8.40542 3.32073i −0.364079 0.143837i
\(534\) 15.2089 + 19.0077i 0.658154 + 0.822543i
\(535\) 6.71804i 0.290446i
\(536\) 7.32282 3.57073i 0.316298 0.154232i
\(537\) −17.8124 −0.768660
\(538\) −18.2261 22.7785i −0.785783 0.982050i
\(539\) 22.1300 + 2.48225i 0.953208 + 0.106918i
\(540\) 0.392180 1.74446i 0.0168767 0.0750698i
\(541\) −4.63441 −0.199249 −0.0996243 0.995025i \(-0.531764\pi\)
−0.0996243 + 0.995025i \(0.531764\pi\)
\(542\) −15.5434 + 12.4370i −0.667646 + 0.534214i
\(543\) 16.7924i 0.720632i
\(544\) 32.5127 7.70032i 1.39397 0.330149i
\(545\) 9.96318i 0.426776i
\(546\) 1.98506 + 6.44961i 0.0849529 + 0.276018i
\(547\) 17.5177 0.749002 0.374501 0.927226i \(-0.377814\pi\)
0.374501 + 0.927226i \(0.377814\pi\)
\(548\) −28.1068 6.31879i −1.20066 0.269925i
\(549\) 32.2913i 1.37816i
\(550\) 6.68275 + 10.5854i 0.284953 + 0.451362i
\(551\) −3.75789 −0.160091
\(552\) −28.2348 + 13.7678i −1.20175 + 0.585995i
\(553\) 4.50399i 0.191529i
\(554\) 28.8681 23.0987i 1.22649 0.981369i
\(555\) 10.6436i 0.451794i
\(556\) 4.78878 21.3011i 0.203090 0.903368i
\(557\) 34.5051 1.46203 0.731014 0.682363i \(-0.239048\pi\)
0.731014 + 0.682363i \(0.239048\pi\)
\(558\) 25.4604 + 31.8197i 1.07782 + 1.34704i
\(559\) −28.4714 11.2482i −1.20421 0.475749i
\(560\) 5.35114 + 2.53410i 0.226127 + 0.107085i
\(561\) −48.2008 5.40653i −2.03504 0.228264i
\(562\) −20.1887 25.2313i −0.851610 1.06432i
\(563\) 3.29489 0.138863 0.0694314 0.997587i \(-0.477881\pi\)
0.0694314 + 0.997587i \(0.477881\pi\)
\(564\) −48.7929 10.9693i −2.05455 0.461892i
\(565\) 45.1904i 1.90118i
\(566\) −11.6134 14.5141i −0.488148 0.610074i
\(567\) 4.59243i 0.192864i
\(568\) −7.87792 + 3.84141i −0.330550 + 0.161182i
\(569\) 36.4540i 1.52823i 0.645080 + 0.764115i \(0.276824\pi\)
−0.645080 + 0.764115i \(0.723176\pi\)
\(570\) −41.9852 + 33.5943i −1.75857 + 1.40711i
\(571\) 35.0455 1.46661 0.733305 0.679900i \(-0.237977\pi\)
0.733305 + 0.679900i \(0.237977\pi\)
\(572\) 15.5730 18.1516i 0.651141 0.758957i
\(573\) −5.25765 −0.219642
\(574\) 1.47945 1.18377i 0.0617510 0.0494098i
\(575\) 11.9716i 0.499250i
\(576\) −15.4217 + 19.7313i −0.642572 + 0.822139i
\(577\) 22.6920i 0.944681i −0.881416 0.472340i \(-0.843409\pi\)
0.881416 0.472340i \(-0.156591\pi\)
\(578\) 15.8037 + 19.7510i 0.657347 + 0.821535i
\(579\) 32.5662i 1.35341i
\(580\) −0.823255 + 3.66194i −0.0341838 + 0.152054i
\(581\) 1.51384 0.0628048
\(582\) 4.97134 + 6.21304i 0.206069 + 0.257539i
\(583\) 14.4649 + 1.62248i 0.599077 + 0.0671964i
\(584\) −24.0071 + 11.7063i −0.993421 + 0.484409i
\(585\) −11.4846 + 29.0698i −0.474832 + 1.20189i
\(586\) 9.84443 + 12.3033i 0.406670 + 0.508245i
\(587\) −23.1795 −0.956722 −0.478361 0.878163i \(-0.658769\pi\)
−0.478361 + 0.878163i \(0.658769\pi\)
\(588\) 32.4390 + 7.29274i 1.33776 + 0.300748i
\(589\) 51.0457i 2.10330i
\(590\) −16.7562 + 13.4074i −0.689842 + 0.551974i
\(591\) 6.11855i 0.251683i
\(592\) −2.65751 + 5.61176i −0.109223 + 0.230642i
\(593\) −1.34031 −0.0550399 −0.0275200 0.999621i \(-0.508761\pi\)
−0.0275200 + 0.999621i \(0.508761\pi\)
\(594\) 1.28039 0.808333i 0.0525350 0.0331663i
\(595\) 8.74284i 0.358421i
\(596\) 7.64966 34.0266i 0.313342 1.39379i
\(597\) 43.6990 1.78848
\(598\) 21.8599 6.72807i 0.893919 0.275131i
\(599\) 34.7876i 1.42138i −0.703504 0.710691i \(-0.748382\pi\)
0.703504 0.710691i \(-0.251618\pi\)
\(600\) 8.19189 + 16.7998i 0.334433 + 0.685851i
\(601\) 34.3990i 1.40317i 0.712588 + 0.701583i \(0.247523\pi\)
−0.712588 + 0.701583i \(0.752477\pi\)
\(602\) 5.01129 4.00976i 0.204245 0.163426i
\(603\) −9.01677 −0.367191
\(604\) −22.7933 5.12425i −0.927447 0.208503i
\(605\) −6.74876 + 29.7051i −0.274376 + 1.20768i
\(606\) −37.8260 47.2739i −1.53657 1.92037i
\(607\) 14.0802 0.571498 0.285749 0.958305i \(-0.407758\pi\)
0.285749 + 0.958305i \(0.407758\pi\)
\(608\) 30.5244 7.22940i 1.23793 0.293191i
\(609\) 0.896852i 0.0363423i
\(610\) 25.2398 + 31.5440i 1.02193 + 1.27718i
\(611\) 33.8663 + 13.3796i 1.37008 + 0.541280i
\(612\) −36.0787 8.11098i −1.45839 0.327867i
\(613\) 10.9545 0.442447 0.221224 0.975223i \(-0.428995\pi\)
0.221224 + 0.975223i \(0.428995\pi\)
\(614\) 31.8214 25.4617i 1.28421 1.02755i
\(615\) 17.1867 0.693035
\(616\) 1.68157 + 4.72377i 0.0677524 + 0.190326i
\(617\) 6.00315i 0.241678i 0.992672 + 0.120839i \(0.0385584\pi\)
−0.992672 + 0.120839i \(0.961442\pi\)
\(618\) 35.2444 + 44.0475i 1.41774 + 1.77185i
\(619\) 13.0392 0.524088 0.262044 0.965056i \(-0.415603\pi\)
0.262044 + 0.965056i \(0.415603\pi\)
\(620\) −49.7424 11.1828i −1.99770 0.449111i
\(621\) 1.44806 0.0581087
\(622\) −16.3015 + 13.0436i −0.653630 + 0.522999i
\(623\) 3.71603 0.148880
\(624\) 26.0724 24.3998i 1.04373 0.976775i
\(625\) −31.2215 −1.24886
\(626\) 10.9691 + 13.7089i 0.438413 + 0.547917i
\(627\) −45.2531 5.07589i −1.80723 0.202711i
\(628\) 3.93971 17.5243i 0.157211 0.699297i
\(629\) −9.16864 −0.365578
\(630\) −4.09404 5.11662i −0.163111 0.203851i
\(631\) −19.0168 −0.757046 −0.378523 0.925592i \(-0.623568\pi\)
−0.378523 + 0.925592i \(0.623568\pi\)
\(632\) 21.4223 10.4459i 0.852134 0.415515i
\(633\) 62.0100i 2.46468i
\(634\) 9.00187 7.20281i 0.357510 0.286060i
\(635\) 37.8797i 1.50321i
\(636\) 21.2033 + 4.76678i 0.840764 + 0.189015i
\(637\) −22.5153 8.89515i −0.892090 0.352439i
\(638\) −2.68776 + 1.69683i −0.106410 + 0.0671783i
\(639\) 9.70028 0.383737
\(640\) −0.357732 31.3288i −0.0141406 1.23838i
\(641\) −18.2023 −0.718949 −0.359475 0.933155i \(-0.617044\pi\)
−0.359475 + 0.933155i \(0.617044\pi\)
\(642\) −6.63257 + 5.30702i −0.261767 + 0.209451i
\(643\) 18.4562 0.727840 0.363920 0.931430i \(-0.381438\pi\)
0.363920 + 0.931430i \(0.381438\pi\)
\(644\) −1.05176 + 4.67837i −0.0414453 + 0.184354i
\(645\) 58.2160 2.29225
\(646\) 28.9390 + 36.1672i 1.13859 + 1.42298i
\(647\) 16.4584i 0.647047i 0.946220 + 0.323524i \(0.104868\pi\)
−0.946220 + 0.323524i \(0.895132\pi\)
\(648\) −21.8430 + 10.6510i −0.858072 + 0.418411i
\(649\) −18.0604 2.02577i −0.708933 0.0795186i
\(650\) −4.00324 13.0068i −0.157020 0.510168i
\(651\) 12.1825 0.477469
\(652\) −4.95582 + 22.0441i −0.194085 + 0.863315i
\(653\) −2.39687 −0.0937967 −0.0468983 0.998900i \(-0.514934\pi\)
−0.0468983 + 0.998900i \(0.514934\pi\)
\(654\) −9.83641 + 7.87056i −0.384634 + 0.307763i
\(655\) 14.5894i 0.570054i
\(656\) −9.06159 4.29123i −0.353796 0.167544i
\(657\) 29.5605 1.15327
\(658\) −5.96085 + 4.76954i −0.232378 + 0.185936i
\(659\) −37.1638 −1.44770 −0.723848 0.689959i \(-0.757629\pi\)
−0.723848 + 0.689959i \(0.757629\pi\)
\(660\) −14.8601 + 42.9857i −0.578427 + 1.67322i
\(661\) 47.4011i 1.84369i 0.387562 + 0.921844i \(0.373317\pi\)
−0.387562 + 0.921844i \(0.626683\pi\)
\(662\) −9.37518 11.7168i −0.364377 0.455388i
\(663\) 49.0400 + 19.3743i 1.90456 + 0.752435i
\(664\) −3.51099 7.20029i −0.136253 0.279425i
\(665\) 8.20817i 0.318299i
\(666\) 5.36582 4.29343i 0.207921 0.166367i
\(667\) −3.03974 −0.117699
\(668\) 16.6436 + 3.74171i 0.643960 + 0.144771i
\(669\) 3.29475i 0.127382i
\(670\) 8.80811 7.04777i 0.340287 0.272279i
\(671\) −3.81358 + 33.9992i −0.147222 + 1.31252i
\(672\) 1.72536 + 7.28490i 0.0665572 + 0.281021i
\(673\) 5.26521i 0.202959i −0.994838 0.101479i \(-0.967642\pi\)
0.994838 0.101479i \(-0.0323576\pi\)
\(674\) −10.5863 + 8.47056i −0.407768 + 0.326274i
\(675\) 0.861604i 0.0331632i
\(676\) −21.5003 + 14.6197i −0.826936 + 0.562296i
\(677\) 0.333277i 0.0128089i −0.999979 0.00640444i \(-0.997961\pi\)
0.999979 0.00640444i \(-0.00203861\pi\)
\(678\) 44.6155 35.6989i 1.71345 1.37101i
\(679\) 1.21466 0.0466143
\(680\) 41.5835 20.2768i 1.59466 0.777582i
\(681\) 46.9237 1.79812
\(682\) −23.0491 36.5096i −0.882597 1.39802i
\(683\) −2.49175 −0.0953442 −0.0476721 0.998863i \(-0.515180\pi\)
−0.0476721 + 0.998863i \(0.515180\pi\)
\(684\) −33.8722 7.61495i −1.29514 0.291165i
\(685\) −39.8892 −1.52409
\(686\) 8.09453 6.47680i 0.309051 0.247286i
\(687\) −28.0148 −1.06883
\(688\) −30.6941 14.5355i −1.17020 0.554162i
\(689\) −14.7168 5.81417i −0.560665 0.221502i
\(690\) −33.9617 + 27.1743i −1.29290 + 1.03451i
\(691\) −39.4033 −1.49897 −0.749486 0.662020i \(-0.769699\pi\)
−0.749486 + 0.662020i \(0.769699\pi\)
\(692\) −25.4608 5.72395i −0.967876 0.217592i
\(693\) 0.618584 5.51487i 0.0234981 0.209493i
\(694\) 13.9593 + 17.4460i 0.529889 + 0.662241i
\(695\) 30.2305i 1.14671i
\(696\) −4.26569 + 2.08003i −0.161691 + 0.0788432i
\(697\) 14.8051i 0.560783i
\(698\) 16.5448 + 20.6773i 0.626232 + 0.782647i
\(699\) −67.0362 −2.53554
\(700\) 2.78366 + 0.625805i 0.105212 + 0.0236532i
\(701\) 14.3122i 0.540565i −0.962781 0.270283i \(-0.912883\pi\)
0.962781 0.270283i \(-0.0871171\pi\)
\(702\) −1.57328 + 0.484224i −0.0593795 + 0.0182759i
\(703\) −8.60793 −0.324654
\(704\) 18.5677 18.9537i 0.699796 0.714343i
\(705\) −69.2470 −2.60799
\(706\) 4.59688 3.67817i 0.173006 0.138430i
\(707\) −9.24210 −0.347585
\(708\) −26.4736 5.95163i −0.994939 0.223676i
\(709\) 26.4836i 0.994612i −0.867575 0.497306i \(-0.834323\pi\)
0.867575 0.497306i \(-0.165677\pi\)
\(710\) −9.47581 + 7.58202i −0.355621 + 0.284548i
\(711\) −26.3778 −0.989246
\(712\) −8.61841 17.6745i −0.322989 0.662381i
\(713\) 41.2906i 1.54635i
\(714\) −8.63160 + 6.90654i −0.323030 + 0.258471i
\(715\) 15.5252 29.2511i 0.580610 1.09393i
\(716\) 14.0379 + 3.15590i 0.524619 + 0.117942i
\(717\) −36.2858 −1.35512
\(718\) −10.9331 + 8.74806i −0.408019 + 0.326475i
\(719\) 28.7663i 1.07280i 0.843963 + 0.536401i \(0.180217\pi\)
−0.843963 + 0.536401i \(0.819783\pi\)
\(720\) −14.8411 + 31.3392i −0.553093 + 1.16794i
\(721\) 8.61135 0.320703
\(722\) 10.3817 + 12.9748i 0.386369 + 0.482873i
\(723\) 18.2614i 0.679148i
\(724\) −2.97520 + 13.2341i −0.110572 + 0.491840i
\(725\) 1.80866i 0.0671720i
\(726\) −34.6585 + 16.8031i −1.28630 + 0.623622i
\(727\) 23.8682i 0.885221i 0.896714 + 0.442610i \(0.145948\pi\)
−0.896714 + 0.442610i \(0.854052\pi\)
\(728\) −0.421714 5.43462i −0.0156298 0.201420i
\(729\) 29.2937 1.08495
\(730\) −28.8765 + 23.1054i −1.06877 + 0.855168i
\(731\) 50.1488i 1.85482i
\(732\) −11.2041 + 49.8373i −0.414116 + 1.84204i
\(733\) 0.489259 0.0180712 0.00903560 0.999959i \(-0.497124\pi\)
0.00903560 + 0.999959i \(0.497124\pi\)
\(734\) −4.56193 + 3.65021i −0.168384 + 0.134732i
\(735\) 46.0375 1.69812
\(736\) 24.6910 5.84783i 0.910124 0.215554i
\(737\) 9.49368 + 1.06487i 0.349704 + 0.0392252i
\(738\) 6.93283 + 8.66446i 0.255201 + 0.318943i
\(739\) 4.59628i 0.169077i 0.996420 + 0.0845384i \(0.0269416\pi\)
−0.996420 + 0.0845384i \(0.973058\pi\)
\(740\) −1.88577 + 8.38816i −0.0693224 + 0.308355i
\(741\) 46.0409 + 18.1894i 1.69136 + 0.668206i
\(742\) 2.59032 2.07263i 0.0950937 0.0760888i
\(743\) 38.4847i 1.41187i 0.708278 + 0.705934i \(0.249472\pi\)
−0.708278 + 0.705934i \(0.750528\pi\)
\(744\) −28.2543 57.9435i −1.03585 2.12431i
\(745\) 48.2906i 1.76923i
\(746\) 38.0354 30.4338i 1.39257 1.11426i
\(747\) 8.86590i 0.324386i
\(748\) 37.0290 + 12.8008i 1.35391 + 0.468045i
\(749\) 1.29668i 0.0473795i
\(750\) −14.1221 17.6494i −0.515665 0.644464i
\(751\) 2.60106i 0.0949141i 0.998873 + 0.0474571i \(0.0151117\pi\)
−0.998873 + 0.0474571i \(0.984888\pi\)
\(752\) 36.5101 + 17.2898i 1.33139 + 0.630493i
\(753\) 6.87691 0.250609
\(754\) 3.30259 1.01647i 0.120273 0.0370177i
\(755\) −32.3483 −1.17727
\(756\) 0.0756962 0.336706i 0.00275304 0.0122459i
\(757\) −15.6223 −0.567802 −0.283901 0.958854i \(-0.591629\pi\)
−0.283901 + 0.958854i \(0.591629\pi\)
\(758\) 25.9156 + 32.3887i 0.941299 + 1.17641i
\(759\) −36.6050 4.10586i −1.32868 0.149033i
\(760\) 39.0405 19.0368i 1.41615 0.690537i
\(761\) 16.2114 0.587662 0.293831 0.955857i \(-0.405070\pi\)
0.293831 + 0.955857i \(0.405070\pi\)
\(762\) −37.3978 + 29.9236i −1.35478 + 1.08402i
\(763\) 1.92303i 0.0696184i
\(764\) 4.14354 + 0.931525i 0.149908 + 0.0337014i
\(765\) −51.2029 −1.85124
\(766\) 20.9314 + 26.1595i 0.756284 + 0.945183i
\(767\) 18.3748 + 7.25936i 0.663477 + 0.262120i
\(768\) 30.6476 25.1018i 1.10590 0.905785i
\(769\) 12.0546 0.434700 0.217350 0.976094i \(-0.430259\pi\)
0.217350 + 0.976094i \(0.430259\pi\)
\(770\) 3.70631 + 5.87075i 0.133566 + 0.211567i
\(771\) 37.5057i 1.35074i
\(772\) −5.76992 + 25.6653i −0.207664 + 0.923715i
\(773\) 29.6851i 1.06770i −0.845579 0.533850i \(-0.820745\pi\)
0.845579 0.533850i \(-0.179255\pi\)
\(774\) 23.4834 + 29.3489i 0.844092 + 1.05492i
\(775\) −24.5682 −0.882514
\(776\) −2.81710 5.77728i −0.101128 0.207392i
\(777\) 2.05436i 0.0736996i
\(778\) 15.9822 + 19.9741i 0.572990 + 0.716107i
\(779\) 13.8997i 0.498007i
\(780\) 27.8114 40.8806i 0.995808 1.46376i
\(781\) −10.2133 1.14560i −0.365462 0.0409927i
\(782\) 23.4086 + 29.2555i 0.837091 + 1.04617i
\(783\) 0.218772 0.00781828
\(784\) −24.2730 11.4948i −0.866893 0.410528i
\(785\) 24.8705i 0.887667i
\(786\) 14.4037 11.5251i 0.513765 0.411086i
\(787\) 6.17918i 0.220264i 0.993917 + 0.110132i \(0.0351274\pi\)
−0.993917 + 0.110132i \(0.964873\pi\)
\(788\) −1.08405 + 4.82201i −0.0386178 + 0.171777i
\(789\) 8.57605i 0.305315i
\(790\) 25.7674 20.6177i 0.916764 0.733544i
\(791\) 8.72239i 0.310132i
\(792\) −27.6650 + 9.84820i −0.983033 + 0.349941i
\(793\) 13.6660 34.5911i 0.485292 1.22837i
\(794\) −29.9450 + 23.9604i −1.06271 + 0.850322i
\(795\) 30.0917 1.06724
\(796\) −34.4390 7.74237i −1.22066 0.274421i
\(797\) −10.8368 −0.383861 −0.191930 0.981409i \(-0.561475\pi\)
−0.191930 + 0.981409i \(0.561475\pi\)
\(798\) −8.10373 + 6.48416i −0.286869 + 0.229537i
\(799\) 59.6512i 2.11031i
\(800\) −3.47949 14.6913i −0.123019 0.519416i
\(801\) 21.7631i 0.768962i
\(802\) 33.9670 27.1785i 1.19942 0.959708i
\(803\) −31.1240 3.49108i −1.09834 0.123198i
\(804\) 13.9162 + 3.12855i 0.490787 + 0.110336i
\(805\) 6.63955i 0.234013i
\(806\) 13.8074 + 44.8611i 0.486344 + 1.58016i
\(807\) 51.0748i 1.79792i
\(808\) 21.4348 + 43.9582i 0.754073 + 1.54644i
\(809\) 17.7739i 0.624897i −0.949935 0.312448i \(-0.898851\pi\)
0.949935 0.312448i \(-0.101149\pi\)
\(810\) −26.2734 + 21.0225i −0.923152 + 0.738656i
\(811\) 49.2510i 1.72944i −0.502256 0.864719i \(-0.667497\pi\)
0.502256 0.864719i \(-0.332503\pi\)
\(812\) −0.158900 + 0.706806i −0.00557629 + 0.0248040i
\(813\) −34.8520 −1.22231
\(814\) −6.15667 + 3.88682i −0.215791 + 0.136233i
\(815\) 31.2850i 1.09587i
\(816\) 52.8684 + 25.0365i 1.85076 + 0.876451i
\(817\) 47.0819i 1.64719i
\(818\) −26.9221 33.6465i −0.941308 1.17642i
\(819\) −2.21670 + 5.61088i −0.0774577 + 0.196060i
\(820\) −13.5448 3.04506i −0.473005 0.106338i
\(821\) −30.7585 −1.07348 −0.536739 0.843748i \(-0.680344\pi\)
−0.536739 + 0.843748i \(0.680344\pi\)
\(822\) −31.5110 39.3816i −1.09907 1.37359i
\(823\) 12.7499i 0.444433i −0.974997 0.222217i \(-0.928671\pi\)
0.974997 0.222217i \(-0.0713292\pi\)
\(824\) −19.9719 40.9581i −0.695753 1.42684i
\(825\) −2.44301 + 21.7802i −0.0850547 + 0.758289i
\(826\) −3.23418 + 2.58781i −0.112532 + 0.0900416i
\(827\) 15.8622i 0.551584i −0.961217 0.275792i \(-0.911060\pi\)
0.961217 0.275792i \(-0.0889400\pi\)
\(828\) −27.3991 6.15970i −0.952185 0.214064i
\(829\) 48.1345 1.67178 0.835890 0.548897i \(-0.184952\pi\)
0.835890 + 0.548897i \(0.184952\pi\)
\(830\) −6.92984 8.66073i −0.240538 0.300618i
\(831\) 64.7291 2.24543
\(832\) −24.8706 + 14.6100i −0.862233 + 0.506512i
\(833\) 39.6579i 1.37407i
\(834\) 29.8459 23.8811i 1.03348 0.826934i
\(835\) 23.6206 0.817424
\(836\) 34.7645 + 12.0180i 1.20235 + 0.415651i
\(837\) 2.97172i 0.102718i
\(838\) 4.38441 3.50816i 0.151457 0.121188i
\(839\) −31.6487 −1.09264 −0.546318 0.837578i \(-0.683971\pi\)
−0.546318 + 0.837578i \(0.683971\pi\)
\(840\) 4.54330 + 9.31734i 0.156759 + 0.321479i
\(841\) 28.5408 0.984164
\(842\) 22.8398 18.2752i 0.787112 0.629804i
\(843\) 56.5746i 1.94853i
\(844\) 10.9866 48.8699i 0.378175 1.68217i
\(845\) −24.6052 + 26.2799i −0.846445 + 0.904055i
\(846\) −27.9331 34.9100i −0.960359 1.20023i
\(847\) −1.30260 + 5.73350i −0.0447580 + 0.197006i
\(848\) −15.8657 7.51338i −0.544829 0.258010i
\(849\) 32.5441i 1.11691i
\(850\) 17.4072 13.9283i 0.597061 0.477735i
\(851\) −6.96292 −0.238686
\(852\) −14.9711 3.36571i −0.512902 0.115307i
\(853\) −42.8801 −1.46819 −0.734094 0.679048i \(-0.762393\pi\)
−0.734094 + 0.679048i \(0.762393\pi\)
\(854\) 4.87163 + 6.08844i 0.166704 + 0.208342i
\(855\) −48.0715 −1.64401
\(856\) 6.16738 3.00732i 0.210797 0.102788i
\(857\) 37.0942i 1.26711i 0.773696 + 0.633557i \(0.218406\pi\)
−0.773696 + 0.633557i \(0.781594\pi\)
\(858\) 41.1433 7.77963i 1.40461 0.265592i
\(859\) 53.4127i 1.82242i 0.411944 + 0.911209i \(0.364850\pi\)
−0.411944 + 0.911209i \(0.635150\pi\)
\(860\) −45.8799 10.3144i −1.56449 0.351719i
\(861\) 3.31728 0.113052
\(862\) −31.8801 + 25.5087i −1.08584 + 0.868831i
\(863\) 13.3427 0.454190 0.227095 0.973873i \(-0.427077\pi\)
0.227095 + 0.973873i \(0.427077\pi\)
\(864\) −1.77703 + 0.420873i −0.0604559 + 0.0143184i
\(865\) −36.1340 −1.22859
\(866\) −0.846605 1.05806i −0.0287688 0.0359545i
\(867\) 44.2865i 1.50405i
\(868\) −9.60098 2.15843i −0.325879 0.0732620i
\(869\) 27.7730 + 3.11521i 0.942135 + 0.105676i
\(870\) −5.13091 + 4.10547i −0.173954 + 0.139189i
\(871\) −9.65897 3.81598i −0.327282 0.129299i
\(872\) 9.14651 4.46000i 0.309740 0.151035i
\(873\) 7.11371i 0.240763i
\(874\) 21.9771 + 27.4663i 0.743385 + 0.929062i
\(875\) −3.45048 −0.116648
\(876\) −45.6228 10.2566i −1.54145 0.346540i
\(877\) −7.39316 −0.249649 −0.124825 0.992179i \(-0.539837\pi\)
−0.124825 + 0.992179i \(0.539837\pi\)
\(878\) 1.08498 + 1.35598i 0.0366164 + 0.0457622i
\(879\) 27.5869i 0.930484i
\(880\) 19.3272 31.2441i 0.651518 1.05324i
\(881\) 1.04846 0.0353235 0.0176618 0.999844i \(-0.494378\pi\)
0.0176618 + 0.999844i \(0.494378\pi\)
\(882\) 18.5708 + 23.2092i 0.625310 + 0.781495i
\(883\) 16.7074i 0.562249i 0.959671 + 0.281124i \(0.0907073\pi\)
−0.959671 + 0.281124i \(0.909293\pi\)
\(884\) −35.2156 23.9575i −1.18443 0.805777i
\(885\) −37.5714 −1.26295
\(886\) 34.7268 27.7865i 1.16667 0.933505i
\(887\) 53.5161 1.79690 0.898448 0.439080i \(-0.144696\pi\)
0.898448 + 0.439080i \(0.144696\pi\)
\(888\) −9.77113 + 4.76457i −0.327897 + 0.159888i
\(889\) 7.31131i 0.245214i
\(890\) −17.0107 21.2595i −0.570199 0.712620i
\(891\) −28.3183 3.17637i −0.948700 0.106413i
\(892\) −0.583747 + 2.59658i −0.0195453 + 0.0869400i
\(893\) 56.0032i 1.87407i
\(894\) 47.6762 38.1479i 1.59453 1.27586i
\(895\) 19.9225 0.665937
\(896\) −0.0690473 6.04690i −0.00230671 0.202013i
\(897\) 37.2423 + 14.7134i 1.24349 + 0.491265i
\(898\) 4.81508 3.85276i 0.160681 0.128568i
\(899\) 6.23817i 0.208054i
\(900\) −3.66505 + 16.3026i −0.122168 + 0.543421i
\(901\) 25.9218i 0.863579i
\(902\) −6.27625 9.94150i −0.208976 0.331016i
\(903\) 11.2365 0.373928
\(904\) −41.4863 + 20.2294i −1.37981 + 0.672820i
\(905\) 18.7818i 0.624328i
\(906\) −25.5540 31.9367i −0.848975 1.06103i
\(907\) 20.6013i 0.684054i −0.939690 0.342027i \(-0.888887\pi\)
0.939690 0.342027i \(-0.111113\pi\)
\(908\) −36.9804 8.31371i −1.22724 0.275900i
\(909\) 54.1268i 1.79527i
\(910\) −2.22023 7.21368i −0.0735999 0.239131i
\(911\) 16.0253i 0.530941i 0.964119 + 0.265470i \(0.0855272\pi\)
−0.964119 + 0.265470i \(0.914473\pi\)
\(912\) 49.6352 + 23.5053i 1.64359 + 0.778339i
\(913\) 1.04706 9.33483i 0.0346525 0.308938i
\(914\) −26.6691 33.3303i −0.882135 1.10247i
\(915\) 70.7292i 2.33823i
\(916\) 22.0783 + 4.96352i 0.729489 + 0.163999i
\(917\) 2.81595i 0.0929910i
\(918\) −1.68474 2.10554i −0.0556046 0.0694931i
\(919\) 15.6755 0.517088 0.258544 0.966000i \(-0.416757\pi\)
0.258544 + 0.966000i \(0.416757\pi\)
\(920\) 31.5797 15.3988i 1.04115 0.507683i
\(921\) 71.3511 2.35110
\(922\) −28.7880 35.9785i −0.948084 1.18489i
\(923\) 10.3912 + 4.10525i 0.342029 + 0.135126i
\(924\) −2.86820 + 8.29684i −0.0943568 + 0.272946i
\(925\) 4.14297i 0.136220i
\(926\) −3.56171 4.45132i −0.117045 0.146280i
\(927\) 50.4328i 1.65643i
\(928\) 3.73031 0.883487i 0.122453 0.0290019i
\(929\) 17.5641i 0.576258i 0.957592 + 0.288129i \(0.0930332\pi\)
−0.957592 + 0.288129i \(0.906967\pi\)
\(930\) −55.7671 69.6963i −1.82868 2.28543i
\(931\) 37.2326i 1.22025i
\(932\) 52.8310 + 11.8771i 1.73054 + 0.389049i
\(933\) −36.5518 −1.19665
\(934\) 3.76561 3.01303i 0.123214 0.0985895i
\(935\) 53.9111 + 6.04702i 1.76308 + 0.197759i
\(936\) 31.8281 2.46979i 1.04033 0.0807276i
\(937\) 51.2539i 1.67439i −0.546904 0.837195i \(-0.684194\pi\)
0.546904 0.837195i \(-0.315806\pi\)
\(938\) 1.70009 1.36032i 0.0555099 0.0444160i
\(939\) 30.7386i 1.00312i
\(940\) 54.5733 + 12.2688i 1.77999 + 0.400165i
\(941\) −5.44008 −0.177342 −0.0886708 0.996061i \(-0.528262\pi\)
−0.0886708 + 0.996061i \(0.528262\pi\)
\(942\) 24.5541 19.6468i 0.800016 0.640129i
\(943\) 11.2434i 0.366135i
\(944\) 19.8093 + 9.38092i 0.644737 + 0.305323i
\(945\) 0.477853i 0.0155446i
\(946\) −21.2594 33.6746i −0.691201 1.09485i
\(947\) −21.5672 −0.700841 −0.350420 0.936593i \(-0.613961\pi\)
−0.350420 + 0.936593i \(0.613961\pi\)
\(948\) 40.7107 + 9.15233i 1.32222 + 0.297254i
\(949\) 31.6659 + 12.5103i 1.02792 + 0.406101i
\(950\) 16.3426 13.0765i 0.530224 0.424257i
\(951\) 20.1843 0.654522
\(952\) 8.02620 3.91372i 0.260131 0.126844i
\(953\) 7.87118i 0.254972i 0.991840 + 0.127486i \(0.0406909\pi\)
−0.991840 + 0.127486i \(0.959309\pi\)
\(954\) 12.1385 + 15.1703i 0.392998 + 0.491158i
\(955\) 5.88051 0.190289
\(956\) 28.5967 + 6.42894i 0.924885 + 0.207927i
\(957\) −5.53027 0.620312i −0.178768 0.0200518i
\(958\) −7.99337 + 6.39586i −0.258254 + 0.206641i
\(959\) −7.69917 −0.248619
\(960\) 33.7790 43.2185i 1.09021 1.39487i
\(961\) 53.7368 1.73345
\(962\) 7.56500 2.32836i 0.243906 0.0750694i
\(963\) −7.59405 −0.244715
\(964\) 3.23546 14.3917i 0.104207 0.463527i
\(965\) 36.4242i 1.17254i
\(966\) −6.55508 + 5.24501i −0.210906 + 0.168756i
\(967\) 2.04860i 0.0658785i 0.999457 + 0.0329392i \(0.0104868\pi\)
−0.999457 + 0.0329392i \(0.989513\pi\)
\(968\) 30.2913 7.10187i 0.973600 0.228263i
\(969\) 81.0953i 2.60516i
\(970\) −5.56028 6.94909i −0.178530 0.223122i
\(971\) 24.7936i 0.795663i 0.917458 + 0.397832i \(0.130237\pi\)
−0.917458 + 0.397832i \(0.869763\pi\)
\(972\) −43.3999 9.75689i −1.39205 0.312953i
\(973\) 5.83492i 0.187059i
\(974\) −19.8246 24.7762i −0.635221 0.793881i
\(975\) 8.75453 22.1594i 0.280369 0.709668i
\(976\) 17.6599 37.2915i 0.565278 1.19367i
\(977\) 41.2555i 1.31988i 0.751318 + 0.659940i \(0.229418\pi\)
−0.751318 + 0.659940i \(0.770582\pi\)
\(978\) −30.8870 + 24.7141i −0.987657 + 0.790269i
\(979\) 2.57021 22.9142i 0.0821442 0.732341i
\(980\) −36.2820 8.15669i −1.15899 0.260556i
\(981\) −11.2623 −0.359579
\(982\) −18.6674 23.3300i −0.595700 0.744490i
\(983\) −27.3410 −0.872042 −0.436021 0.899936i \(-0.643613\pi\)
−0.436021 + 0.899936i \(0.643613\pi\)
\(984\) −7.69360 15.7779i −0.245263 0.502982i
\(985\) 6.84340i 0.218049i
\(986\) 3.53656 + 4.41990i 0.112627 + 0.140758i
\(987\) −13.3656 −0.425433
\(988\) −33.0620 22.4923i −1.05184 0.715577i
\(989\) 38.0844i 1.21101i
\(990\) −34.3823 + 21.7062i −1.09274 + 0.689868i
\(991\) 10.0759i 0.320072i 0.987111 + 0.160036i \(0.0511611\pi\)
−0.987111 + 0.160036i \(0.948839\pi\)
\(992\) 12.0010 + 50.6711i 0.381031 + 1.60881i
\(993\) 26.2719i 0.833715i
\(994\) −1.82896 + 1.46344i −0.0580112 + 0.0464174i
\(995\) −48.8759 −1.54947
\(996\) 3.07620 13.6833i 0.0974733 0.433573i
\(997\) 33.7038i 1.06741i −0.845670 0.533706i \(-0.820799\pi\)
0.845670 0.533706i \(-0.179201\pi\)
\(998\) −7.41353 9.26523i −0.234671 0.293286i
\(999\) 0.501126 0.0158549
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.571.18 yes 56
4.3 odd 2 inner 572.2.b.c.571.20 yes 56
11.10 odd 2 inner 572.2.b.c.571.40 yes 56
13.12 even 2 inner 572.2.b.c.571.39 yes 56
44.43 even 2 inner 572.2.b.c.571.38 yes 56
52.51 odd 2 inner 572.2.b.c.571.37 yes 56
143.142 odd 2 inner 572.2.b.c.571.17 56
572.571 even 2 inner 572.2.b.c.571.19 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
572.2.b.c.571.17 56 143.142 odd 2 inner
572.2.b.c.571.18 yes 56 1.1 even 1 trivial
572.2.b.c.571.19 yes 56 572.571 even 2 inner
572.2.b.c.571.20 yes 56 4.3 odd 2 inner
572.2.b.c.571.37 yes 56 52.51 odd 2 inner
572.2.b.c.571.38 yes 56 44.43 even 2 inner
572.2.b.c.571.39 yes 56 13.12 even 2 inner
572.2.b.c.571.40 yes 56 11.10 odd 2 inner