Properties

Label 882.2.l.c.227.19
Level $882$
Weight $2$
Character 882.227
Analytic conductor $7.043$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,2,Mod(227,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([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("882.227");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.l (of order \(6\), degree \(2\), not 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: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 227.19
Character \(\chi\) \(=\) 882.227
Dual form 882.2.l.c.509.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} +(0.765075 + 1.55392i) q^{3} -1.00000 q^{4} +(0.474556 - 0.821956i) q^{5} +(-1.55392 + 0.765075i) q^{6} -1.00000i q^{8} +(-1.82932 + 2.37773i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(0.765075 + 1.55392i) q^{3} -1.00000 q^{4} +(0.474556 - 0.821956i) q^{5} +(-1.55392 + 0.765075i) q^{6} -1.00000i q^{8} +(-1.82932 + 2.37773i) q^{9} +(0.821956 + 0.474556i) q^{10} +(-1.51873 + 0.876838i) q^{11} +(-0.765075 - 1.55392i) q^{12} +(-0.720756 + 0.416129i) q^{13} +(1.64032 + 0.108564i) q^{15} +1.00000 q^{16} +(-2.73638 + 4.73955i) q^{17} +(-2.37773 - 1.82932i) q^{18} +(-3.21232 + 1.85463i) q^{19} +(-0.474556 + 0.821956i) q^{20} +(-0.876838 - 1.51873i) q^{22} +(0.888998 + 0.513263i) q^{23} +(1.55392 - 0.765075i) q^{24} +(2.04959 + 3.55000i) q^{25} +(-0.416129 - 0.720756i) q^{26} +(-5.09436 - 1.02347i) q^{27} +(-6.58867 - 3.80397i) q^{29} +(-0.108564 + 1.64032i) q^{30} +11.0016i q^{31} +1.00000i q^{32} +(-2.52447 - 1.68913i) q^{33} +(-4.73955 - 2.73638i) q^{34} +(1.82932 - 2.37773i) q^{36} +(-2.19830 - 3.80756i) q^{37} +(-1.85463 - 3.21232i) q^{38} +(-1.19806 - 0.801626i) q^{39} +(-0.821956 - 0.474556i) q^{40} +(4.05647 + 7.02601i) q^{41} +(3.08463 - 5.34273i) q^{43} +(1.51873 - 0.876838i) q^{44} +(1.08627 + 2.63199i) q^{45} +(-0.513263 + 0.888998i) q^{46} +6.80125 q^{47} +(0.765075 + 1.55392i) q^{48} +(-3.55000 + 2.04959i) q^{50} +(-9.45841 - 0.625999i) q^{51} +(0.720756 - 0.416129i) q^{52} +(1.88177 + 1.08644i) q^{53} +(1.02347 - 5.09436i) q^{54} +1.66444i q^{55} +(-5.33961 - 3.57275i) q^{57} +(3.80397 - 6.58867i) q^{58} -10.8659 q^{59} +(-1.64032 - 0.108564i) q^{60} +1.09663i q^{61} -11.0016 q^{62} -1.00000 q^{64} +0.789907i q^{65} +(1.68913 - 2.52447i) q^{66} +14.4481 q^{67} +(2.73638 - 4.73955i) q^{68} +(-0.117419 + 1.77412i) q^{69} -11.0131i q^{71} +(2.37773 + 1.82932i) q^{72} +(3.16204 + 1.82561i) q^{73} +(3.80756 - 2.19830i) q^{74} +(-3.94831 + 5.90091i) q^{75} +(3.21232 - 1.85463i) q^{76} +(0.801626 - 1.19806i) q^{78} +9.84819 q^{79} +(0.474556 - 0.821956i) q^{80} +(-2.30717 - 8.69925i) q^{81} +(-7.02601 + 4.05647i) q^{82} +(2.41103 - 4.17603i) q^{83} +(2.59713 + 4.49837i) q^{85} +(5.34273 + 3.08463i) q^{86} +(0.870230 - 13.1486i) q^{87} +(0.876838 + 1.51873i) q^{88} +(-2.15943 - 3.74024i) q^{89} +(-2.63199 + 1.08627i) q^{90} +(-0.888998 - 0.513263i) q^{92} +(-17.0957 + 8.41708i) q^{93} +6.80125i q^{94} +3.52051i q^{95} +(-1.55392 + 0.765075i) q^{96} +(3.90396 + 2.25395i) q^{97} +(0.693358 - 5.21514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0.765075 + 1.55392i 0.441716 + 0.897155i
\(4\) −1.00000 −0.500000
\(5\) 0.474556 0.821956i 0.212228 0.367590i −0.740183 0.672405i \(-0.765261\pi\)
0.952412 + 0.304815i \(0.0985947\pi\)
\(6\) −1.55392 + 0.765075i −0.634384 + 0.312341i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −1.82932 + 2.37773i −0.609773 + 0.792576i
\(10\) 0.821956 + 0.474556i 0.259925 + 0.150068i
\(11\) −1.51873 + 0.876838i −0.457914 + 0.264377i −0.711167 0.703024i \(-0.751833\pi\)
0.253253 + 0.967400i \(0.418500\pi\)
\(12\) −0.765075 1.55392i −0.220858 0.448577i
\(13\) −0.720756 + 0.416129i −0.199902 + 0.115413i −0.596610 0.802532i \(-0.703486\pi\)
0.396708 + 0.917945i \(0.370153\pi\)
\(14\) 0 0
\(15\) 1.64032 + 0.108564i 0.423530 + 0.0280310i
\(16\) 1.00000 0.250000
\(17\) −2.73638 + 4.73955i −0.663670 + 1.14951i 0.315975 + 0.948768i \(0.397669\pi\)
−0.979644 + 0.200742i \(0.935665\pi\)
\(18\) −2.37773 1.82932i −0.560436 0.431175i
\(19\) −3.21232 + 1.85463i −0.736957 + 0.425482i −0.820962 0.570983i \(-0.806562\pi\)
0.0840051 + 0.996465i \(0.473229\pi\)
\(20\) −0.474556 + 0.821956i −0.106114 + 0.183795i
\(21\) 0 0
\(22\) −0.876838 1.51873i −0.186942 0.323794i
\(23\) 0.888998 + 0.513263i 0.185369 + 0.107023i 0.589813 0.807540i \(-0.299202\pi\)
−0.404444 + 0.914563i \(0.632535\pi\)
\(24\) 1.55392 0.765075i 0.317192 0.156170i
\(25\) 2.04959 + 3.55000i 0.409918 + 0.710000i
\(26\) −0.416129 0.720756i −0.0816096 0.141352i
\(27\) −5.09436 1.02347i −0.980410 0.196968i
\(28\) 0 0
\(29\) −6.58867 3.80397i −1.22348 0.706379i −0.257826 0.966191i \(-0.583006\pi\)
−0.965659 + 0.259812i \(0.916339\pi\)
\(30\) −0.108564 + 1.64032i −0.0198209 + 0.299481i
\(31\) 11.0016i 1.97595i 0.154602 + 0.987977i \(0.450591\pi\)
−0.154602 + 0.987977i \(0.549409\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −2.52447 1.68913i −0.439455 0.294040i
\(34\) −4.73955 2.73638i −0.812826 0.469285i
\(35\) 0 0
\(36\) 1.82932 2.37773i 0.304887 0.396288i
\(37\) −2.19830 3.80756i −0.361398 0.625959i 0.626794 0.779185i \(-0.284367\pi\)
−0.988191 + 0.153226i \(0.951034\pi\)
\(38\) −1.85463 3.21232i −0.300861 0.521107i
\(39\) −1.19806 0.801626i −0.191844 0.128363i
\(40\) −0.821956 0.474556i −0.129963 0.0750340i
\(41\) 4.05647 + 7.02601i 0.633514 + 1.09728i 0.986828 + 0.161774i \(0.0517216\pi\)
−0.353314 + 0.935505i \(0.614945\pi\)
\(42\) 0 0
\(43\) 3.08463 5.34273i 0.470401 0.814759i −0.529026 0.848606i \(-0.677443\pi\)
0.999427 + 0.0338470i \(0.0107759\pi\)
\(44\) 1.51873 0.876838i 0.228957 0.132188i
\(45\) 1.08627 + 2.63199i 0.161932 + 0.392353i
\(46\) −0.513263 + 0.888998i −0.0756766 + 0.131076i
\(47\) 6.80125 0.992064 0.496032 0.868304i \(-0.334790\pi\)
0.496032 + 0.868304i \(0.334790\pi\)
\(48\) 0.765075 + 1.55392i 0.110429 + 0.224289i
\(49\) 0 0
\(50\) −3.55000 + 2.04959i −0.502046 + 0.289856i
\(51\) −9.45841 0.625999i −1.32444 0.0876573i
\(52\) 0.720756 0.416129i 0.0999509 0.0577067i
\(53\) 1.88177 + 1.08644i 0.258480 + 0.149234i 0.623641 0.781711i \(-0.285653\pi\)
−0.365161 + 0.930944i \(0.618986\pi\)
\(54\) 1.02347 5.09436i 0.139277 0.693255i
\(55\) 1.66444i 0.224433i
\(56\) 0 0
\(57\) −5.33961 3.57275i −0.707249 0.473222i
\(58\) 3.80397 6.58867i 0.499486 0.865134i
\(59\) −10.8659 −1.41462 −0.707311 0.706902i \(-0.750092\pi\)
−0.707311 + 0.706902i \(0.750092\pi\)
\(60\) −1.64032 0.108564i −0.211765 0.0140155i
\(61\) 1.09663i 0.140409i 0.997533 + 0.0702043i \(0.0223651\pi\)
−0.997533 + 0.0702043i \(0.977635\pi\)
\(62\) −11.0016 −1.39721
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.789907i 0.0979759i
\(66\) 1.68913 2.52447i 0.207918 0.310741i
\(67\) 14.4481 1.76512 0.882559 0.470202i \(-0.155819\pi\)
0.882559 + 0.470202i \(0.155819\pi\)
\(68\) 2.73638 4.73955i 0.331835 0.574755i
\(69\) −0.117419 + 1.77412i −0.0141355 + 0.213578i
\(70\) 0 0
\(71\) 11.0131i 1.30701i −0.756922 0.653505i \(-0.773298\pi\)
0.756922 0.653505i \(-0.226702\pi\)
\(72\) 2.37773 + 1.82932i 0.280218 + 0.215587i
\(73\) 3.16204 + 1.82561i 0.370089 + 0.213671i 0.673497 0.739190i \(-0.264791\pi\)
−0.303408 + 0.952861i \(0.598125\pi\)
\(74\) 3.80756 2.19830i 0.442620 0.255547i
\(75\) −3.94831 + 5.90091i −0.455912 + 0.681379i
\(76\) 3.21232 1.85463i 0.368478 0.212741i
\(77\) 0 0
\(78\) 0.801626 1.19806i 0.0907663 0.135654i
\(79\) 9.84819 1.10801 0.554004 0.832514i \(-0.313099\pi\)
0.554004 + 0.832514i \(0.313099\pi\)
\(80\) 0.474556 0.821956i 0.0530570 0.0918975i
\(81\) −2.30717 8.69925i −0.256353 0.966583i
\(82\) −7.02601 + 4.05647i −0.775893 + 0.447962i
\(83\) 2.41103 4.17603i 0.264645 0.458379i −0.702825 0.711363i \(-0.748078\pi\)
0.967471 + 0.252983i \(0.0814117\pi\)
\(84\) 0 0
\(85\) 2.59713 + 4.49837i 0.281699 + 0.487916i
\(86\) 5.34273 + 3.08463i 0.576121 + 0.332624i
\(87\) 0.870230 13.1486i 0.0932984 1.40967i
\(88\) 0.876838 + 1.51873i 0.0934712 + 0.161897i
\(89\) −2.15943 3.74024i −0.228899 0.396465i 0.728583 0.684957i \(-0.240179\pi\)
−0.957482 + 0.288493i \(0.906846\pi\)
\(90\) −2.63199 + 1.08627i −0.277436 + 0.114503i
\(91\) 0 0
\(92\) −0.888998 0.513263i −0.0926845 0.0535114i
\(93\) −17.0957 + 8.41708i −1.77274 + 0.872811i
\(94\) 6.80125i 0.701495i
\(95\) 3.52051i 0.361197i
\(96\) −1.55392 + 0.765075i −0.158596 + 0.0780851i
\(97\) 3.90396 + 2.25395i 0.396387 + 0.228854i 0.684924 0.728615i \(-0.259836\pi\)
−0.288537 + 0.957469i \(0.593169\pi\)
\(98\) 0 0
\(99\) 0.693358 5.21514i 0.0696851 0.524141i
\(100\) −2.04959 3.55000i −0.204959 0.355000i
\(101\) −6.33624 10.9747i −0.630480 1.09202i −0.987454 0.157909i \(-0.949525\pi\)
0.356974 0.934114i \(-0.383808\pi\)
\(102\) 0.625999 9.45841i 0.0619831 0.936522i
\(103\) 7.33341 + 4.23394i 0.722582 + 0.417183i 0.815702 0.578472i \(-0.196351\pi\)
−0.0931202 + 0.995655i \(0.529684\pi\)
\(104\) 0.416129 + 0.720756i 0.0408048 + 0.0706760i
\(105\) 0 0
\(106\) −1.08644 + 1.88177i −0.105524 + 0.182773i
\(107\) −1.28657 + 0.742804i −0.124378 + 0.0718096i −0.560898 0.827885i \(-0.689544\pi\)
0.436520 + 0.899694i \(0.356211\pi\)
\(108\) 5.09436 + 1.02347i 0.490205 + 0.0984838i
\(109\) 7.60276 13.1684i 0.728213 1.26130i −0.229425 0.973326i \(-0.573685\pi\)
0.957638 0.287975i \(-0.0929820\pi\)
\(110\) −1.66444 −0.158698
\(111\) 4.23477 6.32904i 0.401947 0.600726i
\(112\) 0 0
\(113\) −17.0031 + 9.81676i −1.59952 + 0.923483i −0.607941 + 0.793982i \(0.708004\pi\)
−0.991579 + 0.129501i \(0.958662\pi\)
\(114\) 3.57275 5.33961i 0.334618 0.500101i
\(115\) 0.843760 0.487145i 0.0786810 0.0454265i
\(116\) 6.58867 + 3.80397i 0.611742 + 0.353190i
\(117\) 0.329053 2.47500i 0.0304210 0.228813i
\(118\) 10.8659i 1.00029i
\(119\) 0 0
\(120\) 0.108564 1.64032i 0.00991047 0.149740i
\(121\) −3.96231 + 6.86292i −0.360210 + 0.623902i
\(122\) −1.09663 −0.0992838
\(123\) −7.81434 + 11.6788i −0.704595 + 1.05305i
\(124\) 11.0016i 0.987977i
\(125\) 8.63615 0.772441
\(126\) 0 0
\(127\) 18.7051 1.65981 0.829903 0.557907i \(-0.188395\pi\)
0.829903 + 0.557907i \(0.188395\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 10.6621 + 0.705666i 0.938748 + 0.0621305i
\(130\) −0.789907 −0.0692794
\(131\) −3.32193 + 5.75375i −0.290238 + 0.502707i −0.973866 0.227124i \(-0.927068\pi\)
0.683628 + 0.729831i \(0.260401\pi\)
\(132\) 2.52447 + 1.68913i 0.219727 + 0.147020i
\(133\) 0 0
\(134\) 14.4481i 1.24813i
\(135\) −3.25881 + 3.70164i −0.280474 + 0.318587i
\(136\) 4.73955 + 2.73638i 0.406413 + 0.234643i
\(137\) −17.6798 + 10.2074i −1.51049 + 0.872080i −0.510562 + 0.859841i \(0.670563\pi\)
−0.999925 + 0.0122395i \(0.996104\pi\)
\(138\) −1.77412 0.117419i −0.151023 0.00999534i
\(139\) 10.9829 6.34099i 0.931559 0.537836i 0.0442550 0.999020i \(-0.485909\pi\)
0.887304 + 0.461184i \(0.152575\pi\)
\(140\) 0 0
\(141\) 5.20346 + 10.5686i 0.438211 + 0.890035i
\(142\) 11.0131 0.924196
\(143\) 0.729755 1.26397i 0.0610252 0.105699i
\(144\) −1.82932 + 2.37773i −0.152443 + 0.198144i
\(145\) −6.25339 + 3.61040i −0.519316 + 0.299827i
\(146\) −1.82561 + 3.16204i −0.151088 + 0.261693i
\(147\) 0 0
\(148\) 2.19830 + 3.80756i 0.180699 + 0.312979i
\(149\) 17.1827 + 9.92046i 1.40767 + 0.812716i 0.995163 0.0982404i \(-0.0313214\pi\)
0.412503 + 0.910956i \(0.364655\pi\)
\(150\) −5.90091 3.94831i −0.481807 0.322378i
\(151\) −0.872422 1.51108i −0.0709967 0.122970i 0.828342 0.560223i \(-0.189285\pi\)
−0.899338 + 0.437253i \(0.855951\pi\)
\(152\) 1.85463 + 3.21232i 0.150431 + 0.260553i
\(153\) −6.26364 15.1765i −0.506385 1.22695i
\(154\) 0 0
\(155\) 9.04287 + 5.22090i 0.726341 + 0.419353i
\(156\) 1.19806 + 0.801626i 0.0959218 + 0.0641815i
\(157\) 9.49564i 0.757835i 0.925431 + 0.378917i \(0.123704\pi\)
−0.925431 + 0.378917i \(0.876296\pi\)
\(158\) 9.84819i 0.783480i
\(159\) −0.248543 + 3.75532i −0.0197108 + 0.297816i
\(160\) 0.821956 + 0.474556i 0.0649813 + 0.0375170i
\(161\) 0 0
\(162\) 8.69925 2.30717i 0.683478 0.181269i
\(163\) −5.92061 10.2548i −0.463738 0.803217i 0.535406 0.844595i \(-0.320159\pi\)
−0.999144 + 0.0413777i \(0.986825\pi\)
\(164\) −4.05647 7.02601i −0.316757 0.548639i
\(165\) −2.58640 + 1.27342i −0.201351 + 0.0991355i
\(166\) 4.17603 + 2.41103i 0.324123 + 0.187133i
\(167\) 1.73229 + 3.00041i 0.134048 + 0.232179i 0.925234 0.379398i \(-0.123869\pi\)
−0.791185 + 0.611577i \(0.790536\pi\)
\(168\) 0 0
\(169\) −6.15367 + 10.6585i −0.473359 + 0.819883i
\(170\) −4.49837 + 2.59713i −0.345009 + 0.199191i
\(171\) 1.46655 11.0307i 0.112150 0.843542i
\(172\) −3.08463 + 5.34273i −0.235201 + 0.407379i
\(173\) 3.09982 0.235675 0.117838 0.993033i \(-0.462404\pi\)
0.117838 + 0.993033i \(0.462404\pi\)
\(174\) 13.1486 + 0.870230i 0.996790 + 0.0659719i
\(175\) 0 0
\(176\) −1.51873 + 0.876838i −0.114478 + 0.0660941i
\(177\) −8.31325 16.8848i −0.624862 1.26914i
\(178\) 3.74024 2.15943i 0.280343 0.161856i
\(179\) 0.500470 + 0.288947i 0.0374069 + 0.0215969i 0.518587 0.855025i \(-0.326458\pi\)
−0.481180 + 0.876622i \(0.659792\pi\)
\(180\) −1.08627 2.63199i −0.0809659 0.196177i
\(181\) 26.0581i 1.93688i 0.249238 + 0.968442i \(0.419820\pi\)
−0.249238 + 0.968442i \(0.580180\pi\)
\(182\) 0 0
\(183\) −1.70407 + 0.839001i −0.125968 + 0.0620207i
\(184\) 0.513263 0.888998i 0.0378383 0.0655378i
\(185\) −4.17286 −0.306795
\(186\) −8.41708 17.0957i −0.617171 1.25351i
\(187\) 9.59745i 0.701835i
\(188\) −6.80125 −0.496032
\(189\) 0 0
\(190\) −3.52051 −0.255405
\(191\) 1.77964i 0.128770i 0.997925 + 0.0643852i \(0.0205086\pi\)
−0.997925 + 0.0643852i \(0.979491\pi\)
\(192\) −0.765075 1.55392i −0.0552145 0.112144i
\(193\) −1.48335 −0.106774 −0.0533871 0.998574i \(-0.517002\pi\)
−0.0533871 + 0.998574i \(0.517002\pi\)
\(194\) −2.25395 + 3.90396i −0.161824 + 0.280288i
\(195\) −1.22745 + 0.604338i −0.0878995 + 0.0432775i
\(196\) 0 0
\(197\) 2.44809i 0.174419i 0.996190 + 0.0872096i \(0.0277950\pi\)
−0.996190 + 0.0872096i \(0.972205\pi\)
\(198\) 5.21514 + 0.693358i 0.370624 + 0.0492748i
\(199\) −9.47403 5.46984i −0.671596 0.387746i 0.125085 0.992146i \(-0.460080\pi\)
−0.796681 + 0.604400i \(0.793413\pi\)
\(200\) 3.55000 2.04959i 0.251023 0.144928i
\(201\) 11.0539 + 22.4512i 0.779681 + 1.58358i
\(202\) 10.9747 6.33624i 0.772177 0.445816i
\(203\) 0 0
\(204\) 9.45841 + 0.625999i 0.662221 + 0.0438287i
\(205\) 7.70010 0.537798
\(206\) −4.23394 + 7.33341i −0.294993 + 0.510943i
\(207\) −2.84666 + 1.17487i −0.197857 + 0.0816593i
\(208\) −0.720756 + 0.416129i −0.0499755 + 0.0288534i
\(209\) 3.25243 5.63337i 0.224975 0.389668i
\(210\) 0 0
\(211\) 12.7481 + 22.0804i 0.877617 + 1.52008i 0.853949 + 0.520357i \(0.174201\pi\)
0.0236678 + 0.999720i \(0.492466\pi\)
\(212\) −1.88177 1.08644i −0.129240 0.0746169i
\(213\) 17.1134 8.42582i 1.17259 0.577328i
\(214\) −0.742804 1.28657i −0.0507770 0.0879484i
\(215\) −2.92766 5.07085i −0.199665 0.345829i
\(216\) −1.02347 + 5.09436i −0.0696386 + 0.346627i
\(217\) 0 0
\(218\) 13.1684 + 7.60276i 0.891875 + 0.514924i
\(219\) −0.417642 + 6.31028i −0.0282216 + 0.426409i
\(220\) 1.66444i 0.112216i
\(221\) 4.55475i 0.306385i
\(222\) 6.32904 + 4.23477i 0.424777 + 0.284219i
\(223\) −13.3108 7.68501i −0.891359 0.514626i −0.0169720 0.999856i \(-0.505403\pi\)
−0.874387 + 0.485230i \(0.838736\pi\)
\(224\) 0 0
\(225\) −12.1903 1.62071i −0.812686 0.108047i
\(226\) −9.81676 17.0031i −0.653001 1.13103i
\(227\) −4.17388 7.22937i −0.277030 0.479830i 0.693615 0.720346i \(-0.256017\pi\)
−0.970645 + 0.240515i \(0.922684\pi\)
\(228\) 5.33961 + 3.57275i 0.353625 + 0.236611i
\(229\) 11.3671 + 6.56281i 0.751161 + 0.433683i 0.826113 0.563504i \(-0.190547\pi\)
−0.0749523 + 0.997187i \(0.523880\pi\)
\(230\) 0.487145 + 0.843760i 0.0321214 + 0.0556359i
\(231\) 0 0
\(232\) −3.80397 + 6.58867i −0.249743 + 0.432567i
\(233\) 9.84350 5.68315i 0.644869 0.372315i −0.141619 0.989921i \(-0.545231\pi\)
0.786488 + 0.617606i \(0.211897\pi\)
\(234\) 2.47500 + 0.329053i 0.161796 + 0.0215109i
\(235\) 3.22758 5.59033i 0.210544 0.364673i
\(236\) 10.8659 0.707311
\(237\) 7.53460 + 15.3033i 0.489425 + 0.994054i
\(238\) 0 0
\(239\) 4.67039 2.69645i 0.302102 0.174419i −0.341285 0.939960i \(-0.610862\pi\)
0.643387 + 0.765541i \(0.277529\pi\)
\(240\) 1.64032 + 0.108564i 0.105882 + 0.00700776i
\(241\) 12.1233 6.99936i 0.780928 0.450869i −0.0558314 0.998440i \(-0.517781\pi\)
0.836759 + 0.547572i \(0.184448\pi\)
\(242\) −6.86292 3.96231i −0.441165 0.254707i
\(243\) 11.7528 10.2407i 0.753940 0.656944i
\(244\) 1.09663i 0.0702043i
\(245\) 0 0
\(246\) −11.6788 7.81434i −0.744616 0.498224i
\(247\) 1.54353 2.67348i 0.0982127 0.170109i
\(248\) 11.0016 0.698605
\(249\) 8.33384 + 0.551570i 0.528135 + 0.0349543i
\(250\) 8.63615i 0.546198i
\(251\) 16.5094 1.04207 0.521033 0.853536i \(-0.325547\pi\)
0.521033 + 0.853536i \(0.325547\pi\)
\(252\) 0 0
\(253\) −1.80019 −0.113177
\(254\) 18.7051i 1.17366i
\(255\) −5.00309 + 7.47732i −0.313306 + 0.468248i
\(256\) 1.00000 0.0625000
\(257\) −3.06000 + 5.30007i −0.190878 + 0.330610i −0.945541 0.325502i \(-0.894467\pi\)
0.754664 + 0.656112i \(0.227800\pi\)
\(258\) −0.705666 + 10.6621i −0.0439329 + 0.663795i
\(259\) 0 0
\(260\) 0.789907i 0.0489879i
\(261\) 21.0976 8.70738i 1.30591 0.538973i
\(262\) −5.75375 3.32193i −0.355468 0.205229i
\(263\) −14.1668 + 8.17923i −0.873565 + 0.504353i −0.868531 0.495634i \(-0.834936\pi\)
−0.00503369 + 0.999987i \(0.501602\pi\)
\(264\) −1.68913 + 2.52447i −0.103959 + 0.155371i
\(265\) 1.78601 1.03115i 0.109714 0.0633432i
\(266\) 0 0
\(267\) 4.15990 6.21714i 0.254582 0.380483i
\(268\) −14.4481 −0.882559
\(269\) −2.65845 + 4.60457i −0.162088 + 0.280745i −0.935617 0.353015i \(-0.885156\pi\)
0.773529 + 0.633761i \(0.218490\pi\)
\(270\) −3.70164 3.25881i −0.225275 0.198325i
\(271\) 14.2825 8.24602i 0.867601 0.500910i 0.00105086 0.999999i \(-0.499666\pi\)
0.866550 + 0.499090i \(0.166332\pi\)
\(272\) −2.73638 + 4.73955i −0.165917 + 0.287377i
\(273\) 0 0
\(274\) −10.2074 17.6798i −0.616654 1.06808i
\(275\) −6.22554 3.59432i −0.375414 0.216746i
\(276\) 0.117419 1.77412i 0.00706777 0.106789i
\(277\) −7.31402 12.6682i −0.439457 0.761161i 0.558191 0.829713i \(-0.311496\pi\)
−0.997648 + 0.0685513i \(0.978162\pi\)
\(278\) 6.34099 + 10.9829i 0.380308 + 0.658712i
\(279\) −26.1589 20.1255i −1.56609 1.20488i
\(280\) 0 0
\(281\) 3.62307 + 2.09178i 0.216134 + 0.124785i 0.604159 0.796864i \(-0.293509\pi\)
−0.388025 + 0.921649i \(0.626842\pi\)
\(282\) −10.5686 + 5.20346i −0.629350 + 0.309862i
\(283\) 9.70591i 0.576957i 0.957486 + 0.288478i \(0.0931493\pi\)
−0.957486 + 0.288478i \(0.906851\pi\)
\(284\) 11.0131i 0.653505i
\(285\) −5.47059 + 2.69346i −0.324050 + 0.159547i
\(286\) 1.26397 + 0.729755i 0.0747403 + 0.0431513i
\(287\) 0 0
\(288\) −2.37773 1.82932i −0.140109 0.107794i
\(289\) −6.47555 11.2160i −0.380915 0.659764i
\(290\) −3.61040 6.25339i −0.212010 0.367212i
\(291\) −0.515633 + 7.79087i −0.0302270 + 0.456709i
\(292\) −3.16204 1.82561i −0.185045 0.106836i
\(293\) 1.01377 + 1.75591i 0.0592253 + 0.102581i 0.894118 0.447832i \(-0.147804\pi\)
−0.834893 + 0.550413i \(0.814470\pi\)
\(294\) 0 0
\(295\) −5.15650 + 8.93131i −0.300223 + 0.520001i
\(296\) −3.80756 + 2.19830i −0.221310 + 0.127773i
\(297\) 8.63437 2.91255i 0.501017 0.169003i
\(298\) −9.92046 + 17.1827i −0.574677 + 0.995370i
\(299\) −0.854335 −0.0494075
\(300\) 3.94831 5.90091i 0.227956 0.340689i
\(301\) 0 0
\(302\) 1.51108 0.872422i 0.0869528 0.0502022i
\(303\) 12.2061 18.2425i 0.701220 1.04800i
\(304\) −3.21232 + 1.85463i −0.184239 + 0.106371i
\(305\) 0.901378 + 0.520411i 0.0516128 + 0.0297986i
\(306\) 15.1765 6.26364i 0.867584 0.358068i
\(307\) 9.79004i 0.558747i 0.960183 + 0.279374i \(0.0901268\pi\)
−0.960183 + 0.279374i \(0.909873\pi\)
\(308\) 0 0
\(309\) −0.968595 + 14.6348i −0.0551014 + 0.832545i
\(310\) −5.22090 + 9.04287i −0.296527 + 0.513600i
\(311\) 13.7039 0.777076 0.388538 0.921433i \(-0.372980\pi\)
0.388538 + 0.921433i \(0.372980\pi\)
\(312\) −0.801626 + 1.19806i −0.0453832 + 0.0678270i
\(313\) 18.8585i 1.06595i −0.846132 0.532974i \(-0.821074\pi\)
0.846132 0.532974i \(-0.178926\pi\)
\(314\) −9.49564 −0.535870
\(315\) 0 0
\(316\) −9.84819 −0.554004
\(317\) 7.86426i 0.441701i −0.975308 0.220850i \(-0.929117\pi\)
0.975308 0.220850i \(-0.0708832\pi\)
\(318\) −3.75532 0.248543i −0.210588 0.0139376i
\(319\) 13.3419 0.747000
\(320\) −0.474556 + 0.821956i −0.0265285 + 0.0459487i
\(321\) −2.13858 1.43093i −0.119364 0.0798667i
\(322\) 0 0
\(323\) 20.2999i 1.12952i
\(324\) 2.30717 + 8.69925i 0.128176 + 0.483292i
\(325\) −2.95451 1.70579i −0.163887 0.0946202i
\(326\) 10.2548 5.92061i 0.567960 0.327912i
\(327\) 26.2792 + 1.73928i 1.45325 + 0.0961821i
\(328\) 7.02601 4.05647i 0.387947 0.223981i
\(329\) 0 0
\(330\) −1.27342 2.58640i −0.0700994 0.142376i
\(331\) 22.7350 1.24963 0.624813 0.780774i \(-0.285175\pi\)
0.624813 + 0.780774i \(0.285175\pi\)
\(332\) −2.41103 + 4.17603i −0.132323 + 0.229190i
\(333\) 13.0747 + 1.73830i 0.716490 + 0.0952582i
\(334\) −3.00041 + 1.73229i −0.164175 + 0.0947866i
\(335\) 6.85644 11.8757i 0.374608 0.648839i
\(336\) 0 0
\(337\) −10.0639 17.4312i −0.548217 0.949539i −0.998397 0.0566014i \(-0.981974\pi\)
0.450180 0.892938i \(-0.351360\pi\)
\(338\) −10.6585 6.15367i −0.579745 0.334716i
\(339\) −28.2631 18.9109i −1.53504 1.02710i
\(340\) −2.59713 4.49837i −0.140849 0.243958i
\(341\) −9.64666 16.7085i −0.522396 0.904816i
\(342\) 11.0307 + 1.46655i 0.596474 + 0.0793019i
\(343\) 0 0
\(344\) −5.34273 3.08463i −0.288061 0.166312i
\(345\) 1.40252 + 0.938431i 0.0755093 + 0.0505234i
\(346\) 3.09982i 0.166647i
\(347\) 22.6395i 1.21535i −0.794185 0.607677i \(-0.792102\pi\)
0.794185 0.607677i \(-0.207898\pi\)
\(348\) −0.870230 + 13.1486i −0.0466492 + 0.704837i
\(349\) −13.3378 7.70058i −0.713955 0.412202i 0.0985684 0.995130i \(-0.468574\pi\)
−0.812524 + 0.582928i \(0.801907\pi\)
\(350\) 0 0
\(351\) 4.09769 1.38224i 0.218719 0.0737783i
\(352\) −0.876838 1.51873i −0.0467356 0.0809485i
\(353\) 15.6132 + 27.0429i 0.831009 + 1.43935i 0.897239 + 0.441545i \(0.145570\pi\)
−0.0662300 + 0.997804i \(0.521097\pi\)
\(354\) 16.8848 8.31325i 0.897414 0.441844i
\(355\) −9.05225 5.22632i −0.480444 0.277384i
\(356\) 2.15943 + 3.74024i 0.114449 + 0.198232i
\(357\) 0 0
\(358\) −0.288947 + 0.500470i −0.0152713 + 0.0264507i
\(359\) 1.39179 0.803552i 0.0734560 0.0424098i −0.462822 0.886451i \(-0.653163\pi\)
0.536278 + 0.844041i \(0.319830\pi\)
\(360\) 2.63199 1.08627i 0.138718 0.0572515i
\(361\) −2.62067 + 4.53913i −0.137930 + 0.238902i
\(362\) −26.0581 −1.36958
\(363\) −13.6959 0.906453i −0.718847 0.0475765i
\(364\) 0 0
\(365\) 3.00114 1.73271i 0.157087 0.0906941i
\(366\) −0.839001 1.70407i −0.0438553 0.0890730i
\(367\) −16.1877 + 9.34599i −0.844992 + 0.487856i −0.858958 0.512046i \(-0.828888\pi\)
0.0139659 + 0.999902i \(0.495554\pi\)
\(368\) 0.888998 + 0.513263i 0.0463422 + 0.0267557i
\(369\) −24.1265 3.20765i −1.25598 0.166984i
\(370\) 4.17286i 0.216937i
\(371\) 0 0
\(372\) 17.0957 8.41708i 0.886368 0.436405i
\(373\) −18.7682 + 32.5075i −0.971781 + 1.68317i −0.281609 + 0.959529i \(0.590868\pi\)
−0.690173 + 0.723645i \(0.742465\pi\)
\(374\) 9.59745 0.496272
\(375\) 6.60731 + 13.4199i 0.341200 + 0.692999i
\(376\) 6.80125i 0.350748i
\(377\) 6.33177 0.326103
\(378\) 0 0
\(379\) −8.63192 −0.443392 −0.221696 0.975116i \(-0.571159\pi\)
−0.221696 + 0.975116i \(0.571159\pi\)
\(380\) 3.52051i 0.180599i
\(381\) 14.3108 + 29.0661i 0.733164 + 1.48910i
\(382\) −1.77964 −0.0910545
\(383\) −4.19997 + 7.27456i −0.214608 + 0.371713i −0.953151 0.302494i \(-0.902181\pi\)
0.738543 + 0.674206i \(0.235514\pi\)
\(384\) 1.55392 0.765075i 0.0792980 0.0390426i
\(385\) 0 0
\(386\) 1.48335i 0.0755007i
\(387\) 7.06078 + 17.1080i 0.358920 + 0.869647i
\(388\) −3.90396 2.25395i −0.198193 0.114427i
\(389\) 12.3475 7.12883i 0.626043 0.361446i −0.153175 0.988199i \(-0.548950\pi\)
0.779218 + 0.626753i \(0.215617\pi\)
\(390\) −0.604338 1.22745i −0.0306018 0.0621544i
\(391\) −4.86527 + 2.80897i −0.246047 + 0.142056i
\(392\) 0 0
\(393\) −11.4824 0.759954i −0.579209 0.0383346i
\(394\) −2.44809 −0.123333
\(395\) 4.67352 8.09477i 0.235150 0.407292i
\(396\) −0.693358 + 5.21514i −0.0348426 + 0.262071i
\(397\) −22.2162 + 12.8265i −1.11500 + 0.643744i −0.940119 0.340846i \(-0.889287\pi\)
−0.174879 + 0.984590i \(0.555953\pi\)
\(398\) 5.46984 9.47403i 0.274178 0.474890i
\(399\) 0 0
\(400\) 2.04959 + 3.55000i 0.102480 + 0.177500i
\(401\) 22.5981 + 13.0470i 1.12849 + 0.651536i 0.943556 0.331214i \(-0.107458\pi\)
0.184938 + 0.982750i \(0.440791\pi\)
\(402\) −22.4512 + 11.0539i −1.11976 + 0.551318i
\(403\) −4.57810 7.92951i −0.228052 0.394997i
\(404\) 6.33624 + 10.9747i 0.315240 + 0.546011i
\(405\) −8.24528 2.23189i −0.409711 0.110904i
\(406\) 0 0
\(407\) 6.67722 + 3.85510i 0.330978 + 0.191090i
\(408\) −0.625999 + 9.45841i −0.0309915 + 0.468261i
\(409\) 30.8308i 1.52448i −0.647292 0.762242i \(-0.724099\pi\)
0.647292 0.762242i \(-0.275901\pi\)
\(410\) 7.70010i 0.380281i
\(411\) −29.3879 19.6635i −1.44960 0.969929i
\(412\) −7.33341 4.23394i −0.361291 0.208591i
\(413\) 0 0
\(414\) −1.17487 2.84666i −0.0577418 0.139906i
\(415\) −2.28834 3.96353i −0.112330 0.194562i
\(416\) −0.416129 0.720756i −0.0204024 0.0353380i
\(417\) 18.2561 + 12.2152i 0.894007 + 0.598182i
\(418\) 5.63337 + 3.25243i 0.275537 + 0.159081i
\(419\) −13.9168 24.1047i −0.679883 1.17759i −0.975016 0.222135i \(-0.928697\pi\)
0.295133 0.955456i \(-0.404636\pi\)
\(420\) 0 0
\(421\) 7.39960 12.8165i 0.360634 0.624637i −0.627431 0.778672i \(-0.715894\pi\)
0.988065 + 0.154035i \(0.0492269\pi\)
\(422\) −22.0804 + 12.7481i −1.07486 + 0.620569i
\(423\) −12.4417 + 16.1715i −0.604934 + 0.786286i
\(424\) 1.08644 1.88177i 0.0527621 0.0913866i
\(425\) −22.4339 −1.08820
\(426\) 8.42582 + 17.1134i 0.408232 + 0.829147i
\(427\) 0 0
\(428\) 1.28657 0.742804i 0.0621889 0.0359048i
\(429\) 2.52243 + 0.166945i 0.121784 + 0.00806019i
\(430\) 5.07085 2.92766i 0.244538 0.141184i
\(431\) −24.7338 14.2801i −1.19139 0.687847i −0.232765 0.972533i \(-0.574777\pi\)
−0.958621 + 0.284686i \(0.908111\pi\)
\(432\) −5.09436 1.02347i −0.245103 0.0492419i
\(433\) 18.0220i 0.866080i 0.901375 + 0.433040i \(0.142559\pi\)
−0.901375 + 0.433040i \(0.857441\pi\)
\(434\) 0 0
\(435\) −10.3946 6.95503i −0.498382 0.333468i
\(436\) −7.60276 + 13.1684i −0.364106 + 0.630651i
\(437\) −3.80766 −0.182145
\(438\) −6.31028 0.417642i −0.301517 0.0199557i
\(439\) 24.5104i 1.16982i −0.811099 0.584909i \(-0.801130\pi\)
0.811099 0.584909i \(-0.198870\pi\)
\(440\) 1.66444 0.0793489
\(441\) 0 0
\(442\) 4.55475 0.216647
\(443\) 10.5547i 0.501469i −0.968056 0.250734i \(-0.919328\pi\)
0.968056 0.250734i \(-0.0806720\pi\)
\(444\) −4.23477 + 6.32904i −0.200973 + 0.300363i
\(445\) −4.09908 −0.194315
\(446\) 7.68501 13.3108i 0.363896 0.630286i
\(447\) −2.26949 + 34.2905i −0.107343 + 1.62188i
\(448\) 0 0
\(449\) 17.2540i 0.814267i −0.913369 0.407133i \(-0.866528\pi\)
0.913369 0.407133i \(-0.133472\pi\)
\(450\) 1.62071 12.1903i 0.0764011 0.574656i
\(451\) −12.3213 7.11373i −0.580190 0.334973i
\(452\) 17.0031 9.81676i 0.799760 0.461742i
\(453\) 1.68062 2.51176i 0.0789626 0.118013i
\(454\) 7.22937 4.17388i 0.339291 0.195890i
\(455\) 0 0
\(456\) −3.57275 + 5.33961i −0.167309 + 0.250050i
\(457\) 1.37536 0.0643368 0.0321684 0.999482i \(-0.489759\pi\)
0.0321684 + 0.999482i \(0.489759\pi\)
\(458\) −6.56281 + 11.3671i −0.306660 + 0.531151i
\(459\) 18.7909 21.3444i 0.877084 0.996269i
\(460\) −0.843760 + 0.487145i −0.0393405 + 0.0227132i
\(461\) −18.7031 + 32.3947i −0.871088 + 1.50877i −0.0102165 + 0.999948i \(0.503252\pi\)
−0.860872 + 0.508822i \(0.830081\pi\)
\(462\) 0 0
\(463\) −5.18312 8.97742i −0.240880 0.417216i 0.720085 0.693886i \(-0.244103\pi\)
−0.960965 + 0.276669i \(0.910769\pi\)
\(464\) −6.58867 3.80397i −0.305871 0.176595i
\(465\) −1.19438 + 18.0463i −0.0553880 + 0.836875i
\(466\) 5.68315 + 9.84350i 0.263267 + 0.455991i
\(467\) −18.1423 31.4234i −0.839527 1.45410i −0.890291 0.455393i \(-0.849499\pi\)
0.0507637 0.998711i \(-0.483834\pi\)
\(468\) −0.329053 + 2.47500i −0.0152105 + 0.114407i
\(469\) 0 0
\(470\) 5.59033 + 3.22758i 0.257862 + 0.148877i
\(471\) −14.7554 + 7.26488i −0.679895 + 0.334748i
\(472\) 10.8659i 0.500145i
\(473\) 10.8189i 0.497452i
\(474\) −15.3033 + 7.53460i −0.702902 + 0.346076i
\(475\) −13.1679 7.60248i −0.604184 0.348826i
\(476\) 0 0
\(477\) −6.02561 + 2.48688i −0.275894 + 0.113867i
\(478\) 2.69645 + 4.67039i 0.123333 + 0.213619i
\(479\) 11.5975 + 20.0875i 0.529905 + 0.917822i 0.999391 + 0.0348822i \(0.0111056\pi\)
−0.469487 + 0.882939i \(0.655561\pi\)
\(480\) −0.108564 + 1.64032i −0.00495523 + 0.0748702i
\(481\) 3.16887 + 1.82955i 0.144488 + 0.0834202i
\(482\) 6.99936 + 12.1233i 0.318812 + 0.552199i
\(483\) 0 0
\(484\) 3.96231 6.86292i 0.180105 0.311951i
\(485\) 3.70529 2.13925i 0.168249 0.0971385i
\(486\) 10.2407 + 11.7528i 0.464529 + 0.533116i
\(487\) −14.3695 + 24.8887i −0.651144 + 1.12781i 0.331701 + 0.943384i \(0.392377\pi\)
−0.982846 + 0.184430i \(0.940956\pi\)
\(488\) 1.09663 0.0496419
\(489\) 11.4054 17.0458i 0.515770 0.770839i
\(490\) 0 0
\(491\) 21.0143 12.1326i 0.948364 0.547538i 0.0557919 0.998442i \(-0.482232\pi\)
0.892572 + 0.450904i \(0.148898\pi\)
\(492\) 7.81434 11.6788i 0.352298 0.526523i
\(493\) 36.0582 20.8182i 1.62398 0.937605i
\(494\) 2.67348 + 1.54353i 0.120285 + 0.0694468i
\(495\) −3.95758 3.04479i −0.177880 0.136853i
\(496\) 11.0016i 0.493988i
\(497\) 0 0
\(498\) −0.551570 + 8.33384i −0.0247164 + 0.373448i
\(499\) −13.2911 + 23.0209i −0.594992 + 1.03056i 0.398556 + 0.917144i \(0.369511\pi\)
−0.993548 + 0.113412i \(0.963822\pi\)
\(500\) −8.63615 −0.386221
\(501\) −3.33706 + 4.98737i −0.149089 + 0.222819i
\(502\) 16.5094i 0.736852i
\(503\) −33.9478 −1.51366 −0.756829 0.653613i \(-0.773252\pi\)
−0.756829 + 0.653613i \(0.773252\pi\)
\(504\) 0 0
\(505\) −12.0276 −0.535222
\(506\) 1.80019i 0.0800284i
\(507\) −21.2704 1.40777i −0.944652 0.0625212i
\(508\) −18.7051 −0.829903
\(509\) −5.70574 + 9.88263i −0.252902 + 0.438040i −0.964324 0.264726i \(-0.914719\pi\)
0.711421 + 0.702766i \(0.248052\pi\)
\(510\) −7.47732 5.00309i −0.331101 0.221541i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 18.2629 6.16045i 0.806326 0.271990i
\(514\) −5.30007 3.06000i −0.233776 0.134971i
\(515\) 6.96023 4.01849i 0.306704 0.177076i
\(516\) −10.6621 0.705666i −0.469374 0.0310652i
\(517\) −10.3292 + 5.96359i −0.454280 + 0.262278i
\(518\) 0 0
\(519\) 2.37160 + 4.81687i 0.104101 + 0.211437i
\(520\) 0.789907 0.0346397
\(521\) 9.24387 16.0108i 0.404981 0.701448i −0.589338 0.807887i \(-0.700611\pi\)
0.994319 + 0.106439i \(0.0339447\pi\)
\(522\) 8.70738 + 21.0976i 0.381112 + 0.923416i
\(523\) −0.133147 + 0.0768726i −0.00582212 + 0.00336140i −0.502908 0.864340i \(-0.667737\pi\)
0.497086 + 0.867701i \(0.334403\pi\)
\(524\) 3.32193 5.75375i 0.145119 0.251354i
\(525\) 0 0
\(526\) −8.17923 14.1668i −0.356631 0.617704i
\(527\) −52.1428 30.1047i −2.27138 1.31138i
\(528\) −2.52447 1.68913i −0.109864 0.0735100i
\(529\) −10.9731 19.0060i −0.477092 0.826348i
\(530\) 1.03115 + 1.78601i 0.0447904 + 0.0775792i
\(531\) 19.8773 25.8362i 0.862600 1.12120i
\(532\) 0 0
\(533\) −5.84746 3.37603i −0.253281 0.146232i
\(534\) 6.21714 + 4.15990i 0.269042 + 0.180016i
\(535\) 1.41001i 0.0609600i
\(536\) 14.4481i 0.624063i
\(537\) −0.0661020 + 0.998756i −0.00285251 + 0.0430995i
\(538\) −4.60457 2.65845i −0.198517 0.114614i
\(539\) 0 0
\(540\) 3.25881 3.70164i 0.140237 0.159293i
\(541\) 17.9635 + 31.1136i 0.772309 + 1.33768i 0.936294 + 0.351216i \(0.114232\pi\)
−0.163985 + 0.986463i \(0.552435\pi\)
\(542\) 8.24602 + 14.2825i 0.354197 + 0.613487i
\(543\) −40.4922 + 19.9364i −1.73769 + 0.855553i
\(544\) −4.73955 2.73638i −0.203206 0.117321i
\(545\) −7.21588 12.4983i −0.309094 0.535367i
\(546\) 0 0
\(547\) 10.2216 17.7043i 0.437044 0.756983i −0.560416 0.828211i \(-0.689359\pi\)
0.997460 + 0.0712286i \(0.0226920\pi\)
\(548\) 17.6798 10.2074i 0.755244 0.436040i
\(549\) −2.60748 2.00608i −0.111284 0.0856174i
\(550\) 3.59432 6.22554i 0.153262 0.265458i
\(551\) 28.2199 1.20221
\(552\) 1.77412 + 0.117419i 0.0755114 + 0.00499767i
\(553\) 0 0
\(554\) 12.6682 7.31402i 0.538222 0.310743i
\(555\) −3.19255 6.48428i −0.135516 0.275242i
\(556\) −10.9829 + 6.34099i −0.465780 + 0.268918i
\(557\) 18.8181 + 10.8646i 0.797348 + 0.460349i 0.842543 0.538629i \(-0.181058\pi\)
−0.0451952 + 0.998978i \(0.514391\pi\)
\(558\) 20.1255 26.1589i 0.851982 1.10739i
\(559\) 5.13441i 0.217162i
\(560\) 0 0
\(561\) 14.9136 7.34277i 0.629654 0.310012i
\(562\) −2.09178 + 3.62307i −0.0882365 + 0.152830i
\(563\) 20.8519 0.878805 0.439402 0.898290i \(-0.355190\pi\)
0.439402 + 0.898290i \(0.355190\pi\)
\(564\) −5.20346 10.5686i −0.219105 0.445017i
\(565\) 18.6344i 0.783957i
\(566\) −9.70591 −0.407970
\(567\) 0 0
\(568\) −11.0131 −0.462098
\(569\) 11.6914i 0.490128i −0.969507 0.245064i \(-0.921191\pi\)
0.969507 0.245064i \(-0.0788090\pi\)
\(570\) −2.69346 5.47059i −0.112816 0.229138i
\(571\) 13.5544 0.567235 0.283617 0.958938i \(-0.408465\pi\)
0.283617 + 0.958938i \(0.408465\pi\)
\(572\) −0.729755 + 1.26397i −0.0305126 + 0.0528494i
\(573\) −2.76542 + 1.36156i −0.115527 + 0.0568800i
\(574\) 0 0
\(575\) 4.20792i 0.175483i
\(576\) 1.82932 2.37773i 0.0762217 0.0990720i
\(577\) −20.0748 11.5902i −0.835727 0.482507i 0.0200828 0.999798i \(-0.493607\pi\)
−0.855809 + 0.517291i \(0.826940\pi\)
\(578\) 11.2160 6.47555i 0.466523 0.269347i
\(579\) −1.13488 2.30501i −0.0471639 0.0957929i
\(580\) 6.25339 3.61040i 0.259658 0.149914i
\(581\) 0 0
\(582\) −7.79087 0.515633i −0.322942 0.0213737i
\(583\) −3.81052 −0.157816
\(584\) 1.82561 3.16204i 0.0755442 0.130846i
\(585\) −1.87818 1.44499i −0.0776533 0.0597431i
\(586\) −1.75591 + 1.01377i −0.0725358 + 0.0418786i
\(587\) 4.22194 7.31262i 0.174258 0.301824i −0.765646 0.643262i \(-0.777581\pi\)
0.939904 + 0.341438i \(0.110914\pi\)
\(588\) 0 0
\(589\) −20.4040 35.3408i −0.840733 1.45619i
\(590\) −8.93131 5.15650i −0.367696 0.212290i
\(591\) −3.80413 + 1.87297i −0.156481 + 0.0770438i
\(592\) −2.19830 3.80756i −0.0903494 0.156490i
\(593\) 16.3255 + 28.2765i 0.670407 + 1.16118i 0.977789 + 0.209592i \(0.0672136\pi\)
−0.307382 + 0.951586i \(0.599453\pi\)
\(594\) 2.91255 + 8.63437i 0.119503 + 0.354272i
\(595\) 0 0
\(596\) −17.1827 9.92046i −0.703833 0.406358i
\(597\) 1.25133 18.9067i 0.0512134 0.773800i
\(598\) 0.854335i 0.0349364i
\(599\) 47.9900i 1.96082i −0.196974 0.980409i \(-0.563112\pi\)
0.196974 0.980409i \(-0.436888\pi\)
\(600\) 5.90091 + 3.94831i 0.240904 + 0.161189i
\(601\) −20.1783 11.6499i −0.823090 0.475211i 0.0283909 0.999597i \(-0.490962\pi\)
−0.851481 + 0.524386i \(0.824295\pi\)
\(602\) 0 0
\(603\) −26.4302 + 34.3537i −1.07632 + 1.39899i
\(604\) 0.872422 + 1.51108i 0.0354983 + 0.0614849i
\(605\) 3.76068 + 6.51369i 0.152893 + 0.264819i
\(606\) 18.2425 + 12.2061i 0.741049 + 0.495838i
\(607\) 21.3385 + 12.3198i 0.866101 + 0.500044i 0.866051 0.499956i \(-0.166651\pi\)
5.03773e−5 1.00000i \(0.499984\pi\)
\(608\) −1.85463 3.21232i −0.0752153 0.130277i
\(609\) 0 0
\(610\) −0.520411 + 0.901378i −0.0210708 + 0.0364957i
\(611\) −4.90204 + 2.83020i −0.198315 + 0.114497i
\(612\) 6.26364 + 15.1765i 0.253193 + 0.613474i
\(613\) −17.2009 + 29.7928i −0.694736 + 1.20332i 0.275533 + 0.961291i \(0.411146\pi\)
−0.970270 + 0.242027i \(0.922188\pi\)
\(614\) −9.79004 −0.395094
\(615\) 5.89115 + 11.9653i 0.237554 + 0.482488i
\(616\) 0 0
\(617\) −22.4321 + 12.9512i −0.903083 + 0.521395i −0.878199 0.478295i \(-0.841255\pi\)
−0.0248838 + 0.999690i \(0.507922\pi\)
\(618\) −14.6348 0.968595i −0.588698 0.0389626i
\(619\) −10.1907 + 5.88361i −0.409599 + 0.236482i −0.690618 0.723220i \(-0.742661\pi\)
0.281018 + 0.959702i \(0.409328\pi\)
\(620\) −9.04287 5.22090i −0.363170 0.209676i
\(621\) −4.00357 3.52461i −0.160658 0.141438i
\(622\) 13.7039i 0.549476i
\(623\) 0 0
\(624\) −1.19806 0.801626i −0.0479609 0.0320907i
\(625\) −6.14962 + 10.6515i −0.245985 + 0.426058i
\(626\) 18.8585 0.753739
\(627\) 11.2421 + 0.744054i 0.448968 + 0.0297146i
\(628\) 9.49564i 0.378917i
\(629\) 24.0615 0.959394
\(630\) 0 0
\(631\) 16.4353 0.654277 0.327139 0.944976i \(-0.393916\pi\)
0.327139 + 0.944976i \(0.393916\pi\)
\(632\) 9.84819i 0.391740i
\(633\) −24.5578 + 36.7027i −0.976087 + 1.45880i
\(634\) 7.86426 0.312329
\(635\) 8.87661 15.3747i 0.352258 0.610128i
\(636\) 0.248543 3.75532i 0.00985538 0.148908i
\(637\) 0 0
\(638\) 13.3419i 0.528209i
\(639\) 26.1861 + 20.1464i 1.03590 + 0.796980i
\(640\) −0.821956 0.474556i −0.0324907 0.0187585i
\(641\) −13.4048 + 7.73929i −0.529460 + 0.305684i −0.740796 0.671730i \(-0.765552\pi\)
0.211337 + 0.977413i \(0.432218\pi\)
\(642\) 1.43093 2.13858i 0.0564743 0.0844031i
\(643\) 3.28185 1.89478i 0.129423 0.0747226i −0.433890 0.900966i \(-0.642860\pi\)
0.563314 + 0.826243i \(0.309526\pi\)
\(644\) 0 0
\(645\) 5.63981 8.42893i 0.222067 0.331889i
\(646\) 20.2999 0.798690
\(647\) 11.0730 19.1789i 0.435323 0.754002i −0.561999 0.827138i \(-0.689967\pi\)
0.997322 + 0.0731360i \(0.0233007\pi\)
\(648\) −8.69925 + 2.30717i −0.341739 + 0.0906343i
\(649\) 16.5024 9.52765i 0.647775 0.373993i
\(650\) 1.70579 2.95451i 0.0669066 0.115886i
\(651\) 0 0
\(652\) 5.92061 + 10.2548i 0.231869 + 0.401609i
\(653\) −6.54842 3.78073i −0.256259 0.147951i 0.366368 0.930470i \(-0.380601\pi\)
−0.622627 + 0.782519i \(0.713935\pi\)
\(654\) −1.73928 + 26.2792i −0.0680110 + 1.02760i
\(655\) 3.15289 + 5.46096i 0.123193 + 0.213377i
\(656\) 4.05647 + 7.02601i 0.158379 + 0.274320i
\(657\) −10.1252 + 4.17886i −0.395021 + 0.163033i
\(658\) 0 0
\(659\) −12.2514 7.07334i −0.477246 0.275538i 0.242022 0.970271i \(-0.422189\pi\)
−0.719268 + 0.694733i \(0.755523\pi\)
\(660\) 2.58640 1.27342i 0.100675 0.0495678i
\(661\) 22.9586i 0.892985i −0.894787 0.446492i \(-0.852673\pi\)
0.894787 0.446492i \(-0.147327\pi\)
\(662\) 22.7350i 0.883620i
\(663\) 7.07770 3.48472i 0.274875 0.135335i
\(664\) −4.17603 2.41103i −0.162062 0.0935663i
\(665\) 0 0
\(666\) −1.73830 + 13.0747i −0.0673577 + 0.506635i
\(667\) −3.90488 6.76344i −0.151197 0.261882i
\(668\) −1.73229 3.00041i −0.0670242 0.116089i
\(669\) 1.75809 26.5635i 0.0679717 1.02701i
\(670\) 11.8757 + 6.85644i 0.458799 + 0.264888i
\(671\) −0.961563 1.66548i −0.0371207 0.0642950i
\(672\) 0 0
\(673\) −1.86542 + 3.23100i −0.0719066 + 0.124546i −0.899737 0.436433i \(-0.856242\pi\)
0.827830 + 0.560979i \(0.189575\pi\)
\(674\) 17.4312 10.0639i 0.671426 0.387648i
\(675\) −6.80803 20.1827i −0.262041 0.776831i
\(676\) 6.15367 10.6585i 0.236680 0.409941i
\(677\) 47.5314 1.82678 0.913390 0.407087i \(-0.133455\pi\)
0.913390 + 0.407087i \(0.133455\pi\)
\(678\) 18.9109 28.2631i 0.726269 1.08544i
\(679\) 0 0
\(680\) 4.49837 2.59713i 0.172505 0.0995955i
\(681\) 8.04052 12.0169i 0.308113 0.460488i
\(682\) 16.7085 9.64666i 0.639802 0.369390i
\(683\) 28.5275 + 16.4704i 1.09158 + 0.630222i 0.933996 0.357284i \(-0.116297\pi\)
0.157580 + 0.987506i \(0.449631\pi\)
\(684\) −1.46655 + 11.0307i −0.0560749 + 0.421771i
\(685\) 19.3760i 0.740320i
\(686\) 0 0
\(687\) −1.50137 + 22.6846i −0.0572807 + 0.865472i
\(688\) 3.08463 5.34273i 0.117600 0.203690i
\(689\) −1.80839 −0.0688943
\(690\) −0.938431 + 1.40252i −0.0357254 + 0.0533931i
\(691\) 7.93611i 0.301904i 0.988541 + 0.150952i \(0.0482339\pi\)
−0.988541 + 0.150952i \(0.951766\pi\)
\(692\) −3.09982 −0.117838
\(693\) 0 0
\(694\) 22.6395 0.859385
\(695\) 12.0366i 0.456576i
\(696\) −13.1486 0.870230i −0.498395 0.0329860i
\(697\) −44.4002 −1.68178
\(698\) 7.70058 13.3378i 0.291471 0.504843i
\(699\) 16.3622 + 10.9480i 0.618874 + 0.414090i
\(700\) 0 0
\(701\) 25.1838i 0.951180i 0.879667 + 0.475590i \(0.157765\pi\)
−0.879667 + 0.475590i \(0.842235\pi\)
\(702\) 1.38224 + 4.09769i 0.0521691 + 0.154657i
\(703\) 14.1233 + 8.15406i 0.532669 + 0.307536i
\(704\) 1.51873 0.876838i 0.0572392 0.0330471i
\(705\) 11.1562 + 0.738369i 0.420168 + 0.0278086i
\(706\) −27.0429 + 15.6132i −1.01777 + 0.587612i
\(707\) 0 0
\(708\) 8.31325 + 16.8848i 0.312431 + 0.634568i
\(709\) 21.5021 0.807530 0.403765 0.914863i \(-0.367701\pi\)
0.403765 + 0.914863i \(0.367701\pi\)
\(710\) 5.22632 9.05225i 0.196140 0.339725i
\(711\) −18.0155 + 23.4163i −0.675634 + 0.878180i
\(712\) −3.74024 + 2.15943i −0.140171 + 0.0809280i
\(713\) −5.64674 + 9.78044i −0.211472 + 0.366280i
\(714\) 0 0
\(715\) −0.692620 1.19965i −0.0259025 0.0448645i
\(716\) −0.500470 0.288947i −0.0187035 0.0107984i
\(717\) 7.76326 + 5.19441i 0.289924 + 0.193989i
\(718\) 0.803552 + 1.39179i 0.0299883 + 0.0519412i
\(719\) 8.30671 + 14.3876i 0.309788 + 0.536569i 0.978316 0.207119i \(-0.0664086\pi\)
−0.668528 + 0.743687i \(0.733075\pi\)
\(720\) 1.08627 + 2.63199i 0.0404829 + 0.0980884i
\(721\) 0 0
\(722\) −4.53913 2.62067i −0.168929 0.0975312i
\(723\) 20.1516 + 13.4835i 0.749447 + 0.501457i
\(724\) 26.0581i 0.968442i
\(725\) 31.1863i 1.15823i
\(726\) 0.906453 13.6959i 0.0336416 0.508302i
\(727\) 39.4866 + 22.7976i 1.46448 + 0.845517i 0.999213 0.0396542i \(-0.0126256\pi\)
0.465265 + 0.885171i \(0.345959\pi\)
\(728\) 0 0
\(729\) 24.9050 + 10.4279i 0.922408 + 0.386218i
\(730\) 1.73271 + 3.00114i 0.0641304 + 0.111077i
\(731\) 16.8814 + 29.2395i 0.624382 + 1.08146i
\(732\) 1.70407 0.839001i 0.0629841 0.0310104i
\(733\) 14.3262 + 8.27123i 0.529150 + 0.305505i 0.740670 0.671869i \(-0.234508\pi\)
−0.211520 + 0.977374i \(0.567841\pi\)
\(734\) −9.34599 16.1877i −0.344967 0.597500i
\(735\) 0 0
\(736\) −0.513263 + 0.888998i −0.0189191 + 0.0327689i
\(737\) −21.9427 + 12.6686i −0.808271 + 0.466656i
\(738\) 3.20765 24.1265i 0.118075 0.888110i
\(739\) 7.75506 13.4322i 0.285274 0.494110i −0.687401 0.726278i \(-0.741249\pi\)
0.972676 + 0.232168i \(0.0745819\pi\)
\(740\) 4.17286 0.153397
\(741\) 5.33528 + 0.353112i 0.195997 + 0.0129719i
\(742\) 0 0
\(743\) 36.0654 20.8224i 1.32311 0.763899i 0.338888 0.940827i \(-0.389949\pi\)
0.984224 + 0.176928i \(0.0566160\pi\)
\(744\) 8.41708 + 17.0957i 0.308585 + 0.626757i
\(745\) 16.3084 9.41564i 0.597492 0.344962i
\(746\) −32.5075 18.7682i −1.19018 0.687153i
\(747\) 5.51892 + 13.3721i 0.201927 + 0.489259i
\(748\) 9.59745i 0.350917i
\(749\) 0 0
\(750\) −13.4199 + 6.60731i −0.490024 + 0.241265i
\(751\) 6.21569 10.7659i 0.226814 0.392853i −0.730048 0.683395i \(-0.760503\pi\)
0.956862 + 0.290543i \(0.0938359\pi\)
\(752\) 6.80125 0.248016
\(753\) 12.6310 + 25.6543i 0.460298 + 0.934895i
\(754\) 6.33177i 0.230589i
\(755\) −1.65605 −0.0602699
\(756\) 0 0
\(757\) 24.8661 0.903775 0.451887 0.892075i \(-0.350751\pi\)
0.451887 + 0.892075i \(0.350751\pi\)
\(758\) 8.63192i 0.313526i
\(759\) −1.37728 2.79735i −0.0499922 0.101538i
\(760\) 3.52051 0.127702
\(761\) −5.68277 + 9.84285i −0.206000 + 0.356803i −0.950451 0.310874i \(-0.899378\pi\)
0.744451 + 0.667678i \(0.232711\pi\)
\(762\) −29.0661 + 14.3108i −1.05296 + 0.518425i
\(763\) 0 0
\(764\) 1.77964i 0.0643852i
\(765\) −15.4469 2.05368i −0.558483 0.0742509i
\(766\) −7.27456 4.19997i −0.262841 0.151751i
\(767\) 7.83169 4.52163i 0.282786 0.163266i
\(768\) 0.765075 + 1.55392i 0.0276073 + 0.0560722i
\(769\) 29.8857 17.2545i 1.07771 0.622214i 0.147429 0.989073i \(-0.452900\pi\)
0.930277 + 0.366859i \(0.119567\pi\)
\(770\) 0 0
\(771\) −10.5770 0.700033i −0.380922 0.0252111i
\(772\) 1.48335 0.0533871
\(773\) −10.6262 + 18.4051i −0.382197 + 0.661984i −0.991376 0.131048i \(-0.958166\pi\)
0.609179 + 0.793033i \(0.291499\pi\)
\(774\) −17.1080 + 7.06078i −0.614933 + 0.253795i
\(775\) −39.0558 + 22.5489i −1.40293 + 0.809980i
\(776\) 2.25395 3.90396i 0.0809121 0.140144i
\(777\) 0 0
\(778\) 7.12883 + 12.3475i 0.255581 + 0.442679i
\(779\) −26.0614 15.0465i −0.933745 0.539098i
\(780\) 1.22745 0.604338i 0.0439498 0.0216388i
\(781\) 9.65667 + 16.7258i 0.345543 + 0.598498i
\(782\) −2.80897 4.86527i −0.100448 0.173982i
\(783\) 29.6718 + 26.1221i 1.06038 + 0.933528i
\(784\) 0 0
\(785\) 7.80500 + 4.50622i 0.278572 + 0.160834i
\(786\) 0.759954 11.4824i 0.0271067 0.409563i
\(787\) 11.9663i 0.426551i −0.976992 0.213276i \(-0.931587\pi\)
0.976992 0.213276i \(-0.0684132\pi\)
\(788\) 2.44809i 0.0872096i
\(789\) −23.5485 15.7564i −0.838351 0.560942i
\(790\) 8.09477 + 4.67352i 0.287999 + 0.166276i
\(791\) 0 0
\(792\) −5.21514 0.693358i −0.185312 0.0246374i
\(793\) −0.456338 0.790400i −0.0162050 0.0280679i
\(794\) −12.8265 22.2162i −0.455196 0.788422i
\(795\) 2.96876 + 1.98640i 0.105291 + 0.0704504i
\(796\) 9.47403 + 5.46984i 0.335798 + 0.193873i
\(797\) −2.86820 4.96786i −0.101597 0.175971i 0.810746 0.585398i \(-0.199062\pi\)
−0.912343 + 0.409427i \(0.865728\pi\)
\(798\) 0 0
\(799\) −18.6108 + 32.2348i −0.658403 + 1.14039i
\(800\) −3.55000 + 2.04959i −0.125511 + 0.0724640i
\(801\) 12.8436 + 1.70756i 0.453805 + 0.0603338i
\(802\) −13.0470 + 22.5981i −0.460706 + 0.797966i
\(803\) −6.40305 −0.225959
\(804\) −11.0539 22.4512i −0.389841 0.791792i
\(805\) 0 0
\(806\) 7.92951 4.57810i 0.279305 0.161257i
\(807\) −9.18903 0.608170i −0.323469 0.0214086i
\(808\) −10.9747 + 6.33624i −0.386088 + 0.222908i
\(809\) 27.5185 + 15.8878i 0.967500 + 0.558586i 0.898473 0.439028i \(-0.144677\pi\)
0.0690269 + 0.997615i \(0.478011\pi\)
\(810\) 2.23189 8.24528i 0.0784206 0.289710i
\(811\) 41.2541i 1.44863i −0.689471 0.724314i \(-0.742157\pi\)
0.689471 0.724314i \(-0.257843\pi\)
\(812\) 0 0
\(813\) 23.7408 + 15.8850i 0.832627 + 0.557113i
\(814\) −3.85510 + 6.67722i −0.135121 + 0.234037i
\(815\) −11.2386 −0.393673
\(816\) −9.45841 0.625999i −0.331110 0.0219143i
\(817\) 22.8834i 0.800589i
\(818\) 30.8308 1.07797
\(819\) 0 0
\(820\) −7.70010 −0.268899
\(821\) 13.5045i 0.471309i −0.971837 0.235655i \(-0.924277\pi\)
0.971837 0.235655i \(-0.0757234\pi\)
\(822\) 19.6635 29.3879i 0.685843 1.02502i
\(823\) −18.9133 −0.659277 −0.329638 0.944107i \(-0.606927\pi\)
−0.329638 + 0.944107i \(0.606927\pi\)
\(824\) 4.23394 7.33341i 0.147496 0.255471i
\(825\) 0.822268 12.4239i 0.0286277 0.432545i
\(826\) 0 0
\(827\) 33.8495i 1.17706i 0.808475 + 0.588531i \(0.200293\pi\)
−0.808475 + 0.588531i \(0.799707\pi\)
\(828\) 2.84666 1.17487i 0.0989284 0.0408296i
\(829\) −21.8963 12.6418i −0.760489 0.439068i 0.0689825 0.997618i \(-0.478025\pi\)
−0.829471 + 0.558550i \(0.811358\pi\)
\(830\) 3.96353 2.28834i 0.137576 0.0794296i
\(831\) 14.0896 21.0575i 0.488764 0.730478i
\(832\) 0.720756 0.416129i 0.0249877 0.0144267i
\(833\) 0 0
\(834\) −12.2152 + 18.2561i −0.422979 + 0.632159i
\(835\) 3.28827 0.113795
\(836\) −3.25243 + 5.63337i −0.112487 + 0.194834i
\(837\) 11.2599 56.0463i 0.389199 1.93724i
\(838\) 24.1047 13.9168i 0.832683 0.480750i
\(839\) −1.28248 + 2.22133i −0.0442763 + 0.0766888i −0.887314 0.461165i \(-0.847432\pi\)
0.843038 + 0.537854i \(0.180765\pi\)
\(840\) 0 0
\(841\) 14.4404 + 25.0114i 0.497943 + 0.862463i
\(842\) 12.8165 + 7.39960i 0.441685 + 0.255007i
\(843\) −0.478535 + 7.23033i −0.0164816 + 0.249026i
\(844\) −12.7481 22.0804i −0.438808 0.760038i
\(845\) 5.84053 + 10.1161i 0.200920 + 0.348004i
\(846\) −16.1715 12.4417i −0.555988 0.427753i
\(847\) 0 0
\(848\) 1.88177 + 1.08644i 0.0646201 + 0.0373084i
\(849\) −15.0822 + 7.42575i −0.517619 + 0.254851i
\(850\) 22.4339i 0.769475i
\(851\) 4.51322i 0.154711i
\(852\) −17.1134 + 8.42582i −0.586295 + 0.288664i
\(853\) 1.98108 + 1.14378i 0.0678310 + 0.0391622i 0.533532 0.845780i \(-0.320864\pi\)
−0.465701 + 0.884942i \(0.654198\pi\)
\(854\) 0 0
\(855\) −8.37082 6.44015i −0.286276 0.220248i
\(856\) 0.742804 + 1.28657i 0.0253885 + 0.0439742i
\(857\) −10.3313 17.8943i −0.352911 0.611259i 0.633847 0.773458i \(-0.281475\pi\)
−0.986758 + 0.162199i \(0.948141\pi\)
\(858\) −0.166945 + 2.52243i −0.00569942 + 0.0861143i
\(859\) −14.3879 8.30688i −0.490910 0.283427i 0.234042 0.972226i \(-0.424805\pi\)
−0.724952 + 0.688800i \(0.758138\pi\)
\(860\) 2.92766 + 5.07085i 0.0998323 + 0.172915i
\(861\) 0 0
\(862\) 14.2801 24.7338i 0.486381 0.842437i
\(863\) −5.54125 + 3.19924i −0.188626 + 0.108904i −0.591339 0.806423i \(-0.701401\pi\)
0.402713 + 0.915326i \(0.368067\pi\)
\(864\) 1.02347 5.09436i 0.0348193 0.173314i
\(865\) 1.47104 2.54792i 0.0500169 0.0866318i
\(866\) −18.0220 −0.612411
\(867\) 12.4744 18.6435i 0.423654 0.633168i
\(868\) 0 0
\(869\) −14.9567 + 8.63526i −0.507372 + 0.292931i
\(870\) 6.95503 10.3946i 0.235798 0.352409i
\(871\) −10.4136 + 6.01228i −0.352850 + 0.203718i
\(872\) −13.1684 7.60276i −0.445937 0.257462i
\(873\) −12.5009 + 5.15934i −0.423090 + 0.174617i
\(874\) 3.80766i 0.128796i
\(875\) 0 0
\(876\) 0.417642 6.31028i 0.0141108 0.213205i
\(877\) −5.08369 + 8.80522i −0.171664 + 0.297331i −0.939002 0.343912i \(-0.888248\pi\)
0.767338 + 0.641243i \(0.221581\pi\)
\(878\) 24.5104 0.827187
\(879\) −1.95292 + 2.91872i −0.0658704 + 0.0984460i
\(880\) 1.66444i 0.0561081i
\(881\) 47.2933 1.59335 0.796675 0.604407i \(-0.206590\pi\)
0.796675 + 0.604407i \(0.206590\pi\)
\(882\) 0 0
\(883\) −16.5706 −0.557645 −0.278822 0.960343i \(-0.589944\pi\)
−0.278822 + 0.960343i \(0.589944\pi\)
\(884\) 4.55475i 0.153193i
\(885\) −17.8236 1.17965i −0.599135 0.0396533i
\(886\) 10.5547 0.354592
\(887\) −11.3965 + 19.7393i −0.382656 + 0.662780i −0.991441 0.130556i \(-0.958324\pi\)
0.608785 + 0.793335i \(0.291657\pi\)
\(888\) −6.32904 4.23477i −0.212389 0.142110i
\(889\) 0 0
\(890\) 4.09908i 0.137402i
\(891\) 11.1318 + 11.1888i 0.372929 + 0.374838i
\(892\) 13.3108 + 7.68501i 0.445679 + 0.257313i
\(893\) −21.8478 + 12.6138i −0.731108 + 0.422105i
\(894\) −34.2905 2.26949i −1.14684 0.0759032i
\(895\) 0.475003 0.274243i 0.0158776 0.00916694i
\(896\) 0 0
\(897\) −0.653630 1.32757i −0.0218241 0.0443261i
\(898\) 17.2540 0.575774
\(899\) 41.8499 72.4862i 1.39577 2.41755i
\(900\) 12.1903 + 1.62071i 0.406343 + 0.0540237i
\(901\) −10.2985 + 5.94581i −0.343091 + 0.198084i
\(902\) 7.11373 12.3213i 0.236861 0.410256i
\(903\) 0 0
\(904\) 9.81676 + 17.0031i 0.326501 + 0.565516i
\(905\) 21.4186 + 12.3660i 0.711979 + 0.411061i
\(906\) 2.51176 + 1.68062i 0.0834476 + 0.0558350i
\(907\) 24.0653 + 41.6824i 0.799077 + 1.38404i 0.920218 + 0.391406i \(0.128011\pi\)
−0.121142 + 0.992635i \(0.538656\pi\)
\(908\) 4.17388 + 7.22937i 0.138515 + 0.239915i
\(909\) 37.6858 + 5.01037i 1.24996 + 0.166184i
\(910\) 0 0
\(911\) 20.5958 + 11.8910i 0.682368 + 0.393966i 0.800747 0.599003i \(-0.204436\pi\)
−0.118378 + 0.992969i \(0.537770\pi\)
\(912\) −5.33961 3.57275i −0.176812 0.118305i
\(913\) 8.45635i 0.279864i
\(914\) 1.37536i 0.0454930i
\(915\) −0.119054 + 1.79882i −0.00393580 + 0.0594672i
\(916\) −11.3671 6.56281i −0.375580 0.216841i
\(917\) 0 0
\(918\) 21.3444 + 18.7909i 0.704469 + 0.620192i
\(919\) −10.9692 18.9992i −0.361841 0.626727i 0.626423 0.779483i \(-0.284518\pi\)
−0.988264 + 0.152757i \(0.951185\pi\)
\(920\) −0.487145 0.843760i −0.0160607 0.0278179i
\(921\) −15.2129 + 7.49011i −0.501283 + 0.246808i
\(922\) −32.3947 18.7031i −1.06686 0.615953i
\(923\) 4.58286 + 7.93774i 0.150847 + 0.261274i
\(924\) 0 0
\(925\) 9.01122 15.6079i 0.296287 0.513184i
\(926\) 8.97742 5.18312i 0.295016 0.170328i
\(927\) −23.4823 + 9.69160i −0.771261 + 0.318314i
\(928\) 3.80397 6.58867i 0.124871 0.216284i
\(929\) −50.4538 −1.65534 −0.827668 0.561217i \(-0.810333\pi\)
−0.827668 + 0.561217i \(0.810333\pi\)
\(930\) −18.0463 1.19438i −0.591760 0.0391653i
\(931\) 0 0
\(932\) −9.84350 + 5.68315i −0.322435 + 0.186158i
\(933\) 10.4845 + 21.2947i 0.343247 + 0.697158i
\(934\) 31.4234 18.1423i 1.02821 0.593635i
\(935\) −7.88868 4.55453i −0.257987 0.148949i
\(936\) −2.47500 0.329053i −0.0808978 0.0107554i
\(937\) 42.6251i 1.39250i −0.717799 0.696250i \(-0.754850\pi\)
0.717799 0.696250i \(-0.245150\pi\)
\(938\) 0 0
\(939\) 29.3046 14.4282i 0.956320 0.470847i
\(940\) −3.22758 + 5.59033i −0.105272 + 0.182336i
\(941\) −55.0404 −1.79427 −0.897133 0.441761i \(-0.854354\pi\)
−0.897133 + 0.441761i \(0.854354\pi\)
\(942\) −7.26488 14.7554i −0.236703 0.480758i
\(943\) 8.32815i 0.271202i
\(944\) −10.8659 −0.353656
\(945\) 0 0
\(946\) −10.8189 −0.351752
\(947\) 25.6884i 0.834760i 0.908732 + 0.417380i \(0.137052\pi\)
−0.908732 + 0.417380i \(0.862948\pi\)
\(948\) −7.53460 15.3033i −0.244712 0.497027i
\(949\) −3.03875 −0.0986421
\(950\) 7.60248 13.1679i 0.246657 0.427223i
\(951\) 12.2204 6.01675i 0.396274 0.195106i
\(952\) 0 0
\(953\) 17.3463i 0.561903i 0.959722 + 0.280952i \(0.0906500\pi\)
−0.959722 + 0.280952i \(0.909350\pi\)
\(954\) −2.48688 6.02561i −0.0805158 0.195086i
\(955\) 1.46279 + 0.844541i 0.0473347 + 0.0273287i
\(956\) −4.67039 + 2.69645i −0.151051 + 0.0872094i
\(957\) 10.2075 + 20.7321i 0.329962 + 0.670175i
\(958\) −20.0875 + 11.5975i −0.648998 + 0.374699i
\(959\) 0 0
\(960\) −1.64032 0.108564i −0.0529412 0.00350388i
\(961\) −90.0362 −2.90439
\(962\) −1.82955 + 3.16887i −0.0589870 + 0.102169i
\(963\) 0.587371 4.41795i 0.0189278 0.142366i
\(964\) −12.1233 + 6.99936i −0.390464 + 0.225434i
\(965\) −0.703935 + 1.21925i −0.0226605 + 0.0392491i
\(966\) 0 0
\(967\) 2.61334 + 4.52644i 0.0840393 + 0.145560i 0.904981 0.425451i \(-0.139885\pi\)
−0.820942 + 0.571011i \(0.806551\pi\)
\(968\) 6.86292 + 3.96231i 0.220583 + 0.127353i
\(969\) 31.5444 15.5310i 1.01335 0.498927i
\(970\) 2.13925 + 3.70529i 0.0686873 + 0.118970i
\(971\) 14.2195 + 24.6289i 0.456326 + 0.790379i 0.998763 0.0497167i \(-0.0158319\pi\)
−0.542438 + 0.840096i \(0.682499\pi\)
\(972\) −11.7528 + 10.2407i −0.376970 + 0.328472i
\(973\) 0 0
\(974\) −24.8887 14.3695i −0.797485 0.460428i
\(975\) 0.390231 5.89613i 0.0124974 0.188827i
\(976\) 1.09663i 0.0351021i
\(977\) 24.3217i 0.778119i 0.921213 + 0.389059i \(0.127200\pi\)
−0.921213 + 0.389059i \(0.872800\pi\)
\(978\) 17.0458 + 11.4054i 0.545065 + 0.364704i
\(979\) 6.55917 + 3.78694i 0.209632 + 0.121031i
\(980\) 0 0
\(981\) 17.4029 + 42.1665i 0.555632 + 1.34627i
\(982\) 12.1326 + 21.0143i 0.387168 + 0.670595i
\(983\) 13.4186 + 23.2417i 0.427987 + 0.741295i 0.996694 0.0812449i \(-0.0258896\pi\)
−0.568707 + 0.822540i \(0.692556\pi\)
\(984\) 11.6788 + 7.81434i 0.372308 + 0.249112i
\(985\) 2.01222 + 1.16176i 0.0641147 + 0.0370166i
\(986\) 20.8182 + 36.0582i 0.662987 + 1.14833i
\(987\) 0 0
\(988\) −1.54353 + 2.67348i −0.0491063 + 0.0850547i
\(989\) 5.48446 3.16645i 0.174396 0.100687i
\(990\) 3.04479 3.95758i 0.0967697 0.125780i
\(991\) −3.51093 + 6.08111i −0.111528 + 0.193173i −0.916387 0.400294i \(-0.868908\pi\)
0.804858 + 0.593467i \(0.202241\pi\)
\(992\) −11.0016 −0.349303
\(993\) 17.3940 + 35.3283i 0.551980 + 1.12111i
\(994\) 0 0
\(995\) −8.99193 + 5.19149i −0.285063 + 0.164581i
\(996\) −8.33384 0.551570i −0.264068 0.0174772i
\(997\) 9.60463 5.54524i 0.304182 0.175619i −0.340138 0.940375i \(-0.610474\pi\)
0.644320 + 0.764756i \(0.277141\pi\)
\(998\) −23.0209 13.2911i −0.728713 0.420723i
\(999\) 7.30197 + 21.6470i 0.231024 + 0.684880i
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 882.2.l.c.227.19 48
3.2 odd 2 2646.2.l.c.521.5 48
7.2 even 3 882.2.t.c.803.13 48
7.3 odd 6 882.2.m.c.587.3 yes 48
7.4 even 3 882.2.m.c.587.10 yes 48
7.5 odd 6 882.2.t.c.803.24 48
7.6 odd 2 inner 882.2.l.c.227.18 48
9.4 even 3 2646.2.t.c.2285.7 48
9.5 odd 6 882.2.t.c.815.24 48
21.2 odd 6 2646.2.t.c.1979.8 48
21.5 even 6 2646.2.t.c.1979.7 48
21.11 odd 6 2646.2.m.c.1763.15 48
21.17 even 6 2646.2.m.c.1763.16 48
21.20 even 2 2646.2.l.c.521.6 48
63.4 even 3 2646.2.m.c.881.16 48
63.5 even 6 inner 882.2.l.c.509.7 48
63.13 odd 6 2646.2.t.c.2285.8 48
63.23 odd 6 inner 882.2.l.c.509.6 48
63.31 odd 6 2646.2.m.c.881.15 48
63.32 odd 6 882.2.m.c.293.3 48
63.40 odd 6 2646.2.l.c.1097.5 48
63.41 even 6 882.2.t.c.815.13 48
63.58 even 3 2646.2.l.c.1097.6 48
63.59 even 6 882.2.m.c.293.10 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
882.2.l.c.227.18 48 7.6 odd 2 inner
882.2.l.c.227.19 48 1.1 even 1 trivial
882.2.l.c.509.6 48 63.23 odd 6 inner
882.2.l.c.509.7 48 63.5 even 6 inner
882.2.m.c.293.3 48 63.32 odd 6
882.2.m.c.293.10 yes 48 63.59 even 6
882.2.m.c.587.3 yes 48 7.3 odd 6
882.2.m.c.587.10 yes 48 7.4 even 3
882.2.t.c.803.13 48 7.2 even 3
882.2.t.c.803.24 48 7.5 odd 6
882.2.t.c.815.13 48 63.41 even 6
882.2.t.c.815.24 48 9.5 odd 6
2646.2.l.c.521.5 48 3.2 odd 2
2646.2.l.c.521.6 48 21.20 even 2
2646.2.l.c.1097.5 48 63.40 odd 6
2646.2.l.c.1097.6 48 63.58 even 3
2646.2.m.c.881.15 48 63.31 odd 6
2646.2.m.c.881.16 48 63.4 even 3
2646.2.m.c.1763.15 48 21.11 odd 6
2646.2.m.c.1763.16 48 21.17 even 6
2646.2.t.c.1979.7 48 21.5 even 6
2646.2.t.c.1979.8 48 21.2 odd 6
2646.2.t.c.2285.7 48 9.4 even 3
2646.2.t.c.2285.8 48 63.13 odd 6