Properties

Label 242.4.c.q.9.2
Level $242$
Weight $4$
Character 242.9
Analytic conductor $14.278$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [242,4,Mod(3,242)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(242, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("242.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 242 = 2 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 242.c (of order \(5\), degree \(4\), 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: \(14.2784622214\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 71x^{6} - 141x^{5} + 2911x^{4} + 2710x^{3} + 75340x^{2} + 169400x + 5856400 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 22)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 9.2
Root \(2.22300 - 6.84169i\) of defining polynomial
Character \(\chi\) \(=\) 242.9
Dual form 242.4.c.q.27.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.618034 - 1.90211i) q^{2} +(6.31989 - 4.59167i) q^{3} +(-3.23607 - 2.35114i) q^{4} +(4.60996 + 14.1880i) q^{5} +(-4.82797 - 14.8590i) q^{6} +(17.6106 + 12.7948i) q^{7} +(-6.47214 + 4.70228i) q^{8} +(10.5141 - 32.3592i) q^{9} +O(q^{10})\) \(q+(0.618034 - 1.90211i) q^{2} +(6.31989 - 4.59167i) q^{3} +(-3.23607 - 2.35114i) q^{4} +(4.60996 + 14.1880i) q^{5} +(-4.82797 - 14.8590i) q^{6} +(17.6106 + 12.7948i) q^{7} +(-6.47214 + 4.70228i) q^{8} +(10.5141 - 32.3592i) q^{9} +29.8363 q^{10} -31.2473 q^{12} +(13.6056 - 41.8736i) q^{13} +(35.2211 - 25.5896i) q^{14} +(94.2810 + 68.4992i) q^{15} +(4.94427 + 15.2169i) q^{16} +(7.69900 + 23.6951i) q^{17} +(-55.0527 - 39.9982i) q^{18} +(17.7638 - 12.9061i) q^{19} +(18.4398 - 56.7520i) q^{20} +170.046 q^{21} +177.749 q^{23} +(-19.3119 + 59.4358i) q^{24} +(-78.9203 + 57.3389i) q^{25} +(-71.2397 - 51.7587i) q^{26} +(-16.9569 - 52.1881i) q^{27} +(-26.9065 - 82.8098i) q^{28} +(-120.864 - 87.8130i) q^{29} +(188.562 - 136.998i) q^{30} +(23.2207 - 71.4658i) q^{31} +32.0000 q^{32} +49.8290 q^{34} +(-100.349 + 308.842i) q^{35} +(-110.105 + 79.9963i) q^{36} +(-179.874 - 130.686i) q^{37} +(-13.5703 - 41.7652i) q^{38} +(-106.284 - 327.109i) q^{39} +(-96.5522 - 70.1493i) q^{40} +(-204.779 + 148.781i) q^{41} +(105.094 - 323.448i) q^{42} -130.623 q^{43} +507.582 q^{45} +(109.855 - 338.099i) q^{46} +(-403.775 + 293.360i) q^{47} +(101.118 + 73.4667i) q^{48} +(40.4316 + 124.436i) q^{49} +(60.2897 + 185.553i) q^{50} +(157.457 + 114.399i) q^{51} +(-142.479 + 103.517i) q^{52} +(3.99933 - 12.3087i) q^{53} -109.748 q^{54} -174.143 q^{56} +(53.0044 - 163.131i) q^{57} +(-241.728 + 175.626i) q^{58} +(-28.7697 - 20.9024i) q^{59} +(-144.049 - 443.336i) q^{60} +(-166.357 - 511.995i) q^{61} +(-121.585 - 88.3366i) q^{62} +(599.190 - 435.337i) q^{63} +(19.7771 - 60.8676i) q^{64} +656.824 q^{65} -519.621 q^{67} +(30.7960 - 94.7804i) q^{68} +(1123.35 - 816.165i) q^{69} +(525.434 + 381.750i) q^{70} +(24.2420 + 74.6091i) q^{71} +(84.1131 + 258.873i) q^{72} +(925.571 + 672.467i) q^{73} +(-359.748 + 261.372i) q^{74} +(-235.486 + 724.752i) q^{75} -87.8290 q^{76} -687.886 q^{78} +(-238.730 + 734.735i) q^{79} +(-193.104 + 140.299i) q^{80} +(396.416 + 288.013i) q^{81} +(156.438 + 481.465i) q^{82} +(-166.017 - 510.947i) q^{83} +(-550.282 - 399.803i) q^{84} +(-300.694 + 218.467i) q^{85} +(-80.7296 + 248.460i) q^{86} -1167.06 q^{87} +667.089 q^{89} +(313.703 - 965.477i) q^{90} +(775.368 - 563.338i) q^{91} +(-575.208 - 417.913i) q^{92} +(-181.395 - 558.278i) q^{93} +(308.457 + 949.332i) q^{94} +(265.003 + 192.536i) q^{95} +(202.237 - 146.933i) q^{96} +(-55.5161 + 170.861i) q^{97} +261.679 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} + 3 q^{3} - 8 q^{4} + 5 q^{5} - 14 q^{6} + q^{7} - 16 q^{8} - 21 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} + 3 q^{3} - 8 q^{4} + 5 q^{5} - 14 q^{6} + q^{7} - 16 q^{8} - 21 q^{9} + 100 q^{10} + 32 q^{12} - 7 q^{13} + 2 q^{14} + 211 q^{15} - 32 q^{16} - 161 q^{17} - 162 q^{18} + 272 q^{19} + 20 q^{20} + 50 q^{21} + 628 q^{23} - 56 q^{24} - 17 q^{25} + 96 q^{26} - 528 q^{27} - 16 q^{28} - 33 q^{29} + 422 q^{30} + 323 q^{31} + 256 q^{32} + 208 q^{34} + 697 q^{35} - 324 q^{36} + 49 q^{37} - 576 q^{38} - 391 q^{39} - 240 q^{40} - 361 q^{41} + 1430 q^{42} - 1442 q^{43} + 2652 q^{45} + 416 q^{46} - 1069 q^{47} + 48 q^{48} - 709 q^{49} + 76 q^{50} + 1332 q^{51} + 192 q^{52} - 281 q^{53} + 1144 q^{54} + 48 q^{56} + 438 q^{57} - 66 q^{58} - 128 q^{59} - 1116 q^{60} + 617 q^{61} - 1044 q^{62} - 694 q^{63} - 128 q^{64} + 138 q^{65} + 578 q^{67} - 644 q^{68} - 310 q^{69} + 34 q^{70} + 115 q^{71} - 168 q^{72} + 1487 q^{73} + 98 q^{74} - 1852 q^{75} + 128 q^{76} - 4152 q^{78} - 71 q^{79} - 480 q^{80} + 1630 q^{81} + 658 q^{82} - 1942 q^{83} - 2960 q^{84} + 329 q^{85} + 2426 q^{86} - 2122 q^{87} - 2202 q^{89} - 1286 q^{90} + 4523 q^{91} - 2088 q^{92} + 6019 q^{93} + 1332 q^{94} + 793 q^{95} + 96 q^{96} - 5128 q^{97} + 3292 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/242\mathbb{Z}\right)^\times\).

\(n\) \(123\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.618034 1.90211i 0.218508 0.672499i
\(3\) 6.31989 4.59167i 1.21626 0.883667i 0.220479 0.975392i \(-0.429238\pi\)
0.995784 + 0.0917244i \(0.0292379\pi\)
\(4\) −3.23607 2.35114i −0.404508 0.293893i
\(5\) 4.60996 + 14.1880i 0.412327 + 1.26901i 0.914620 + 0.404315i \(0.132490\pi\)
−0.502293 + 0.864698i \(0.667510\pi\)
\(6\) −4.82797 14.8590i −0.328502 1.01102i
\(7\) 17.6106 + 12.7948i 0.950881 + 0.690856i 0.951015 0.309144i \(-0.100043\pi\)
−0.000134039 1.00000i \(0.500043\pi\)
\(8\) −6.47214 + 4.70228i −0.286031 + 0.207813i
\(9\) 10.5141 32.3592i 0.389412 1.19849i
\(10\) 29.8363 0.943506
\(11\) 0 0
\(12\) −31.2473 −0.751692
\(13\) 13.6056 41.8736i 0.290270 0.893358i −0.694500 0.719493i \(-0.744374\pi\)
0.984769 0.173865i \(-0.0556258\pi\)
\(14\) 35.2211 25.5896i 0.672374 0.488509i
\(15\) 94.2810 + 68.4992i 1.62288 + 1.17909i
\(16\) 4.94427 + 15.2169i 0.0772542 + 0.237764i
\(17\) 7.69900 + 23.6951i 0.109840 + 0.338053i 0.990836 0.135071i \(-0.0431262\pi\)
−0.880996 + 0.473124i \(0.843126\pi\)
\(18\) −55.0527 39.9982i −0.720892 0.523759i
\(19\) 17.7638 12.9061i 0.214489 0.155835i −0.475353 0.879795i \(-0.657680\pi\)
0.689842 + 0.723960i \(0.257680\pi\)
\(20\) 18.4398 56.7520i 0.206164 0.634506i
\(21\) 170.046 1.76701
\(22\) 0 0
\(23\) 177.749 1.61145 0.805723 0.592293i \(-0.201777\pi\)
0.805723 + 0.592293i \(0.201777\pi\)
\(24\) −19.3119 + 59.4358i −0.164251 + 0.505512i
\(25\) −78.9203 + 57.3389i −0.631362 + 0.458711i
\(26\) −71.2397 51.7587i −0.537356 0.390412i
\(27\) −16.9569 52.1881i −0.120865 0.371985i
\(28\) −26.9065 82.8098i −0.181602 0.558914i
\(29\) −120.864 87.8130i −0.773928 0.562292i 0.129223 0.991616i \(-0.458752\pi\)
−0.903151 + 0.429324i \(0.858752\pi\)
\(30\) 188.562 136.998i 1.14755 0.833745i
\(31\) 23.2207 71.4658i 0.134534 0.414053i −0.860983 0.508633i \(-0.830151\pi\)
0.995517 + 0.0945803i \(0.0301509\pi\)
\(32\) 32.0000 0.176777
\(33\) 0 0
\(34\) 49.8290 0.251341
\(35\) −100.349 + 308.842i −0.484630 + 1.49154i
\(36\) −110.105 + 79.9963i −0.509748 + 0.370353i
\(37\) −179.874 130.686i −0.799219 0.580667i 0.111466 0.993768i \(-0.464445\pi\)
−0.910685 + 0.413102i \(0.864445\pi\)
\(38\) −13.5703 41.7652i −0.0579315 0.178295i
\(39\) −106.284 327.109i −0.436387 1.34306i
\(40\) −96.5522 70.1493i −0.381656 0.277289i
\(41\) −204.779 + 148.781i −0.780029 + 0.566724i −0.904988 0.425438i \(-0.860120\pi\)
0.124959 + 0.992162i \(0.460120\pi\)
\(42\) 105.094 323.448i 0.386106 1.18831i
\(43\) −130.623 −0.463253 −0.231626 0.972805i \(-0.574405\pi\)
−0.231626 + 0.972805i \(0.574405\pi\)
\(44\) 0 0
\(45\) 507.582 1.68146
\(46\) 109.855 338.099i 0.352114 1.08369i
\(47\) −403.775 + 293.360i −1.25312 + 0.910445i −0.998399 0.0565693i \(-0.981984\pi\)
−0.254722 + 0.967014i \(0.581984\pi\)
\(48\) 101.118 + 73.4667i 0.304066 + 0.220917i
\(49\) 40.4316 + 124.436i 0.117876 + 0.362786i
\(50\) 60.2897 + 185.553i 0.170525 + 0.524822i
\(51\) 157.457 + 114.399i 0.432321 + 0.314100i
\(52\) −142.479 + 103.517i −0.379968 + 0.276063i
\(53\) 3.99933 12.3087i 0.0103651 0.0319005i −0.945740 0.324924i \(-0.894661\pi\)
0.956105 + 0.293023i \(0.0946613\pi\)
\(54\) −109.748 −0.276569
\(55\) 0 0
\(56\) −174.143 −0.415550
\(57\) 53.0044 163.131i 0.123169 0.379074i
\(58\) −241.728 + 175.626i −0.547250 + 0.397600i
\(59\) −28.7697 20.9024i −0.0634831 0.0461232i 0.555591 0.831456i \(-0.312492\pi\)
−0.619074 + 0.785332i \(0.712492\pi\)
\(60\) −144.049 443.336i −0.309943 0.953907i
\(61\) −166.357 511.995i −0.349178 1.07466i −0.959309 0.282359i \(-0.908883\pi\)
0.610131 0.792301i \(-0.291117\pi\)
\(62\) −121.585 88.3366i −0.249053 0.180948i
\(63\) 599.190 435.337i 1.19827 0.870592i
\(64\) 19.7771 60.8676i 0.0386271 0.118882i
\(65\) 656.824 1.25337
\(66\) 0 0
\(67\) −519.621 −0.947491 −0.473745 0.880662i \(-0.657098\pi\)
−0.473745 + 0.880662i \(0.657098\pi\)
\(68\) 30.7960 94.7804i 0.0549201 0.169027i
\(69\) 1123.35 816.165i 1.95994 1.42398i
\(70\) 525.434 + 381.750i 0.897162 + 0.651826i
\(71\) 24.2420 + 74.6091i 0.0405210 + 0.124711i 0.969271 0.245997i \(-0.0791152\pi\)
−0.928750 + 0.370708i \(0.879115\pi\)
\(72\) 84.1131 + 258.873i 0.137678 + 0.423730i
\(73\) 925.571 + 672.467i 1.48397 + 1.07817i 0.976250 + 0.216648i \(0.0695123\pi\)
0.507722 + 0.861521i \(0.330488\pi\)
\(74\) −359.748 + 261.372i −0.565133 + 0.410593i
\(75\) −235.486 + 724.752i −0.362555 + 1.11583i
\(76\) −87.8290 −0.132562
\(77\) 0 0
\(78\) −687.886 −0.998561
\(79\) −238.730 + 734.735i −0.339990 + 1.04638i 0.624222 + 0.781247i \(0.285416\pi\)
−0.964212 + 0.265134i \(0.914584\pi\)
\(80\) −193.104 + 140.299i −0.269872 + 0.196073i
\(81\) 396.416 + 288.013i 0.543780 + 0.395079i
\(82\) 156.438 + 481.465i 0.210678 + 0.648402i
\(83\) −166.017 510.947i −0.219551 0.675708i −0.998799 0.0489926i \(-0.984399\pi\)
0.779248 0.626715i \(-0.215601\pi\)
\(84\) −550.282 399.803i −0.714770 0.519311i
\(85\) −300.694 + 218.467i −0.383704 + 0.278777i
\(86\) −80.7296 + 248.460i −0.101224 + 0.311537i
\(87\) −1167.06 −1.43818
\(88\) 0 0
\(89\) 667.089 0.794509 0.397255 0.917708i \(-0.369963\pi\)
0.397255 + 0.917708i \(0.369963\pi\)
\(90\) 313.703 965.477i 0.367413 1.13078i
\(91\) 775.368 563.338i 0.893194 0.648943i
\(92\) −575.208 417.913i −0.651843 0.473592i
\(93\) −181.395 558.278i −0.202256 0.622481i
\(94\) 308.457 + 949.332i 0.338456 + 1.04166i
\(95\) 265.003 + 192.536i 0.286197 + 0.207934i
\(96\) 202.237 146.933i 0.215007 0.156212i
\(97\) −55.5161 + 170.861i −0.0581114 + 0.178848i −0.975899 0.218224i \(-0.929974\pi\)
0.917787 + 0.397072i \(0.129974\pi\)
\(98\) 261.679 0.269730
\(99\) 0 0
\(100\) 390.203 0.390203
\(101\) 126.924 390.633i 0.125044 0.384846i −0.868865 0.495049i \(-0.835150\pi\)
0.993909 + 0.110203i \(0.0351502\pi\)
\(102\) 314.914 228.798i 0.305697 0.222102i
\(103\) −1106.46 803.890i −1.05847 0.769026i −0.0846679 0.996409i \(-0.526983\pi\)
−0.973805 + 0.227383i \(0.926983\pi\)
\(104\) 108.845 + 334.989i 0.102626 + 0.315850i
\(105\) 783.907 + 2412.62i 0.728586 + 2.24236i
\(106\) −20.9408 15.2144i −0.0191882 0.0139410i
\(107\) −319.756 + 232.317i −0.288897 + 0.209896i −0.722789 0.691069i \(-0.757140\pi\)
0.433892 + 0.900965i \(0.357140\pi\)
\(108\) −67.8277 + 208.752i −0.0604326 + 0.185993i
\(109\) −505.826 −0.444490 −0.222245 0.974991i \(-0.571338\pi\)
−0.222245 + 0.974991i \(0.571338\pi\)
\(110\) 0 0
\(111\) −1736.85 −1.48518
\(112\) −107.626 + 331.239i −0.0908011 + 0.279457i
\(113\) −1243.96 + 903.793i −1.03560 + 0.752404i −0.969421 0.245404i \(-0.921079\pi\)
−0.0661744 + 0.997808i \(0.521079\pi\)
\(114\) −277.535 201.641i −0.228013 0.165661i
\(115\) 819.416 + 2521.90i 0.664443 + 2.04494i
\(116\) 184.664 + 568.337i 0.147807 + 0.454903i
\(117\) −1211.95 880.530i −0.957645 0.695770i
\(118\) −57.5395 + 41.8049i −0.0448893 + 0.0326140i
\(119\) −167.591 + 515.791i −0.129101 + 0.397332i
\(120\) −932.302 −0.709226
\(121\) 0 0
\(122\) −1076.69 −0.799005
\(123\) −611.031 + 1880.56i −0.447925 + 1.37857i
\(124\) −243.170 + 176.673i −0.176107 + 0.127949i
\(125\) 331.285 + 240.693i 0.237048 + 0.172226i
\(126\) −457.740 1408.78i −0.323641 0.996064i
\(127\) 215.487 + 663.202i 0.150562 + 0.463383i 0.997684 0.0680154i \(-0.0216667\pi\)
−0.847122 + 0.531399i \(0.821667\pi\)
\(128\) −103.554 75.2365i −0.0715077 0.0519534i
\(129\) −825.525 + 599.779i −0.563437 + 0.409361i
\(130\) 405.940 1249.35i 0.273871 0.842889i
\(131\) 259.910 0.173347 0.0866735 0.996237i \(-0.472376\pi\)
0.0866735 + 0.996237i \(0.472376\pi\)
\(132\) 0 0
\(133\) 477.962 0.311613
\(134\) −321.144 + 988.379i −0.207034 + 0.637186i
\(135\) 662.273 481.170i 0.422218 0.306759i
\(136\) −161.250 117.155i −0.101670 0.0738673i
\(137\) −643.856 1981.58i −0.401520 1.23575i −0.923766 0.382958i \(-0.874906\pi\)
0.522245 0.852795i \(-0.325094\pi\)
\(138\) −858.167 2641.17i −0.529362 1.62921i
\(139\) 140.307 + 101.939i 0.0856163 + 0.0622039i 0.629770 0.776782i \(-0.283149\pi\)
−0.544154 + 0.838986i \(0.683149\pi\)
\(140\) 1050.87 763.500i 0.634389 0.460911i
\(141\) −1204.80 + 3708.00i −0.719594 + 2.21468i
\(142\) 156.897 0.0927220
\(143\) 0 0
\(144\) 544.391 0.315041
\(145\) 688.711 2119.63i 0.394444 1.21397i
\(146\) 1851.14 1344.93i 1.04933 0.762380i
\(147\) 826.891 + 600.772i 0.463951 + 0.337080i
\(148\) 274.823 + 845.818i 0.152637 + 0.469769i
\(149\) 138.766 + 427.077i 0.0762961 + 0.234815i 0.981930 0.189246i \(-0.0606042\pi\)
−0.905634 + 0.424061i \(0.860604\pi\)
\(150\) 1233.02 + 895.842i 0.671172 + 0.487635i
\(151\) 23.0859 16.7729i 0.0124418 0.00903947i −0.581547 0.813513i \(-0.697552\pi\)
0.593989 + 0.804473i \(0.297552\pi\)
\(152\) −54.2813 + 167.061i −0.0289658 + 0.0891474i
\(153\) 847.702 0.447926
\(154\) 0 0
\(155\) 1121.00 0.580910
\(156\) −425.137 + 1308.44i −0.218194 + 0.671531i
\(157\) −1394.63 + 1013.26i −0.708941 + 0.515076i −0.882832 0.469689i \(-0.844366\pi\)
0.173891 + 0.984765i \(0.444366\pi\)
\(158\) 1250.01 + 908.182i 0.629399 + 0.457285i
\(159\) −31.2420 96.1531i −0.0155827 0.0479587i
\(160\) 147.519 + 454.016i 0.0728898 + 0.224332i
\(161\) 3130.26 + 2274.27i 1.53229 + 1.11328i
\(162\) 792.831 576.026i 0.384510 0.279363i
\(163\) 1025.39 3155.82i 0.492727 1.51646i −0.327743 0.944767i \(-0.606288\pi\)
0.820470 0.571690i \(-0.193712\pi\)
\(164\) 1012.49 0.482084
\(165\) 0 0
\(166\) −1074.48 −0.502386
\(167\) 931.871 2868.00i 0.431799 1.32894i −0.464533 0.885556i \(-0.653778\pi\)
0.896332 0.443384i \(-0.146222\pi\)
\(168\) −1100.56 + 799.606i −0.505419 + 0.367208i
\(169\) 209.120 + 151.934i 0.0951842 + 0.0691554i
\(170\) 229.710 + 706.973i 0.103635 + 0.318955i
\(171\) −230.862 710.519i −0.103242 0.317747i
\(172\) 422.706 + 307.114i 0.187390 + 0.136147i
\(173\) −1787.45 + 1298.66i −0.785534 + 0.570724i −0.906635 0.421917i \(-0.861357\pi\)
0.121101 + 0.992640i \(0.461357\pi\)
\(174\) −721.281 + 2219.87i −0.314254 + 0.967173i
\(175\) −2123.47 −0.917254
\(176\) 0 0
\(177\) −277.799 −0.117970
\(178\) 412.284 1268.88i 0.173607 0.534306i
\(179\) 1837.95 1335.35i 0.767457 0.557590i −0.133731 0.991018i \(-0.542696\pi\)
0.901189 + 0.433427i \(0.142696\pi\)
\(180\) −1642.57 1193.40i −0.680166 0.494169i
\(181\) −192.961 593.873i −0.0792413 0.243880i 0.903586 0.428406i \(-0.140925\pi\)
−0.982828 + 0.184527i \(0.940925\pi\)
\(182\) −592.328 1823.00i −0.241243 0.742471i
\(183\) −3402.27 2471.89i −1.37433 0.998512i
\(184\) −1150.42 + 835.826i −0.460923 + 0.334880i
\(185\) 1024.96 3154.51i 0.407333 1.25364i
\(186\) −1174.02 −0.462812
\(187\) 0 0
\(188\) 1996.37 0.774471
\(189\) 369.116 1136.02i 0.142059 0.437214i
\(190\) 530.005 385.071i 0.202372 0.147032i
\(191\) 1087.48 + 790.100i 0.411975 + 0.299317i 0.774401 0.632695i \(-0.218051\pi\)
−0.362426 + 0.932013i \(0.618051\pi\)
\(192\) −154.495 475.487i −0.0580714 0.178725i
\(193\) −1428.82 4397.46i −0.532895 1.64008i −0.748154 0.663526i \(-0.769059\pi\)
0.215258 0.976557i \(-0.430941\pi\)
\(194\) 290.686 + 211.196i 0.107578 + 0.0781597i
\(195\) 4151.06 3015.92i 1.52443 1.10756i
\(196\) 161.726 497.743i 0.0589382 0.181393i
\(197\) −664.691 −0.240392 −0.120196 0.992750i \(-0.538352\pi\)
−0.120196 + 0.992750i \(0.538352\pi\)
\(198\) 0 0
\(199\) −3042.82 −1.08392 −0.541959 0.840405i \(-0.682317\pi\)
−0.541959 + 0.840405i \(0.682317\pi\)
\(200\) 241.159 742.211i 0.0852625 0.262411i
\(201\) −3283.95 + 2385.93i −1.15240 + 0.837266i
\(202\) −664.584 482.849i −0.231485 0.168184i
\(203\) −1004.93 3092.87i −0.347451 1.06934i
\(204\) −240.573 740.407i −0.0825660 0.254112i
\(205\) −3054.93 2219.53i −1.04081 0.756190i
\(206\) −2212.92 + 1607.78i −0.748454 + 0.543783i
\(207\) 1868.88 5751.81i 0.627517 1.93130i
\(208\) 704.457 0.234833
\(209\) 0 0
\(210\) 5073.55 1.66718
\(211\) −800.851 + 2464.77i −0.261293 + 0.804178i 0.731231 + 0.682130i \(0.238946\pi\)
−0.992524 + 0.122048i \(0.961054\pi\)
\(212\) −41.8815 + 30.4287i −0.0135681 + 0.00985779i
\(213\) 495.787 + 360.210i 0.159487 + 0.115874i
\(214\) 244.272 + 751.792i 0.0780285 + 0.240147i
\(215\) −602.168 1853.28i −0.191012 0.587873i
\(216\) 355.151 + 258.032i 0.111875 + 0.0812817i
\(217\) 1323.32 961.449i 0.413977 0.300772i
\(218\) −312.618 + 962.139i −0.0971245 + 0.298919i
\(219\) 8937.26 2.75764
\(220\) 0 0
\(221\) 1096.95 0.333886
\(222\) −1073.43 + 3303.69i −0.324523 + 0.998779i
\(223\) −2133.54 + 1550.11i −0.640684 + 0.465484i −0.860085 0.510150i \(-0.829590\pi\)
0.219401 + 0.975635i \(0.429590\pi\)
\(224\) 563.538 + 409.434i 0.168094 + 0.122127i
\(225\) 1025.66 + 3156.66i 0.303900 + 0.935308i
\(226\) 950.304 + 2924.73i 0.279705 + 0.860843i
\(227\) 202.796 + 147.340i 0.0592954 + 0.0430806i 0.617038 0.786933i \(-0.288332\pi\)
−0.557743 + 0.830014i \(0.688332\pi\)
\(228\) −555.070 + 403.282i −0.161230 + 0.117140i
\(229\) 556.018 1711.25i 0.160449 0.493810i −0.838224 0.545327i \(-0.816406\pi\)
0.998672 + 0.0515169i \(0.0164056\pi\)
\(230\) 5303.37 1.52041
\(231\) 0 0
\(232\) 1195.17 0.338219
\(233\) −982.821 + 3024.81i −0.276338 + 0.850481i 0.712524 + 0.701647i \(0.247552\pi\)
−0.988862 + 0.148833i \(0.952448\pi\)
\(234\) −2423.89 + 1761.06i −0.677157 + 0.491984i
\(235\) −6023.57 4376.38i −1.67206 1.21482i
\(236\) 43.9563 + 135.283i 0.0121242 + 0.0373144i
\(237\) 1864.91 + 5739.61i 0.511135 + 1.57311i
\(238\) 877.517 + 637.553i 0.238996 + 0.173641i
\(239\) 4056.25 2947.04i 1.09781 0.797608i 0.117111 0.993119i \(-0.462637\pi\)
0.980701 + 0.195511i \(0.0626366\pi\)
\(240\) −576.194 + 1773.34i −0.154972 + 0.476953i
\(241\) −6074.13 −1.62352 −0.811761 0.583990i \(-0.801491\pi\)
−0.811761 + 0.583990i \(0.801491\pi\)
\(242\) 0 0
\(243\) 5309.35 1.40163
\(244\) −665.429 + 2047.98i −0.174589 + 0.537330i
\(245\) −1579.10 + 1147.29i −0.411777 + 0.299173i
\(246\) 3199.40 + 2324.50i 0.829212 + 0.602458i
\(247\) −298.741 919.430i −0.0769572 0.236850i
\(248\) 185.765 + 571.727i 0.0475649 + 0.146390i
\(249\) −3395.31 2466.84i −0.864132 0.627829i
\(250\) 662.570 481.385i 0.167618 0.121782i
\(251\) −1721.13 + 5297.09i −0.432816 + 1.33207i 0.462493 + 0.886623i \(0.346955\pi\)
−0.895309 + 0.445447i \(0.853045\pi\)
\(252\) −2962.56 −0.740570
\(253\) 0 0
\(254\) 1394.66 0.344524
\(255\) −897.224 + 2761.37i −0.220339 + 0.678133i
\(256\) −207.108 + 150.473i −0.0505636 + 0.0367366i
\(257\) 4778.90 + 3472.08i 1.15992 + 0.842732i 0.989768 0.142685i \(-0.0455737\pi\)
0.170153 + 0.985418i \(0.445574\pi\)
\(258\) 630.645 + 1940.93i 0.152179 + 0.468359i
\(259\) −1495.58 4602.91i −0.358805 1.10429i
\(260\) −2125.53 1544.29i −0.506998 0.368356i
\(261\) −4112.34 + 2987.79i −0.975277 + 0.708580i
\(262\) 160.633 494.379i 0.0378777 0.116576i
\(263\) 6853.74 1.60692 0.803459 0.595360i \(-0.202991\pi\)
0.803459 + 0.595360i \(0.202991\pi\)
\(264\) 0 0
\(265\) 193.072 0.0447559
\(266\) 295.397 909.138i 0.0680900 0.209560i
\(267\) 4215.93 3063.05i 0.966333 0.702082i
\(268\) 1681.53 + 1221.70i 0.383268 + 0.278460i
\(269\) 340.340 + 1047.46i 0.0771409 + 0.237415i 0.982190 0.187893i \(-0.0601657\pi\)
−0.905049 + 0.425308i \(0.860166\pi\)
\(270\) −505.932 1557.10i −0.114037 0.350970i
\(271\) −2080.54 1511.60i −0.466362 0.338832i 0.329660 0.944100i \(-0.393066\pi\)
−0.796022 + 0.605268i \(0.793066\pi\)
\(272\) −322.500 + 234.310i −0.0718913 + 0.0522321i
\(273\) 2313.58 7120.46i 0.512909 1.57857i
\(274\) −4167.12 −0.918777
\(275\) 0 0
\(276\) −5554.17 −1.21131
\(277\) 2268.22 6980.85i 0.492000 1.51422i −0.329581 0.944127i \(-0.606908\pi\)
0.821581 0.570092i \(-0.193092\pi\)
\(278\) 280.613 203.878i 0.0605398 0.0439848i
\(279\) −2068.43 1502.80i −0.443848 0.322475i
\(280\) −802.791 2470.74i −0.171343 0.527338i
\(281\) 2315.45 + 7126.21i 0.491559 + 1.51286i 0.822252 + 0.569124i \(0.192718\pi\)
−0.330693 + 0.943738i \(0.607282\pi\)
\(282\) 6308.43 + 4583.34i 1.33213 + 0.967852i
\(283\) −5253.84 + 3817.14i −1.10356 + 0.801785i −0.981638 0.190754i \(-0.938907\pi\)
−0.121925 + 0.992539i \(0.538907\pi\)
\(284\) 96.9678 298.436i 0.0202605 0.0623554i
\(285\) 2558.85 0.531835
\(286\) 0 0
\(287\) −5509.91 −1.13324
\(288\) 336.452 1035.49i 0.0688390 0.211865i
\(289\) 3472.52 2522.93i 0.706802 0.513522i
\(290\) −3606.14 2620.01i −0.730206 0.530525i
\(291\) 433.681 + 1334.73i 0.0873638 + 0.268878i
\(292\) −1414.15 4352.30i −0.283413 0.872257i
\(293\) −2172.11 1578.13i −0.433092 0.314660i 0.349792 0.936827i \(-0.386252\pi\)
−0.782884 + 0.622168i \(0.786252\pi\)
\(294\) 1653.78 1201.54i 0.328063 0.238352i
\(295\) 163.936 504.544i 0.0323551 0.0995787i
\(296\) 1778.69 0.349271
\(297\) 0 0
\(298\) 898.110 0.174584
\(299\) 2418.38 7443.00i 0.467754 1.43960i
\(300\) 2466.04 1791.68i 0.474590 0.344810i
\(301\) −2300.35 1671.30i −0.440498 0.320041i
\(302\) −17.6361 54.2783i −0.00336041 0.0103423i
\(303\) −991.509 3051.55i −0.187989 0.578571i
\(304\) 284.221 + 206.498i 0.0536223 + 0.0389589i
\(305\) 6497.28 4720.55i 1.21978 0.886223i
\(306\) 523.909 1612.43i 0.0978754 0.301230i
\(307\) −8331.66 −1.54890 −0.774451 0.632633i \(-0.781974\pi\)
−0.774451 + 0.632633i \(0.781974\pi\)
\(308\) 0 0
\(309\) −10683.9 −1.96695
\(310\) 692.818 2132.27i 0.126934 0.390661i
\(311\) 4061.55 2950.89i 0.740545 0.538037i −0.152337 0.988329i \(-0.548680\pi\)
0.892882 + 0.450292i \(0.148680\pi\)
\(312\) 2226.05 + 1617.32i 0.403926 + 0.293470i
\(313\) 933.873 + 2874.16i 0.168644 + 0.519033i 0.999286 0.0377733i \(-0.0120265\pi\)
−0.830642 + 0.556807i \(0.812026\pi\)
\(314\) 1065.40 + 3278.98i 0.191479 + 0.589310i
\(315\) 8938.80 + 6494.42i 1.59887 + 1.16165i
\(316\) 2500.01 1816.36i 0.445052 0.323350i
\(317\) −3257.08 + 10024.3i −0.577085 + 1.77609i 0.0518809 + 0.998653i \(0.483478\pi\)
−0.628966 + 0.777433i \(0.716522\pi\)
\(318\) −202.203 −0.0356571
\(319\) 0 0
\(320\) 954.761 0.166790
\(321\) −954.104 + 2936.43i −0.165897 + 0.510578i
\(322\) 6260.52 4548.54i 1.08349 0.787205i
\(323\) 442.576 + 321.550i 0.0762402 + 0.0553917i
\(324\) −605.669 1864.06i −0.103853 0.319626i
\(325\) 1327.23 + 4084.81i 0.226528 + 0.697183i
\(326\) −5368.99 3900.80i −0.912150 0.662716i
\(327\) −3196.77 + 2322.59i −0.540617 + 0.392781i
\(328\) 625.750 1925.86i 0.105339 0.324201i
\(329\) −10864.2 −1.82055
\(330\) 0 0
\(331\) 309.871 0.0514563 0.0257281 0.999669i \(-0.491810\pi\)
0.0257281 + 0.999669i \(0.491810\pi\)
\(332\) −664.067 + 2043.79i −0.109775 + 0.337854i
\(333\) −6120.11 + 4446.52i −1.00715 + 0.731736i
\(334\) −4879.34 3545.05i −0.799358 0.580768i
\(335\) −2395.43 7372.39i −0.390676 1.20238i
\(336\) 840.756 + 2587.58i 0.136509 + 0.420131i
\(337\) 9032.40 + 6562.42i 1.46002 + 1.06076i 0.983358 + 0.181677i \(0.0581525\pi\)
0.476659 + 0.879088i \(0.341848\pi\)
\(338\) 418.239 303.869i 0.0673054 0.0489002i
\(339\) −3711.80 + 11423.7i −0.594682 + 1.83024i
\(340\) 1486.71 0.237142
\(341\) 0 0
\(342\) −1494.17 −0.236244
\(343\) 1427.13 4392.25i 0.224658 0.691425i
\(344\) 845.412 614.227i 0.132504 0.0962701i
\(345\) 16758.4 + 12175.7i 2.61519 + 1.90005i
\(346\) 1365.49 + 4202.55i 0.212165 + 0.652978i
\(347\) −777.327 2392.37i −0.120257 0.370112i 0.872750 0.488167i \(-0.162334\pi\)
−0.993007 + 0.118055i \(0.962334\pi\)
\(348\) 3776.67 + 2743.91i 0.581756 + 0.422670i
\(349\) −9203.85 + 6686.99i −1.41166 + 1.02563i −0.418587 + 0.908177i \(0.637474\pi\)
−0.993078 + 0.117457i \(0.962526\pi\)
\(350\) −1312.38 + 4039.08i −0.200427 + 0.616852i
\(351\) −2416.01 −0.367400
\(352\) 0 0
\(353\) 6210.08 0.936343 0.468172 0.883638i \(-0.344913\pi\)
0.468172 + 0.883638i \(0.344913\pi\)
\(354\) −171.689 + 528.405i −0.0257773 + 0.0793344i
\(355\) −946.799 + 687.889i −0.141552 + 0.102843i
\(356\) −2158.75 1568.42i −0.321386 0.233500i
\(357\) 1309.19 + 4029.27i 0.194088 + 0.597343i
\(358\) −1404.07 4321.28i −0.207283 0.637952i
\(359\) −2012.43 1462.12i −0.295856 0.214952i 0.429948 0.902854i \(-0.358532\pi\)
−0.725804 + 0.687902i \(0.758532\pi\)
\(360\) −3285.14 + 2386.79i −0.480950 + 0.349430i
\(361\) −1970.56 + 6064.77i −0.287296 + 0.884207i
\(362\) −1248.87 −0.181324
\(363\) 0 0
\(364\) −3833.63 −0.552024
\(365\) −5274.11 + 16232.0i −0.756328 + 2.32774i
\(366\) −6804.54 + 4943.79i −0.971801 + 0.706055i
\(367\) −5436.21 3949.64i −0.773209 0.561770i 0.129724 0.991550i \(-0.458591\pi\)
−0.902933 + 0.429781i \(0.858591\pi\)
\(368\) 878.840 + 2704.79i 0.124491 + 0.383144i
\(369\) 2661.35 + 8190.80i 0.375459 + 1.15554i
\(370\) −5366.77 3899.19i −0.754068 0.547862i
\(371\) 227.918 165.592i 0.0318946 0.0231728i
\(372\) −725.582 + 2233.11i −0.101128 + 0.311240i
\(373\) 8614.37 1.19580 0.597902 0.801569i \(-0.296001\pi\)
0.597902 + 0.801569i \(0.296001\pi\)
\(374\) 0 0
\(375\) 3198.87 0.440503
\(376\) 1233.83 3797.33i 0.169228 0.520831i
\(377\) −5321.47 + 3866.28i −0.726976 + 0.528179i
\(378\) −1932.72 1404.20i −0.262985 0.191070i
\(379\) −2474.95 7617.10i −0.335434 1.03236i −0.966508 0.256637i \(-0.917386\pi\)
0.631074 0.775723i \(-0.282614\pi\)
\(380\) −404.888 1246.12i −0.0546587 0.168222i
\(381\) 4407.06 + 3201.92i 0.592600 + 0.430549i
\(382\) 2174.96 1580.20i 0.291310 0.211649i
\(383\) 2475.83 7619.82i 0.330310 1.01659i −0.638676 0.769476i \(-0.720517\pi\)
0.968986 0.247115i \(-0.0794826\pi\)
\(384\) −999.912 −0.132882
\(385\) 0 0
\(386\) −9247.52 −1.21940
\(387\) −1373.39 + 4226.86i −0.180396 + 0.555203i
\(388\) 581.372 422.392i 0.0760688 0.0552672i
\(389\) −6496.09 4719.68i −0.846696 0.615160i 0.0775373 0.996989i \(-0.475294\pi\)
−0.924233 + 0.381829i \(0.875294\pi\)
\(390\) −3171.13 9759.72i −0.411734 1.26719i
\(391\) 1368.49 + 4211.78i 0.177001 + 0.544754i
\(392\) −846.811 615.244i −0.109108 0.0792717i
\(393\) 1642.60 1193.42i 0.210836 0.153181i
\(394\) −410.801 + 1264.32i −0.0525276 + 0.161663i
\(395\) −11524.9 −1.46806
\(396\) 0 0
\(397\) 4435.00 0.560670 0.280335 0.959902i \(-0.409554\pi\)
0.280335 + 0.959902i \(0.409554\pi\)
\(398\) −1880.57 + 5787.79i −0.236845 + 0.728934i
\(399\) 3020.67 2194.64i 0.379004 0.275363i
\(400\) −1262.72 917.423i −0.157841 0.114678i
\(401\) −1214.19 3736.90i −0.151207 0.465366i 0.846550 0.532309i \(-0.178675\pi\)
−0.997757 + 0.0669429i \(0.978675\pi\)
\(402\) 2508.72 + 7721.03i 0.311252 + 0.957936i
\(403\) −2676.60 1944.67i −0.330847 0.240374i
\(404\) −1329.17 + 965.697i −0.163685 + 0.118924i
\(405\) −2258.86 + 6952.07i −0.277145 + 0.852965i
\(406\) −6504.07 −0.795054
\(407\) 0 0
\(408\) −1557.02 −0.188931
\(409\) 4500.59 13851.4i 0.544107 1.67459i −0.178996 0.983850i \(-0.557285\pi\)
0.723103 0.690740i \(-0.242715\pi\)
\(410\) −6109.85 + 4439.07i −0.735961 + 0.534707i
\(411\) −13167.9 9567.02i −1.58035 1.14819i
\(412\) 1690.52 + 5202.89i 0.202150 + 0.622155i
\(413\) −239.208 736.208i −0.0285004 0.0877153i
\(414\) −9785.57 7109.63i −1.16168 0.844008i
\(415\) 6483.98 4710.89i 0.766955 0.557225i
\(416\) 435.378 1339.96i 0.0513129 0.157925i
\(417\) 1354.79 0.159099
\(418\) 0 0
\(419\) 4028.77 0.469734 0.234867 0.972028i \(-0.424535\pi\)
0.234867 + 0.972028i \(0.424535\pi\)
\(420\) 3135.63 9650.47i 0.364293 1.12118i
\(421\) 6898.98 5012.40i 0.798659 0.580260i −0.111861 0.993724i \(-0.535681\pi\)
0.910521 + 0.413464i \(0.135681\pi\)
\(422\) 4193.31 + 3046.62i 0.483714 + 0.351439i
\(423\) 5247.54 + 16150.3i 0.603177 + 1.85639i
\(424\) 31.9946 + 98.4694i 0.00366462 + 0.0112785i
\(425\) −1966.26 1428.57i −0.224418 0.163049i
\(426\) 991.574 720.420i 0.112774 0.0819354i
\(427\) 3621.24 11145.0i 0.410408 1.26310i
\(428\) 1580.96 0.178548
\(429\) 0 0
\(430\) −3897.31 −0.437082
\(431\) −4145.53 + 12758.6i −0.463302 + 1.42590i 0.397803 + 0.917471i \(0.369773\pi\)
−0.861105 + 0.508427i \(0.830227\pi\)
\(432\) 710.301 516.064i 0.0791074 0.0574749i
\(433\) −3343.11 2428.91i −0.371038 0.269575i 0.386603 0.922246i \(-0.373648\pi\)
−0.757641 + 0.652671i \(0.773648\pi\)
\(434\) −1010.93 3111.32i −0.111811 0.344120i
\(435\) −5380.08 16558.2i −0.593000 1.82507i
\(436\) 1636.89 + 1189.27i 0.179800 + 0.130632i
\(437\) 3157.50 2294.06i 0.345637 0.251120i
\(438\) 5523.53 16999.7i 0.602567 1.85451i
\(439\) −3358.46 −0.365126 −0.182563 0.983194i \(-0.558439\pi\)
−0.182563 + 0.983194i \(0.558439\pi\)
\(440\) 0 0
\(441\) 4451.74 0.480698
\(442\) 677.952 2086.52i 0.0729568 0.224538i
\(443\) 357.383 259.654i 0.0383290 0.0278477i −0.568456 0.822714i \(-0.692459\pi\)
0.606785 + 0.794866i \(0.292459\pi\)
\(444\) 5620.57 + 4083.58i 0.600767 + 0.436483i
\(445\) 3075.25 + 9464.66i 0.327598 + 1.00824i
\(446\) 1629.88 + 5016.26i 0.173043 + 0.532571i
\(447\) 2837.98 + 2061.91i 0.300295 + 0.218177i
\(448\) 1127.08 818.869i 0.118860 0.0863569i
\(449\) −126.227 + 388.486i −0.0132673 + 0.0408325i −0.957471 0.288530i \(-0.906834\pi\)
0.944204 + 0.329362i \(0.106834\pi\)
\(450\) 6638.23 0.695398
\(451\) 0 0
\(452\) 6150.49 0.640033
\(453\) 68.8849 212.006i 0.00714458 0.0219888i
\(454\) 405.592 294.680i 0.0419282 0.0304626i
\(455\) 11567.0 + 8403.95i 1.19181 + 0.865897i
\(456\) 424.036 + 1305.05i 0.0435467 + 0.134023i
\(457\) −470.585 1448.31i −0.0481686 0.148248i 0.924079 0.382201i \(-0.124834\pi\)
−0.972248 + 0.233953i \(0.924834\pi\)
\(458\) −2911.35 2115.22i −0.297027 0.215803i
\(459\) 1106.05 803.592i 0.112475 0.0817178i
\(460\) 3277.66 10087.6i 0.332221 1.02247i
\(461\) 13861.4 1.40041 0.700203 0.713944i \(-0.253093\pi\)
0.700203 + 0.713944i \(0.253093\pi\)
\(462\) 0 0
\(463\) −6502.26 −0.652669 −0.326334 0.945254i \(-0.605814\pi\)
−0.326334 + 0.945254i \(0.605814\pi\)
\(464\) 738.656 2273.35i 0.0739036 0.227452i
\(465\) 7084.62 5147.27i 0.706540 0.513331i
\(466\) 5146.12 + 3738.87i 0.511565 + 0.371674i
\(467\) 131.015 + 403.223i 0.0129821 + 0.0399548i 0.957338 0.288971i \(-0.0933132\pi\)
−0.944356 + 0.328926i \(0.893313\pi\)
\(468\) 1851.69 + 5698.91i 0.182894 + 0.562890i
\(469\) −9150.83 6648.46i −0.900951 0.654579i
\(470\) −12047.1 + 8752.76i −1.18233 + 0.859010i
\(471\) −4161.37 + 12807.4i −0.407104 + 1.25294i
\(472\) 284.491 0.0277431
\(473\) 0 0
\(474\) 12070.0 1.16960
\(475\) −661.898 + 2037.11i −0.0639368 + 0.196777i
\(476\) 1755.03 1275.11i 0.168995 0.122782i
\(477\) −356.249 258.830i −0.0341961 0.0248449i
\(478\) −3098.70 9536.82i −0.296509 0.912561i
\(479\) −1408.29 4334.29i −0.134335 0.413442i 0.861151 0.508350i \(-0.169744\pi\)
−0.995486 + 0.0949081i \(0.969744\pi\)
\(480\) 3016.99 + 2191.97i 0.286888 + 0.208436i
\(481\) −7919.59 + 5753.92i −0.750732 + 0.545439i
\(482\) −3754.02 + 11553.7i −0.354753 + 1.09182i
\(483\) 30225.6 2.84744
\(484\) 0 0
\(485\) −2680.10 −0.250922
\(486\) 3281.36 10099.0i 0.306267 0.942592i
\(487\) 5427.63 3943.41i 0.505030 0.366926i −0.305905 0.952062i \(-0.598959\pi\)
0.810935 + 0.585136i \(0.198959\pi\)
\(488\) 3484.23 + 2531.44i 0.323204 + 0.234822i
\(489\) −8010.13 24652.6i −0.740758 2.27982i
\(490\) 1206.33 + 3712.70i 0.111217 + 0.342291i
\(491\) 11753.1 + 8539.14i 1.08027 + 0.784859i 0.977729 0.209870i \(-0.0673040\pi\)
0.102537 + 0.994729i \(0.467304\pi\)
\(492\) 6398.80 4649.00i 0.586341 0.426002i
\(493\) 1150.20 3539.96i 0.105076 0.323391i
\(494\) −1933.49 −0.176097
\(495\) 0 0
\(496\) 1202.30 0.108840
\(497\) −527.695 + 1624.08i −0.0476265 + 0.146579i
\(498\) −6790.62 + 4933.67i −0.611034 + 0.443942i
\(499\) 7847.09 + 5701.24i 0.703976 + 0.511468i 0.881225 0.472698i \(-0.156720\pi\)
−0.177249 + 0.984166i \(0.556720\pi\)
\(500\) −506.158 1557.79i −0.0452722 0.139333i
\(501\) −7279.61 22404.3i −0.649159 1.99791i
\(502\) 9011.95 + 6547.57i 0.801241 + 0.582136i
\(503\) 12707.4 9232.43i 1.12643 0.818397i 0.141256 0.989973i \(-0.454886\pi\)
0.985171 + 0.171576i \(0.0548859\pi\)
\(504\) −1830.96 + 5635.12i −0.161820 + 0.498032i
\(505\) 6127.41 0.539933
\(506\) 0 0
\(507\) 2019.25 0.176879
\(508\) 861.950 2652.81i 0.0752812 0.231692i
\(509\) 1192.56 866.443i 0.103849 0.0754507i −0.534649 0.845074i \(-0.679556\pi\)
0.638498 + 0.769624i \(0.279556\pi\)
\(510\) 4697.93 + 3413.24i 0.407898 + 0.296355i
\(511\) 7695.74 + 23685.0i 0.666222 + 2.05042i
\(512\) 158.217 + 486.941i 0.0136568 + 0.0420312i
\(513\) −974.766 708.209i −0.0838928 0.0609517i
\(514\) 9557.81 6944.15i 0.820188 0.595902i
\(515\) 6304.85 19404.3i 0.539466 1.66031i
\(516\) 4081.62 0.348223
\(517\) 0 0
\(518\) −9679.57 −0.821035
\(519\) −5333.48 + 16414.8i −0.451086 + 1.38830i
\(520\) −4251.05 + 3088.57i −0.358502 + 0.260467i
\(521\) 7501.89 + 5450.44i 0.630832 + 0.458326i 0.856688 0.515834i \(-0.172518\pi\)
−0.225856 + 0.974161i \(0.572518\pi\)
\(522\) 3141.55 + 9668.69i 0.263413 + 0.810703i
\(523\) 1311.01 + 4034.86i 0.109610 + 0.337346i 0.990785 0.135445i \(-0.0432464\pi\)
−0.881174 + 0.472791i \(0.843246\pi\)
\(524\) −841.087 611.085i −0.0701203 0.0509454i
\(525\) −13420.1 + 9750.28i −1.11562 + 0.810547i
\(526\) 4235.84 13036.6i 0.351125 1.08065i
\(527\) 1872.17 0.154749
\(528\) 0 0
\(529\) 19427.7 1.59676
\(530\) 119.325 367.245i 0.00977953 0.0300983i
\(531\) −978.875 + 711.194i −0.0799992 + 0.0581228i
\(532\) −1546.72 1123.76i −0.126050 0.0915809i
\(533\) 3443.86 + 10599.1i 0.279869 + 0.861348i
\(534\) −3220.68 9912.25i −0.260997 0.803268i
\(535\) −4770.17 3465.73i −0.385481 0.280068i
\(536\) 3363.06 2443.41i 0.271011 0.196901i
\(537\) 5484.16 16878.5i 0.440706 1.35635i
\(538\) 2202.73 0.176517
\(539\) 0 0
\(540\) −3274.46 −0.260945
\(541\) 2014.87 6201.13i 0.160122 0.492805i −0.838522 0.544868i \(-0.816580\pi\)
0.998644 + 0.0520633i \(0.0165798\pi\)
\(542\) −4161.09 + 3023.21i −0.329768 + 0.239590i
\(543\) −3946.36 2867.20i −0.311887 0.226599i
\(544\) 246.368 + 758.243i 0.0194172 + 0.0597599i
\(545\) −2331.84 7176.66i −0.183275 0.564063i
\(546\) −12114.1 8801.38i −0.949513 0.689861i
\(547\) 5154.07 3744.65i 0.402874 0.292705i −0.367836 0.929890i \(-0.619901\pi\)
0.770711 + 0.637185i \(0.219901\pi\)
\(548\) −2575.42 + 7926.34i −0.200760 + 0.617876i
\(549\) −18316.8 −1.42394
\(550\) 0 0
\(551\) −3280.33 −0.253624
\(552\) −3432.67 + 10564.7i −0.264681 + 0.814605i
\(553\) −13605.0 + 9884.59i −1.04619 + 0.760100i
\(554\) −11876.5 8628.81i −0.910804 0.661738i
\(555\) −8006.81 24642.4i −0.612379 1.88471i
\(556\) −214.370 659.762i −0.0163513 0.0503240i
\(557\) 4938.23 + 3587.84i 0.375655 + 0.272929i 0.759552 0.650447i \(-0.225418\pi\)
−0.383897 + 0.923376i \(0.625418\pi\)
\(558\) −4136.86 + 3005.61i −0.313848 + 0.228024i
\(559\) −1777.20 + 5469.67i −0.134468 + 0.413851i
\(560\) −5195.77 −0.392074
\(561\) 0 0
\(562\) 14985.9 1.12481
\(563\) 4200.34 12927.3i 0.314429 0.967711i −0.661561 0.749892i \(-0.730106\pi\)
0.975989 0.217820i \(-0.0698945\pi\)
\(564\) 12616.9 9166.69i 0.941961 0.684375i
\(565\) −18557.6 13482.9i −1.38181 1.00395i
\(566\) 4013.57 + 12352.5i 0.298062 + 0.917341i
\(567\) 3296.03 + 10144.1i 0.244127 + 0.751347i
\(568\) −507.730 368.888i −0.0375068 0.0272503i
\(569\) 13913.1 10108.5i 1.02508 0.744761i 0.0577589 0.998331i \(-0.481605\pi\)
0.967317 + 0.253569i \(0.0816045\pi\)
\(570\) 1581.46 4867.22i 0.116210 0.357659i
\(571\) −2475.65 −0.181441 −0.0907203 0.995876i \(-0.528917\pi\)
−0.0907203 + 0.995876i \(0.528917\pi\)
\(572\) 0 0
\(573\) 10500.6 0.765567
\(574\) −3405.31 + 10480.5i −0.247622 + 0.762101i
\(575\) −14028.0 + 10191.9i −1.01741 + 0.739188i
\(576\) −1761.69 1279.94i −0.127437 0.0925883i
\(577\) −6285.32 19344.2i −0.453485 1.39568i −0.872904 0.487892i \(-0.837766\pi\)
0.419419 0.907793i \(-0.362234\pi\)
\(578\) −2652.77 8164.38i −0.190901 0.587532i
\(579\) −29221.7 21230.8i −2.09743 1.52387i
\(580\) −7212.27 + 5240.02i −0.516333 + 0.375138i
\(581\) 3613.83 11122.2i 0.258050 0.794196i
\(582\) 2806.85 0.199910
\(583\) 0 0
\(584\) −9152.55 −0.648519
\(585\) 6905.94 21254.3i 0.488078 1.50215i
\(586\) −4344.22 + 3156.26i −0.306242 + 0.222498i
\(587\) 11988.4 + 8710.07i 0.842953 + 0.612441i 0.923194 0.384334i \(-0.125569\pi\)
−0.0802411 + 0.996775i \(0.525569\pi\)
\(588\) −1263.38 3888.28i −0.0886068 0.272704i
\(589\) −509.862 1569.19i −0.0356681 0.109775i
\(590\) −858.382 623.651i −0.0598967 0.0435175i
\(591\) −4200.77 + 3052.04i −0.292380 + 0.212427i
\(592\) 1099.29 3383.27i 0.0763186 0.234885i
\(593\) −11123.2 −0.770281 −0.385140 0.922858i \(-0.625847\pi\)
−0.385140 + 0.922858i \(0.625847\pi\)
\(594\) 0 0
\(595\) −8090.63 −0.557451
\(596\) 555.062 1708.31i 0.0381481 0.117408i
\(597\) −19230.3 + 13971.6i −1.31833 + 0.957824i
\(598\) −12662.8 9200.06i −0.865920 0.629127i
\(599\) 2560.26 + 7879.67i 0.174640 + 0.537487i 0.999617 0.0276796i \(-0.00881183\pi\)
−0.824977 + 0.565167i \(0.808812\pi\)
\(600\) −1883.89 5798.01i −0.128182 0.394505i
\(601\) 22101.0 + 16057.3i 1.50003 + 1.08984i 0.970370 + 0.241625i \(0.0776803\pi\)
0.529660 + 0.848210i \(0.322320\pi\)
\(602\) −4600.70 + 3342.60i −0.311479 + 0.226303i
\(603\) −5463.37 + 16814.5i −0.368965 + 1.13556i
\(604\) −114.143 −0.00768944
\(605\) 0 0
\(606\) −6417.18 −0.430165
\(607\) −5045.53 + 15528.6i −0.337384 + 1.03836i 0.628152 + 0.778091i \(0.283812\pi\)
−0.965536 + 0.260270i \(0.916188\pi\)
\(608\) 568.441 412.997i 0.0379167 0.0275481i
\(609\) −20552.5 14932.3i −1.36754 0.993574i
\(610\) −4963.48 15276.0i −0.329452 1.01395i
\(611\) 6790.45 + 20898.9i 0.449611 + 1.38376i
\(612\) −2743.22 1993.07i −0.181190 0.131642i
\(613\) −17009.8 + 12358.4i −1.12075 + 0.814274i −0.984323 0.176376i \(-0.943563\pi\)
−0.136429 + 0.990650i \(0.543563\pi\)
\(614\) −5149.25 + 15847.8i −0.338448 + 1.04163i
\(615\) −29498.2 −1.93412
\(616\) 0 0
\(617\) 871.824 0.0568854 0.0284427 0.999595i \(-0.490945\pi\)
0.0284427 + 0.999595i \(0.490945\pi\)
\(618\) −6603.02 + 20322.0i −0.429793 + 1.32277i
\(619\) −7602.75 + 5523.72i −0.493668 + 0.358671i −0.806593 0.591107i \(-0.798691\pi\)
0.312925 + 0.949778i \(0.398691\pi\)
\(620\) −3627.64 2635.64i −0.234983 0.170725i
\(621\) −3014.08 9276.38i −0.194768 0.599434i
\(622\) −3102.75 9549.28i −0.200014 0.615581i
\(623\) 11747.8 + 8535.29i 0.755484 + 0.548891i
\(624\) 4452.09 3234.63i 0.285619 0.207514i
\(625\) −5655.84 + 17406.9i −0.361974 + 1.11404i
\(626\) 6044.15 0.385899
\(627\) 0 0
\(628\) 6895.44 0.438150
\(629\) 1711.77 5268.28i 0.108510 0.333959i
\(630\) 17877.6 12988.8i 1.13057 0.821409i
\(631\) 11759.8 + 8544.01i 0.741919 + 0.539036i 0.893311 0.449438i \(-0.148376\pi\)
−0.151393 + 0.988474i \(0.548376\pi\)
\(632\) −1909.84 5877.88i −0.120205 0.369952i
\(633\) 6256.10 + 19254.3i 0.392824 + 1.20899i
\(634\) 17054.3 + 12390.7i 1.06832 + 0.776178i
\(635\) −8416.12 + 6114.67i −0.525958 + 0.382131i
\(636\) −124.968 + 384.612i −0.00779136 + 0.0239794i
\(637\) 5760.67 0.358314
\(638\) 0 0
\(639\) 2669.17 0.165244
\(640\) 590.075 1816.06i 0.0364449 0.112166i
\(641\) 9238.70 6712.31i 0.569277 0.413604i −0.265565 0.964093i \(-0.585559\pi\)
0.834843 + 0.550489i \(0.185559\pi\)
\(642\) 4995.76 + 3629.63i 0.307113 + 0.223131i
\(643\) 7407.11 + 22796.7i 0.454289 + 1.39816i 0.871968 + 0.489563i \(0.162844\pi\)
−0.417679 + 0.908595i \(0.637156\pi\)
\(644\) −4782.61 14719.4i −0.292642 0.900659i
\(645\) −12315.3 8947.58i −0.751805 0.546218i
\(646\) 885.152 643.100i 0.0539100 0.0391679i
\(647\) 2569.24 7907.32i 0.156117 0.480478i −0.842156 0.539234i \(-0.818714\pi\)
0.998272 + 0.0587569i \(0.0187137\pi\)
\(648\) −3919.97 −0.237641
\(649\) 0 0
\(650\) 8590.04 0.518353
\(651\) 3948.59 12152.5i 0.237723 0.731635i
\(652\) −10738.0 + 7801.60i −0.644988 + 0.468611i
\(653\) 24334.7 + 17680.2i 1.45833 + 1.05954i 0.983794 + 0.179303i \(0.0573843\pi\)
0.474536 + 0.880236i \(0.342616\pi\)
\(654\) 2442.11 + 7516.05i 0.146016 + 0.449390i
\(655\) 1198.17 + 3687.60i 0.0714757 + 0.219980i
\(656\) −3276.47 2380.50i −0.195007 0.141681i
\(657\) 31492.1 22880.3i 1.87005 1.35867i
\(658\) −6714.44 + 20664.9i −0.397806 + 1.22432i
\(659\) 10041.6 0.593572 0.296786 0.954944i \(-0.404085\pi\)
0.296786 + 0.954944i \(0.404085\pi\)
\(660\) 0 0
\(661\) 1402.50 0.0825281 0.0412640 0.999148i \(-0.486862\pi\)
0.0412640 + 0.999148i \(0.486862\pi\)
\(662\) 191.511 589.409i 0.0112436 0.0346043i
\(663\) 6932.60 5036.83i 0.406093 0.295044i
\(664\) 3477.10 + 2526.26i 0.203219 + 0.147648i
\(665\) 2203.39 + 6781.32i 0.128487 + 0.395441i
\(666\) 4675.35 + 14389.3i 0.272021 + 0.837196i
\(667\) −21483.5 15608.7i −1.24714 0.906102i
\(668\) −9758.68 + 7090.10i −0.565232 + 0.410665i
\(669\) −6366.17 + 19593.1i −0.367908 + 1.13230i
\(670\) −15503.6 −0.893963
\(671\) 0 0
\(672\) 5441.49 0.312366
\(673\) −6299.43 + 19387.7i −0.360810 + 1.11046i 0.591753 + 0.806119i \(0.298436\pi\)
−0.952563 + 0.304341i \(0.901564\pi\)
\(674\) 18064.8 13124.8i 1.03239 0.750074i
\(675\) 4330.65 + 3146.40i 0.246944 + 0.179415i
\(676\) −319.507 983.340i −0.0181786 0.0559479i
\(677\) 2282.09 + 7023.55i 0.129554 + 0.398725i 0.994703 0.102789i \(-0.0327766\pi\)
−0.865149 + 0.501514i \(0.832777\pi\)
\(678\) 19435.2 + 14120.5i 1.10089 + 0.799846i
\(679\) −3163.81 + 2298.64i −0.178815 + 0.129917i
\(680\) 918.838 2827.89i 0.0518174 0.159478i
\(681\) 1958.19 0.110188
\(682\) 0 0
\(683\) −25844.0 −1.44787 −0.723935 0.689868i \(-0.757668\pi\)
−0.723935 + 0.689868i \(0.757668\pi\)
\(684\) −923.446 + 2842.07i −0.0516211 + 0.158873i
\(685\) 25146.5 18270.0i 1.40263 1.01907i
\(686\) −7472.53 5429.11i −0.415893 0.302164i
\(687\) −4343.51 13368.0i −0.241216 0.742386i
\(688\) −645.837 1987.68i −0.0357882 0.110145i
\(689\) −460.996 334.933i −0.0254899 0.0185195i
\(690\) 33516.7 24351.3i 1.84922 1.34353i
\(691\) 2607.73 8025.78i 0.143564 0.441845i −0.853259 0.521487i \(-0.825378\pi\)
0.996824 + 0.0796417i \(0.0253776\pi\)
\(692\) 8837.64 0.485486
\(693\) 0 0
\(694\) −5030.97 −0.275177
\(695\) −799.499 + 2460.60i −0.0436356 + 0.134296i
\(696\) 7553.35 5487.83i 0.411363 0.298873i
\(697\) −5101.98 3706.80i −0.277261 0.201442i
\(698\) 7031.12 + 21639.6i 0.381278 + 1.17345i
\(699\) 7677.62 + 23629.3i 0.415442 + 1.27860i
\(700\) 6871.70 + 4992.58i 0.371037 + 0.269574i
\(701\) −10503.8 + 7631.43i −0.565937 + 0.411177i −0.833627 0.552328i \(-0.813740\pi\)
0.267690 + 0.963505i \(0.413740\pi\)
\(702\) −1493.18 + 4595.53i −0.0802798 + 0.247076i
\(703\) −4881.90 −0.261912
\(704\) 0 0
\(705\) −58163.2 −3.10717
\(706\) 3838.04 11812.3i 0.204598 0.629689i
\(707\) 7233.28 5255.29i 0.384775 0.279555i
\(708\) 898.976 + 653.144i 0.0477197 + 0.0346704i
\(709\) −5537.15 17041.6i −0.293303 0.902695i −0.983786 0.179346i \(-0.942602\pi\)
0.690483 0.723349i \(-0.257398\pi\)
\(710\) 723.290 + 2226.06i 0.0382318 + 0.117665i
\(711\) 21265.4 + 15450.2i 1.12168 + 0.814948i
\(712\) −4317.49 + 3136.84i −0.227254 + 0.165110i
\(713\) 4127.45 12703.0i 0.216794 0.667224i
\(714\) 8473.24 0.444122
\(715\) 0 0
\(716\) −9087.33 −0.474315
\(717\) 12103.2 37250.0i 0.630410 1.94020i
\(718\) −4024.87 + 2924.24i −0.209202 + 0.151994i
\(719\) −2845.59 2067.45i −0.147598 0.107236i 0.511536 0.859262i \(-0.329077\pi\)
−0.659133 + 0.752026i \(0.729077\pi\)
\(720\) 2509.62 + 7723.82i 0.129900 + 0.399791i
\(721\) −9199.75 28313.9i −0.475196 1.46250i
\(722\) 10318.0 + 7496.47i 0.531851 + 0.386412i
\(723\) −38387.8 + 27890.4i −1.97463 + 1.43465i
\(724\) −771.844 + 2375.49i −0.0396207 + 0.121940i
\(725\) 14573.7 0.746559
\(726\) 0 0
\(727\) −29438.9 −1.50183 −0.750913 0.660401i \(-0.770386\pi\)
−0.750913 + 0.660401i \(0.770386\pi\)
\(728\) −2369.31 + 7292.00i −0.120622 + 0.371235i
\(729\) 22851.3 16602.5i 1.16097 0.843492i
\(730\) 27615.6 + 20063.9i 1.40014 + 1.01726i
\(731\) −1005.67 3095.13i −0.0508837 0.156604i
\(732\) 5198.21 + 15998.4i 0.262474 + 0.807813i
\(733\) 2779.70 + 2019.57i 0.140069 + 0.101766i 0.655613 0.755097i \(-0.272410\pi\)
−0.515544 + 0.856863i \(0.672410\pi\)
\(734\) −10872.4 + 7899.28i −0.546742 + 0.397231i
\(735\) −4711.81 + 14501.5i −0.236459 + 0.727747i
\(736\) 5687.97 0.284866
\(737\) 0 0
\(738\) 17224.6 0.859143
\(739\) 10383.5 31957.2i 0.516866 1.59075i −0.262995 0.964797i \(-0.584710\pi\)
0.779861 0.625953i \(-0.215290\pi\)
\(740\) −10733.5 + 7798.37i −0.533206 + 0.387397i
\(741\) −6109.73 4438.98i −0.302897 0.220067i
\(742\) −174.114 535.867i −0.00861444 0.0265125i
\(743\) 368.875 + 1135.28i 0.0182136 + 0.0560557i 0.959750 0.280855i \(-0.0906180\pi\)
−0.941537 + 0.336911i \(0.890618\pi\)
\(744\) 3799.20 + 2760.28i 0.187211 + 0.136017i
\(745\) −5419.66 + 3937.61i −0.266525 + 0.193641i
\(746\) 5323.97 16385.5i 0.261293 0.804177i
\(747\) −18279.4 −0.895324
\(748\) 0 0
\(749\) −8603.54 −0.419715
\(750\) 1977.01 6084.60i 0.0962535 0.296238i
\(751\) −19828.5 + 14406.2i −0.963451 + 0.699988i −0.953950 0.299967i \(-0.903024\pi\)
−0.00950152 + 0.999955i \(0.503024\pi\)
\(752\) −6460.40 4693.76i −0.313280 0.227611i
\(753\) 13445.1 + 41379.9i 0.650688 + 2.00261i
\(754\) 4065.25 + 12511.5i 0.196349 + 0.604302i
\(755\) 344.399 + 250.221i 0.0166013 + 0.0120615i
\(756\) −3865.43 + 2808.40i −0.185958 + 0.135107i
\(757\) 3338.57 10275.0i 0.160294 0.493333i −0.838365 0.545109i \(-0.816488\pi\)
0.998659 + 0.0517762i \(0.0164882\pi\)
\(758\) −16018.2 −0.767555
\(759\) 0 0
\(760\) −2620.49 −0.125073
\(761\) −2526.49 + 7775.75i −0.120349 + 0.370395i −0.993025 0.117904i \(-0.962383\pi\)
0.872676 + 0.488299i \(0.162383\pi\)
\(762\) 8814.12 6403.83i 0.419031 0.304444i
\(763\) −8907.88 6471.96i −0.422657 0.307078i
\(764\) −1661.52 5113.63i −0.0786802 0.242153i
\(765\) 3907.87 + 12027.2i 0.184692 + 0.568424i
\(766\) −12963.6 9418.61i −0.611481 0.444267i
\(767\) −1266.69 + 920.304i −0.0596317 + 0.0433250i
\(768\) −617.980 + 1901.95i −0.0290357 + 0.0893627i
\(769\) 28895.9 1.35502 0.677511 0.735513i \(-0.263059\pi\)
0.677511 + 0.735513i \(0.263059\pi\)
\(770\) 0 0
\(771\) 46144.8 2.15547
\(772\) −5715.28 + 17589.8i −0.266448 + 0.820041i
\(773\) 14559.7 10578.3i 0.677460 0.492203i −0.195054 0.980792i \(-0.562488\pi\)
0.872514 + 0.488589i \(0.162488\pi\)
\(774\) 7191.17 + 5224.69i 0.333955 + 0.242633i
\(775\) 2265.19 + 6971.55i 0.104991 + 0.323130i
\(776\) −444.129 1366.89i −0.0205455 0.0632325i
\(777\) −30586.9 22222.7i −1.41223 1.02604i
\(778\) −12992.2 + 9439.36i −0.598704 + 0.434984i
\(779\) −1717.47 + 5285.83i −0.0789919 + 0.243112i
\(780\) −20524.0 −0.942148
\(781\) 0 0
\(782\) 8857.06 0.405023
\(783\) −2533.30 + 7796.71i −0.115623 + 0.355851i
\(784\) −1693.62 + 1230.49i −0.0771511 + 0.0560536i
\(785\) −20805.3 15115.9i −0.945954 0.687276i
\(786\) −1254.84 3861.99i −0.0569448 0.175258i
\(787\) 4906.17 + 15099.6i 0.222219 + 0.683918i 0.998562 + 0.0536084i \(0.0170723\pi\)
−0.776343 + 0.630310i \(0.782928\pi\)
\(788\) 2150.98 + 1562.78i 0.0972407 + 0.0706495i
\(789\) 43314.9 31470.1i 1.95444 1.41998i
\(790\) −7122.81 + 21921.7i −0.320782 + 0.987267i
\(791\) −33470.8 −1.50453
\(792\) 0 0
\(793\) −23702.5 −1.06141
\(794\) 2740.98 8435.86i 0.122511 0.377050i
\(795\) 1220.19 886.523i 0.0544350 0.0395494i
\(796\) 9846.78 + 7154.10i 0.438454 + 0.318556i
\(797\) 5098.07 + 15690.2i 0.226578 + 0.697336i 0.998128 + 0.0611668i \(0.0194822\pi\)
−0.771549 + 0.636170i \(0.780518\pi\)
\(798\) −2307.59 7102.02i −0.102365 0.315049i
\(799\) −10059.9 7308.91i −0.445422 0.323618i
\(800\) −2525.45 + 1834.85i −0.111610 + 0.0810895i
\(801\) 7013.87 21586.5i 0.309392 0.952210i
\(802\) −7858.41 −0.345998
\(803\) 0 0
\(804\) 16236.7 0.712221
\(805\) −17836.9 + 54896.4i −0.780955 + 2.40353i
\(806\) −5353.21 + 3889.33i −0.233944 + 0.169970i
\(807\) 6960.50 + 5057.10i 0.303620 + 0.220593i
\(808\) 1015.39 + 3125.06i 0.0442097 + 0.136063i
\(809\) 2812.97 + 8657.42i 0.122248 + 0.376241i 0.993390 0.114791i \(-0.0366199\pi\)
−0.871142 + 0.491032i \(0.836620\pi\)
\(810\) 11827.6 + 8593.23i 0.513060 + 0.372760i
\(811\) 29590.8 21499.0i 1.28123 0.930865i 0.281636 0.959521i \(-0.409123\pi\)
0.999589 + 0.0286567i \(0.00912297\pi\)
\(812\) −4019.74 + 12371.5i −0.173726 + 0.534672i
\(813\) −20089.6 −0.866633
\(814\) 0 0
\(815\) 49501.7 2.12757
\(816\) −962.291 + 2961.63i −0.0412830 + 0.127056i
\(817\) −2320.36 + 1685.84i −0.0993626 + 0.0721912i
\(818\) −23565.4 17121.3i −1.00727 0.731823i
\(819\) −10076.8 31013.3i −0.429930 1.32319i
\(820\) 4667.51 + 14365.1i 0.198776 + 0.611771i
\(821\) −2948.23 2142.01i −0.125328 0.0910558i 0.523356 0.852114i \(-0.324680\pi\)
−0.648683 + 0.761059i \(0.724680\pi\)
\(822\) −26335.8 + 19134.0i −1.11748 + 0.811894i
\(823\) −5221.12 + 16068.9i −0.221138 + 0.680593i 0.777523 + 0.628855i \(0.216476\pi\)
−0.998661 + 0.0517380i \(0.983524\pi\)
\(824\) 10941.3 0.462570
\(825\) 0 0
\(826\) −1548.19 −0.0652160
\(827\) 11983.1 36880.1i 0.503860 1.55072i −0.298817 0.954310i \(-0.596592\pi\)
0.802678 0.596413i \(-0.203408\pi\)
\(828\) −19571.1 + 14219.3i −0.821430 + 0.596804i
\(829\) 10027.2 + 7285.20i 0.420096 + 0.305218i 0.777677 0.628665i \(-0.216398\pi\)
−0.357580 + 0.933882i \(0.616398\pi\)
\(830\) −4953.32 15244.8i −0.207147 0.637534i
\(831\) −17718.9 54533.1i −0.739665 2.27645i
\(832\) −2279.67 1656.28i −0.0949920 0.0690157i
\(833\) −2637.23 + 1916.06i −0.109694 + 0.0796970i
\(834\) 837.308 2576.97i 0.0347645 0.106994i
\(835\) 44987.1 1.86448
\(836\) 0 0
\(837\) −4123.41 −0.170282
\(838\) 2489.92 7663.18i 0.102641 0.315895i
\(839\) −19872.6 + 14438.3i −0.817732 + 0.594117i −0.916062 0.401037i \(-0.868650\pi\)
0.0983299 + 0.995154i \(0.468650\pi\)
\(840\) −16418.4 11928.6i −0.674390 0.489973i
\(841\) −639.584 1968.44i −0.0262243 0.0807100i
\(842\) −5270.35 16220.5i −0.215711 0.663889i
\(843\) 47354.6 + 34405.1i 1.93473 + 1.40566i
\(844\) 8386.62 6093.24i 0.342037 0.248505i
\(845\) −1191.61 + 3667.40i −0.0485120 + 0.149305i
\(846\) 33962.8 1.38022
\(847\) 0 0
\(848\) 207.074 0.00838554
\(849\) −15676.7 + 48247.8i −0.633712 + 1.95036i
\(850\) −3932.52 + 2857.14i −0.158687 + 0.115293i
\(851\) −31972.4 23229.3i −1.28790 0.935712i
\(852\) −757.495 2331.33i −0.0304593 0.0937442i
\(853\) 3772.37 + 11610.1i 0.151422 + 0.466030i 0.997781 0.0665834i \(-0.0212098\pi\)
−0.846358 + 0.532614i \(0.821210\pi\)
\(854\) −18961.1 13776.0i −0.759759 0.551997i
\(855\) 9016.57 6550.92i 0.360655 0.262031i
\(856\) 977.089 3007.17i 0.0390143 0.120074i
\(857\) −7281.72 −0.290244 −0.145122 0.989414i \(-0.546357\pi\)
−0.145122 + 0.989414i \(0.546357\pi\)
\(858\) 0 0
\(859\) 5927.39 0.235437 0.117718 0.993047i \(-0.462442\pi\)
0.117718 + 0.993047i \(0.462442\pi\)
\(860\) −2408.67 + 7413.13i −0.0955058 + 0.293937i
\(861\) −34822.0 + 25299.7i −1.37832 + 1.00141i
\(862\) 21706.3 + 15770.5i 0.857679 + 0.623140i
\(863\) −11916.3 36674.5i −0.470028 1.44660i −0.852547 0.522651i \(-0.824943\pi\)
0.382518 0.923948i \(-0.375057\pi\)
\(864\) −542.622 1670.02i −0.0213662 0.0657583i
\(865\) −26665.4 19373.6i −1.04815 0.761527i
\(866\) −6686.22 + 4857.82i −0.262364 + 0.190618i
\(867\) 10361.5 31889.3i 0.405875 1.24916i
\(868\) −6542.86 −0.255852
\(869\) 0 0
\(870\) −34820.6 −1.35693
\(871\) −7069.75 + 21758.4i −0.275028 + 0.846449i
\(872\) 3273.78 2378.54i 0.127138 0.0923709i
\(873\) 4945.22 + 3592.91i 0.191719 + 0.139292i
\(874\) −2412.11 7423.72i −0.0933535 0.287312i
\(875\) 2754.49 + 8477.46i 0.106422 + 0.327532i
\(876\) −28921.6 21012.8i −1.11549 0.810451i
\(877\) 23067.2 16759.3i 0.888170 0.645293i −0.0472301 0.998884i \(-0.515039\pi\)
0.935400 + 0.353591i \(0.115039\pi\)
\(878\) −2075.64 + 6388.16i −0.0797830 + 0.245547i
\(879\) −20973.7 −0.804809
\(880\) 0 0
\(881\) 40747.6 1.55826 0.779128 0.626865i \(-0.215662\pi\)
0.779128 + 0.626865i \(0.215662\pi\)
\(882\) 2751.33 8467.72i 0.105036 0.323268i
\(883\) 2908.89 2113.43i 0.110863 0.0805467i −0.530972 0.847389i \(-0.678173\pi\)
0.641835 + 0.766842i \(0.278173\pi\)
\(884\) −3549.80 2579.08i −0.135060 0.0981266i
\(885\) −1280.64 3941.41i −0.0486421 0.149705i
\(886\) −273.016 840.257i −0.0103523 0.0318612i
\(887\) −6241.81 4534.94i −0.236279 0.171667i 0.463345 0.886178i \(-0.346649\pi\)
−0.699624 + 0.714511i \(0.746649\pi\)
\(888\) 11241.1 8167.16i 0.424806 0.308640i
\(889\) −4690.70 + 14436.5i −0.176964 + 0.544639i
\(890\) 19903.5 0.749624
\(891\) 0 0
\(892\) 10548.8 0.395965
\(893\) −3386.43 + 10422.4i −0.126901 + 0.390561i
\(894\) 5675.96 4123.82i 0.212341 0.154274i
\(895\) 27418.8 + 19920.9i 1.02403 + 0.744003i
\(896\) −861.009 2649.91i −0.0321030 0.0988029i
\(897\) −18891.9 58143.4i −0.703214 2.16427i
\(898\) 660.932 + 480.195i 0.0245608 + 0.0178445i
\(899\) −9082.17 + 6598.58i −0.336938 + 0.244800i
\(900\) 4102.65 12626.7i 0.151950 0.467654i
\(901\) 322.446 0.0119226
\(902\) 0 0
\(903\) −22212.0 −0.818571
\(904\) 3801.21 11698.9i 0.139852 0.430421i
\(905\) 7536.32 5475.46i 0.276813 0.201117i
\(906\) −360.686 262.054i −0.0132263 0.00960944i
\(907\) −10418.1 32063.6i −0.381398 1.17382i −0.939060 0.343753i \(-0.888302\pi\)
0.557662 0.830068i \(-0.311698\pi\)
\(908\) −309.845 953.605i −0.0113244 0.0348530i
\(909\) −11306.1 8214.33i −0.412539 0.299727i
\(910\) 23134.1 16807.9i 0.842733 0.612282i
\(911\) 4644.75 14295.1i 0.168922 0.519887i −0.830382 0.557194i \(-0.811878\pi\)
0.999304 + 0.0373070i \(0.0118780\pi\)
\(912\) 2744.42 0.0996455
\(913\) 0 0
\(914\) −3045.69 −0.110222
\(915\) 19386.9 59666.7i 0.700449 2.15576i
\(916\) −5822.70 + 4230.44i −0.210030 + 0.152596i
\(917\) 4577.16 + 3325.50i 0.164832 + 0.119758i
\(918\) −844.947 2600.48i −0.0303784 0.0934952i
\(919\) 5281.31 + 16254.2i 0.189570 + 0.583435i 0.999997 0.00240379i \(-0.000765151\pi\)
−0.810428 + 0.585839i \(0.800765\pi\)
\(920\) −17162.1 12469.0i −0.615018 0.446837i
\(921\) −52655.2 + 38256.3i −1.88387 + 1.36871i
\(922\) 8566.79 26365.9i 0.306000 0.941771i
\(923\) 3453.98 0.123173
\(924\) 0 0
\(925\) 21689.1 0.770955
\(926\) −4018.62 + 12368.0i −0.142613 + 0.438919i
\(927\) −37646.7 + 27351.9i −1.33385 + 0.969099i
\(928\) −3867.65 2810.01i −0.136812 0.0994001i
\(929\) 4066.74 + 12516.1i 0.143623 + 0.442025i 0.996831 0.0795446i \(-0.0253466\pi\)
−0.853209 + 0.521570i \(0.825347\pi\)
\(930\) −5412.16 16656.9i −0.190830 0.587314i
\(931\) 2324.20 + 1688.63i 0.0818182 + 0.0594444i
\(932\) 10292.2 7477.75i 0.361731 0.262813i
\(933\) 12119.0 37298.6i 0.425252 1.30879i
\(934\) 847.946 0.0297063
\(935\) 0 0
\(936\) 11984.4 0.418506
\(937\) −1253.46 + 3857.76i −0.0437021 + 0.134501i −0.970527 0.240993i \(-0.922527\pi\)
0.926825 + 0.375494i \(0.122527\pi\)
\(938\) −18301.7 + 13296.9i −0.637068 + 0.462857i
\(939\) 19099.2 + 13876.4i 0.663768 + 0.482256i
\(940\) 9203.20 + 28324.5i 0.319335 + 0.982813i
\(941\) −10320.4 31763.0i −0.357531 1.10037i −0.954527 0.298123i \(-0.903639\pi\)
0.596996 0.802244i \(-0.296361\pi\)
\(942\) 21789.2 + 15830.8i 0.753643 + 0.547553i
\(943\) −36399.3 + 26445.7i −1.25697 + 0.913245i
\(944\) 175.825 541.134i 0.00606209 0.0186572i
\(945\) 17819.5 0.613405
\(946\) 0 0
\(947\) 25660.8 0.880533 0.440267 0.897867i \(-0.354884\pi\)
0.440267 + 0.897867i \(0.354884\pi\)
\(948\) 7459.65 22958.4i 0.255568 0.786557i
\(949\) 40751.6 29607.8i 1.39394 1.01276i
\(950\) 3465.74 + 2518.01i 0.118362 + 0.0859948i
\(951\) 25443.7 + 78307.8i 0.867581 + 2.67014i
\(952\) −1340.73 4126.33i −0.0456441 0.140478i
\(953\) 39522.7 + 28714.9i 1.34341 + 0.976042i 0.999311 + 0.0371079i \(0.0118145\pi\)
0.344096 + 0.938935i \(0.388185\pi\)
\(954\) −712.498 + 517.660i −0.0241803 + 0.0175680i
\(955\) −6196.70 + 19071.5i −0.209969 + 0.646218i
\(956\) −20055.2 −0.678485
\(957\) 0 0
\(958\) −9114.68 −0.307392
\(959\) 14015.4 43134.8i 0.471929 1.45245i
\(960\) 6033.98 4383.95i 0.202860 0.147387i
\(961\) 19533.3 + 14191.7i 0.655677 + 0.476377i
\(962\) 6050.03 + 18620.1i 0.202766 + 0.624049i
\(963\) 4155.61 + 12789.7i 0.139058 + 0.427976i
\(964\) 19656.3 + 14281.1i 0.656728 + 0.477141i
\(965\) 55804.3 40544.2i 1.86156 1.35250i
\(966\) 18680.4 57492.5i 0.622188 1.91490i
\(967\) 48861.8 1.62491 0.812456 0.583023i \(-0.198130\pi\)
0.812456 + 0.583023i \(0.198130\pi\)
\(968\) 0 0
\(969\) 4273.48 0.141676
\(970\) −1656.39 + 5097.85i −0.0548284 + 0.168745i
\(971\) −28224.6 + 20506.4i −0.932822 + 0.677735i −0.946682 0.322169i \(-0.895588\pi\)
0.0138603 + 0.999904i \(0.495588\pi\)
\(972\) −17181.4 12483.0i −0.566970 0.411928i
\(973\) 1166.59 + 3590.40i 0.0384370 + 0.118297i
\(974\) −4146.34 12761.1i −0.136404 0.419808i
\(975\) 27144.1 + 19721.3i 0.891596 + 0.647782i
\(976\) 6968.46 5062.88i 0.228540 0.166044i
\(977\) −5875.16 + 18081.9i −0.192388 + 0.592109i 0.807609 + 0.589718i \(0.200761\pi\)
−0.999997 + 0.00239112i \(0.999239\pi\)
\(978\) −51842.7 −1.69504
\(979\) 0 0
\(980\) 7807.52 0.254492
\(981\) −5318.33 + 16368.1i −0.173090 + 0.532716i
\(982\) 23506.2 17078.3i 0.763864 0.554979i
\(983\) 6025.47 + 4377.76i 0.195506 + 0.142044i 0.681232 0.732068i \(-0.261445\pi\)
−0.485726 + 0.874111i \(0.661445\pi\)
\(984\) −4888.24 15044.5i −0.158365 0.487399i
\(985\) −3064.20 9430.63i −0.0991202 0.305061i
\(986\) −6022.54 4375.63i −0.194520 0.141327i
\(987\) −68660.5 + 49884.8i −2.21427 + 1.60876i
\(988\) −1194.96 + 3677.72i −0.0384786 + 0.118425i
\(989\) −23218.2 −0.746506
\(990\) 0 0
\(991\) 5313.37 0.170318 0.0851588 0.996367i \(-0.472860\pi\)
0.0851588 + 0.996367i \(0.472860\pi\)
\(992\) 743.061 2286.91i 0.0237825 0.0731949i
\(993\) 1958.35 1422.82i 0.0625844 0.0454702i
\(994\) 2763.05 + 2007.47i 0.0881676 + 0.0640575i
\(995\) −14027.3 43171.5i −0.446929 1.37551i
\(996\) 5187.57 + 15965.7i 0.165035 + 0.507924i
\(997\) 43301.8 + 31460.6i 1.37551 + 0.999365i 0.997284 + 0.0736504i \(0.0234649\pi\)
0.378223 + 0.925714i \(0.376535\pi\)
\(998\) 15694.2 11402.5i 0.497786 0.361663i
\(999\) −3770.14 + 11603.3i −0.119401 + 0.367480i
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 242.4.c.q.9.2 8
11.2 odd 10 242.4.c.r.3.1 8
11.3 even 5 242.4.c.n.81.1 8
11.4 even 5 242.4.a.o.1.1 4
11.5 even 5 inner 242.4.c.q.27.2 8
11.6 odd 10 22.4.c.b.5.2 8
11.7 odd 10 242.4.a.n.1.1 4
11.8 odd 10 242.4.c.r.81.1 8
11.9 even 5 242.4.c.n.3.1 8
11.10 odd 2 22.4.c.b.9.2 yes 8
33.17 even 10 198.4.f.d.181.1 8
33.26 odd 10 2178.4.a.bt.1.1 4
33.29 even 10 2178.4.a.by.1.1 4
33.32 even 2 198.4.f.d.163.1 8
44.7 even 10 1936.4.a.bn.1.4 4
44.15 odd 10 1936.4.a.bm.1.4 4
44.39 even 10 176.4.m.b.49.1 8
44.43 even 2 176.4.m.b.97.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.4.c.b.5.2 8 11.6 odd 10
22.4.c.b.9.2 yes 8 11.10 odd 2
176.4.m.b.49.1 8 44.39 even 10
176.4.m.b.97.1 8 44.43 even 2
198.4.f.d.163.1 8 33.32 even 2
198.4.f.d.181.1 8 33.17 even 10
242.4.a.n.1.1 4 11.7 odd 10
242.4.a.o.1.1 4 11.4 even 5
242.4.c.n.3.1 8 11.9 even 5
242.4.c.n.81.1 8 11.3 even 5
242.4.c.q.9.2 8 1.1 even 1 trivial
242.4.c.q.27.2 8 11.5 even 5 inner
242.4.c.r.3.1 8 11.2 odd 10
242.4.c.r.81.1 8 11.8 odd 10
1936.4.a.bm.1.4 4 44.15 odd 10
1936.4.a.bn.1.4 4 44.7 even 10
2178.4.a.bt.1.1 4 33.26 odd 10
2178.4.a.by.1.1 4 33.29 even 10