Properties

Label 63.4.g.a.4.18
Level $63$
Weight $4$
Character 63.4
Analytic conductor $3.717$
Analytic rank $0$
Dimension $44$
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] = [63,4,Mod(4,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.g (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 4.18
Character \(\chi\) \(=\) 63.4
Dual form 63.4.g.a.16.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.68671 - 2.92146i) q^{2} +(0.0520064 - 5.19589i) q^{3} +(-1.68996 - 2.92710i) q^{4} -9.74532 q^{5} +(-15.0919 - 8.91589i) q^{6} +(0.158327 - 18.5196i) q^{7} +15.5854 q^{8} +(-26.9946 - 0.540440i) q^{9} +O(q^{10})\) \(q+(1.68671 - 2.92146i) q^{2} +(0.0520064 - 5.19589i) q^{3} +(-1.68996 - 2.92710i) q^{4} -9.74532 q^{5} +(-15.0919 - 8.91589i) q^{6} +(0.158327 - 18.5196i) q^{7} +15.5854 q^{8} +(-26.9946 - 0.540440i) q^{9} +(-16.4375 + 28.4706i) q^{10} +38.9123 q^{11} +(-15.2968 + 8.62865i) q^{12} +(-31.2817 + 54.1816i) q^{13} +(-53.8372 - 31.6997i) q^{14} +(-0.506819 + 50.6356i) q^{15} +(39.8078 - 68.9491i) q^{16} +(63.3614 - 109.745i) q^{17} +(-47.1109 + 77.9521i) q^{18} +(22.7332 + 39.3751i) q^{19} +(16.4692 + 28.5256i) q^{20} +(-96.2175 - 1.78579i) q^{21} +(65.6337 - 113.681i) q^{22} +153.865 q^{23} +(0.810542 - 80.9801i) q^{24} -30.0287 q^{25} +(105.526 + 182.777i) q^{26} +(-4.21196 + 140.233i) q^{27} +(-54.4763 + 30.8340i) q^{28} +(27.4655 + 47.5716i) q^{29} +(147.075 + 86.8882i) q^{30} +(-54.8509 - 95.0045i) q^{31} +(-71.9464 - 124.615i) q^{32} +(2.02369 - 202.184i) q^{33} +(-213.744 - 370.216i) q^{34} +(-1.54295 + 180.479i) q^{35} +(44.0380 + 79.9293i) q^{36} +(144.482 + 250.249i) q^{37} +153.377 q^{38} +(279.895 + 165.354i) q^{39} -151.885 q^{40} +(-11.3009 + 19.5738i) q^{41} +(-167.508 + 278.084i) q^{42} +(23.9450 + 41.4740i) q^{43} +(-65.7604 - 113.900i) q^{44} +(263.071 + 5.26676i) q^{45} +(259.525 - 449.510i) q^{46} +(-193.385 + 334.953i) q^{47} +(-356.182 - 210.423i) q^{48} +(-342.950 - 5.86430i) q^{49} +(-50.6496 + 87.7278i) q^{50} +(-566.929 - 334.926i) q^{51} +211.460 q^{52} +(-133.617 + 231.431i) q^{53} +(402.581 + 248.837i) q^{54} -379.213 q^{55} +(2.46759 - 288.635i) q^{56} +(205.771 - 116.072i) q^{57} +185.305 q^{58} +(-193.371 - 334.929i) q^{59} +(149.072 - 84.0889i) q^{60} +(-17.8409 + 30.9013i) q^{61} -370.070 q^{62} +(-14.2827 + 499.843i) q^{63} +151.514 q^{64} +(304.851 - 528.017i) q^{65} +(-587.260 - 346.938i) q^{66} +(-17.8513 - 30.9194i) q^{67} -428.314 q^{68} +(8.00195 - 799.465i) q^{69} +(524.661 + 308.923i) q^{70} -146.355 q^{71} +(-420.722 - 8.42297i) q^{72} +(-364.856 + 631.948i) q^{73} +974.792 q^{74} +(-1.56169 + 156.026i) q^{75} +(76.8367 - 133.085i) q^{76} +(6.16087 - 720.640i) q^{77} +(955.177 - 538.798i) q^{78} +(-250.675 + 434.183i) q^{79} +(-387.939 + 671.931i) q^{80} +(728.416 + 29.1779i) q^{81} +(38.1227 + 66.0304i) q^{82} +(169.622 + 293.794i) q^{83} +(157.377 + 284.657i) q^{84} +(-617.477 + 1069.50i) q^{85} +161.553 q^{86} +(248.605 - 140.234i) q^{87} +606.465 q^{88} +(-104.209 - 180.495i) q^{89} +(459.110 - 759.669i) q^{90} +(998.467 + 587.903i) q^{91} +(-260.026 - 450.378i) q^{92} +(-496.486 + 280.058i) q^{93} +(652.368 + 1129.94i) q^{94} +(-221.543 - 383.723i) q^{95} +(-651.227 + 367.345i) q^{96} +(-56.7013 - 98.2095i) q^{97} +(-595.588 + 992.024i) q^{98} +(-1050.42 - 21.0297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q + q^{2} - q^{3} - 79 q^{4} + 38 q^{5} - 20 q^{6} - 7 q^{7} - 24 q^{8} - 31 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 44 q + q^{2} - q^{3} - 79 q^{4} + 38 q^{5} - 20 q^{6} - 7 q^{7} - 24 q^{8} - 31 q^{9} - 18 q^{10} - 10 q^{11} - 41 q^{12} - 14 q^{13} - 79 q^{14} + 119 q^{15} - 247 q^{16} - 162 q^{17} + 157 q^{18} + 58 q^{19} - 362 q^{20} + 166 q^{21} - 18 q^{22} + 186 q^{23} + 414 q^{24} + 698 q^{25} - 266 q^{26} + 272 q^{27} - 172 q^{28} + 248 q^{29} + 616 q^{30} + 61 q^{31} - 163 q^{32} + 23 q^{33} + 6 q^{34} + 289 q^{35} - 806 q^{36} - 86 q^{37} + 1522 q^{38} - 565 q^{39} + 36 q^{40} - 692 q^{41} + 395 q^{42} - 86 q^{43} - 443 q^{44} - 1483 q^{45} - 270 q^{46} - 1005 q^{47} - 1013 q^{48} - 277 q^{49} + 239 q^{50} - 1719 q^{51} + 670 q^{52} + 258 q^{53} + 910 q^{54} - 870 q^{55} + 714 q^{56} + 566 q^{57} - 474 q^{58} - 1665 q^{59} + 4 q^{60} + 439 q^{61} + 1812 q^{62} + 493 q^{63} + 872 q^{64} - 613 q^{65} + 3073 q^{66} + 295 q^{67} + 2748 q^{68} + 1389 q^{69} - 1044 q^{70} + 636 q^{71} + 981 q^{72} - 338 q^{73} - 2238 q^{74} - 1064 q^{75} + 1006 q^{76} - 2909 q^{77} + 157 q^{78} + 133 q^{79} - 4817 q^{80} + 1325 q^{81} + 6 q^{82} - 1356 q^{83} - 7081 q^{84} + 483 q^{85} + 6686 q^{86} + 2774 q^{87} - 738 q^{88} - 2200 q^{89} + 2665 q^{90} + 1552 q^{91} - 396 q^{92} + 4365 q^{93} - 1191 q^{94} + 3083 q^{95} - 1468 q^{96} - 266 q^{97} + 3601 q^{98} - 5395 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.68671 2.92146i 0.596341 1.03289i −0.397015 0.917812i \(-0.629954\pi\)
0.993356 0.115081i \(-0.0367128\pi\)
\(3\) 0.0520064 5.19589i 0.0100086 0.999950i
\(4\) −1.68996 2.92710i −0.211246 0.365888i
\(5\) −9.74532 −0.871648 −0.435824 0.900032i \(-0.643543\pi\)
−0.435824 + 0.900032i \(0.643543\pi\)
\(6\) −15.0919 8.91589i −1.02687 0.606649i
\(7\) 0.158327 18.5196i 0.00854886 0.999963i
\(8\) 15.5854 0.688785
\(9\) −26.9946 0.540440i −0.999800 0.0200163i
\(10\) −16.4375 + 28.4706i −0.519800 + 0.900319i
\(11\) 38.9123 1.06659 0.533296 0.845929i \(-0.320953\pi\)
0.533296 + 0.845929i \(0.320953\pi\)
\(12\) −15.2968 + 8.62865i −0.367984 + 0.207573i
\(13\) −31.2817 + 54.1816i −0.667384 + 1.15594i 0.311249 + 0.950328i \(0.399253\pi\)
−0.978633 + 0.205615i \(0.934081\pi\)
\(14\) −53.8372 31.6997i −1.02776 0.605149i
\(15\) −0.506819 + 50.6356i −0.00872401 + 0.871604i
\(16\) 39.8078 68.9491i 0.621996 1.07733i
\(17\) 63.3614 109.745i 0.903964 1.56571i 0.0816621 0.996660i \(-0.473977\pi\)
0.822302 0.569051i \(-0.192689\pi\)
\(18\) −47.1109 + 77.9521i −0.616896 + 1.02075i
\(19\) 22.7332 + 39.3751i 0.274493 + 0.475435i 0.970007 0.243077i \(-0.0781568\pi\)
−0.695514 + 0.718512i \(0.744823\pi\)
\(20\) 16.4692 + 28.5256i 0.184132 + 0.318926i
\(21\) −96.2175 1.78579i −0.999828 0.0185567i
\(22\) 65.6337 113.681i 0.636052 1.10167i
\(23\) 153.865 1.39491 0.697457 0.716627i \(-0.254315\pi\)
0.697457 + 0.716627i \(0.254315\pi\)
\(24\) 0.810542 80.9801i 0.00689380 0.688750i
\(25\) −30.0287 −0.240230
\(26\) 105.526 + 182.777i 0.795977 + 1.37867i
\(27\) −4.21196 + 140.233i −0.0300219 + 0.999549i
\(28\) −54.4763 + 30.8340i −0.367681 + 0.208110i
\(29\) 27.4655 + 47.5716i 0.175869 + 0.304615i 0.940462 0.339899i \(-0.110393\pi\)
−0.764592 + 0.644514i \(0.777060\pi\)
\(30\) 147.075 + 86.8882i 0.895072 + 0.528785i
\(31\) −54.8509 95.0045i −0.317791 0.550430i 0.662236 0.749295i \(-0.269608\pi\)
−0.980027 + 0.198866i \(0.936274\pi\)
\(32\) −71.9464 124.615i −0.397452 0.688406i
\(33\) 2.02369 202.184i 0.0106751 1.06654i
\(34\) −213.744 370.216i −1.07814 1.86740i
\(35\) −1.54295 + 180.479i −0.00745159 + 0.871616i
\(36\) 44.0380 + 79.9293i 0.203880 + 0.370043i
\(37\) 144.482 + 250.249i 0.641962 + 1.11191i 0.984994 + 0.172588i \(0.0552129\pi\)
−0.343032 + 0.939324i \(0.611454\pi\)
\(38\) 153.377 0.654765
\(39\) 279.895 + 165.354i 1.14921 + 0.678920i
\(40\) −151.885 −0.600378
\(41\) −11.3009 + 19.5738i −0.0430465 + 0.0745587i −0.886746 0.462257i \(-0.847040\pi\)
0.843699 + 0.536816i \(0.180373\pi\)
\(42\) −167.508 + 278.084i −0.615406 + 1.02165i
\(43\) 23.9450 + 41.4740i 0.0849204 + 0.147086i 0.905357 0.424651i \(-0.139603\pi\)
−0.820437 + 0.571737i \(0.806270\pi\)
\(44\) −65.7604 113.900i −0.225313 0.390253i
\(45\) 263.071 + 5.26676i 0.871473 + 0.0174472i
\(46\) 259.525 449.510i 0.831845 1.44080i
\(47\) −193.385 + 334.953i −0.600173 + 1.03953i 0.392622 + 0.919700i \(0.371568\pi\)
−0.992794 + 0.119830i \(0.961765\pi\)
\(48\) −356.182 210.423i −1.07105 0.632748i
\(49\) −342.950 5.86430i −0.999854 0.0170971i
\(50\) −50.6496 + 87.7278i −0.143259 + 0.248132i
\(51\) −566.929 334.926i −1.55659 0.919589i
\(52\) 211.460 0.563928
\(53\) −133.617 + 231.431i −0.346296 + 0.599802i −0.985588 0.169162i \(-0.945894\pi\)
0.639293 + 0.768964i \(0.279227\pi\)
\(54\) 402.581 + 248.837i 1.01452 + 0.627082i
\(55\) −379.213 −0.929692
\(56\) 2.46759 288.635i 0.00588832 0.688759i
\(57\) 205.771 116.072i 0.478159 0.269720i
\(58\) 185.305 0.419513
\(59\) −193.371 334.929i −0.426691 0.739051i 0.569886 0.821724i \(-0.306987\pi\)
−0.996577 + 0.0826735i \(0.973654\pi\)
\(60\) 149.072 84.0889i 0.320753 0.180931i
\(61\) −17.8409 + 30.9013i −0.0374473 + 0.0648607i −0.884142 0.467219i \(-0.845256\pi\)
0.846694 + 0.532080i \(0.178589\pi\)
\(62\) −370.070 −0.758047
\(63\) −14.2827 + 499.843i −0.0285627 + 0.999592i
\(64\) 151.514 0.295925
\(65\) 304.851 528.017i 0.581724 1.00758i
\(66\) −587.260 346.938i −1.09525 0.647047i
\(67\) −17.8513 30.9194i −0.0325506 0.0563792i 0.849291 0.527925i \(-0.177030\pi\)
−0.881842 + 0.471545i \(0.843696\pi\)
\(68\) −428.314 −0.763834
\(69\) 8.00195 799.465i 0.0139612 1.39484i
\(70\) 524.661 + 308.923i 0.895843 + 0.527477i
\(71\) −146.355 −0.244636 −0.122318 0.992491i \(-0.539033\pi\)
−0.122318 + 0.992491i \(0.539033\pi\)
\(72\) −420.722 8.42297i −0.688647 0.0137869i
\(73\) −364.856 + 631.948i −0.584974 + 1.01320i 0.409905 + 0.912128i \(0.365562\pi\)
−0.994879 + 0.101076i \(0.967771\pi\)
\(74\) 974.792 1.53131
\(75\) −1.56169 + 156.026i −0.00240437 + 0.240218i
\(76\) 76.8367 133.085i 0.115971 0.200867i
\(77\) 6.16087 720.640i 0.00911814 1.06655i
\(78\) 955.177 538.798i 1.38657 0.782139i
\(79\) −250.675 + 434.183i −0.357002 + 0.618346i −0.987459 0.157879i \(-0.949535\pi\)
0.630456 + 0.776225i \(0.282868\pi\)
\(80\) −387.939 + 671.931i −0.542162 + 0.939052i
\(81\) 728.416 + 29.1779i 0.999199 + 0.0400245i
\(82\) 38.1227 + 66.0304i 0.0513408 + 0.0889249i
\(83\) 169.622 + 293.794i 0.224319 + 0.388532i 0.956115 0.292992i \(-0.0946510\pi\)
−0.731796 + 0.681524i \(0.761318\pi\)
\(84\) 157.377 + 284.657i 0.204420 + 0.369745i
\(85\) −617.477 + 1069.50i −0.787938 + 1.36475i
\(86\) 161.553 0.202566
\(87\) 248.605 140.234i 0.306360 0.172812i
\(88\) 606.465 0.734652
\(89\) −104.209 180.495i −0.124113 0.214971i 0.797273 0.603619i \(-0.206275\pi\)
−0.921386 + 0.388649i \(0.872942\pi\)
\(90\) 459.110 759.669i 0.537717 0.889735i
\(91\) 998.467 + 587.903i 1.15020 + 0.677242i
\(92\) −260.026 450.378i −0.294669 0.510382i
\(93\) −496.486 + 280.058i −0.553583 + 0.312266i
\(94\) 652.368 + 1129.94i 0.715816 + 1.23983i
\(95\) −221.543 383.723i −0.239261 0.414412i
\(96\) −651.227 + 367.345i −0.692350 + 0.390542i
\(97\) −56.7013 98.2095i −0.0593520 0.102801i 0.834823 0.550519i \(-0.185570\pi\)
−0.894175 + 0.447718i \(0.852237\pi\)
\(98\) −595.588 + 992.024i −0.613913 + 1.02255i
\(99\) −1050.42 21.0297i −1.06638 0.0213492i
\(100\) 50.7475 + 87.8972i 0.0507475 + 0.0878972i
\(101\) 1078.01 1.06204 0.531019 0.847360i \(-0.321809\pi\)
0.531019 + 0.847360i \(0.321809\pi\)
\(102\) −1934.72 + 1091.34i −1.87809 + 1.05940i
\(103\) 1710.37 1.63619 0.818097 0.575080i \(-0.195029\pi\)
0.818097 + 0.575080i \(0.195029\pi\)
\(104\) −487.539 + 844.442i −0.459684 + 0.796196i
\(105\) 937.671 + 17.4031i 0.871498 + 0.0161749i
\(106\) 450.745 + 780.713i 0.413021 + 0.715373i
\(107\) −410.398 710.830i −0.370791 0.642229i 0.618896 0.785473i \(-0.287580\pi\)
−0.989687 + 0.143244i \(0.954247\pi\)
\(108\) 417.594 224.660i 0.372065 0.200166i
\(109\) 1064.55 1843.85i 0.935460 1.62026i 0.161648 0.986848i \(-0.448319\pi\)
0.773812 0.633416i \(-0.218348\pi\)
\(110\) −639.621 + 1107.86i −0.554414 + 0.960273i
\(111\) 1307.78 737.696i 1.11828 0.630802i
\(112\) −1270.61 748.140i −1.07197 0.631183i
\(113\) 203.179 351.917i 0.169146 0.292970i −0.768974 0.639280i \(-0.779232\pi\)
0.938120 + 0.346311i \(0.112566\pi\)
\(114\) 7.97660 796.932i 0.00655331 0.654732i
\(115\) −1499.46 −1.21587
\(116\) 92.8314 160.789i 0.0743033 0.128697i
\(117\) 873.719 1445.70i 0.690388 1.14235i
\(118\) −1304.64 −1.01781
\(119\) −2022.40 1190.80i −1.55793 0.917316i
\(120\) −7.89899 + 789.178i −0.00600897 + 0.600348i
\(121\) 183.168 0.137617
\(122\) 60.1846 + 104.243i 0.0446628 + 0.0773582i
\(123\) 101.115 + 59.7363i 0.0741242 + 0.0437906i
\(124\) −185.392 + 321.109i −0.134264 + 0.232552i
\(125\) 1510.80 1.08104
\(126\) 1436.18 + 884.815i 1.01544 + 0.625600i
\(127\) −2300.05 −1.60706 −0.803529 0.595266i \(-0.797047\pi\)
−0.803529 + 0.595266i \(0.797047\pi\)
\(128\) 831.131 1439.56i 0.573924 0.994066i
\(129\) 216.739 122.259i 0.147929 0.0834440i
\(130\) −1028.39 1781.22i −0.693812 1.20172i
\(131\) −583.702 −0.389300 −0.194650 0.980873i \(-0.562357\pi\)
−0.194650 + 0.980873i \(0.562357\pi\)
\(132\) −595.234 + 335.761i −0.392489 + 0.221395i
\(133\) 732.810 414.776i 0.477764 0.270418i
\(134\) −120.440 −0.0776449
\(135\) 41.0469 1366.61i 0.0261685 0.871255i
\(136\) 987.513 1710.42i 0.622636 1.07844i
\(137\) −168.798 −0.105266 −0.0526328 0.998614i \(-0.516761\pi\)
−0.0526328 + 0.998614i \(0.516761\pi\)
\(138\) −2322.11 1371.84i −1.43240 0.846223i
\(139\) 671.306 1162.74i 0.409636 0.709511i −0.585213 0.810880i \(-0.698989\pi\)
0.994849 + 0.101369i \(0.0323223\pi\)
\(140\) 530.889 300.487i 0.320488 0.181399i
\(141\) 1730.32 + 1022.23i 1.03347 + 0.610547i
\(142\) −246.858 + 427.571i −0.145887 + 0.252683i
\(143\) −1217.24 + 2108.33i −0.711826 + 1.23292i
\(144\) −1111.86 + 1839.74i −0.643436 + 1.06466i
\(145\) −267.660 463.601i −0.153296 0.265517i
\(146\) 1230.81 + 2131.82i 0.697688 + 1.20843i
\(147\) −48.3059 + 1781.63i −0.0271034 + 0.999633i
\(148\) 488.337 845.825i 0.271223 0.469773i
\(149\) −721.359 −0.396618 −0.198309 0.980140i \(-0.563545\pi\)
−0.198309 + 0.980140i \(0.563545\pi\)
\(150\) 453.190 + 267.733i 0.246685 + 0.145735i
\(151\) −2867.01 −1.54513 −0.772563 0.634938i \(-0.781026\pi\)
−0.772563 + 0.634938i \(0.781026\pi\)
\(152\) 354.307 + 613.677i 0.189066 + 0.327472i
\(153\) −1769.72 + 2928.28i −0.935123 + 1.54730i
\(154\) −2094.93 1233.51i −1.09620 0.645447i
\(155\) 534.540 + 925.850i 0.277002 + 0.479781i
\(156\) 10.9973 1098.72i 0.00564415 0.563899i
\(157\) 375.097 + 649.686i 0.190675 + 0.330259i 0.945474 0.325697i \(-0.105599\pi\)
−0.754799 + 0.655956i \(0.772266\pi\)
\(158\) 845.632 + 1464.68i 0.425790 + 0.737491i
\(159\) 1195.54 + 706.294i 0.596306 + 0.352282i
\(160\) 701.141 + 1214.41i 0.346438 + 0.600048i
\(161\) 24.3610 2849.51i 0.0119249 1.39486i
\(162\) 1313.87 2078.83i 0.637204 1.00820i
\(163\) 1400.06 + 2424.98i 0.672769 + 1.16527i 0.977116 + 0.212709i \(0.0682285\pi\)
−0.304347 + 0.952561i \(0.598438\pi\)
\(164\) 76.3926 0.0363735
\(165\) −19.7215 + 1970.35i −0.00930495 + 0.929646i
\(166\) 1144.41 0.535082
\(167\) −0.0790177 + 0.136863i −3.66142e−5 + 6.34176e-5i −0.866044 0.499968i \(-0.833345\pi\)
0.866007 + 0.500032i \(0.166678\pi\)
\(168\) −1499.59 27.8322i −0.688666 0.0127816i
\(169\) −858.594 1487.13i −0.390803 0.676890i
\(170\) 2083.01 + 3607.87i 0.939760 + 1.62771i
\(171\) −592.394 1075.20i −0.264921 0.480834i
\(172\) 80.9324 140.179i 0.0358781 0.0621427i
\(173\) −631.310 + 1093.46i −0.277443 + 0.480545i −0.970748 0.240099i \(-0.922820\pi\)
0.693306 + 0.720644i \(0.256154\pi\)
\(174\) 9.63705 962.825i 0.00419875 0.419492i
\(175\) −4.75436 + 556.119i −0.00205369 + 0.240221i
\(176\) 1549.01 2682.97i 0.663416 1.14907i
\(177\) −1750.31 + 987.317i −0.743284 + 0.419273i
\(178\) −703.078 −0.296056
\(179\) 1457.18 2523.91i 0.608462 1.05389i −0.383032 0.923735i \(-0.625120\pi\)
0.991494 0.130152i \(-0.0415465\pi\)
\(180\) −429.164 778.937i −0.177711 0.322547i
\(181\) 870.971 0.357673 0.178836 0.983879i \(-0.442767\pi\)
0.178836 + 0.983879i \(0.442767\pi\)
\(182\) 3401.66 1925.36i 1.38543 0.784162i
\(183\) 159.632 + 94.3062i 0.0644827 + 0.0380946i
\(184\) 2398.05 0.960795
\(185\) −1408.02 2438.76i −0.559565 0.969196i
\(186\) −19.2460 + 1922.84i −0.00758702 + 0.758009i
\(187\) 2465.54 4270.44i 0.964160 1.66997i
\(188\) 1307.26 0.507135
\(189\) 2596.39 + 100.206i 0.999256 + 0.0385658i
\(190\) −1494.71 −0.570725
\(191\) −1588.84 + 2751.95i −0.601907 + 1.04253i 0.390625 + 0.920550i \(0.372259\pi\)
−0.992532 + 0.121983i \(0.961075\pi\)
\(192\) 7.87969 787.249i 0.00296181 0.295911i
\(193\) 851.492 + 1474.83i 0.317574 + 0.550054i 0.979981 0.199090i \(-0.0637985\pi\)
−0.662407 + 0.749144i \(0.730465\pi\)
\(194\) −382.554 −0.141576
\(195\) −2727.66 1611.43i −1.00170 0.591779i
\(196\) 562.408 + 1013.76i 0.204959 + 0.369446i
\(197\) 254.870 0.0921763 0.0460881 0.998937i \(-0.485324\pi\)
0.0460881 + 0.998937i \(0.485324\pi\)
\(198\) −1833.19 + 3033.30i −0.657976 + 1.08872i
\(199\) −386.703 + 669.790i −0.137752 + 0.238594i −0.926645 0.375937i \(-0.877321\pi\)
0.788893 + 0.614530i \(0.210654\pi\)
\(200\) −468.010 −0.165466
\(201\) −161.582 + 91.1456i −0.0567022 + 0.0319846i
\(202\) 1818.28 3149.36i 0.633337 1.09697i
\(203\) 885.355 501.118i 0.306107 0.173259i
\(204\) −22.2751 + 2225.47i −0.00764494 + 0.763795i
\(205\) 110.131 190.753i 0.0375214 0.0649890i
\(206\) 2884.90 4996.79i 0.975730 1.69001i
\(207\) −4153.52 83.1546i −1.39463 0.0279210i
\(208\) 2490.51 + 4313.69i 0.830221 + 1.43798i
\(209\) 884.602 + 1532.18i 0.292771 + 0.507095i
\(210\) 1632.42 2710.02i 0.536417 0.890519i
\(211\) −1834.55 + 3177.54i −0.598558 + 1.03673i 0.394476 + 0.918906i \(0.370926\pi\)
−0.993034 + 0.117827i \(0.962407\pi\)
\(212\) 903.230 0.292614
\(213\) −7.61141 + 760.445i −0.00244847 + 0.244624i
\(214\) −2768.88 −0.884472
\(215\) −233.352 404.177i −0.0740207 0.128208i
\(216\) −65.6451 + 2185.59i −0.0206786 + 0.688474i
\(217\) −1768.13 + 1000.77i −0.553126 + 0.313074i
\(218\) −3591.16 6220.07i −1.11571 1.93246i
\(219\) 3264.56 + 1928.62i 1.00730 + 0.595086i
\(220\) 640.857 + 1110.00i 0.196393 + 0.340163i
\(221\) 3964.11 + 6866.03i 1.20658 + 2.08986i
\(222\) 50.6955 5064.91i 0.0153264 1.53124i
\(223\) 1002.18 + 1735.83i 0.300947 + 0.521256i 0.976351 0.216192i \(-0.0693639\pi\)
−0.675404 + 0.737448i \(0.736031\pi\)
\(224\) −2319.21 + 1312.69i −0.691779 + 0.391552i
\(225\) 810.613 + 16.2287i 0.240182 + 0.00480850i
\(226\) −685.409 1187.16i −0.201738 0.349420i
\(227\) −3396.02 −0.992958 −0.496479 0.868049i \(-0.665374\pi\)
−0.496479 + 0.868049i \(0.665374\pi\)
\(228\) −687.500 406.157i −0.199696 0.117975i
\(229\) −5153.79 −1.48721 −0.743606 0.668618i \(-0.766886\pi\)
−0.743606 + 0.668618i \(0.766886\pi\)
\(230\) −2529.15 + 4380.62i −0.725076 + 1.25587i
\(231\) −3744.05 69.4891i −1.06641 0.0197924i
\(232\) 428.061 + 741.424i 0.121136 + 0.209814i
\(233\) −3053.12 5288.16i −0.858441 1.48686i −0.873416 0.486976i \(-0.838100\pi\)
0.0149746 0.999888i \(-0.495233\pi\)
\(234\) −2749.86 4991.02i −0.768222 1.39433i
\(235\) 1884.60 3264.22i 0.523139 0.906104i
\(236\) −653.581 + 1132.03i −0.180273 + 0.312242i
\(237\) 2242.93 + 1325.06i 0.614742 + 0.363173i
\(238\) −6890.08 + 3899.84i −1.87655 + 1.06214i
\(239\) −1301.70 + 2254.62i −0.352302 + 0.610205i −0.986652 0.162840i \(-0.947934\pi\)
0.634350 + 0.773046i \(0.281268\pi\)
\(240\) 3471.10 + 2050.64i 0.933578 + 0.551533i
\(241\) 2322.27 0.620707 0.310354 0.950621i \(-0.399553\pi\)
0.310354 + 0.950621i \(0.399553\pi\)
\(242\) 308.950 535.118i 0.0820665 0.142143i
\(243\) 189.487 3783.25i 0.0500232 0.998748i
\(244\) 120.602 0.0316423
\(245\) 3342.16 + 57.1495i 0.871521 + 0.0149026i
\(246\) 345.070 194.647i 0.0894343 0.0504482i
\(247\) −2844.54 −0.732768
\(248\) −854.874 1480.69i −0.218889 0.379127i
\(249\) 1535.35 866.060i 0.390757 0.220419i
\(250\) 2548.29 4413.76i 0.644671 1.11660i
\(251\) −476.889 −0.119924 −0.0599621 0.998201i \(-0.519098\pi\)
−0.0599621 + 0.998201i \(0.519098\pi\)
\(252\) 1487.23 802.910i 0.371773 0.200709i
\(253\) 5987.23 1.48780
\(254\) −3879.51 + 6719.51i −0.958354 + 1.65992i
\(255\) 5524.90 + 3263.96i 1.35679 + 0.801558i
\(256\) −2197.69 3806.52i −0.536546 0.929326i
\(257\) 3736.85 0.906997 0.453499 0.891257i \(-0.350176\pi\)
0.453499 + 0.891257i \(0.350176\pi\)
\(258\) 8.40179 839.411i 0.00202741 0.202556i
\(259\) 4657.39 2636.12i 1.11736 0.632433i
\(260\) −2060.75 −0.491546
\(261\) −715.710 1299.02i −0.169737 0.308074i
\(262\) −984.535 + 1705.26i −0.232156 + 0.402105i
\(263\) 1009.13 0.236600 0.118300 0.992978i \(-0.462256\pi\)
0.118300 + 0.992978i \(0.462256\pi\)
\(264\) 31.5400 3151.12i 0.00735286 0.734615i
\(265\) 1302.14 2255.37i 0.301848 0.522816i
\(266\) 24.2838 2840.48i 0.00559749 0.654741i
\(267\) −943.251 + 532.070i −0.216202 + 0.121956i
\(268\) −60.3362 + 104.505i −0.0137523 + 0.0238197i
\(269\) −4069.36 + 7048.33i −0.922354 + 1.59756i −0.126591 + 0.991955i \(0.540403\pi\)
−0.795763 + 0.605608i \(0.792930\pi\)
\(270\) −3923.28 2425.00i −0.884308 0.546595i
\(271\) 3384.69 + 5862.46i 0.758692 + 1.31409i 0.943518 + 0.331321i \(0.107494\pi\)
−0.184826 + 0.982771i \(0.559172\pi\)
\(272\) −5044.55 8737.41i −1.12452 1.94773i
\(273\) 3106.61 5157.35i 0.688720 1.14336i
\(274\) −284.713 + 493.137i −0.0627742 + 0.108728i
\(275\) −1168.49 −0.256227
\(276\) −2353.64 + 1327.64i −0.513306 + 0.289546i
\(277\) −6519.00 −1.41404 −0.707019 0.707194i \(-0.749961\pi\)
−0.707019 + 0.707194i \(0.749961\pi\)
\(278\) −2264.59 3922.39i −0.488566 0.846221i
\(279\) 1429.33 + 2594.25i 0.306709 + 0.556680i
\(280\) −24.0475 + 2812.84i −0.00513254 + 0.600356i
\(281\) −3138.53 5436.10i −0.666296 1.15406i −0.978932 0.204185i \(-0.934545\pi\)
0.312636 0.949873i \(-0.398788\pi\)
\(282\) 5904.95 3330.87i 1.24693 0.703371i
\(283\) −403.166 698.304i −0.0846845 0.146678i 0.820572 0.571543i \(-0.193655\pi\)
−0.905257 + 0.424865i \(0.860322\pi\)
\(284\) 247.335 + 428.397i 0.0516783 + 0.0895094i
\(285\) −2005.31 + 1131.16i −0.416786 + 0.235101i
\(286\) 4106.27 + 7112.27i 0.848982 + 1.47048i
\(287\) 360.709 + 212.387i 0.0741880 + 0.0436823i
\(288\) 1874.82 + 3402.81i 0.383593 + 0.696224i
\(289\) −5572.82 9652.42i −1.13430 1.96467i
\(290\) −1805.86 −0.365668
\(291\) −513.235 + 289.506i −0.103390 + 0.0583201i
\(292\) 2466.37 0.494293
\(293\) 3084.92 5343.24i 0.615095 1.06538i −0.375272 0.926915i \(-0.622451\pi\)
0.990368 0.138462i \(-0.0442158\pi\)
\(294\) 5123.48 + 3146.21i 1.01635 + 0.624117i
\(295\) 1884.46 + 3263.99i 0.371924 + 0.644192i
\(296\) 2251.80 + 3900.24i 0.442174 + 0.765868i
\(297\) −163.897 + 5456.78i −0.0320211 + 1.06611i
\(298\) −1216.72 + 2107.42i −0.236519 + 0.409664i
\(299\) −4813.16 + 8336.63i −0.930943 + 1.61244i
\(300\) 459.343 259.107i 0.0884007 0.0498652i
\(301\) 771.871 436.885i 0.147807 0.0836599i
\(302\) −4835.81 + 8375.87i −0.921423 + 1.59595i
\(303\) 56.0633 5601.21i 0.0106296 1.06198i
\(304\) 3619.84 0.682933
\(305\) 173.865 301.143i 0.0326409 0.0565357i
\(306\) 5569.86 + 10109.3i 1.04055 + 1.88860i
\(307\) 4381.77 0.814596 0.407298 0.913295i \(-0.366471\pi\)
0.407298 + 0.913295i \(0.366471\pi\)
\(308\) −2119.80 + 1199.82i −0.392165 + 0.221968i
\(309\) 88.9504 8886.91i 0.0163761 1.63611i
\(310\) 3606.45 0.660750
\(311\) 4231.30 + 7328.83i 0.771495 + 1.33627i 0.936743 + 0.350017i \(0.113824\pi\)
−0.165248 + 0.986252i \(0.552843\pi\)
\(312\) 4362.27 + 2577.12i 0.791555 + 0.467630i
\(313\) −2910.23 + 5040.67i −0.525547 + 0.910273i 0.474011 + 0.880519i \(0.342806\pi\)
−0.999557 + 0.0297543i \(0.990528\pi\)
\(314\) 2530.71 0.454829
\(315\) 139.189 4871.13i 0.0248966 0.871292i
\(316\) 1694.53 0.301661
\(317\) 3207.59 5555.71i 0.568316 0.984353i −0.428416 0.903582i \(-0.640928\pi\)
0.996733 0.0807714i \(-0.0257384\pi\)
\(318\) 4079.94 2301.42i 0.719471 0.405840i
\(319\) 1068.75 + 1851.12i 0.187581 + 0.324900i
\(320\) −1476.55 −0.257943
\(321\) −3714.74 + 2095.41i −0.645908 + 0.364345i
\(322\) −8283.65 4877.46i −1.43363 0.844131i
\(323\) 5761.63 0.992526
\(324\) −1145.59 2181.46i −0.196432 0.374050i
\(325\) 939.350 1627.00i 0.160325 0.277692i
\(326\) 9445.98 1.60480
\(327\) −9525.08 5627.16i −1.61082 0.951630i
\(328\) −176.130 + 305.065i −0.0296498 + 0.0513549i
\(329\) 6172.57 + 3634.44i 1.03436 + 0.609038i
\(330\) 5723.04 + 3381.02i 0.954676 + 0.563997i
\(331\) 414.418 717.794i 0.0688172 0.119195i −0.829564 0.558412i \(-0.811411\pi\)
0.898381 + 0.439217i \(0.144744\pi\)
\(332\) 573.311 993.004i 0.0947727 0.164151i
\(333\) −3764.97 6833.46i −0.619578 1.12454i
\(334\) 0.266559 + 0.461694i 4.36691e−5 + 7.56371e-5i
\(335\) 173.967 + 301.320i 0.0283726 + 0.0491428i
\(336\) −3953.33 + 6563.02i −0.641881 + 1.06560i
\(337\) −2906.88 + 5034.86i −0.469875 + 0.813847i −0.999407 0.0344432i \(-0.989034\pi\)
0.529532 + 0.848290i \(0.322368\pi\)
\(338\) −5792.79 −0.932207
\(339\) −1817.96 1074.00i −0.291262 0.172070i
\(340\) 4174.06 0.665794
\(341\) −2134.37 3696.85i −0.338953 0.587083i
\(342\) −4140.36 82.8911i −0.654634 0.0131060i
\(343\) −162.903 + 6350.36i −0.0256441 + 0.999671i
\(344\) 373.193 + 646.389i 0.0584919 + 0.101311i
\(345\) −77.9816 + 7791.04i −0.0121692 + 1.21581i
\(346\) 2129.67 + 3688.70i 0.330901 + 0.573137i
\(347\) −1661.46 2877.74i −0.257038 0.445202i 0.708409 0.705802i \(-0.249413\pi\)
−0.965447 + 0.260600i \(0.916080\pi\)
\(348\) −830.613 490.704i −0.127947 0.0755877i
\(349\) −376.201 651.599i −0.0577008 0.0999407i 0.835732 0.549137i \(-0.185044\pi\)
−0.893433 + 0.449197i \(0.851710\pi\)
\(350\) 1616.66 + 951.900i 0.246898 + 0.145375i
\(351\) −7466.28 4614.94i −1.13539 0.701787i
\(352\) −2799.60 4849.05i −0.423918 0.734248i
\(353\) −2213.65 −0.333770 −0.166885 0.985976i \(-0.553371\pi\)
−0.166885 + 0.985976i \(0.553371\pi\)
\(354\) −67.8498 + 6778.78i −0.0101869 + 1.01776i
\(355\) 1426.28 0.213236
\(356\) −352.218 + 610.060i −0.0524368 + 0.0908233i
\(357\) −6292.45 + 10446.3i −0.932863 + 1.54867i
\(358\) −4915.67 8514.19i −0.725702 1.25695i
\(359\) −435.090 753.599i −0.0639643 0.110789i 0.832270 0.554371i \(-0.187041\pi\)
−0.896234 + 0.443581i \(0.853708\pi\)
\(360\) 4100.07 + 82.0846i 0.600257 + 0.0120173i
\(361\) 2395.90 4149.82i 0.349308 0.605018i
\(362\) 1469.07 2544.51i 0.213295 0.369438i
\(363\) 9.52590 951.720i 0.00137736 0.137610i
\(364\) 33.4799 3916.15i 0.00482094 0.563907i
\(365\) 3555.63 6158.54i 0.509892 0.883158i
\(366\) 544.764 307.292i 0.0778014 0.0438863i
\(367\) −2528.67 −0.359660 −0.179830 0.983698i \(-0.557555\pi\)
−0.179830 + 0.983698i \(0.557555\pi\)
\(368\) 6125.01 10608.8i 0.867631 1.50278i
\(369\) 315.642 522.278i 0.0445303 0.0736822i
\(370\) −9499.66 −1.33477
\(371\) 4264.85 + 2511.17i 0.596819 + 0.351411i
\(372\) 1658.80 + 979.977i 0.231196 + 0.136585i
\(373\) 5370.58 0.745518 0.372759 0.927928i \(-0.378412\pi\)
0.372759 + 0.927928i \(0.378412\pi\)
\(374\) −8317.28 14406.0i −1.14994 1.99175i
\(375\) 78.5715 7849.98i 0.0108198 1.08099i
\(376\) −3013.99 + 5220.38i −0.413390 + 0.716012i
\(377\) −3436.67 −0.469490
\(378\) 4672.10 7416.23i 0.635732 1.00913i
\(379\) −9923.53 −1.34495 −0.672477 0.740118i \(-0.734770\pi\)
−0.672477 + 0.740118i \(0.734770\pi\)
\(380\) −748.798 + 1296.96i −0.101086 + 0.175085i
\(381\) −119.617 + 11950.8i −0.0160845 + 1.60698i
\(382\) 5359.81 + 9283.46i 0.717884 + 1.24341i
\(383\) 11187.6 1.49259 0.746295 0.665616i \(-0.231831\pi\)
0.746295 + 0.665616i \(0.231831\pi\)
\(384\) −7436.58 4393.33i −0.988272 0.583845i
\(385\) −60.0397 + 7022.87i −0.00794781 + 0.929658i
\(386\) 5744.87 0.757529
\(387\) −623.971 1132.51i −0.0819593 0.148757i
\(388\) −191.646 + 331.941i −0.0250757 + 0.0434324i
\(389\) −1683.37 −0.219410 −0.109705 0.993964i \(-0.534991\pi\)
−0.109705 + 0.993964i \(0.534991\pi\)
\(390\) −9308.51 + 5250.76i −1.20860 + 0.681750i
\(391\) 9749.08 16885.9i 1.26095 2.18403i
\(392\) −5345.02 91.3976i −0.688684 0.0117762i
\(393\) −30.3563 + 3032.85i −0.00389636 + 0.389280i
\(394\) 429.891 744.593i 0.0549685 0.0952083i
\(395\) 2442.91 4231.25i 0.311180 0.538980i
\(396\) 1713.62 + 3110.23i 0.217456 + 0.394685i
\(397\) −1775.41 3075.09i −0.224446 0.388752i 0.731707 0.681619i \(-0.238724\pi\)
−0.956153 + 0.292867i \(0.905391\pi\)
\(398\) 1304.51 + 2259.48i 0.164295 + 0.284566i
\(399\) −2117.02 3829.17i −0.265623 0.480447i
\(400\) −1195.38 + 2070.45i −0.149422 + 0.258806i
\(401\) −3801.66 −0.473431 −0.236716 0.971579i \(-0.576071\pi\)
−0.236716 + 0.971579i \(0.576071\pi\)
\(402\) −6.26365 + 625.793i −0.000777120 + 0.0776411i
\(403\) 6863.32 0.848354
\(404\) −1821.80 3155.44i −0.224351 0.388587i
\(405\) −7098.65 284.348i −0.870950 0.0348873i
\(406\) 29.3388 3431.77i 0.00358636 0.419498i
\(407\) 5622.11 + 9737.78i 0.684712 + 1.18596i
\(408\) −8835.82 5219.97i −1.07215 0.633399i
\(409\) −6622.39 11470.3i −0.800626 1.38673i −0.919204 0.393781i \(-0.871167\pi\)
0.118578 0.992945i \(-0.462166\pi\)
\(410\) −371.518 643.488i −0.0447511 0.0775112i
\(411\) −8.77858 + 877.056i −0.00105357 + 0.105260i
\(412\) −2890.47 5006.44i −0.345639 0.598664i
\(413\) −6233.35 + 3528.12i −0.742671 + 0.420357i
\(414\) −7248.70 + 11994.1i −0.860517 + 1.42386i
\(415\) −1653.02 2863.12i −0.195527 0.338663i
\(416\) 9002.44 1.06101
\(417\) −6006.54 3548.50i −0.705376 0.416717i
\(418\) 5968.26 0.698367
\(419\) 1435.52 2486.39i 0.167374 0.289900i −0.770122 0.637897i \(-0.779805\pi\)
0.937496 + 0.347997i \(0.113138\pi\)
\(420\) −1533.69 2774.07i −0.178182 0.322288i
\(421\) −441.098 764.004i −0.0510637 0.0884449i 0.839364 0.543570i \(-0.182928\pi\)
−0.890427 + 0.455125i \(0.849594\pi\)
\(422\) 6188.70 + 10719.1i 0.713890 + 1.23649i
\(423\) 5401.37 8937.40i 0.620860 1.02731i
\(424\) −2082.47 + 3606.95i −0.238523 + 0.413134i
\(425\) −1902.66 + 3295.50i −0.217159 + 0.376130i
\(426\) 2208.77 + 1304.89i 0.251210 + 0.148408i
\(427\) 569.454 + 335.298i 0.0645382 + 0.0380005i
\(428\) −1387.12 + 2402.55i −0.156656 + 0.271336i
\(429\) 10891.3 + 6434.32i 1.22573 + 0.724130i
\(430\) −1574.38 −0.176566
\(431\) −4337.40 + 7512.59i −0.484745 + 0.839603i −0.999846 0.0175265i \(-0.994421\pi\)
0.515102 + 0.857129i \(0.327754\pi\)
\(432\) 9501.26 + 5872.77i 1.05817 + 0.654059i
\(433\) −10521.0 −1.16769 −0.583843 0.811866i \(-0.698452\pi\)
−0.583843 + 0.811866i \(0.698452\pi\)
\(434\) −58.5920 + 6853.54i −0.00648043 + 0.758019i
\(435\) −2422.74 + 1366.62i −0.267038 + 0.150631i
\(436\) −7196.19 −0.790447
\(437\) 3497.84 + 6058.44i 0.382894 + 0.663191i
\(438\) 11140.7 6284.28i 1.21535 0.685559i
\(439\) 5603.51 9705.56i 0.609205 1.05517i −0.382167 0.924093i \(-0.624822\pi\)
0.991372 0.131080i \(-0.0418445\pi\)
\(440\) −5910.19 −0.640358
\(441\) 9254.62 + 343.648i 0.999311 + 0.0371070i
\(442\) 26745.2 2.87814
\(443\) 1280.39 2217.70i 0.137321 0.237847i −0.789161 0.614187i \(-0.789484\pi\)
0.926482 + 0.376340i \(0.122817\pi\)
\(444\) −4369.42 2581.34i −0.467035 0.275912i
\(445\) 1015.55 + 1758.98i 0.108183 + 0.187379i
\(446\) 6761.57 0.717869
\(447\) −37.5153 + 3748.10i −0.00396960 + 0.396598i
\(448\) 23.9887 2805.97i 0.00252982 0.295915i
\(449\) 10296.7 1.08225 0.541126 0.840941i \(-0.317998\pi\)
0.541126 + 0.840941i \(0.317998\pi\)
\(450\) 1414.68 2340.80i 0.148197 0.245214i
\(451\) −439.745 + 761.660i −0.0459130 + 0.0795237i
\(452\) −1373.46 −0.142926
\(453\) −149.103 + 14896.7i −0.0154646 + 1.54505i
\(454\) −5728.08 + 9921.33i −0.592142 + 1.02562i
\(455\) −9730.38 5729.30i −1.00257 0.590316i
\(456\) 3207.03 1809.02i 0.329348 0.185779i
\(457\) −7182.41 + 12440.3i −0.735184 + 1.27338i 0.219459 + 0.975622i \(0.429571\pi\)
−0.954643 + 0.297754i \(0.903762\pi\)
\(458\) −8692.93 + 15056.6i −0.886886 + 1.53613i
\(459\) 15123.0 + 9347.59i 1.53787 + 0.950562i
\(460\) 2534.04 + 4389.08i 0.256848 + 0.444874i
\(461\) −2747.56 4758.92i −0.277585 0.480792i 0.693199 0.720746i \(-0.256201\pi\)
−0.970784 + 0.239955i \(0.922867\pi\)
\(462\) −6518.12 + 10820.9i −0.656386 + 1.08968i
\(463\) 3667.94 6353.05i 0.368172 0.637692i −0.621108 0.783725i \(-0.713317\pi\)
0.989280 + 0.146033i \(0.0466506\pi\)
\(464\) 4373.36 0.437561
\(465\) 4838.42 2729.26i 0.482529 0.272186i
\(466\) −20598.9 −2.04769
\(467\) 1503.29 + 2603.77i 0.148959 + 0.258004i 0.930843 0.365420i \(-0.119074\pi\)
−0.781884 + 0.623424i \(0.785741\pi\)
\(468\) −5708.28 114.281i −0.563815 0.0112877i
\(469\) −575.441 + 325.704i −0.0566554 + 0.0320674i
\(470\) −6357.54 11011.6i −0.623939 1.08069i
\(471\) 3395.21 1915.17i 0.332151 0.187360i
\(472\) −3013.77 5220.00i −0.293898 0.509047i
\(473\) 931.755 + 1613.85i 0.0905754 + 0.156881i
\(474\) 7654.29 4317.64i 0.741715 0.418388i
\(475\) −682.649 1182.38i −0.0659413 0.114214i
\(476\) −67.8137 + 7932.19i −0.00652990 + 0.763806i
\(477\) 3732.00 6175.17i 0.358232 0.592750i
\(478\) 4391.19 + 7605.76i 0.420185 + 0.727781i
\(479\) 10603.8 1.01148 0.505740 0.862686i \(-0.331219\pi\)
0.505740 + 0.862686i \(0.331219\pi\)
\(480\) 6346.42 3579.90i 0.603485 0.340415i
\(481\) −18078.5 −1.71374
\(482\) 3916.99 6784.42i 0.370153 0.641124i
\(483\) −14804.5 274.770i −1.39467 0.0258850i
\(484\) −309.547 536.151i −0.0290709 0.0503523i
\(485\) 552.572 + 957.083i 0.0517340 + 0.0896060i
\(486\) −10733.0 6934.82i −1.00177 0.647263i
\(487\) 7160.77 12402.8i 0.666294 1.15406i −0.312638 0.949872i \(-0.601213\pi\)
0.978933 0.204183i \(-0.0654538\pi\)
\(488\) −278.057 + 481.609i −0.0257932 + 0.0446751i
\(489\) 12672.7 7148.46i 1.17194 0.661072i
\(490\) 5804.20 9667.59i 0.535116 0.891301i
\(491\) −2111.73 + 3657.62i −0.194096 + 0.336184i −0.946604 0.322399i \(-0.895511\pi\)
0.752508 + 0.658583i \(0.228844\pi\)
\(492\) 3.97291 396.928i 0.000364050 0.0363717i
\(493\) 6961.01 0.635919
\(494\) −4797.91 + 8310.22i −0.436980 + 0.756871i
\(495\) 10236.7 + 204.942i 0.929506 + 0.0186090i
\(496\) −8733.96 −0.790658
\(497\) −23.1720 + 2710.44i −0.00209136 + 0.244627i
\(498\) 59.5168 5946.25i 0.00535545 0.535055i
\(499\) 18697.4 1.67738 0.838690 0.544610i \(-0.183322\pi\)
0.838690 + 0.544610i \(0.183322\pi\)
\(500\) −2553.21 4422.28i −0.228366 0.395541i
\(501\) 0.707014 + 0.417685i 6.30480e−5 + 3.72471e-5i
\(502\) −804.372 + 1393.21i −0.0715157 + 0.123869i
\(503\) −7096.25 −0.629038 −0.314519 0.949251i \(-0.601843\pi\)
−0.314519 + 0.949251i \(0.601843\pi\)
\(504\) −222.602 + 7790.26i −0.0196735 + 0.688504i
\(505\) −10505.5 −0.925723
\(506\) 10098.7 17491.5i 0.887238 1.53674i
\(507\) −7771.61 + 4383.82i −0.680768 + 0.384008i
\(508\) 3887.00 + 6732.48i 0.339484 + 0.588003i
\(509\) −6419.73 −0.559037 −0.279518 0.960140i \(-0.590175\pi\)
−0.279518 + 0.960140i \(0.590175\pi\)
\(510\) 18854.4 10635.4i 1.63704 0.923422i
\(511\) 11645.7 + 6857.03i 1.00817 + 0.593614i
\(512\) −1529.38 −0.132011
\(513\) −5617.44 + 3022.10i −0.483462 + 0.260095i
\(514\) 6302.97 10917.1i 0.540880 0.936831i
\(515\) −16668.1 −1.42619
\(516\) −724.146 427.806i −0.0617805 0.0364983i
\(517\) −7525.06 + 13033.8i −0.640139 + 1.10875i
\(518\) 154.336 18052.7i 0.0130910 1.53126i
\(519\) 5648.67 + 3337.08i 0.477744 + 0.282238i
\(520\) 4751.22 8229.36i 0.400682 0.694002i
\(521\) 4877.13 8447.45i 0.410117 0.710344i −0.584785 0.811188i \(-0.698821\pi\)
0.994902 + 0.100844i \(0.0321544\pi\)
\(522\) −5002.23 100.146i −0.419429 0.00839709i
\(523\) −2134.28 3696.68i −0.178443 0.309072i 0.762905 0.646511i \(-0.223773\pi\)
−0.941347 + 0.337439i \(0.890439\pi\)
\(524\) 986.436 + 1708.56i 0.0822379 + 0.142440i
\(525\) 2889.29 + 53.6249i 0.240188 + 0.00445787i
\(526\) 1702.11 2948.15i 0.141094 0.244383i
\(527\) −13901.7 −1.14909
\(528\) −13859.8 8188.03i −1.14237 0.674883i
\(529\) 11507.4 0.945784
\(530\) −4392.65 7608.30i −0.360009 0.623553i
\(531\) 5038.96 + 9145.76i 0.411813 + 0.747443i
\(532\) −2452.51 1444.05i −0.199868 0.117684i
\(533\) −707.025 1224.60i −0.0574571 0.0995186i
\(534\) −36.5646 + 3653.12i −0.00296312 + 0.296041i
\(535\) 3999.46 + 6927.26i 0.323199 + 0.559798i
\(536\) −278.220 481.892i −0.0224203 0.0388331i
\(537\) −13038.2 7702.60i −1.04774 0.618979i
\(538\) 13727.6 + 23777.0i 1.10007 + 1.90539i
\(539\) −13345.0 228.194i −1.06644 0.0182356i
\(540\) −4069.59 + 2189.38i −0.324310 + 0.174474i
\(541\) 10185.3 + 17641.4i 0.809426 + 1.40197i 0.913262 + 0.407373i \(0.133555\pi\)
−0.103836 + 0.994594i \(0.533112\pi\)
\(542\) 22835.9 1.80976
\(543\) 45.2961 4525.47i 0.00357982 0.357655i
\(544\) −18234.5 −1.43713
\(545\) −10374.4 + 17968.9i −0.815392 + 1.41230i
\(546\) −9827.08 17774.8i −0.770256 1.39321i
\(547\) −1046.82 1813.14i −0.0818258 0.141726i 0.822208 0.569187i \(-0.192742\pi\)
−0.904034 + 0.427460i \(0.859408\pi\)
\(548\) 285.263 + 494.089i 0.0222369 + 0.0385154i
\(549\) 498.307 824.525i 0.0387381 0.0640981i
\(550\) −1970.89 + 3413.69i −0.152799 + 0.264655i
\(551\) −1248.76 + 2162.91i −0.0965498 + 0.167229i
\(552\) 124.714 12460.0i 0.00961625 0.960747i
\(553\) 8001.19 + 4711.15i 0.615272 + 0.362275i
\(554\) −10995.6 + 19045.0i −0.843249 + 1.46055i
\(555\) −12744.8 + 7189.08i −0.974748 + 0.549837i
\(556\) −4537.94 −0.346135
\(557\) 844.740 1463.13i 0.0642599 0.111301i −0.832106 0.554617i \(-0.812865\pi\)
0.896365 + 0.443316i \(0.146198\pi\)
\(558\) 9989.88 + 200.000i 0.757895 + 0.0151733i
\(559\) −2996.16 −0.226698
\(560\) 12382.5 + 7290.86i 0.934383 + 0.550170i
\(561\) −22060.5 13032.8i −1.66024 0.980826i
\(562\) −21175.1 −1.58936
\(563\) −6454.60 11179.7i −0.483178 0.836888i 0.516636 0.856205i \(-0.327184\pi\)
−0.999813 + 0.0193169i \(0.993851\pi\)
\(564\) 67.9857 6792.36i 0.00507574 0.507110i
\(565\) −1980.05 + 3429.55i −0.147436 + 0.255367i
\(566\) −2720.09 −0.202004
\(567\) 655.690 13485.3i 0.0485651 0.998820i
\(568\) −2281.01 −0.168501
\(569\) 13211.4 22882.8i 0.973377 1.68594i 0.288185 0.957575i \(-0.406948\pi\)
0.685191 0.728363i \(-0.259719\pi\)
\(570\) −77.7345 + 7766.35i −0.00571218 + 0.570696i
\(571\) 6392.78 + 11072.6i 0.468528 + 0.811515i 0.999353 0.0359669i \(-0.0114511\pi\)
−0.530825 + 0.847482i \(0.678118\pi\)
\(572\) 8228.40 0.601480
\(573\) 14216.2 + 8398.54i 1.03646 + 0.612311i
\(574\) 1228.89 695.562i 0.0893606 0.0505787i
\(575\) −4620.36 −0.335100
\(576\) −4090.05 81.8841i −0.295866 0.00592333i
\(577\) −2294.12 + 3973.54i −0.165521 + 0.286691i −0.936840 0.349758i \(-0.886264\pi\)
0.771319 + 0.636449i \(0.219597\pi\)
\(578\) −37598.9 −2.70572
\(579\) 7707.33 4347.56i 0.553205 0.312053i
\(580\) −904.672 + 1566.94i −0.0647663 + 0.112179i
\(581\) 5467.81 3094.82i 0.390435 0.220989i
\(582\) −19.8953 + 1987.71i −0.00141698 + 0.141569i
\(583\) −5199.34 + 9005.52i −0.369356 + 0.639743i
\(584\) −5686.43 + 9849.18i −0.402921 + 0.697880i
\(585\) −8514.68 + 14088.8i −0.601775 + 0.995730i
\(586\) −10406.7 18025.0i −0.733613 1.27066i
\(587\) 10298.2 + 17837.0i 0.724111 + 1.25420i 0.959339 + 0.282256i \(0.0910829\pi\)
−0.235228 + 0.971940i \(0.575584\pi\)
\(588\) 5296.64 2869.49i 0.371479 0.201251i
\(589\) 2493.88 4319.52i 0.174462 0.302178i
\(590\) 12714.2 0.887175
\(591\) 13.2549 1324.28i 0.000922559 0.0921717i
\(592\) 23005.9 1.59719
\(593\) −3894.55 6745.56i −0.269697 0.467128i 0.699087 0.715037i \(-0.253590\pi\)
−0.968783 + 0.247909i \(0.920257\pi\)
\(594\) 15665.3 + 9682.82i 1.08208 + 0.668840i
\(595\) 19709.0 + 11604.7i 1.35796 + 0.799577i
\(596\) 1219.07 + 2111.49i 0.0837837 + 0.145118i
\(597\) 3460.04 + 2044.10i 0.237203 + 0.140133i
\(598\) 16236.8 + 28122.9i 1.11032 + 1.92313i
\(599\) −10937.0 18943.4i −0.746031 1.29216i −0.949712 0.313126i \(-0.898624\pi\)
0.203681 0.979037i \(-0.434709\pi\)
\(600\) −24.3395 + 2431.73i −0.00165609 + 0.165458i
\(601\) −13992.6 24235.9i −0.949702 1.64493i −0.746052 0.665888i \(-0.768053\pi\)
−0.203650 0.979044i \(-0.565281\pi\)
\(602\) 25.5782 2991.89i 0.00173171 0.202559i
\(603\) 465.179 + 844.304i 0.0314155 + 0.0570195i
\(604\) 4845.15 + 8392.04i 0.326401 + 0.565343i
\(605\) −1785.03 −0.119953
\(606\) −16269.2 9611.40i −1.09058 0.644284i
\(607\) −4683.46 −0.313172 −0.156586 0.987664i \(-0.550049\pi\)
−0.156586 + 0.987664i \(0.550049\pi\)
\(608\) 3271.15 5665.80i 0.218195 0.377925i
\(609\) −2557.71 4626.27i −0.170187 0.307826i
\(610\) −586.518 1015.88i −0.0389302 0.0674291i
\(611\) −12098.8 20955.8i −0.801091 1.38753i
\(612\) 11562.2 + 231.478i 0.763681 + 0.0152891i
\(613\) −13144.7 + 22767.2i −0.866082 + 1.50010i −0.000113990 1.00000i \(0.500036\pi\)
−0.865968 + 0.500099i \(0.833297\pi\)
\(614\) 7390.77 12801.2i 0.485777 0.841391i
\(615\) −985.403 582.150i −0.0646102 0.0381700i
\(616\) 96.0197 11231.5i 0.00628043 0.734625i
\(617\) −215.459 + 373.186i −0.0140584 + 0.0243499i −0.872969 0.487776i \(-0.837808\pi\)
0.858911 + 0.512126i \(0.171142\pi\)
\(618\) −25812.8 15249.5i −1.68016 0.992596i
\(619\) −17378.1 −1.12841 −0.564205 0.825635i \(-0.690817\pi\)
−0.564205 + 0.825635i \(0.690817\pi\)
\(620\) 1806.71 3129.31i 0.117031 0.202703i
\(621\) −648.072 + 21576.9i −0.0418780 + 1.39428i
\(622\) 28547.9 1.84030
\(623\) −3359.19 + 1901.32i −0.216024 + 0.122271i
\(624\) 22543.0 12716.1i 1.44622 0.815787i
\(625\) −10969.7 −0.702060
\(626\) 9817.42 + 17004.3i 0.626810 + 1.08567i
\(627\) 8007.03 4516.62i 0.510000 0.287681i
\(628\) 1267.80 2195.89i 0.0805585 0.139531i
\(629\) 36618.2 2.32124
\(630\) −13996.1 8622.81i −0.885105 0.545303i
\(631\) −176.931 −0.0111625 −0.00558123 0.999984i \(-0.501777\pi\)
−0.00558123 + 0.999984i \(0.501777\pi\)
\(632\) −3906.88 + 6766.92i −0.245898 + 0.425907i
\(633\) 16414.7 + 9697.38i 1.03069 + 0.608904i
\(634\) −10820.5 18741.7i −0.677821 1.17402i
\(635\) 22414.7 1.40079
\(636\) 46.9738 4693.09i 0.00292867 0.292599i
\(637\) 11045.8 18398.1i 0.687050 1.14436i
\(638\) 7210.65 0.447449
\(639\) 3950.80 + 79.0961i 0.244587 + 0.00489670i
\(640\) −8099.64 + 14029.0i −0.500260 + 0.866475i
\(641\) −21029.9 −1.29583 −0.647917 0.761711i \(-0.724360\pi\)
−0.647917 + 0.761711i \(0.724360\pi\)
\(642\) −144.000 + 14386.8i −0.00885236 + 0.884428i
\(643\) −6304.53 + 10919.8i −0.386666 + 0.669725i −0.991999 0.126247i \(-0.959707\pi\)
0.605333 + 0.795973i \(0.293040\pi\)
\(644\) −8381.99 + 4744.27i −0.512883 + 0.290295i
\(645\) −2112.20 + 1191.45i −0.128942 + 0.0727338i
\(646\) 9718.19 16832.4i 0.591884 1.02517i
\(647\) −5084.38 + 8806.41i −0.308945 + 0.535109i −0.978132 0.207985i \(-0.933309\pi\)
0.669187 + 0.743094i \(0.266643\pi\)
\(648\) 11352.7 + 454.750i 0.688233 + 0.0275683i
\(649\) −7524.52 13032.8i −0.455105 0.788265i
\(650\) −3168.82 5488.55i −0.191217 0.331198i
\(651\) 5107.96 + 9239.05i 0.307522 + 0.556232i
\(652\) 4732.11 8196.26i 0.284239 0.492316i
\(653\) 17327.5 1.03841 0.519203 0.854651i \(-0.326229\pi\)
0.519203 + 0.854651i \(0.326229\pi\)
\(654\) −32505.6 + 18335.8i −1.94353 + 1.09631i
\(655\) 5688.36 0.339333
\(656\) 899.728 + 1558.38i 0.0535495 + 0.0927505i
\(657\) 10190.7 16862.0i 0.605137 1.00129i
\(658\) 21029.2 11902.7i 1.24590 0.705190i
\(659\) 7431.15 + 12871.1i 0.439266 + 0.760831i 0.997633 0.0687629i \(-0.0219052\pi\)
−0.558367 + 0.829594i \(0.688572\pi\)
\(660\) 5800.75 3272.09i 0.342112 0.192979i
\(661\) −15644.7 27097.4i −0.920588 1.59451i −0.798507 0.601985i \(-0.794377\pi\)
−0.122081 0.992520i \(-0.538957\pi\)
\(662\) −1398.01 2421.42i −0.0820771 0.142162i
\(663\) 35881.3 20240.0i 2.10183 1.18561i
\(664\) 2643.63 + 4578.91i 0.154507 + 0.267615i
\(665\) −7141.47 + 4042.12i −0.416442 + 0.235709i
\(666\) −26314.1 526.816i −1.53101 0.0306512i
\(667\) 4225.97 + 7319.60i 0.245323 + 0.424911i
\(668\) 0.534148 3.09383e−5
\(669\) 9071.33 5116.97i 0.524242 0.295715i
\(670\) 1173.73 0.0676791
\(671\) −694.229 + 1202.44i −0.0399410 + 0.0691798i
\(672\) 6699.97 + 12118.6i 0.384609 + 0.695663i
\(673\) 2162.02 + 3744.73i 0.123833 + 0.214485i 0.921276 0.388909i \(-0.127148\pi\)
−0.797443 + 0.603394i \(0.793815\pi\)
\(674\) 9806.11 + 16984.7i 0.560411 + 0.970661i
\(675\) 126.480 4211.01i 0.00721215 0.240121i
\(676\) −2901.99 + 5026.39i −0.165111 + 0.285980i
\(677\) 2404.70 4165.07i 0.136514 0.236450i −0.789661 0.613544i \(-0.789743\pi\)
0.926175 + 0.377094i \(0.123077\pi\)
\(678\) −6204.02 + 3499.57i −0.351421 + 0.198230i
\(679\) −1827.78 + 1034.53i −0.103304 + 0.0584710i
\(680\) −9623.63 + 16668.6i −0.542720 + 0.940018i
\(681\) −176.615 + 17645.3i −0.00993816 + 0.992908i
\(682\) −14400.3 −0.808526
\(683\) −13158.2 + 22790.8i −0.737169 + 1.27681i 0.216596 + 0.976261i \(0.430504\pi\)
−0.953765 + 0.300553i \(0.902829\pi\)
\(684\) −2146.10 + 3551.05i −0.119968 + 0.198506i
\(685\) 1644.99 0.0917545
\(686\) 18277.6 + 11187.1i 1.01726 + 0.622633i
\(687\) −268.030 + 26778.5i −0.0148850 + 1.48714i
\(688\) 3812.79 0.211281
\(689\) −8359.53 14479.1i −0.462224 0.800596i
\(690\) 22629.7 + 13369.0i 1.24855 + 0.737609i
\(691\) −1095.59 + 1897.63i −0.0603161 + 0.104470i −0.894607 0.446854i \(-0.852544\pi\)
0.834291 + 0.551325i \(0.185878\pi\)
\(692\) 4267.56 0.234434
\(693\) −555.772 + 19450.0i −0.0304647 + 1.06616i
\(694\) −11209.6 −0.613128
\(695\) −6542.10 + 11331.2i −0.357059 + 0.618444i
\(696\) 3874.62 2185.60i 0.211016 0.119030i
\(697\) 1432.08 + 2480.44i 0.0778250 + 0.134797i
\(698\) −2538.16 −0.137637
\(699\) −27635.5 + 15588.7i −1.49538 + 0.843517i
\(700\) 1635.85 925.905i 0.0883278 0.0499942i
\(701\) 7938.38 0.427715 0.213858 0.976865i \(-0.431397\pi\)
0.213858 + 0.976865i \(0.431397\pi\)
\(702\) −26075.8 + 14028.4i −1.40195 + 0.754228i
\(703\) −6569.06 + 11377.9i −0.352428 + 0.610423i
\(704\) 5895.75 0.315631
\(705\) −16862.5 9961.94i −0.900823 0.532182i
\(706\) −3733.79 + 6467.11i −0.199041 + 0.344749i
\(707\) 170.678 19964.3i 0.00907921 1.06200i
\(708\) 5847.94 + 3454.81i 0.310422 + 0.183389i
\(709\) −11439.3 + 19813.4i −0.605940 + 1.04952i 0.385962 + 0.922515i \(0.373870\pi\)
−0.991902 + 0.127004i \(0.959464\pi\)
\(710\) 2405.71 4166.82i 0.127162 0.220251i
\(711\) 7001.53 11585.1i 0.369308 0.611077i
\(712\) −1624.14 2813.09i −0.0854875 0.148069i
\(713\) −8439.62 14617.8i −0.443291 0.767802i
\(714\) 19904.8 + 36002.9i 1.04330 + 1.88708i
\(715\) 11862.4 20546.3i 0.620462 1.07467i
\(716\) −9850.32 −0.514139
\(717\) 11647.1 + 6880.77i 0.606649 + 0.358392i
\(718\) −2935.48 −0.152578
\(719\) −5773.81 10000.5i −0.299481 0.518716i 0.676536 0.736409i \(-0.263480\pi\)
−0.976017 + 0.217693i \(0.930147\pi\)
\(720\) 10835.4 17928.8i 0.560849 0.928012i
\(721\) 270.798 31675.4i 0.0139876 1.63613i
\(722\) −8082.37 13999.1i −0.416613 0.721595i
\(723\) 120.773 12066.3i 0.00621244 0.620676i
\(724\) −1471.91 2549.42i −0.0755568 0.130868i
\(725\) −824.753 1428.51i −0.0422491 0.0731775i
\(726\) −2764.35 1633.10i −0.141315 0.0834850i
\(727\) −9053.60 15681.3i −0.461870 0.799982i 0.537184 0.843465i \(-0.319488\pi\)
−0.999054 + 0.0434827i \(0.986155\pi\)
\(728\) 15561.5 + 9162.71i 0.792237 + 0.466474i
\(729\) −19647.5 1181.31i −0.998197 0.0600168i
\(730\) −11994.6 20775.3i −0.608139 1.05333i
\(731\) 6068.75 0.307060
\(732\) 6.27206 626.633i 0.000316697 0.0316408i
\(733\) 23101.1 1.16406 0.582032 0.813166i \(-0.302258\pi\)
0.582032 + 0.813166i \(0.302258\pi\)
\(734\) −4265.12 + 7387.41i −0.214480 + 0.371491i
\(735\) 470.756 17362.5i 0.0236246 0.871328i
\(736\) −11070.0 19173.8i −0.554411 0.960267i
\(737\) −694.636 1203.15i −0.0347181 0.0601336i
\(738\) −993.421 1803.07i −0.0495506 0.0899347i
\(739\) −5479.70 + 9491.12i −0.272766 + 0.472444i −0.969569 0.244818i \(-0.921272\pi\)
0.696803 + 0.717262i \(0.254605\pi\)
\(740\) −4759.00 + 8242.84i −0.236411 + 0.409477i
\(741\) −147.934 + 14779.9i −0.00733401 + 0.732731i
\(742\) 14529.8 8224.00i 0.718878 0.406890i
\(743\) −2774.77 + 4806.05i −0.137008 + 0.237304i −0.926363 0.376633i \(-0.877082\pi\)
0.789355 + 0.613937i \(0.210415\pi\)
\(744\) −7737.94 + 4364.83i −0.381299 + 0.215084i
\(745\) 7029.87 0.345711
\(746\) 9058.60 15690.0i 0.444583 0.770040i
\(747\) −4420.11 8022.53i −0.216497 0.392944i
\(748\) −16666.7 −0.814698
\(749\) −13229.2 + 7487.85i −0.645375 + 0.365287i
\(750\) −22800.9 13470.2i −1.11009 0.655814i
\(751\) −16603.6 −0.806754 −0.403377 0.915034i \(-0.632164\pi\)
−0.403377 + 0.915034i \(0.632164\pi\)
\(752\) 15396.5 + 26667.4i 0.746610 + 1.29317i
\(753\) −24.8013 + 2477.86i −0.00120028 + 0.119918i
\(754\) −5796.66 + 10040.1i −0.279976 + 0.484933i
\(755\) 27939.9 1.34681
\(756\) −4094.49 7769.24i −0.196978 0.373763i
\(757\) 2336.31 0.112172 0.0560862 0.998426i \(-0.482138\pi\)
0.0560862 + 0.998426i \(0.482138\pi\)
\(758\) −16738.1 + 28991.2i −0.802052 + 1.38919i
\(759\) 311.375 31109.0i 0.0148909 1.48773i
\(760\) −3452.83 5980.48i −0.164799 0.285441i
\(761\) 10068.8 0.479625 0.239812 0.970819i \(-0.422914\pi\)
0.239812 + 0.970819i \(0.422914\pi\)
\(762\) 34712.1 + 20507.0i 1.65024 + 0.974920i
\(763\) −33978.8 20006.9i −1.61221 0.949277i
\(764\) 10740.3 0.508601
\(765\) 17246.5 28537.0i 0.815098 1.34870i
\(766\) 18870.3 32684.3i 0.890093 1.54169i
\(767\) 24195.9 1.13907
\(768\) −19892.6 + 11221.0i −0.934649 + 0.527218i
\(769\) −1220.38 + 2113.76i −0.0572277 + 0.0991213i −0.893220 0.449620i \(-0.851559\pi\)
0.835992 + 0.548741i \(0.184893\pi\)
\(770\) 20415.8 + 12020.9i 0.955498 + 0.562603i
\(771\) 194.340 19416.3i 0.00907781 0.906952i
\(772\) 2877.98 4984.81i 0.134172 0.232393i
\(773\) 5436.01 9415.44i 0.252936 0.438098i −0.711397 0.702791i \(-0.751937\pi\)
0.964333 + 0.264692i \(0.0852704\pi\)
\(774\) −4361.05 87.3095i −0.202526 0.00405462i
\(775\) 1647.10 + 2852.86i 0.0763428 + 0.132230i
\(776\) −883.713 1530.64i −0.0408807 0.0708075i
\(777\) −13454.8 24336.4i −0.621219 1.12363i
\(778\) −2839.35 + 4917.91i −0.130843 + 0.226627i
\(779\) −1027.63 −0.0472638
\(780\) −107.172 + 10707.4i −0.00491971 + 0.491522i
\(781\) −5695.01 −0.260927
\(782\) −32887.7 56963.2i −1.50391 2.60486i
\(783\) −6786.79 + 3651.20i −0.309758 + 0.166645i
\(784\) −14056.4 + 23412.6i −0.640324 + 1.06654i
\(785\) −3655.44 6331.40i −0.166201 0.287869i
\(786\) 8809.17 + 5204.22i 0.399762 + 0.236168i
\(787\) −9740.91 16871.7i −0.441202 0.764184i 0.556577 0.830796i \(-0.312114\pi\)
−0.997779 + 0.0666120i \(0.978781\pi\)
\(788\) −430.721 746.031i −0.0194718 0.0337262i
\(789\) 52.4814 5243.35i 0.00236805 0.236588i
\(790\) −8240.96 14273.8i −0.371139 0.642832i
\(791\) −6485.19 3818.52i −0.291513 0.171645i
\(792\) −16371.3 327.757i −0.734504 0.0147050i
\(793\) −1116.19 1933.29i −0.0499835 0.0865740i
\(794\) −11978.4 −0.535385
\(795\) −11650.9 6883.06i −0.519769 0.307066i
\(796\) 2614.06 0.116398
\(797\) 1644.31 2848.02i 0.0730794 0.126577i −0.827170 0.561952i \(-0.810051\pi\)
0.900249 + 0.435374i \(0.143384\pi\)
\(798\) −14757.6 273.899i −0.654652 0.0121503i
\(799\) 24506.3 + 42446.1i 1.08507 + 1.87939i
\(800\) 2160.46 + 3742.02i 0.0954797 + 0.165376i
\(801\) 2715.52 + 4928.70i 0.119786 + 0.217412i
\(802\) −6412.29 + 11106.4i −0.282327 + 0.489004i
\(803\) −14197.4 + 24590.6i −0.623928 + 1.08068i
\(804\) 539.861 + 318.936i 0.0236809 + 0.0139900i
\(805\) −237.405 + 27769.4i −0.0103943 + 1.21583i
\(806\) 11576.4 20050.9i 0.505908 0.876259i
\(807\) 36410.8 + 21510.5i 1.58825 + 0.938297i
\(808\) 16801.2 0.731515
\(809\) 14785.3 25608.8i 0.642549 1.11293i −0.342313 0.939586i \(-0.611210\pi\)
0.984862 0.173341i \(-0.0554562\pi\)
\(810\) −12804.1 + 20258.8i −0.555418 + 0.878793i
\(811\) −1910.74 −0.0827313 −0.0413656 0.999144i \(-0.513171\pi\)
−0.0413656 + 0.999144i \(0.513171\pi\)
\(812\) −2963.04 1744.66i −0.128057 0.0754008i
\(813\) 30636.7 17281.6i 1.32162 0.745501i
\(814\) 37931.4 1.63329
\(815\) −13644.1 23632.2i −0.586418 1.01571i
\(816\) −45661.0 + 25756.5i −1.95889 + 1.10497i
\(817\) −1088.69 + 1885.67i −0.0466201 + 0.0807483i
\(818\) −44680.1 −1.90979
\(819\) −26635.5 16409.8i −1.13641 0.700129i
\(820\) −744.471 −0.0317049
\(821\) 16782.8 29068.7i 0.713428 1.23569i −0.250135 0.968211i \(-0.580475\pi\)
0.963563 0.267482i \(-0.0861917\pi\)
\(822\) 2547.48 + 1504.98i 0.108094 + 0.0638593i
\(823\) 19668.3 + 34066.5i 0.833042 + 1.44287i 0.895614 + 0.444831i \(0.146736\pi\)
−0.0625721 + 0.998040i \(0.519930\pi\)
\(824\) 26656.9 1.12699
\(825\) −60.7688 + 6071.33i −0.00256448 + 0.256214i
\(826\) −206.560 + 24161.4i −0.00870114 + 1.01778i
\(827\) 36017.5 1.51445 0.757226 0.653153i \(-0.226554\pi\)
0.757226 + 0.653153i \(0.226554\pi\)
\(828\) 6775.89 + 12298.3i 0.284394 + 0.516178i
\(829\) −1351.86 + 2341.49i −0.0566369 + 0.0980980i −0.892954 0.450148i \(-0.851371\pi\)
0.836317 + 0.548246i \(0.184704\pi\)
\(830\) −11152.7 −0.466403
\(831\) −339.030 + 33872.0i −0.0141526 + 1.41397i
\(832\) −4739.61 + 8209.25i −0.197496 + 0.342073i
\(833\) −22373.3 + 37265.5i −0.930601 + 1.55003i
\(834\) −20498.1 + 11562.6i −0.851069 + 0.480072i
\(835\) 0.770052 1.33377i 3.19147e−5 5.52779e-5i
\(836\) 2989.89 5178.65i 0.123693 0.214243i
\(837\) 13553.8 7291.74i 0.559722 0.301123i
\(838\) −4842.59 8387.62i −0.199624 0.345758i
\(839\) −14788.7 25614.8i −0.608537 1.05402i −0.991482 0.130245i \(-0.958424\pi\)
0.382945 0.923771i \(-0.374910\pi\)
\(840\) 14614.0 + 271.234i 0.600274 + 0.0111410i
\(841\) 10685.8 18508.3i 0.438140 0.758880i
\(842\) −2976.01 −0.121805
\(843\) −28408.6 + 16024.8i −1.16067 + 0.654712i
\(844\) 12401.3 0.505771
\(845\) 8367.27 + 14492.5i 0.340642 + 0.590010i
\(846\) −16999.8 30854.7i −0.690855 1.25391i
\(847\) 29.0004 3392.19i 0.00117647 0.137612i
\(848\) 10638.0 + 18425.5i 0.430789 + 0.746149i
\(849\) −3649.28 + 2058.49i −0.147518 + 0.0832123i
\(850\) 6418.46 + 11117.1i 0.259002 + 0.448604i
\(851\) 22230.6 + 38504.5i 0.895482 + 1.55102i
\(852\) 2238.77 1262.85i 0.0900221 0.0507798i
\(853\) 1776.98 + 3077.82i 0.0713279 + 0.123544i 0.899484 0.436955i \(-0.143943\pi\)
−0.828156 + 0.560498i \(0.810610\pi\)
\(854\) 1940.06 1098.09i 0.0777372 0.0439998i
\(855\) 5773.07 + 10478.2i 0.230918 + 0.419118i
\(856\) −6396.22 11078.6i −0.255395 0.442357i
\(857\) 13277.7 0.529237 0.264619 0.964353i \(-0.414754\pi\)
0.264619 + 0.964353i \(0.414754\pi\)
\(858\) 37168.1 20965.9i 1.47890 0.834222i
\(859\) 36198.1 1.43779 0.718896 0.695117i \(-0.244648\pi\)
0.718896 + 0.695117i \(0.244648\pi\)
\(860\) −788.712 + 1366.09i −0.0312731 + 0.0541666i
\(861\) 1122.30 1863.16i 0.0444227 0.0737471i
\(862\) 14631.8 + 25343.1i 0.578147 + 1.00138i
\(863\) 8941.47 + 15487.1i 0.352689 + 0.610876i 0.986720 0.162432i \(-0.0519339\pi\)
−0.634030 + 0.773308i \(0.718601\pi\)
\(864\) 17778.1 9564.38i 0.700028 0.376605i
\(865\) 6152.32 10656.1i 0.241832 0.418866i
\(866\) −17745.9 + 30736.8i −0.696340 + 1.20610i
\(867\) −50442.7 + 28453.8i −1.97592 + 1.11458i
\(868\) 5917.45 + 3484.23i 0.231395 + 0.136247i
\(869\) −9754.36 + 16895.0i −0.380776 + 0.659523i
\(870\) −93.9162 + 9383.04i −0.00365984 + 0.365649i
\(871\) 2233.68 0.0868949
\(872\) 16591.4 28737.2i 0.644330 1.11601i
\(873\) 1477.55 + 2681.77i 0.0572824 + 0.103968i
\(874\) 23599.3 0.913341
\(875\) 239.201 27979.5i 0.00924169 1.08100i
\(876\) 128.267 12815.0i 0.00494720 0.494268i
\(877\) −10938.4 −0.421166 −0.210583 0.977576i \(-0.567536\pi\)
−0.210583 + 0.977576i \(0.567536\pi\)
\(878\) −18903.0 32740.9i −0.726587 1.25849i
\(879\) −27602.5 16306.8i −1.05917 0.625727i
\(880\) −15095.6 + 26146.4i −0.578265 + 1.00158i
\(881\) −16145.8 −0.617442 −0.308721 0.951153i \(-0.599901\pi\)
−0.308721 + 0.951153i \(0.599901\pi\)
\(882\) 16613.8 26457.4i 0.634258 1.01005i
\(883\) −36343.7 −1.38512 −0.692562 0.721359i \(-0.743518\pi\)
−0.692562 + 0.721359i \(0.743518\pi\)
\(884\) 13398.4 23206.7i 0.509770 0.882948i
\(885\) 17057.3 9621.72i 0.647882 0.365458i
\(886\) −4319.29 7481.23i −0.163780 0.283676i
\(887\) 24675.6 0.934077 0.467038 0.884237i \(-0.345321\pi\)
0.467038 + 0.884237i \(0.345321\pi\)
\(888\) 20382.3 11497.3i 0.770255 0.434486i
\(889\) −364.160 + 42595.9i −0.0137385 + 1.60700i
\(890\) 6851.72 0.258057
\(891\) 28344.3 + 1135.38i 1.06574 + 0.0426898i
\(892\) 3387.31 5867.00i 0.127148 0.220226i
\(893\) −17585.1 −0.658972
\(894\) 10886.7 + 6431.55i 0.407276 + 0.240608i
\(895\) −14200.7 + 24596.3i −0.530365 + 0.918618i
\(896\) −26528.5 15620.1i −0.989123 0.582401i
\(897\) 43065.9 + 25442.2i 1.60304 + 0.947035i
\(898\) 17367.5 30081.4i 0.645392 1.11785i
\(899\) 3013.01 5218.69i 0.111779 0.193608i
\(900\) −1322.40 2400.17i −0.0489779 0.0888953i
\(901\) 16932.3 + 29327.6i 0.626078 + 1.08440i
\(902\) 1483.44 + 2569.40i 0.0547597 + 0.0948465i
\(903\) −2229.86 4033.28i −0.0821764 0.148637i
\(904\) 3166.64 5484.78i 0.116505 0.201793i
\(905\) −8487.89 −0.311765
\(906\) 43268.6 + 25561.9i 1.58665 + 0.937350i
\(907\) −16901.6 −0.618753 −0.309377 0.950940i \(-0.600120\pi\)
−0.309377 + 0.950940i \(0.600120\pi\)
\(908\) 5739.15 + 9940.49i 0.209758 + 0.363311i
\(909\) −29100.4 582.598i −1.06182 0.0212580i
\(910\) −33150.3 + 18763.3i −1.20760 + 0.683513i
\(911\) −17861.1 30936.3i −0.649576 1.12510i −0.983224 0.182401i \(-0.941613\pi\)
0.333649 0.942698i \(-0.391720\pi\)
\(912\) 188.255 18808.3i 0.00683524 0.682899i
\(913\) 6600.39 + 11432.2i 0.239256 + 0.414404i
\(914\) 24229.3 + 41966.3i 0.876841 + 1.51873i
\(915\) −1555.66 919.045i −0.0562062 0.0332051i
\(916\) 8709.71 + 15085.7i 0.314167 + 0.544153i
\(917\) −92.4158 + 10809.9i −0.00332807 + 0.389286i
\(918\) 52816.7 28414.6i 1.89892 1.02159i
\(919\) −706.061 1222.93i −0.0253436 0.0438965i 0.853075 0.521788i \(-0.174735\pi\)
−0.878419 + 0.477891i \(0.841401\pi\)
\(920\) −23369.7 −0.837475
\(921\) 227.880 22767.2i 0.00815300 0.814555i
\(922\) −18537.4 −0.662142
\(923\) 4578.24 7929.75i 0.163266 0.282785i
\(924\) 6123.90 + 11076.6i 0.218032 + 0.394367i
\(925\) −4338.59 7514.66i −0.154218 0.267114i
\(926\) −12373.5 21431.5i −0.439112 0.760564i
\(927\) −46170.8 924.353i −1.63587 0.0327505i
\(928\) 3952.09 6845.22i 0.139799 0.242139i
\(929\) 6295.72 10904.5i 0.222342 0.385108i −0.733177 0.680038i \(-0.761963\pi\)
0.955519 + 0.294930i \(0.0952964\pi\)
\(930\) 187.558 18738.7i 0.00661321 0.660717i
\(931\) −7565.45 13637.0i −0.266324 0.480059i
\(932\) −10319.3 + 17873.6i −0.362684 + 0.628187i
\(933\) 38299.8 21604.2i 1.34392 0.758082i
\(934\) 10142.4 0.355321
\(935\) −24027.4 + 41616.8i −0.840408 + 1.45563i
\(936\) 13617.3 22531.9i 0.475529 0.786835i
\(937\) 48310.9 1.68436 0.842182 0.539193i \(-0.181271\pi\)
0.842182 + 0.539193i \(0.181271\pi\)
\(938\) −19.0689 + 2230.50i −0.000663776 + 0.0776421i
\(939\) 26039.4 + 15383.4i 0.904968 + 0.534631i
\(940\) −12739.6 −0.442044
\(941\) 10507.2 + 18199.0i 0.364000 + 0.630467i 0.988615 0.150466i \(-0.0480773\pi\)
−0.624615 + 0.780933i \(0.714744\pi\)
\(942\) 131.613 13149.3i 0.00455222 0.454807i
\(943\) −1738.81 + 3011.71i −0.0600462 + 0.104003i
\(944\) −30790.7 −1.06160
\(945\) −25302.6 976.543i −0.871000 0.0336158i
\(946\) 6286.39 0.216055
\(947\) −25990.5 + 45016.9i −0.891845 + 1.54472i −0.0541843 + 0.998531i \(0.517256\pi\)
−0.837661 + 0.546190i \(0.816077\pi\)
\(948\) 88.1265 8804.60i 0.00301921 0.301646i
\(949\) −22826.6 39536.9i −0.780805 1.35239i
\(950\) −4605.72 −0.157294
\(951\) −28700.1 16955.2i −0.978616 0.578140i
\(952\) −31520.0 18559.1i −1.07308 0.631833i
\(953\) −26692.5 −0.907296 −0.453648 0.891181i \(-0.649878\pi\)
−0.453648 + 0.891181i \(0.649878\pi\)
\(954\) −11745.7 21318.6i −0.398619 0.723497i
\(955\) 15483.7 26818.6i 0.524651 0.908722i
\(956\) 8799.33 0.297689
\(957\) 9673.81 5456.82i 0.326761 0.184320i
\(958\) 17885.5 30978.6i 0.603187 1.04475i
\(959\) −26.7253 + 3126.07i −0.000899900 + 0.105262i
\(960\) −76.7901 + 7672.00i −0.00258166 + 0.257930i
\(961\) 8878.26 15377.6i 0.298018 0.516183i
\(962\) −30493.2 + 52815.8i −1.02197 + 1.77011i
\(963\) 10694.4 + 19410.4i 0.357862 + 0.649522i
\(964\) −3924.55 6797.52i −0.131122 0.227109i
\(965\) −8298.07 14372.7i −0.276813 0.479454i
\(966\) −25773.6 + 42787.3i −0.858438 + 1.42511i
\(967\) −17421.6 + 30175.0i −0.579359 + 1.00348i 0.416194 + 0.909276i \(0.363364\pi\)
−0.995553 + 0.0942029i \(0.969970\pi\)
\(968\) 2854.75 0.0947882
\(969\) 299.642 29936.8i 0.00993383 0.992476i
\(970\) 3728.11 0.123405
\(971\) −3963.58 6865.13i −0.130996 0.226892i 0.793065 0.609138i \(-0.208484\pi\)
−0.924061 + 0.382245i \(0.875151\pi\)
\(972\) −11394.2 + 5838.91i −0.375997 + 0.192678i
\(973\) −21427.1 12616.4i −0.705983 0.415687i
\(974\) −24156.2 41839.8i −0.794677 1.37642i
\(975\) −8404.87 4965.38i −0.276073 0.163097i
\(976\) 1420.41 + 2460.22i 0.0465842 + 0.0806862i
\(977\) 3122.04 + 5407.52i 0.102234 + 0.177075i 0.912605 0.408843i \(-0.134068\pi\)
−0.810371 + 0.585918i \(0.800734\pi\)
\(978\) 491.252 49080.3i 0.0160619 1.60472i
\(979\) −4055.00 7023.47i −0.132378 0.229286i
\(980\) −5480.84 9879.42i −0.178652 0.322027i
\(981\) −29733.5 + 49198.7i −0.967704 + 1.60122i
\(982\) 7123.74 + 12338.7i 0.231495 + 0.400961i
\(983\) 8380.12 0.271907 0.135953 0.990715i \(-0.456590\pi\)
0.135953 + 0.990715i \(0.456590\pi\)
\(984\) 1575.93 + 931.015i 0.0510556 + 0.0301623i
\(985\) −2483.79 −0.0803453
\(986\) 11741.2 20336.3i 0.379225 0.656836i
\(987\) 19205.2 31883.0i 0.619360 1.02821i
\(988\) 4807.17 + 8326.26i 0.154794 + 0.268111i
\(989\) 3684.29 + 6381.38i 0.118457 + 0.205173i
\(990\) 17865.0 29560.5i 0.573524 0.948983i
\(991\) 4971.94 8611.66i 0.159373 0.276043i −0.775269 0.631631i \(-0.782386\pi\)
0.934643 + 0.355588i \(0.115719\pi\)
\(992\) −7892.65 + 13670.5i −0.252613 + 0.437538i
\(993\) −3708.03 2190.60i −0.118500 0.0700067i
\(994\) 7879.35 + 4639.41i 0.251426 + 0.148041i
\(995\) 3768.55 6527.32i 0.120071 0.207970i
\(996\) −5129.73 3030.51i −0.163194 0.0964109i
\(997\) 34946.8 1.11011 0.555053 0.831815i \(-0.312698\pi\)
0.555053 + 0.831815i \(0.312698\pi\)
\(998\) 31537.1 54623.9i 1.00029 1.73255i
\(999\) −35701.7 + 19207.0i −1.13068 + 0.608291i
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 63.4.g.a.4.18 44
3.2 odd 2 189.4.g.a.172.5 44
7.2 even 3 63.4.h.a.58.5 yes 44
9.2 odd 6 189.4.h.a.46.18 44
9.7 even 3 63.4.h.a.25.5 yes 44
21.2 odd 6 189.4.h.a.37.18 44
63.2 odd 6 189.4.g.a.100.5 44
63.16 even 3 inner 63.4.g.a.16.18 yes 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.g.a.4.18 44 1.1 even 1 trivial
63.4.g.a.16.18 yes 44 63.16 even 3 inner
63.4.h.a.25.5 yes 44 9.7 even 3
63.4.h.a.58.5 yes 44 7.2 even 3
189.4.g.a.100.5 44 63.2 odd 6
189.4.g.a.172.5 44 3.2 odd 2
189.4.h.a.37.18 44 21.2 odd 6
189.4.h.a.46.18 44 9.2 odd 6