Properties

Label 117.4.g.f.55.5
Level $117$
Weight $4$
Character 117.55
Analytic conductor $6.903$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [117,4,Mod(55,117)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(117, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("117.55");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 117 = 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 117.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: \(6.90322347067\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 52 x^{14} + 1899 x^{12} + 33440 x^{10} + 424113 x^{8} + 2869882 x^{6} + 13705540 x^{4} + 21016320 x^{2} + 24920064 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{4}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 55.5
Root \(0.643348 + 1.11431i\) of defining polynomial
Character \(\chi\) \(=\) 117.55
Dual form 117.4.g.f.100.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.643348 + 1.11431i) q^{2} +(3.17221 - 5.49442i) q^{4} -12.4484 q^{5} +(4.50137 - 7.79659i) q^{7} +18.4569 q^{8} +O(q^{10})\) \(q+(0.643348 + 1.11431i) q^{2} +(3.17221 - 5.49442i) q^{4} -12.4484 q^{5} +(4.50137 - 7.79659i) q^{7} +18.4569 q^{8} +(-8.00866 - 13.8714i) q^{10} +(-25.5387 - 44.2343i) q^{11} +(2.33646 - 46.8139i) q^{13} +11.5838 q^{14} +(-13.5034 - 23.3886i) q^{16} +(-3.43100 + 5.94266i) q^{17} +(41.5585 - 71.9815i) q^{19} +(-39.4890 + 68.3969i) q^{20} +(32.8606 - 56.9162i) q^{22} +(93.7893 + 162.448i) q^{23} +29.9631 q^{25} +(53.6684 - 27.5141i) q^{26} +(-28.5585 - 49.4648i) q^{28} +(-111.807 - 193.656i) q^{29} +57.3882 q^{31} +(91.2024 - 157.967i) q^{32} -8.82930 q^{34} +(-56.0349 + 97.0553i) q^{35} +(78.1293 + 135.324i) q^{37} +106.946 q^{38} -229.759 q^{40} +(111.141 + 192.501i) q^{41} +(-173.987 + 301.354i) q^{43} -324.056 q^{44} +(-120.678 + 209.021i) q^{46} +45.0185 q^{47} +(130.975 + 226.856i) q^{49} +(19.2767 + 33.3882i) q^{50} +(-249.804 - 161.341i) q^{52} -473.516 q^{53} +(317.917 + 550.648i) q^{55} +(83.0813 - 143.901i) q^{56} +(143.862 - 249.176i) q^{58} +(307.747 - 533.034i) q^{59} +(-97.6626 + 169.157i) q^{61} +(36.9206 + 63.9483i) q^{62} +18.6446 q^{64} +(-29.0852 + 582.759i) q^{65} +(177.548 + 307.523i) q^{67} +(21.7677 + 37.7027i) q^{68} -144.200 q^{70} +(381.710 - 661.141i) q^{71} +331.595 q^{73} +(-100.529 + 174.121i) q^{74} +(-263.664 - 456.680i) q^{76} -459.836 q^{77} -207.777 q^{79} +(168.096 + 291.152i) q^{80} +(-143.004 + 247.691i) q^{82} +251.185 q^{83} +(42.7105 - 73.9767i) q^{85} -447.737 q^{86} +(-471.365 - 816.429i) q^{88} +(359.683 + 622.989i) q^{89} +(-354.472 - 228.943i) q^{91} +1190.08 q^{92} +(28.9626 + 50.1647i) q^{94} +(-517.338 + 896.055i) q^{95} +(778.080 - 1347.67i) q^{97} +(-168.526 + 291.895i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 40 q^{4} + 22 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 40 q^{4} + 22 q^{7} - 36 q^{10} + 36 q^{13} - 204 q^{16} - 244 q^{19} - 136 q^{22} + 708 q^{25} + 452 q^{28} + 484 q^{31} - 2584 q^{34} - 1018 q^{37} + 3400 q^{40} - 74 q^{43} + 896 q^{46} - 298 q^{49} - 1676 q^{52} - 1300 q^{55} - 812 q^{58} - 1148 q^{61} + 7272 q^{64} + 2198 q^{67} + 4400 q^{70} - 4352 q^{73} - 6936 q^{76} + 3724 q^{79} - 5436 q^{82} + 890 q^{85} - 3528 q^{88} - 4754 q^{91} + 3104 q^{94} + 4370 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.643348 + 1.11431i 0.227458 + 0.393969i 0.957054 0.289910i \(-0.0936253\pi\)
−0.729596 + 0.683878i \(0.760292\pi\)
\(3\) 0 0
\(4\) 3.17221 5.49442i 0.396526 0.686803i
\(5\) −12.4484 −1.11342 −0.556710 0.830707i \(-0.687937\pi\)
−0.556710 + 0.830707i \(0.687937\pi\)
\(6\) 0 0
\(7\) 4.50137 7.79659i 0.243051 0.420977i −0.718531 0.695495i \(-0.755185\pi\)
0.961582 + 0.274519i \(0.0885185\pi\)
\(8\) 18.4569 0.815687
\(9\) 0 0
\(10\) −8.00866 13.8714i −0.253256 0.438653i
\(11\) −25.5387 44.2343i −0.700019 1.21247i −0.968459 0.249172i \(-0.919841\pi\)
0.268440 0.963296i \(-0.413492\pi\)
\(12\) 0 0
\(13\) 2.33646 46.8139i 0.0498475 0.998757i
\(14\) 11.5838 0.221135
\(15\) 0 0
\(16\) −13.5034 23.3886i −0.210991 0.365448i
\(17\) −3.43100 + 5.94266i −0.0489493 + 0.0847827i −0.889462 0.457009i \(-0.848921\pi\)
0.840513 + 0.541792i \(0.182254\pi\)
\(18\) 0 0
\(19\) 41.5585 71.9815i 0.501799 0.869141i −0.498199 0.867063i \(-0.666005\pi\)
0.999998 0.00207845i \(-0.000661591\pi\)
\(20\) −39.4890 + 68.3969i −0.441500 + 0.764700i
\(21\) 0 0
\(22\) 32.8606 56.9162i 0.318450 0.551571i
\(23\) 93.7893 + 162.448i 0.850279 + 1.47273i 0.880957 + 0.473197i \(0.156900\pi\)
−0.0306776 + 0.999529i \(0.509767\pi\)
\(24\) 0 0
\(25\) 29.9631 0.239705
\(26\) 53.6684 27.5141i 0.404817 0.207537i
\(27\) 0 0
\(28\) −28.5585 49.4648i −0.192752 0.333856i
\(29\) −111.807 193.656i −0.715933 1.24003i −0.962599 0.270932i \(-0.912668\pi\)
0.246665 0.969101i \(-0.420665\pi\)
\(30\) 0 0
\(31\) 57.3882 0.332491 0.166246 0.986084i \(-0.446836\pi\)
0.166246 + 0.986084i \(0.446836\pi\)
\(32\) 91.2024 157.967i 0.503827 0.872654i
\(33\) 0 0
\(34\) −8.82930 −0.0445357
\(35\) −56.0349 + 97.0553i −0.270618 + 0.468724i
\(36\) 0 0
\(37\) 78.1293 + 135.324i 0.347146 + 0.601274i 0.985741 0.168269i \(-0.0538177\pi\)
−0.638596 + 0.769542i \(0.720484\pi\)
\(38\) 106.946 0.456552
\(39\) 0 0
\(40\) −229.759 −0.908203
\(41\) 111.141 + 192.501i 0.423348 + 0.733260i 0.996265 0.0863539i \(-0.0275216\pi\)
−0.572917 + 0.819613i \(0.694188\pi\)
\(42\) 0 0
\(43\) −173.987 + 301.354i −0.617041 + 1.06875i 0.372982 + 0.927839i \(0.378335\pi\)
−0.990023 + 0.140908i \(0.954998\pi\)
\(44\) −324.056 −1.11030
\(45\) 0 0
\(46\) −120.678 + 209.021i −0.386805 + 0.669966i
\(47\) 45.0185 0.139715 0.0698577 0.997557i \(-0.477745\pi\)
0.0698577 + 0.997557i \(0.477745\pi\)
\(48\) 0 0
\(49\) 130.975 + 226.856i 0.381853 + 0.661388i
\(50\) 19.2767 + 33.3882i 0.0545227 + 0.0944361i
\(51\) 0 0
\(52\) −249.804 161.341i −0.666183 0.430268i
\(53\) −473.516 −1.22722 −0.613608 0.789611i \(-0.710282\pi\)
−0.613608 + 0.789611i \(0.710282\pi\)
\(54\) 0 0
\(55\) 317.917 + 550.648i 0.779416 + 1.34999i
\(56\) 83.0813 143.901i 0.198254 0.343385i
\(57\) 0 0
\(58\) 143.862 249.176i 0.325689 0.564110i
\(59\) 307.747 533.034i 0.679072 1.17619i −0.296188 0.955130i \(-0.595716\pi\)
0.975261 0.221058i \(-0.0709511\pi\)
\(60\) 0 0
\(61\) −97.6626 + 169.157i −0.204990 + 0.355054i −0.950130 0.311855i \(-0.899050\pi\)
0.745139 + 0.666909i \(0.232383\pi\)
\(62\) 36.9206 + 63.9483i 0.0756277 + 0.130991i
\(63\) 0 0
\(64\) 18.6446 0.0364151
\(65\) −29.0852 + 582.759i −0.0555012 + 1.11204i
\(66\) 0 0
\(67\) 177.548 + 307.523i 0.323746 + 0.560745i 0.981258 0.192700i \(-0.0617243\pi\)
−0.657512 + 0.753444i \(0.728391\pi\)
\(68\) 21.7677 + 37.7027i 0.0388194 + 0.0672371i
\(69\) 0 0
\(70\) −144.200 −0.246217
\(71\) 381.710 661.141i 0.638038 1.10511i −0.347825 0.937559i \(-0.613080\pi\)
0.985863 0.167554i \(-0.0535869\pi\)
\(72\) 0 0
\(73\) 331.595 0.531647 0.265824 0.964022i \(-0.414356\pi\)
0.265824 + 0.964022i \(0.414356\pi\)
\(74\) −100.529 + 174.121i −0.157922 + 0.273529i
\(75\) 0 0
\(76\) −263.664 456.680i −0.397952 0.689274i
\(77\) −459.836 −0.680561
\(78\) 0 0
\(79\) −207.777 −0.295908 −0.147954 0.988994i \(-0.547269\pi\)
−0.147954 + 0.988994i \(0.547269\pi\)
\(80\) 168.096 + 291.152i 0.234922 + 0.406897i
\(81\) 0 0
\(82\) −143.004 + 247.691i −0.192587 + 0.333571i
\(83\) 251.185 0.332183 0.166091 0.986110i \(-0.446885\pi\)
0.166091 + 0.986110i \(0.446885\pi\)
\(84\) 0 0
\(85\) 42.7105 73.9767i 0.0545012 0.0943988i
\(86\) −447.737 −0.561403
\(87\) 0 0
\(88\) −471.365 816.429i −0.570997 0.988996i
\(89\) 359.683 + 622.989i 0.428385 + 0.741985i 0.996730 0.0808054i \(-0.0257492\pi\)
−0.568345 + 0.822791i \(0.692416\pi\)
\(90\) 0 0
\(91\) −354.472 228.943i −0.408338 0.263733i
\(92\) 1190.08 1.34863
\(93\) 0 0
\(94\) 28.9626 + 50.1647i 0.0317794 + 0.0550435i
\(95\) −517.338 + 896.055i −0.558713 + 0.967719i
\(96\) 0 0
\(97\) 778.080 1347.67i 0.814454 1.41068i −0.0952647 0.995452i \(-0.530370\pi\)
0.909719 0.415224i \(-0.136297\pi\)
\(98\) −168.526 + 291.895i −0.173711 + 0.300876i
\(99\) 0 0
\(100\) 95.0491 164.630i 0.0950491 0.164630i
\(101\) −391.693 678.431i −0.385890 0.668381i 0.606002 0.795463i \(-0.292772\pi\)
−0.991892 + 0.127082i \(0.959439\pi\)
\(102\) 0 0
\(103\) 1033.54 0.988720 0.494360 0.869257i \(-0.335402\pi\)
0.494360 + 0.869257i \(0.335402\pi\)
\(104\) 43.1238 864.039i 0.0406599 0.814673i
\(105\) 0 0
\(106\) −304.635 527.644i −0.279140 0.483484i
\(107\) −120.679 209.022i −0.109033 0.188850i 0.806346 0.591444i \(-0.201442\pi\)
−0.915379 + 0.402594i \(0.868109\pi\)
\(108\) 0 0
\(109\) 1763.93 1.55003 0.775016 0.631941i \(-0.217742\pi\)
0.775016 + 0.631941i \(0.217742\pi\)
\(110\) −409.062 + 708.516i −0.354568 + 0.614131i
\(111\) 0 0
\(112\) −243.136 −0.205126
\(113\) 933.917 1617.59i 0.777482 1.34664i −0.155907 0.987772i \(-0.549830\pi\)
0.933389 0.358867i \(-0.116837\pi\)
\(114\) 0 0
\(115\) −1167.53 2022.22i −0.946718 1.63976i
\(116\) −1418.70 −1.13554
\(117\) 0 0
\(118\) 791.954 0.617841
\(119\) 30.8883 + 53.5002i 0.0237944 + 0.0412130i
\(120\) 0 0
\(121\) −638.952 + 1106.70i −0.480054 + 0.831478i
\(122\) −251.324 −0.186507
\(123\) 0 0
\(124\) 182.047 315.315i 0.131841 0.228356i
\(125\) 1183.06 0.846528
\(126\) 0 0
\(127\) −119.442 206.880i −0.0834551 0.144548i 0.821277 0.570530i \(-0.193262\pi\)
−0.904732 + 0.425982i \(0.859929\pi\)
\(128\) −717.624 1242.96i −0.495544 0.858308i
\(129\) 0 0
\(130\) −668.087 + 342.507i −0.450732 + 0.231076i
\(131\) 1158.72 0.772807 0.386403 0.922330i \(-0.373717\pi\)
0.386403 + 0.922330i \(0.373717\pi\)
\(132\) 0 0
\(133\) −374.140 648.030i −0.243925 0.422491i
\(134\) −228.451 + 395.688i −0.147277 + 0.255092i
\(135\) 0 0
\(136\) −63.3256 + 109.683i −0.0399274 + 0.0691562i
\(137\) −456.260 + 790.265i −0.284532 + 0.492824i −0.972496 0.232921i \(-0.925172\pi\)
0.687963 + 0.725745i \(0.258505\pi\)
\(138\) 0 0
\(139\) −1157.52 + 2004.88i −0.706326 + 1.22339i 0.259884 + 0.965640i \(0.416316\pi\)
−0.966211 + 0.257753i \(0.917018\pi\)
\(140\) 355.508 + 615.759i 0.214614 + 0.371722i
\(141\) 0 0
\(142\) 982.290 0.580507
\(143\) −2130.45 + 1092.21i −1.24586 + 0.638711i
\(144\) 0 0
\(145\) 1391.82 + 2410.71i 0.797134 + 1.38068i
\(146\) 213.331 + 369.500i 0.120927 + 0.209452i
\(147\) 0 0
\(148\) 991.370 0.550609
\(149\) −462.704 + 801.427i −0.254404 + 0.440641i −0.964733 0.263229i \(-0.915213\pi\)
0.710329 + 0.703869i \(0.248546\pi\)
\(150\) 0 0
\(151\) −3523.78 −1.89908 −0.949541 0.313644i \(-0.898450\pi\)
−0.949541 + 0.313644i \(0.898450\pi\)
\(152\) 767.042 1328.55i 0.409311 0.708948i
\(153\) 0 0
\(154\) −295.835 512.401i −0.154799 0.268120i
\(155\) −714.392 −0.370202
\(156\) 0 0
\(157\) 1615.83 0.821384 0.410692 0.911774i \(-0.365287\pi\)
0.410692 + 0.911774i \(0.365287\pi\)
\(158\) −133.673 231.528i −0.0673067 0.116579i
\(159\) 0 0
\(160\) −1135.33 + 1966.44i −0.560971 + 0.971631i
\(161\) 1688.72 0.826644
\(162\) 0 0
\(163\) −504.003 + 872.959i −0.242188 + 0.419481i −0.961337 0.275374i \(-0.911198\pi\)
0.719150 + 0.694855i \(0.244532\pi\)
\(164\) 1410.24 0.671473
\(165\) 0 0
\(166\) 161.600 + 279.899i 0.0755576 + 0.130870i
\(167\) 1177.02 + 2038.66i 0.545392 + 0.944647i 0.998582 + 0.0532328i \(0.0169525\pi\)
−0.453190 + 0.891414i \(0.649714\pi\)
\(168\) 0 0
\(169\) −2186.08 218.757i −0.995030 0.0995710i
\(170\) 109.911 0.0495869
\(171\) 0 0
\(172\) 1103.84 + 1911.92i 0.489345 + 0.847571i
\(173\) 1566.16 2712.67i 0.688284 1.19214i −0.284109 0.958792i \(-0.591698\pi\)
0.972393 0.233350i \(-0.0749688\pi\)
\(174\) 0 0
\(175\) 134.875 233.610i 0.0582604 0.100910i
\(176\) −689.721 + 1194.63i −0.295396 + 0.511641i
\(177\) 0 0
\(178\) −462.802 + 801.597i −0.194879 + 0.337541i
\(179\) −1590.41 2754.67i −0.664093 1.15024i −0.979530 0.201297i \(-0.935484\pi\)
0.315437 0.948947i \(-0.397849\pi\)
\(180\) 0 0
\(181\) 4230.52 1.73731 0.868653 0.495421i \(-0.164986\pi\)
0.868653 + 0.495421i \(0.164986\pi\)
\(182\) 27.0650 542.282i 0.0110230 0.220860i
\(183\) 0 0
\(184\) 1731.06 + 2998.28i 0.693562 + 1.20128i
\(185\) −972.587 1684.57i −0.386519 0.669470i
\(186\) 0 0
\(187\) 350.493 0.137062
\(188\) 142.808 247.351i 0.0554008 0.0959570i
\(189\) 0 0
\(190\) −1331.31 −0.508335
\(191\) −1976.40 + 3423.22i −0.748729 + 1.29684i 0.199703 + 0.979856i \(0.436002\pi\)
−0.948432 + 0.316980i \(0.897331\pi\)
\(192\) 0 0
\(193\) −2521.22 4366.89i −0.940319 1.62868i −0.764863 0.644193i \(-0.777193\pi\)
−0.175456 0.984487i \(-0.556140\pi\)
\(194\) 2002.31 0.741016
\(195\) 0 0
\(196\) 1661.92 0.605658
\(197\) 1786.06 + 3093.55i 0.645947 + 1.11881i 0.984082 + 0.177715i \(0.0568706\pi\)
−0.338135 + 0.941098i \(0.609796\pi\)
\(198\) 0 0
\(199\) −2503.42 + 4336.05i −0.891773 + 1.54460i −0.0540255 + 0.998540i \(0.517205\pi\)
−0.837748 + 0.546057i \(0.816128\pi\)
\(200\) 553.026 0.195524
\(201\) 0 0
\(202\) 503.989 872.935i 0.175547 0.304057i
\(203\) −2013.14 −0.696033
\(204\) 0 0
\(205\) −1383.52 2396.34i −0.471364 0.816426i
\(206\) 664.929 + 1151.69i 0.224892 + 0.389525i
\(207\) 0 0
\(208\) −1126.46 + 577.502i −0.375511 + 0.192512i
\(209\) −4245.40 −1.40508
\(210\) 0 0
\(211\) −879.615 1523.54i −0.286992 0.497084i 0.686099 0.727509i \(-0.259322\pi\)
−0.973090 + 0.230425i \(0.925989\pi\)
\(212\) −1502.09 + 2601.70i −0.486622 + 0.842855i
\(213\) 0 0
\(214\) 155.277 268.948i 0.0496007 0.0859109i
\(215\) 2165.86 3751.38i 0.687026 1.18996i
\(216\) 0 0
\(217\) 258.325 447.433i 0.0808123 0.139971i
\(218\) 1134.82 + 1965.56i 0.352567 + 0.610664i
\(219\) 0 0
\(220\) 4033.99 1.23623
\(221\) 270.183 + 174.503i 0.0822373 + 0.0531147i
\(222\) 0 0
\(223\) −856.260 1483.09i −0.257127 0.445358i 0.708344 0.705868i \(-0.249443\pi\)
−0.965471 + 0.260510i \(0.916109\pi\)
\(224\) −821.071 1422.14i −0.244911 0.424199i
\(225\) 0 0
\(226\) 2403.33 0.707378
\(227\) 1288.33 2231.45i 0.376693 0.652451i −0.613886 0.789394i \(-0.710395\pi\)
0.990579 + 0.136944i \(0.0437280\pi\)
\(228\) 0 0
\(229\) −1963.10 −0.566486 −0.283243 0.959048i \(-0.591410\pi\)
−0.283243 + 0.959048i \(0.591410\pi\)
\(230\) 1502.25 2601.98i 0.430677 0.745954i
\(231\) 0 0
\(232\) −2063.61 3574.28i −0.583978 1.01148i
\(233\) 1078.11 0.303131 0.151565 0.988447i \(-0.451569\pi\)
0.151565 + 0.988447i \(0.451569\pi\)
\(234\) 0 0
\(235\) −560.409 −0.155562
\(236\) −1952.48 3381.79i −0.538539 0.932778i
\(237\) 0 0
\(238\) −39.7439 + 68.8385i −0.0108244 + 0.0187485i
\(239\) −3998.43 −1.08216 −0.541081 0.840970i \(-0.681985\pi\)
−0.541081 + 0.840970i \(0.681985\pi\)
\(240\) 0 0
\(241\) 1787.36 3095.80i 0.477735 0.827461i −0.521939 0.852983i \(-0.674791\pi\)
0.999674 + 0.0255213i \(0.00812457\pi\)
\(242\) −1644.27 −0.436768
\(243\) 0 0
\(244\) 619.612 + 1073.20i 0.162568 + 0.281576i
\(245\) −1630.44 2824.00i −0.425162 0.736403i
\(246\) 0 0
\(247\) −3272.63 2113.70i −0.843047 0.544500i
\(248\) 1059.21 0.271209
\(249\) 0 0
\(250\) 761.119 + 1318.30i 0.192550 + 0.333506i
\(251\) 1075.35 1862.55i 0.270419 0.468380i −0.698550 0.715561i \(-0.746171\pi\)
0.968969 + 0.247181i \(0.0795043\pi\)
\(252\) 0 0
\(253\) 4790.52 8297.42i 1.19042 2.06187i
\(254\) 153.686 266.192i 0.0379650 0.0657574i
\(255\) 0 0
\(256\) 997.943 1728.49i 0.243638 0.421994i
\(257\) 2137.40 + 3702.09i 0.518784 + 0.898560i 0.999762 + 0.0218271i \(0.00694834\pi\)
−0.480978 + 0.876733i \(0.659718\pi\)
\(258\) 0 0
\(259\) 1406.75 0.337496
\(260\) 3109.66 + 2008.44i 0.741742 + 0.479069i
\(261\) 0 0
\(262\) 745.459 + 1291.17i 0.175781 + 0.304462i
\(263\) 4185.82 + 7250.06i 0.981403 + 1.69984i 0.656944 + 0.753940i \(0.271849\pi\)
0.324459 + 0.945900i \(0.394818\pi\)
\(264\) 0 0
\(265\) 5894.52 1.36641
\(266\) 481.405 833.818i 0.110965 0.192198i
\(267\) 0 0
\(268\) 2252.88 0.513495
\(269\) −2539.82 + 4399.10i −0.575672 + 0.997092i 0.420297 + 0.907387i \(0.361926\pi\)
−0.995968 + 0.0897057i \(0.971407\pi\)
\(270\) 0 0
\(271\) −2465.97 4271.18i −0.552756 0.957401i −0.998074 0.0620290i \(-0.980243\pi\)
0.445318 0.895372i \(-0.353090\pi\)
\(272\) 185.321 0.0413115
\(273\) 0 0
\(274\) −1174.14 −0.258876
\(275\) −765.219 1325.40i −0.167798 0.290635i
\(276\) 0 0
\(277\) −2586.26 + 4479.54i −0.560987 + 0.971658i 0.436424 + 0.899741i \(0.356245\pi\)
−0.997411 + 0.0719165i \(0.977088\pi\)
\(278\) −2978.75 −0.642638
\(279\) 0 0
\(280\) −1034.23 + 1791.34i −0.220740 + 0.382332i
\(281\) 217.515 0.0461773 0.0230887 0.999733i \(-0.492650\pi\)
0.0230887 + 0.999733i \(0.492650\pi\)
\(282\) 0 0
\(283\) −2461.49 4263.42i −0.517033 0.895527i −0.999804 0.0197808i \(-0.993703\pi\)
0.482771 0.875746i \(-0.339630\pi\)
\(284\) −2421.73 4194.55i −0.505997 0.876412i
\(285\) 0 0
\(286\) −2587.69 1671.31i −0.535012 0.345548i
\(287\) 2001.14 0.411580
\(288\) 0 0
\(289\) 2432.96 + 4214.00i 0.495208 + 0.857725i
\(290\) −1790.85 + 3101.85i −0.362629 + 0.628092i
\(291\) 0 0
\(292\) 1051.89 1821.92i 0.210812 0.365137i
\(293\) −1321.13 + 2288.26i −0.263416 + 0.456250i −0.967147 0.254216i \(-0.918183\pi\)
0.703731 + 0.710466i \(0.251516\pi\)
\(294\) 0 0
\(295\) −3830.97 + 6635.43i −0.756093 + 1.30959i
\(296\) 1442.03 + 2497.66i 0.283162 + 0.490451i
\(297\) 0 0
\(298\) −1190.72 −0.231465
\(299\) 7823.95 4011.09i 1.51328 0.775810i
\(300\) 0 0
\(301\) 1566.36 + 2713.01i 0.299945 + 0.519519i
\(302\) −2267.02 3926.59i −0.431961 0.748178i
\(303\) 0 0
\(304\) −2244.73 −0.423501
\(305\) 1215.74 2105.73i 0.228240 0.395324i
\(306\) 0 0
\(307\) −3386.22 −0.629517 −0.314759 0.949172i \(-0.601924\pi\)
−0.314759 + 0.949172i \(0.601924\pi\)
\(308\) −1458.70 + 2526.54i −0.269860 + 0.467411i
\(309\) 0 0
\(310\) −459.603 796.056i −0.0842055 0.145848i
\(311\) 3.29813 0.000601349 0.000300675 1.00000i \(-0.499904\pi\)
0.000300675 1.00000i \(0.499904\pi\)
\(312\) 0 0
\(313\) 2882.62 0.520560 0.260280 0.965533i \(-0.416185\pi\)
0.260280 + 0.965533i \(0.416185\pi\)
\(314\) 1039.54 + 1800.54i 0.186830 + 0.323599i
\(315\) 0 0
\(316\) −659.112 + 1141.62i −0.117335 + 0.203231i
\(317\) 1442.70 0.255616 0.127808 0.991799i \(-0.459206\pi\)
0.127808 + 0.991799i \(0.459206\pi\)
\(318\) 0 0
\(319\) −5710.82 + 9891.43i −1.00233 + 1.73609i
\(320\) −232.095 −0.0405454
\(321\) 0 0
\(322\) 1086.43 + 1881.76i 0.188027 + 0.325672i
\(323\) 285.174 + 493.936i 0.0491255 + 0.0850878i
\(324\) 0 0
\(325\) 70.0075 1402.69i 0.0119487 0.239407i
\(326\) −1297.00 −0.220350
\(327\) 0 0
\(328\) 2051.31 + 3552.98i 0.345319 + 0.598111i
\(329\) 202.645 350.991i 0.0339580 0.0588169i
\(330\) 0 0
\(331\) 1912.49 3312.53i 0.317583 0.550070i −0.662400 0.749150i \(-0.730462\pi\)
0.979983 + 0.199080i \(0.0637954\pi\)
\(332\) 796.812 1380.12i 0.131719 0.228144i
\(333\) 0 0
\(334\) −1514.47 + 2623.13i −0.248107 + 0.429735i
\(335\) −2210.20 3828.17i −0.360465 0.624344i
\(336\) 0 0
\(337\) 2290.22 0.370197 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(338\) −1162.65 2576.71i −0.187100 0.414659i
\(339\) 0 0
\(340\) −270.973 469.339i −0.0432223 0.0748631i
\(341\) −1465.62 2538.53i −0.232750 0.403135i
\(342\) 0 0
\(343\) 5446.21 0.857340
\(344\) −3211.26 + 5562.06i −0.503313 + 0.871763i
\(345\) 0 0
\(346\) 4030.35 0.626222
\(347\) −167.496 + 290.112i −0.0259126 + 0.0448820i −0.878691 0.477391i \(-0.841582\pi\)
0.852778 + 0.522273i \(0.174916\pi\)
\(348\) 0 0
\(349\) 4487.64 + 7772.81i 0.688303 + 1.19218i 0.972387 + 0.233376i \(0.0749773\pi\)
−0.284084 + 0.958799i \(0.591689\pi\)
\(350\) 347.086 0.0530072
\(351\) 0 0
\(352\) −9316.77 −1.41075
\(353\) −4962.94 8596.06i −0.748302 1.29610i −0.948636 0.316369i \(-0.897536\pi\)
0.200334 0.979728i \(-0.435797\pi\)
\(354\) 0 0
\(355\) −4751.69 + 8230.16i −0.710404 + 1.23046i
\(356\) 4563.95 0.679463
\(357\) 0 0
\(358\) 2046.37 3544.42i 0.302107 0.523264i
\(359\) −215.661 −0.0317052 −0.0158526 0.999874i \(-0.505046\pi\)
−0.0158526 + 0.999874i \(0.505046\pi\)
\(360\) 0 0
\(361\) −24.7218 42.8195i −0.00360429 0.00624282i
\(362\) 2721.70 + 4714.12i 0.395164 + 0.684444i
\(363\) 0 0
\(364\) −2382.37 + 1221.36i −0.343049 + 0.175870i
\(365\) −4127.83 −0.591947
\(366\) 0 0
\(367\) 1430.76 + 2478.15i 0.203502 + 0.352475i 0.949654 0.313300i \(-0.101434\pi\)
−0.746153 + 0.665775i \(0.768101\pi\)
\(368\) 2532.96 4387.21i 0.358803 0.621465i
\(369\) 0 0
\(370\) 1251.42 2167.53i 0.175834 0.304553i
\(371\) −2131.47 + 3691.81i −0.298276 + 0.516629i
\(372\) 0 0
\(373\) 8.50723 14.7350i 0.00118093 0.00204544i −0.865434 0.501022i \(-0.832957\pi\)
0.866615 + 0.498977i \(0.166291\pi\)
\(374\) 225.489 + 390.558i 0.0311758 + 0.0539981i
\(375\) 0 0
\(376\) 830.902 0.113964
\(377\) −9327.01 + 4781.66i −1.27418 + 0.653231i
\(378\) 0 0
\(379\) 950.983 + 1647.15i 0.128888 + 0.223241i 0.923246 0.384209i \(-0.125526\pi\)
−0.794358 + 0.607450i \(0.792192\pi\)
\(380\) 3282.20 + 5684.95i 0.443088 + 0.767451i
\(381\) 0 0
\(382\) −5086.05 −0.681217
\(383\) −3864.89 + 6694.18i −0.515631 + 0.893099i 0.484205 + 0.874955i \(0.339109\pi\)
−0.999835 + 0.0181440i \(0.994224\pi\)
\(384\) 0 0
\(385\) 5724.23 0.757751
\(386\) 3244.05 5618.85i 0.427766 0.740912i
\(387\) 0 0
\(388\) −4936.46 8550.20i −0.645904 1.11874i
\(389\) 14445.5 1.88282 0.941408 0.337271i \(-0.109504\pi\)
0.941408 + 0.337271i \(0.109504\pi\)
\(390\) 0 0
\(391\) −1287.16 −0.166482
\(392\) 2417.40 + 4187.06i 0.311472 + 0.539486i
\(393\) 0 0
\(394\) −2298.12 + 3980.46i −0.293851 + 0.508966i
\(395\) 2586.50 0.329470
\(396\) 0 0
\(397\) −516.534 + 894.664i −0.0653000 + 0.113103i −0.896827 0.442381i \(-0.854134\pi\)
0.831527 + 0.555484i \(0.187467\pi\)
\(398\) −6442.29 −0.811364
\(399\) 0 0
\(400\) −404.605 700.796i −0.0505756 0.0875995i
\(401\) −2305.86 3993.87i −0.287155 0.497368i 0.685974 0.727626i \(-0.259376\pi\)
−0.973130 + 0.230258i \(0.926043\pi\)
\(402\) 0 0
\(403\) 134.085 2686.57i 0.0165738 0.332078i
\(404\) −4970.12 −0.612061
\(405\) 0 0
\(406\) −1295.15 2243.26i −0.158318 0.274215i
\(407\) 3990.65 6912.00i 0.486017 0.841806i
\(408\) 0 0
\(409\) −1334.28 + 2311.04i −0.161311 + 0.279398i −0.935339 0.353753i \(-0.884905\pi\)
0.774028 + 0.633151i \(0.218239\pi\)
\(410\) 1780.18 3083.36i 0.214431 0.371405i
\(411\) 0 0
\(412\) 3278.62 5678.73i 0.392053 0.679056i
\(413\) −2770.57 4798.76i −0.330098 0.571747i
\(414\) 0 0
\(415\) −3126.86 −0.369859
\(416\) −7181.97 4638.62i −0.846455 0.546700i
\(417\) 0 0
\(418\) −2731.27 4730.70i −0.319596 0.553556i
\(419\) 3094.91 + 5360.55i 0.360851 + 0.625012i 0.988101 0.153806i \(-0.0491531\pi\)
−0.627250 + 0.778818i \(0.715820\pi\)
\(420\) 0 0
\(421\) 8991.13 1.04086 0.520429 0.853905i \(-0.325772\pi\)
0.520429 + 0.853905i \(0.325772\pi\)
\(422\) 1131.80 1960.33i 0.130557 0.226131i
\(423\) 0 0
\(424\) −8739.63 −1.00102
\(425\) −102.803 + 178.060i −0.0117334 + 0.0203228i
\(426\) 0 0
\(427\) 879.230 + 1522.87i 0.0996462 + 0.172592i
\(428\) −1531.28 −0.172937
\(429\) 0 0
\(430\) 5573.61 0.625078
\(431\) 1034.51 + 1791.82i 0.115616 + 0.200253i 0.918026 0.396521i \(-0.129783\pi\)
−0.802410 + 0.596773i \(0.796449\pi\)
\(432\) 0 0
\(433\) 7467.33 12933.8i 0.828769 1.43547i −0.0702363 0.997530i \(-0.522375\pi\)
0.899005 0.437939i \(-0.144291\pi\)
\(434\) 664.772 0.0735256
\(435\) 0 0
\(436\) 5595.54 9691.76i 0.614628 1.06457i
\(437\) 15591.0 1.70668
\(438\) 0 0
\(439\) 3000.12 + 5196.36i 0.326168 + 0.564940i 0.981748 0.190186i \(-0.0609091\pi\)
−0.655580 + 0.755126i \(0.727576\pi\)
\(440\) 5867.75 + 10163.2i 0.635760 + 1.10117i
\(441\) 0 0
\(442\) −20.6293 + 413.334i −0.00221999 + 0.0444803i
\(443\) 5392.60 0.578352 0.289176 0.957276i \(-0.406619\pi\)
0.289176 + 0.957276i \(0.406619\pi\)
\(444\) 0 0
\(445\) −4477.48 7755.23i −0.476973 0.826141i
\(446\) 1101.75 1908.28i 0.116971 0.202600i
\(447\) 0 0
\(448\) 83.9259 145.364i 0.00885073 0.0153299i
\(449\) −3023.30 + 5236.51i −0.317769 + 0.550392i −0.980022 0.198888i \(-0.936267\pi\)
0.662253 + 0.749280i \(0.269600\pi\)
\(450\) 0 0
\(451\) 5676.78 9832.47i 0.592703 1.02659i
\(452\) −5925.15 10262.7i −0.616584 1.06795i
\(453\) 0 0
\(454\) 3315.37 0.342727
\(455\) 4412.61 + 2849.98i 0.454651 + 0.293646i
\(456\) 0 0
\(457\) −507.286 878.646i −0.0519253 0.0899372i 0.838894 0.544294i \(-0.183202\pi\)
−0.890820 + 0.454357i \(0.849869\pi\)
\(458\) −1262.96 2187.51i −0.128852 0.223178i
\(459\) 0 0
\(460\) −14814.6 −1.50159
\(461\) −7989.45 + 13838.1i −0.807171 + 1.39806i 0.107644 + 0.994189i \(0.465669\pi\)
−0.914816 + 0.403872i \(0.867664\pi\)
\(462\) 0 0
\(463\) −128.805 −0.0129289 −0.00646445 0.999979i \(-0.502058\pi\)
−0.00646445 + 0.999979i \(0.502058\pi\)
\(464\) −3019.56 + 5230.03i −0.302111 + 0.523272i
\(465\) 0 0
\(466\) 693.601 + 1201.35i 0.0689494 + 0.119424i
\(467\) −18832.4 −1.86608 −0.933039 0.359776i \(-0.882853\pi\)
−0.933039 + 0.359776i \(0.882853\pi\)
\(468\) 0 0
\(469\) 3196.84 0.314747
\(470\) −360.538 624.471i −0.0353838 0.0612865i
\(471\) 0 0
\(472\) 5680.06 9838.15i 0.553911 0.959402i
\(473\) 17773.6 1.72776
\(474\) 0 0
\(475\) 1245.22 2156.79i 0.120284 0.208337i
\(476\) 391.937 0.0377403
\(477\) 0 0
\(478\) −2572.38 4455.49i −0.246146 0.426338i
\(479\) −4615.79 7994.79i −0.440294 0.762612i 0.557417 0.830233i \(-0.311793\pi\)
−0.997711 + 0.0676205i \(0.978459\pi\)
\(480\) 0 0
\(481\) 6517.59 3341.36i 0.617831 0.316742i
\(482\) 4599.58 0.434658
\(483\) 0 0
\(484\) 4053.77 + 7021.34i 0.380708 + 0.659405i
\(485\) −9685.87 + 16776.4i −0.906830 + 1.57068i
\(486\) 0 0
\(487\) −3616.50 + 6263.97i −0.336508 + 0.582849i −0.983773 0.179416i \(-0.942579\pi\)
0.647265 + 0.762265i \(0.275913\pi\)
\(488\) −1802.55 + 3122.11i −0.167208 + 0.289613i
\(489\) 0 0
\(490\) 2097.88 3633.63i 0.193413 0.335001i
\(491\) −327.565 567.360i −0.0301076 0.0521479i 0.850579 0.525847i \(-0.176252\pi\)
−0.880687 + 0.473699i \(0.842918\pi\)
\(492\) 0 0
\(493\) 1534.44 0.140178
\(494\) 249.876 5006.58i 0.0227580 0.455985i
\(495\) 0 0
\(496\) −774.938 1342.23i −0.0701527 0.121508i
\(497\) −3436.43 5952.08i −0.310151 0.537198i
\(498\) 0 0
\(499\) −4560.07 −0.409092 −0.204546 0.978857i \(-0.565572\pi\)
−0.204546 + 0.978857i \(0.565572\pi\)
\(500\) 3752.91 6500.23i 0.335670 0.581398i
\(501\) 0 0
\(502\) 2767.29 0.246036
\(503\) 4534.34 7853.70i 0.401941 0.696181i −0.592020 0.805924i \(-0.701669\pi\)
0.993960 + 0.109742i \(0.0350025\pi\)
\(504\) 0 0
\(505\) 4875.95 + 8445.40i 0.429657 + 0.744189i
\(506\) 12327.9 1.08308
\(507\) 0 0
\(508\) −1515.58 −0.132368
\(509\) −7940.44 13753.2i −0.691461 1.19765i −0.971359 0.237616i \(-0.923634\pi\)
0.279898 0.960030i \(-0.409699\pi\)
\(510\) 0 0
\(511\) 1492.63 2585.31i 0.129217 0.223811i
\(512\) −8913.89 −0.769418
\(513\) 0 0
\(514\) −2750.19 + 4763.46i −0.236003 + 0.408769i
\(515\) −12866.0 −1.10086
\(516\) 0 0
\(517\) −1149.72 1991.36i −0.0978035 0.169401i
\(518\) 905.033 + 1567.56i 0.0767662 + 0.132963i
\(519\) 0 0
\(520\) −536.823 + 10755.9i −0.0452716 + 0.907074i
\(521\) 10998.0 0.924821 0.462410 0.886666i \(-0.346985\pi\)
0.462410 + 0.886666i \(0.346985\pi\)
\(522\) 0 0
\(523\) −9315.88 16135.6i −0.778882 1.34906i −0.932587 0.360946i \(-0.882454\pi\)
0.153705 0.988117i \(-0.450879\pi\)
\(524\) 3675.69 6366.49i 0.306438 0.530766i
\(525\) 0 0
\(526\) −5385.88 + 9328.62i −0.446456 + 0.773284i
\(527\) −196.899 + 341.039i −0.0162752 + 0.0281895i
\(528\) 0 0
\(529\) −11509.4 + 19934.8i −0.945949 + 1.63843i
\(530\) 3792.23 + 6568.33i 0.310800 + 0.538321i
\(531\) 0 0
\(532\) −4747.40 −0.386891
\(533\) 9271.41 4753.16i 0.753451 0.386270i
\(534\) 0 0
\(535\) 1502.26 + 2602.00i 0.121399 + 0.210270i
\(536\) 3276.99 + 5675.92i 0.264076 + 0.457392i
\(537\) 0 0
\(538\) −6535.96 −0.523764
\(539\) 6689.89 11587.2i 0.534608 0.925969i
\(540\) 0 0
\(541\) −14270.1 −1.13405 −0.567023 0.823702i \(-0.691905\pi\)
−0.567023 + 0.823702i \(0.691905\pi\)
\(542\) 3172.95 5495.71i 0.251457 0.435537i
\(543\) 0 0
\(544\) 625.830 + 1083.97i 0.0493240 + 0.0854317i
\(545\) −21958.1 −1.72584
\(546\) 0 0
\(547\) 14379.7 1.12400 0.562002 0.827136i \(-0.310031\pi\)
0.562002 + 0.827136i \(0.310031\pi\)
\(548\) 2894.70 + 5013.77i 0.225649 + 0.390835i
\(549\) 0 0
\(550\) 984.604 1705.38i 0.0763339 0.132214i
\(551\) −18586.2 −1.43702
\(552\) 0 0
\(553\) −935.281 + 1619.95i −0.0719208 + 0.124570i
\(554\) −6655.46 −0.510404
\(555\) 0 0
\(556\) 7343.77 + 12719.8i 0.560153 + 0.970214i
\(557\) −4517.55 7824.62i −0.343653 0.595224i 0.641455 0.767160i \(-0.278331\pi\)
−0.985108 + 0.171936i \(0.944998\pi\)
\(558\) 0 0
\(559\) 13701.1 + 8849.11i 1.03666 + 0.669548i
\(560\) 3026.65 0.228392
\(561\) 0 0
\(562\) 139.938 + 242.379i 0.0105034 + 0.0181924i
\(563\) −3646.73 + 6316.33i −0.272987 + 0.472827i −0.969625 0.244595i \(-0.921345\pi\)
0.696638 + 0.717422i \(0.254678\pi\)
\(564\) 0 0
\(565\) −11625.8 + 20136.4i −0.865664 + 1.49937i
\(566\) 3167.19 5485.73i 0.235206 0.407389i
\(567\) 0 0
\(568\) 7045.19 12202.6i 0.520439 0.901427i
\(569\) 13207.9 + 22876.7i 0.973117 + 1.68549i 0.686013 + 0.727589i \(0.259359\pi\)
0.287104 + 0.957899i \(0.407307\pi\)
\(570\) 0 0
\(571\) −23940.9 −1.75463 −0.877317 0.479912i \(-0.840669\pi\)
−0.877317 + 0.479912i \(0.840669\pi\)
\(572\) −757.144 + 15170.3i −0.0553458 + 1.10892i
\(573\) 0 0
\(574\) 1287.43 + 2229.89i 0.0936171 + 0.162150i
\(575\) 2810.22 + 4867.44i 0.203816 + 0.353019i
\(576\) 0 0
\(577\) 10182.8 0.734691 0.367346 0.930085i \(-0.380267\pi\)
0.367346 + 0.930085i \(0.380267\pi\)
\(578\) −3130.48 + 5422.14i −0.225278 + 0.390193i
\(579\) 0 0
\(580\) 17660.6 1.26434
\(581\) 1130.68 1958.39i 0.0807373 0.139841i
\(582\) 0 0
\(583\) 12093.0 + 20945.7i 0.859074 + 1.48796i
\(584\) 6120.22 0.433658
\(585\) 0 0
\(586\) −3399.77 −0.239664
\(587\) 9553.74 + 16547.6i 0.671763 + 1.16353i 0.977404 + 0.211381i \(0.0677960\pi\)
−0.305641 + 0.952147i \(0.598871\pi\)
\(588\) 0 0
\(589\) 2384.97 4130.89i 0.166844 0.288982i
\(590\) −9858.58 −0.687917
\(591\) 0 0
\(592\) 2110.03 3654.68i 0.146489 0.253727i
\(593\) 13597.5 0.941621 0.470810 0.882234i \(-0.343962\pi\)
0.470810 + 0.882234i \(0.343962\pi\)
\(594\) 0 0
\(595\) −384.511 665.992i −0.0264931 0.0458874i
\(596\) 2935.59 + 5084.58i 0.201755 + 0.349451i
\(597\) 0 0
\(598\) 9503.13 + 6137.79i 0.649852 + 0.419721i
\(599\) −4150.37 −0.283104 −0.141552 0.989931i \(-0.545209\pi\)
−0.141552 + 0.989931i \(0.545209\pi\)
\(600\) 0 0
\(601\) −9588.73 16608.2i −0.650803 1.12722i −0.982928 0.183988i \(-0.941099\pi\)
0.332126 0.943235i \(-0.392234\pi\)
\(602\) −2015.43 + 3490.82i −0.136450 + 0.236338i
\(603\) 0 0
\(604\) −11178.2 + 19361.1i −0.753035 + 1.30429i
\(605\) 7953.94 13776.6i 0.534502 0.925784i
\(606\) 0 0
\(607\) −3997.18 + 6923.32i −0.267282 + 0.462947i −0.968159 0.250336i \(-0.919459\pi\)
0.700877 + 0.713282i \(0.252792\pi\)
\(608\) −7580.48 13129.8i −0.505640 0.875794i
\(609\) 0 0
\(610\) 3128.59 0.207660
\(611\) 105.184 2107.49i 0.00696446 0.139542i
\(612\) 0 0
\(613\) −7806.69 13521.6i −0.514371 0.890916i −0.999861 0.0166742i \(-0.994692\pi\)
0.485490 0.874242i \(-0.338641\pi\)
\(614\) −2178.52 3773.30i −0.143189 0.248010i
\(615\) 0 0
\(616\) −8487.15 −0.555125
\(617\) 10818.1 18737.5i 0.705868 1.22260i −0.260509 0.965471i \(-0.583890\pi\)
0.966377 0.257128i \(-0.0827762\pi\)
\(618\) 0 0
\(619\) 10394.0 0.674911 0.337456 0.941341i \(-0.390434\pi\)
0.337456 + 0.941341i \(0.390434\pi\)
\(620\) −2266.20 + 3925.17i −0.146795 + 0.254256i
\(621\) 0 0
\(622\) 2.12184 + 3.67514i 0.000136782 + 0.000236913i
\(623\) 6476.25 0.416478
\(624\) 0 0
\(625\) −18472.6 −1.18225
\(626\) 1854.53 + 3212.14i 0.118405 + 0.205084i
\(627\) 0 0
\(628\) 5125.74 8878.05i 0.325700 0.564129i
\(629\) −1072.25 −0.0679702
\(630\) 0 0
\(631\) −2322.07 + 4021.95i −0.146498 + 0.253742i −0.929931 0.367735i \(-0.880134\pi\)
0.783433 + 0.621476i \(0.213467\pi\)
\(632\) −3834.92 −0.241369
\(633\) 0 0
\(634\) 928.160 + 1607.62i 0.0581419 + 0.100705i
\(635\) 1486.87 + 2575.33i 0.0929206 + 0.160943i
\(636\) 0 0
\(637\) 10926.0 5601.43i 0.679600 0.348409i
\(638\) −14696.2 −0.911955
\(639\) 0 0
\(640\) 8933.29 + 15472.9i 0.551749 + 0.955657i
\(641\) 76.9612 133.301i 0.00474225 0.00821383i −0.863645 0.504101i \(-0.831824\pi\)
0.868387 + 0.495887i \(0.165157\pi\)
\(642\) 0 0
\(643\) 4219.02 7307.56i 0.258759 0.448184i −0.707151 0.707063i \(-0.750020\pi\)
0.965910 + 0.258879i \(0.0833531\pi\)
\(644\) 5356.97 9278.54i 0.327786 0.567742i
\(645\) 0 0
\(646\) −366.933 + 635.546i −0.0223479 + 0.0387078i
\(647\) 332.618 + 576.111i 0.0202111 + 0.0350066i 0.875954 0.482395i \(-0.160233\pi\)
−0.855743 + 0.517401i \(0.826900\pi\)
\(648\) 0 0
\(649\) −31437.9 −1.90145
\(650\) 1608.07 824.407i 0.0970366 0.0497475i
\(651\) 0 0
\(652\) 3197.60 + 5538.41i 0.192067 + 0.332670i
\(653\) −11207.4 19411.7i −0.671636 1.16331i −0.977440 0.211213i \(-0.932259\pi\)
0.305805 0.952094i \(-0.401075\pi\)
\(654\) 0 0
\(655\) −14424.2 −0.860458
\(656\) 3001.56 5198.86i 0.178645 0.309423i
\(657\) 0 0
\(658\) 521.485 0.0308960
\(659\) −12792.8 + 22157.8i −0.756202 + 1.30978i 0.188572 + 0.982059i \(0.439614\pi\)
−0.944775 + 0.327721i \(0.893719\pi\)
\(660\) 0 0
\(661\) 6658.75 + 11533.3i 0.391824 + 0.678658i 0.992690 0.120691i \(-0.0385110\pi\)
−0.600866 + 0.799349i \(0.705178\pi\)
\(662\) 4921.59 0.288947
\(663\) 0 0
\(664\) 4636.10 0.270957
\(665\) 4657.45 + 8066.95i 0.271591 + 0.470410i
\(666\) 0 0
\(667\) 20972.6 36325.6i 1.21749 2.10875i
\(668\) 14935.0 0.865048
\(669\) 0 0
\(670\) 2843.85 4925.69i 0.163981 0.284024i
\(671\) 9976.71 0.573989
\(672\) 0 0
\(673\) −4889.14 8468.24i −0.280034 0.485032i 0.691359 0.722511i \(-0.257012\pi\)
−0.971393 + 0.237479i \(0.923679\pi\)
\(674\) 1473.41 + 2552.02i 0.0842042 + 0.145846i
\(675\) 0 0
\(676\) −8136.65 + 11317.3i −0.462941 + 0.643907i
\(677\) −12392.8 −0.703537 −0.351769 0.936087i \(-0.614420\pi\)
−0.351769 + 0.936087i \(0.614420\pi\)
\(678\) 0 0
\(679\) −7004.85 12132.8i −0.395908 0.685732i
\(680\) 788.303 1365.38i 0.0444559 0.0769999i
\(681\) 0 0
\(682\) 1885.81 3266.32i 0.105882 0.183393i
\(683\) −9470.84 + 16404.0i −0.530588 + 0.919006i 0.468775 + 0.883318i \(0.344696\pi\)
−0.999363 + 0.0356881i \(0.988638\pi\)
\(684\) 0 0
\(685\) 5679.71 9837.55i 0.316804 0.548721i
\(686\) 3503.81 + 6068.77i 0.195009 + 0.337765i
\(687\) 0 0
\(688\) 9397.69 0.520761
\(689\) −1106.35 + 22167.1i −0.0611735 + 1.22569i
\(690\) 0 0
\(691\) −16188.8 28039.8i −0.891247 1.54368i −0.838382 0.545083i \(-0.816498\pi\)
−0.0528645 0.998602i \(-0.516835\pi\)
\(692\) −9936.38 17210.3i −0.545844 0.945430i
\(693\) 0 0
\(694\) −431.034 −0.0235761
\(695\) 14409.3 24957.6i 0.786438 1.36215i
\(696\) 0 0
\(697\) −1525.29 −0.0828903
\(698\) −5774.22 + 10001.2i −0.313120 + 0.542339i
\(699\) 0 0
\(700\) −855.702 1482.12i −0.0462035 0.0800269i
\(701\) −6072.34 −0.327174 −0.163587 0.986529i \(-0.552306\pi\)
−0.163587 + 0.986529i \(0.552306\pi\)
\(702\) 0 0
\(703\) 12987.8 0.696789
\(704\) −476.158 824.730i −0.0254913 0.0441522i
\(705\) 0 0
\(706\) 6385.79 11060.5i 0.340414 0.589615i
\(707\) −7052.61 −0.375163
\(708\) 0 0
\(709\) 1699.26 2943.21i 0.0900100 0.155902i −0.817505 0.575921i \(-0.804643\pi\)
0.907515 + 0.420019i \(0.137977\pi\)
\(710\) −12228.0 −0.646348
\(711\) 0 0
\(712\) 6638.63 + 11498.4i 0.349429 + 0.605228i
\(713\) 5382.40 + 9322.59i 0.282710 + 0.489669i
\(714\) 0 0
\(715\) 26520.8 13596.3i 1.38716 0.711153i
\(716\) −20180.4 −1.05332
\(717\) 0 0
\(718\) −138.745 240.314i −0.00721160 0.0124909i
\(719\) 14416.8 24970.6i 0.747782 1.29520i −0.201102 0.979570i \(-0.564452\pi\)
0.948884 0.315626i \(-0.102214\pi\)
\(720\) 0 0
\(721\) 4652.36 8058.13i 0.240309 0.416228i
\(722\) 31.8095 55.0957i 0.00163965 0.00283996i
\(723\) 0 0
\(724\) 13420.1 23244.3i 0.688886 1.19319i
\(725\) −3350.09 5802.52i −0.171613 0.297242i
\(726\) 0 0
\(727\) −12894.7 −0.657822 −0.328911 0.944361i \(-0.606682\pi\)
−0.328911 + 0.944361i \(0.606682\pi\)
\(728\) −6542.45 4225.58i −0.333076 0.215124i
\(729\) 0 0
\(730\) −2655.63 4599.69i −0.134643 0.233209i
\(731\) −1193.90 2067.89i −0.0604075 0.104629i
\(732\) 0 0
\(733\) −23754.7 −1.19700 −0.598499 0.801124i \(-0.704236\pi\)
−0.598499 + 0.801124i \(0.704236\pi\)
\(734\) −1840.95 + 3188.63i −0.0925761 + 0.160347i
\(735\) 0 0
\(736\) 34215.2 1.71357
\(737\) 9068.71 15707.5i 0.453257 0.785064i
\(738\) 0 0
\(739\) 13023.6 + 22557.5i 0.648282 + 1.12286i 0.983533 + 0.180728i \(0.0578455\pi\)
−0.335251 + 0.942129i \(0.608821\pi\)
\(740\) −12341.0 −0.613059
\(741\) 0 0
\(742\) −5485.10 −0.271381
\(743\) 7959.65 + 13786.5i 0.393016 + 0.680725i 0.992846 0.119403i \(-0.0380982\pi\)
−0.599829 + 0.800128i \(0.704765\pi\)
\(744\) 0 0
\(745\) 5759.93 9976.50i 0.283259 0.490618i
\(746\) 21.8924 0.00107445
\(747\) 0 0
\(748\) 1111.84 1925.76i 0.0543486 0.0941345i
\(749\) −2172.88 −0.106002
\(750\) 0 0
\(751\) −1118.79 1937.81i −0.0543613 0.0941566i 0.837564 0.546339i \(-0.183979\pi\)
−0.891926 + 0.452182i \(0.850646\pi\)
\(752\) −607.905 1052.92i −0.0294787 0.0510587i
\(753\) 0 0
\(754\) −11328.8 7316.92i −0.547174 0.353404i
\(755\) 43865.5 2.11448
\(756\) 0 0
\(757\) −1631.95 2826.63i −0.0783545 0.135714i 0.824186 0.566320i \(-0.191633\pi\)
−0.902540 + 0.430606i \(0.858300\pi\)
\(758\) −1223.63 + 2119.38i −0.0586334 + 0.101556i
\(759\) 0 0
\(760\) −9548.45 + 16538.4i −0.455735 + 0.789357i
\(761\) −952.456 + 1649.70i −0.0453699 + 0.0785830i −0.887819 0.460194i \(-0.847780\pi\)
0.842449 + 0.538777i \(0.181113\pi\)
\(762\) 0 0
\(763\) 7940.08 13752.6i 0.376737 0.652527i
\(764\) 12539.1 + 21718.3i 0.593781 + 1.02846i
\(765\) 0 0
\(766\) −9945.88 −0.469137
\(767\) −24234.3 15652.3i −1.14088 0.736858i
\(768\) 0 0
\(769\) −1714.94 2970.36i −0.0804190 0.139290i 0.823011 0.568025i \(-0.192292\pi\)
−0.903430 + 0.428736i \(0.858959\pi\)
\(770\) 3682.68 + 6378.58i 0.172356 + 0.298530i
\(771\) 0 0
\(772\) −31991.4 −1.49144
\(773\) −14121.8 + 24459.6i −0.657082 + 1.13810i 0.324285 + 0.945959i \(0.394876\pi\)
−0.981367 + 0.192141i \(0.938457\pi\)
\(774\) 0 0
\(775\) 1719.53 0.0796997
\(776\) 14360.9 24873.9i 0.664340 1.15067i
\(777\) 0 0
\(778\) 9293.48 + 16096.8i 0.428261 + 0.741770i
\(779\) 18475.4 0.849741
\(780\) 0 0
\(781\) −38993.5 −1.78655
\(782\) −828.094 1434.30i −0.0378677 0.0655888i
\(783\) 0 0
\(784\) 3537.24 6126.68i 0.161135 0.279094i
\(785\) −20114.5 −0.914545
\(786\) 0 0
\(787\) −3313.36 + 5738.91i −0.150074 + 0.259937i −0.931255 0.364369i \(-0.881285\pi\)
0.781180 + 0.624306i \(0.214618\pi\)
\(788\) 22663.0 1.02454
\(789\) 0 0
\(790\) 1664.02 + 2882.16i 0.0749406 + 0.129801i
\(791\) −8407.80 14562.7i −0.377936 0.654603i
\(792\) 0 0
\(793\) 7690.69 + 4967.19i 0.344394 + 0.222434i
\(794\) −1329.25 −0.0594120
\(795\) 0 0
\(796\) 15882.7 + 27509.7i 0.707222 + 1.22495i
\(797\) −10375.4 + 17970.8i −0.461125 + 0.798691i −0.999017 0.0443221i \(-0.985887\pi\)
0.537893 + 0.843013i \(0.319221\pi\)
\(798\) 0 0
\(799\) −154.458 + 267.530i −0.00683898 + 0.0118455i
\(800\) 2732.71 4733.19i 0.120770 0.209179i
\(801\) 0 0
\(802\) 2966.94 5138.90i 0.130631 0.226260i
\(803\) −8468.51 14667.9i −0.372163 0.644606i
\(804\) 0 0
\(805\) −21021.9 −0.920403
\(806\) 3079.93 1578.98i 0.134598 0.0690041i
\(807\) 0 0
\(808\) −7229.43 12521.7i −0.314765 0.545190i
\(809\) 5002.66 + 8664.86i 0.217409 + 0.376564i 0.954015 0.299758i \(-0.0969061\pi\)
−0.736606 + 0.676322i \(0.763573\pi\)
\(810\) 0 0
\(811\) 32773.5 1.41903 0.709515 0.704690i \(-0.248914\pi\)
0.709515 + 0.704690i \(0.248914\pi\)
\(812\) −6386.09 + 11061.0i −0.275995 + 0.478037i
\(813\) 0 0
\(814\) 10269.5 0.442194
\(815\) 6274.04 10867.0i 0.269657 0.467059i
\(816\) 0 0
\(817\) 14461.3 + 25047.7i 0.619261 + 1.07259i
\(818\) −3433.63 −0.146765
\(819\) 0 0
\(820\) −17555.3 −0.747632
\(821\) −1515.87 2625.57i −0.0644388 0.111611i 0.832006 0.554766i \(-0.187192\pi\)
−0.896445 + 0.443155i \(0.853859\pi\)
\(822\) 0 0
\(823\) −15528.5 + 26896.2i −0.657704 + 1.13918i 0.323505 + 0.946226i \(0.395139\pi\)
−0.981209 + 0.192950i \(0.938195\pi\)
\(824\) 19076.0 0.806486
\(825\) 0 0
\(826\) 3564.88 6174.55i 0.150167 0.260097i
\(827\) 8770.13 0.368764 0.184382 0.982855i \(-0.440972\pi\)
0.184382 + 0.982855i \(0.440972\pi\)
\(828\) 0 0
\(829\) 19349.4 + 33514.2i 0.810656 + 1.40410i 0.912406 + 0.409287i \(0.134223\pi\)
−0.101750 + 0.994810i \(0.532444\pi\)
\(830\) −2011.66 3484.30i −0.0841274 0.145713i
\(831\) 0 0
\(832\) 43.5622 872.824i 0.00181520 0.0363699i
\(833\) −1797.50 −0.0747657
\(834\) 0 0
\(835\) −14652.0 25378.1i −0.607251 1.05179i
\(836\) −13467.3 + 23326.0i −0.557149 + 0.965010i
\(837\) 0 0
\(838\) −3982.21 + 6897.40i −0.164157 + 0.284328i
\(839\) −11271.9 + 19523.4i −0.463824 + 0.803366i −0.999148 0.0412806i \(-0.986856\pi\)
0.535324 + 0.844647i \(0.320190\pi\)
\(840\) 0 0
\(841\) −12807.2 + 22182.7i −0.525121 + 0.909535i
\(842\) 5784.43 + 10018.9i 0.236751 + 0.410065i
\(843\) 0 0
\(844\) −11161.3 −0.455198
\(845\) 27213.3 + 2723.18i 1.10789 + 0.110864i
\(846\) 0 0
\(847\) 5752.31 + 9963.29i 0.233355 + 0.404183i
\(848\) 6394.09 + 11074.9i 0.258932 + 0.448483i
\(849\) 0 0
\(850\) −264.553 −0.0106754
\(851\) −14655.4 + 25383.9i −0.590341 + 1.02250i
\(852\) 0 0
\(853\) −7751.80 −0.311156 −0.155578 0.987824i \(-0.549724\pi\)
−0.155578 + 0.987824i \(0.549724\pi\)
\(854\) −1131.30 + 1959.47i −0.0453306 + 0.0785150i
\(855\) 0 0
\(856\) −2227.36 3857.91i −0.0889366 0.154043i
\(857\) −30235.6 −1.20517 −0.602583 0.798056i \(-0.705862\pi\)
−0.602583 + 0.798056i \(0.705862\pi\)
\(858\) 0 0
\(859\) 3568.09 0.141725 0.0708624 0.997486i \(-0.477425\pi\)
0.0708624 + 0.997486i \(0.477425\pi\)
\(860\) −13741.1 23800.3i −0.544847 0.943703i
\(861\) 0 0
\(862\) −1331.10 + 2305.53i −0.0525955 + 0.0910980i
\(863\) 406.509 0.0160345 0.00801723 0.999968i \(-0.497448\pi\)
0.00801723 + 0.999968i \(0.497448\pi\)
\(864\) 0 0
\(865\) −19496.2 + 33768.5i −0.766349 + 1.32736i
\(866\) 19216.4 0.754040
\(867\) 0 0
\(868\) −1638.92 2838.70i −0.0640883 0.111004i
\(869\) 5306.36 + 9190.89i 0.207141 + 0.358780i
\(870\) 0 0
\(871\) 14811.2 7593.22i 0.576185 0.295392i
\(872\) 32556.6 1.26434
\(873\) 0 0
\(874\) 10030.4 + 17373.2i 0.388197 + 0.672377i
\(875\) 5325.38 9223.83i 0.205749 0.356368i
\(876\) 0 0
\(877\) −9480.97 + 16421.5i −0.365051 + 0.632287i −0.988784 0.149350i \(-0.952282\pi\)
0.623733 + 0.781637i \(0.285615\pi\)
\(878\) −3860.24 + 6686.13i −0.148379 + 0.257000i
\(879\) 0 0
\(880\) 8585.94 14871.3i 0.328900 0.569671i
\(881\) −15514.5 26871.8i −0.593298 1.02762i −0.993785 0.111320i \(-0.964492\pi\)
0.400487 0.916303i \(-0.368841\pi\)
\(882\) 0 0
\(883\) 33896.2 1.29184 0.645922 0.763404i \(-0.276473\pi\)
0.645922 + 0.763404i \(0.276473\pi\)
\(884\) 1815.87 930.938i 0.0690886 0.0354195i
\(885\) 0 0
\(886\) 3469.32 + 6009.03i 0.131551 + 0.227853i
\(887\) −886.675 1535.77i −0.0335644 0.0581353i 0.848755 0.528786i \(-0.177353\pi\)
−0.882320 + 0.470651i \(0.844019\pi\)
\(888\) 0 0
\(889\) −2150.62 −0.0811354
\(890\) 5761.16 9978.62i 0.216983 0.375825i
\(891\) 0 0
\(892\) −10864.9 −0.407831
\(893\) 1870.90 3240.50i 0.0701091 0.121432i
\(894\) 0 0
\(895\) 19798.1 + 34291.3i 0.739415 + 1.28070i
\(896\) −12921.2 −0.481770
\(897\) 0 0
\(898\) −7780.14 −0.289116
\(899\) −6416.41 11113.5i −0.238041 0.412300i
\(900\) 0 0
\(901\) 1624.63 2813.94i 0.0600714 0.104047i
\(902\) 14608.6 0.539260
\(903\) 0 0
\(904\) 17237.2 29855.7i 0.634182 1.09844i
\(905\) −52663.3 −1.93435
\(906\) 0 0
\(907\) −7200.82 12472.2i −0.263615 0.456595i 0.703584 0.710612i \(-0.251582\pi\)
−0.967200 + 0.254016i \(0.918248\pi\)
\(908\) −8173.67 14157.2i −0.298737 0.517427i
\(909\) 0 0
\(910\) −336.917 + 6750.55i −0.0122733 + 0.245911i
\(911\) 19324.5 0.702799 0.351400 0.936226i \(-0.385706\pi\)
0.351400 + 0.936226i \(0.385706\pi\)
\(912\) 0 0
\(913\) −6414.95 11111.0i −0.232534 0.402761i
\(914\) 652.723 1130.55i 0.0236216 0.0409139i
\(915\) 0 0
\(916\) −6227.36 + 10786.1i −0.224626 + 0.389064i
\(917\) 5215.81 9034.05i 0.187831 0.325333i
\(918\) 0 0
\(919\) −9324.57 + 16150.6i −0.334700 + 0.579717i −0.983427 0.181304i \(-0.941968\pi\)
0.648727 + 0.761021i \(0.275302\pi\)
\(920\) −21548.9 37323.9i −0.772226 1.33753i
\(921\) 0 0
\(922\) −20560.0 −0.734390
\(923\) −30058.8 19414.1i −1.07194 0.692331i
\(924\) 0 0
\(925\) 2341.00 + 4054.72i 0.0832124 + 0.144128i
\(926\) −82.8666 143.529i −0.00294078 0.00509358i
\(927\) 0 0
\(928\) −40788.3 −1.44283
\(929\) 13663.2 23665.4i 0.482535 0.835775i −0.517264 0.855826i \(-0.673049\pi\)
0.999799 + 0.0200506i \(0.00638272\pi\)
\(930\) 0 0
\(931\) 21772.6 0.766453
\(932\) 3419.99 5923.60i 0.120199 0.208191i
\(933\) 0 0
\(934\) −12115.8 20985.1i −0.424454 0.735176i
\(935\) −4363.08 −0.152608
\(936\) 0 0
\(937\) 28699.1 1.00060 0.500298 0.865853i \(-0.333224\pi\)
0.500298 + 0.865853i \(0.333224\pi\)
\(938\) 2056.68 + 3562.28i 0.0715917 + 0.124000i
\(939\) 0 0
\(940\) −1777.73 + 3079.13i −0.0616844 + 0.106840i
\(941\) 55401.1 1.91926 0.959630 0.281264i \(-0.0907538\pi\)
0.959630 + 0.281264i \(0.0907538\pi\)
\(942\) 0 0
\(943\) −20847.6 + 36109.1i −0.719927 + 1.24695i
\(944\) −16622.6 −0.573113
\(945\) 0 0
\(946\) 11434.6 + 19805.3i 0.392993 + 0.680684i
\(947\) 16629.2 + 28802.6i 0.570619 + 0.988341i 0.996502 + 0.0835631i \(0.0266300\pi\)
−0.425883 + 0.904778i \(0.640037\pi\)
\(948\) 0 0
\(949\) 774.758 15523.3i 0.0265013 0.530986i
\(950\) 3204.44 0.109438
\(951\) 0 0
\(952\) 570.103 + 987.447i 0.0194088 + 0.0336170i
\(953\) 2205.95 3820.81i 0.0749817 0.129872i −0.826097 0.563529i \(-0.809443\pi\)
0.901078 + 0.433656i \(0.142777\pi\)
\(954\) 0 0
\(955\) 24603.0 42613.7i 0.833650 1.44392i
\(956\) −12683.8 + 21969.1i −0.429105 + 0.743232i
\(957\) 0 0
\(958\) 5939.13 10286.9i 0.200297 0.346924i
\(959\) 4107.59 + 7114.55i 0.138312 + 0.239563i
\(960\) 0 0
\(961\) −26497.6 −0.889450
\(962\) 7916.39 + 5112.97i 0.265317 + 0.171360i
\(963\) 0 0
\(964\) −11339.8 19641.1i −0.378869 0.656220i
\(965\) 31385.2 + 54360.8i 1.04697 + 1.81341i
\(966\) 0 0
\(967\) 26014.3 0.865114 0.432557 0.901607i \(-0.357611\pi\)
0.432557 + 0.901607i \(0.357611\pi\)
\(968\) −11793.1 + 20426.2i −0.391574 + 0.678226i
\(969\) 0 0
\(970\) −24925.5 −0.825063
\(971\) −18102.5 + 31354.4i −0.598286 + 1.03626i 0.394788 + 0.918772i \(0.370818\pi\)
−0.993074 + 0.117490i \(0.962515\pi\)
\(972\) 0 0
\(973\) 10420.8 + 18049.4i 0.343347 + 0.594694i
\(974\) −9306.69 −0.306166
\(975\) 0 0
\(976\) 5275.12 0.173005
\(977\) −6958.19 12051.9i −0.227853 0.394653i 0.729319 0.684174i \(-0.239837\pi\)
−0.957172 + 0.289522i \(0.906504\pi\)
\(978\) 0 0
\(979\) 18371.7 31820.7i 0.599756 1.03881i
\(980\) −20688.3 −0.674351
\(981\) 0 0
\(982\) 421.477 730.020i 0.0136964 0.0237229i
\(983\) 13585.3 0.440796 0.220398 0.975410i \(-0.429264\pi\)
0.220398 + 0.975410i \(0.429264\pi\)
\(984\) 0 0
\(985\) −22233.6 38509.8i −0.719210 1.24571i
\(986\) 987.178 + 1709.84i 0.0318846 + 0.0552257i
\(987\) 0 0
\(988\) −21995.0 + 11276.1i −0.708254 + 0.363099i
\(989\) −65272.4 −2.09863
\(990\) 0 0
\(991\) 512.246 + 887.237i 0.0164198 + 0.0284400i 0.874119 0.485713i \(-0.161440\pi\)
−0.857699 + 0.514153i \(0.828107\pi\)
\(992\) 5233.94 9065.46i 0.167518 0.290150i
\(993\) 0 0
\(994\) 4421.65 7658.52i 0.141093 0.244380i
\(995\) 31163.6 53977.0i 0.992919 1.71979i
\(996\) 0 0
\(997\) −9257.43 + 16034.3i −0.294068 + 0.509341i −0.974768 0.223222i \(-0.928343\pi\)
0.680700 + 0.732563i \(0.261676\pi\)
\(998\) −2933.71 5081.34i −0.0930512 0.161169i
\(999\) 0 0
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 117.4.g.f.55.5 yes 16
3.2 odd 2 inner 117.4.g.f.55.4 16
13.3 even 3 1521.4.a.bc.1.4 8
13.9 even 3 inner 117.4.g.f.100.5 yes 16
13.10 even 6 1521.4.a.bd.1.5 8
39.23 odd 6 1521.4.a.bd.1.4 8
39.29 odd 6 1521.4.a.bc.1.5 8
39.35 odd 6 inner 117.4.g.f.100.4 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.4.g.f.55.4 16 3.2 odd 2 inner
117.4.g.f.55.5 yes 16 1.1 even 1 trivial
117.4.g.f.100.4 yes 16 39.35 odd 6 inner
117.4.g.f.100.5 yes 16 13.9 even 3 inner
1521.4.a.bc.1.4 8 13.3 even 3
1521.4.a.bc.1.5 8 39.29 odd 6
1521.4.a.bd.1.4 8 39.23 odd 6
1521.4.a.bd.1.5 8 13.10 even 6