Properties

Label 117.4.g.f.100.4
Level $117$
Weight $4$
Character 117.100
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 100.4
Root \(-0.643348 + 1.11431i\) of defining polynomial
Character \(\chi\) \(=\) 117.100
Dual form 117.4.g.f.55.4

$q$-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 \(\left(\mathbb{Z}/117\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(92\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 \(-0.906375\pi\)
0.729596 + 0.683878i \(0.239708\pi\)
\(3\) 0 0
\(4\) 3.17221 + 5.49442i 0.396526 + 0.686803i
\(5\) 12.4484 1.11342 0.556710 0.830707i \(-0.312063\pi\)
0.556710 + 0.830707i \(0.312063\pi\)
\(6\) 0 0
\(7\) 4.50137 + 7.79659i 0.243051 + 0.420977i 0.961582 0.274519i \(-0.0885185\pi\)
−0.718531 + 0.695495i \(0.755185\pi\)
\(8\) −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 −0.268440 0.963296i \(-0.586508\pi\)
0.968459 0.249172i \(-0.0801586\pi\)
\(12\) 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 \(-0.151079\pi\)
−0.840513 + 0.541792i \(0.817746\pi\)
\(18\) 0 0
\(19\) 41.5585 + 71.9815i 0.501799 + 0.869141i 0.999998 + 0.00207845i \(0.000661591\pi\)
−0.498199 + 0.867063i \(0.666005\pi\)
\(20\) 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 0.0306776 + 0.999529i \(0.490233\pi\)
−0.880957 + 0.473197i \(0.843100\pi\)
\(24\) 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 −0.246665 0.969101i \(-0.579335\pi\)
0.962599 0.270932i \(-0.0873318\pi\)
\(30\) 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 −0.638596 0.769542i \(-0.720484\pi\)
0.985741 + 0.168269i \(0.0538177\pi\)
\(38\) −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 \(-0.972478\pi\)
0.572917 + 0.819613i \(0.305812\pi\)
\(42\) 0 0
\(43\) −173.987 301.354i −0.617041 1.06875i −0.990023 0.140908i \(-0.954998\pi\)
0.372982 0.927839i \(-0.378335\pi\)
\(44\) 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 \(-0.522255\pi\)
−0.0698577 + 0.997557i \(0.522255\pi\)
\(48\) 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 \(-0.289718\pi\)
0.613608 + 0.789611i \(0.289718\pi\)
\(54\) 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 −0.975261 0.221058i \(-0.929049\pi\)
0.296188 0.955130i \(-0.404284\pi\)
\(60\) 0 0
\(61\) −97.6626 169.157i −0.204990 0.355054i 0.745139 0.666909i \(-0.232383\pi\)
−0.950130 + 0.311855i \(0.899050\pi\)
\(62\) −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 −0.657512 0.753444i \(-0.728391\pi\)
0.981258 + 0.192700i \(0.0617243\pi\)
\(68\) −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 −0.985863 0.167554i \(-0.946413\pi\)
0.347825 0.937559i \(-0.386920\pi\)
\(72\) 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 \(-0.553115\pi\)
−0.166091 + 0.986110i \(0.553115\pi\)
\(84\) 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 \(-0.974251\pi\)
0.568345 + 0.822791i \(0.307584\pi\)
\(90\) 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 0.909719 + 0.415224i \(0.136297\pi\)
−0.0952647 + 0.995452i \(0.530370\pi\)
\(98\) 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 \(-0.707228\pi\)
0.991892 + 0.127082i \(0.0405612\pi\)
\(102\) 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 \(-0.798558\pi\)
0.915379 + 0.402594i \(0.131891\pi\)
\(108\) 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 −0.933389 0.358867i \(-0.883163\pi\)
0.155907 0.987772i \(-0.450170\pi\)
\(114\) 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 −0.904732 0.425982i \(-0.859929\pi\)
0.821277 + 0.570530i \(0.193262\pi\)
\(128\) 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 \(-0.626283\pi\)
−0.386403 + 0.922330i \(0.626283\pi\)
\(132\) 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 \(-0.0748284\pi\)
−0.687963 + 0.725745i \(0.741495\pi\)
\(138\) 0 0
\(139\) −1157.52 2004.88i −0.706326 1.22339i −0.966211 0.257753i \(-0.917018\pi\)
0.259884 0.965640i \(-0.416316\pi\)
\(140\) −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 \(-0.0847874\pi\)
−0.710329 + 0.703869i \(0.751454\pi\)
\(150\) 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 0.719150 0.694855i \(-0.244532\pi\)
−0.961337 + 0.275374i \(0.911198\pi\)
\(164\) −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 0.453190 + 0.891414i \(0.350286\pi\)
−0.998582 + 0.0532328i \(0.983047\pi\)
\(168\) 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 −0.972393 0.233350i \(-0.925031\pi\)
0.284109 0.958792i \(-0.408302\pi\)
\(174\) 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 −0.315437 0.948947i \(-0.602151\pi\)
0.979530 0.201297i \(-0.0645156\pi\)
\(180\) 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 0.948432 + 0.316980i \(0.102669\pi\)
−0.199703 + 0.979856i \(0.563998\pi\)
\(192\) 0 0
\(193\) −2521.22 + 4366.89i −0.940319 + 1.62868i −0.175456 + 0.984487i \(0.556140\pi\)
−0.764863 + 0.644193i \(0.777193\pi\)
\(194\) −2002.31 −0.741016
\(195\) 0 0
\(196\) 1661.92 0.605658
\(197\) −1786.06 + 3093.55i −0.645947 + 1.11881i 0.338135 + 0.941098i \(0.390204\pi\)
−0.984082 + 0.177715i \(0.943129\pi\)
\(198\) 0 0
\(199\) −2503.42 4336.05i −0.891773 1.54460i −0.837748 0.546057i \(-0.816128\pi\)
−0.0540255 0.998540i \(-0.517205\pi\)
\(200\) −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 −0.973090 0.230425i \(-0.925989\pi\)
0.686099 + 0.727509i \(0.259322\pi\)
\(212\) 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 −0.965471 0.260510i \(-0.916109\pi\)
0.708344 + 0.705868i \(0.249443\pi\)
\(224\) 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 \(-0.289605\pi\)
−0.990579 + 0.136944i \(0.956272\pi\)
\(228\) 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 \(-0.548431\pi\)
−0.151565 + 0.988447i \(0.548431\pi\)
\(234\) 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 \(-0.318015\pi\)
0.541081 + 0.840970i \(0.318015\pi\)
\(240\) 0 0
\(241\) 1787.36 + 3095.80i 0.477735 + 0.827461i 0.999674 0.0255213i \(-0.00812457\pi\)
−0.521939 + 0.852983i \(0.674791\pi\)
\(242\) 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 \(-0.253829\pi\)
−0.968969 + 0.247181i \(0.920496\pi\)
\(252\) 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 0.480978 + 0.876733i \(0.340282\pi\)
−0.999762 + 0.0218271i \(0.993052\pi\)
\(258\) 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 −0.324459 + 0.945900i \(0.605182\pi\)
−0.656944 + 0.753940i \(0.728151\pi\)
\(264\) 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 0.995968 + 0.0897057i \(0.0285926\pi\)
−0.420297 + 0.907387i \(0.638074\pi\)
\(270\) 0 0
\(271\) −2465.97 + 4271.18i −0.552756 + 0.957401i 0.445318 + 0.895372i \(0.353090\pi\)
−0.998074 + 0.0620290i \(0.980243\pi\)
\(272\) −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 −0.997411 0.0719165i \(-0.977088\pi\)
0.436424 0.899741i \(-0.356245\pi\)
\(278\) 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 \(-0.507350\pi\)
−0.0230887 + 0.999733i \(0.507350\pi\)
\(282\) 0 0
\(283\) −2461.49 + 4263.42i −0.517033 + 0.895527i 0.482771 + 0.875746i \(0.339630\pi\)
−0.999804 + 0.0197808i \(0.993703\pi\)
\(284\) 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 \(-0.0818174\pi\)
−0.703731 + 0.710466i \(0.748484\pi\)
\(294\) 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 \(-0.500096\pi\)
−0.000300675 1.00000i \(0.500096\pi\)
\(312\) 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 \(-0.540794\pi\)
−0.127808 + 0.991799i \(0.540794\pi\)
\(318\) 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 0.979983 0.199080i \(-0.0637954\pi\)
−0.662400 + 0.749150i \(0.730462\pi\)
\(332\) −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 \(-0.158418\pi\)
−0.852778 + 0.522273i \(0.825084\pi\)
\(348\) 0 0
\(349\) 4487.64 7772.81i 0.688303 1.19218i −0.284084 0.958799i \(-0.591689\pi\)
0.972387 0.233376i \(-0.0749773\pi\)
\(350\) −347.086 −0.0530072
\(351\) 0 0
\(352\) −9316.77 −1.41075
\(353\) 4962.94 8596.06i 0.748302 1.29610i −0.200334 0.979728i \(-0.564203\pi\)
0.948636 0.316369i \(-0.102464\pi\)
\(354\) 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 \(-0.494954\pi\)
0.0158526 + 0.999874i \(0.494954\pi\)
\(360\) 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 −0.746153 0.665775i \(-0.768101\pi\)
0.949654 + 0.313300i \(0.101434\pi\)
\(368\) −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 0.866615 0.498977i \(-0.166291\pi\)
−0.865434 + 0.501022i \(0.832957\pi\)
\(374\) −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 −0.794358 0.607450i \(-0.792192\pi\)
0.923246 + 0.384209i \(0.125526\pi\)
\(380\) −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 0.999835 + 0.0181440i \(0.00577574\pi\)
−0.484205 + 0.874955i \(0.660891\pi\)
\(384\) 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 \(-0.890496\pi\)
−0.941408 + 0.337271i \(0.890496\pi\)
\(390\) 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 0.831527 0.555484i \(-0.187467\pi\)
−0.896827 + 0.442381i \(0.854134\pi\)
\(398\) 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 \(-0.740624\pi\)
0.973130 + 0.230258i \(0.0739571\pi\)
\(402\) 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 0.774028 0.633151i \(-0.218239\pi\)
−0.935339 + 0.353753i \(0.884905\pi\)
\(410\) −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 \(-0.950847\pi\)
0.627250 + 0.778818i \(0.284180\pi\)
\(420\) 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 \(-0.870217\pi\)
0.802410 + 0.596773i \(0.203551\pi\)
\(432\) 0 0
\(433\) 7467.33 + 12933.8i 0.828769 + 1.43547i 0.899005 + 0.437939i \(0.144291\pi\)
−0.0702363 + 0.997530i \(0.522375\pi\)
\(434\) −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 −0.655580 0.755126i \(-0.727576\pi\)
0.981748 + 0.190186i \(0.0609091\pi\)
\(440\) −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 \(-0.593381\pi\)
−0.289176 + 0.957276i \(0.593381\pi\)
\(444\) 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 \(-0.0637329\pi\)
−0.662253 + 0.749280i \(0.730400\pi\)
\(450\) 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 −0.890820 0.454357i \(-0.849869\pi\)
0.838894 + 0.544294i \(0.183202\pi\)
\(458\) 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 0.914816 + 0.403872i \(0.132336\pi\)
−0.107644 + 0.994189i \(0.534331\pi\)
\(462\) 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 \(-0.117147\pi\)
0.933039 + 0.359776i \(0.117147\pi\)
\(468\) 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 \(-0.688207\pi\)
0.997711 + 0.0676205i \(0.0215407\pi\)
\(480\) 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 0.647265 0.762265i \(-0.275913\pi\)
−0.983773 + 0.179416i \(0.942579\pi\)
\(488\) 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 \(-0.823748\pi\)
0.880687 + 0.473699i \(0.157082\pi\)
\(492\) 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 \(-0.298331\pi\)
−0.993960 + 0.109742i \(0.964997\pi\)
\(504\) 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 −0.279898 0.960030i \(-0.590301\pi\)
0.971359 0.237616i \(-0.0763661\pi\)
\(510\) 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 \(-0.653015\pi\)
−0.462410 + 0.886666i \(0.653015\pi\)
\(522\) 0 0
\(523\) −9315.88 + 16135.6i −0.778882 + 1.34906i 0.153705 + 0.988117i \(0.450879\pi\)
−0.932587 + 0.360946i \(0.882454\pi\)
\(524\) −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 \(-0.721669\pi\)
0.985108 + 0.171936i \(0.0550023\pi\)
\(558\) 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 \(-0.0786551\pi\)
−0.696638 + 0.717422i \(0.745322\pi\)
\(564\) 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 −0.287104 + 0.957899i \(0.592693\pi\)
−0.686013 + 0.727589i \(0.740641\pi\)
\(570\) 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 0.305641 + 0.952147i \(0.401129\pi\)
−0.977404 + 0.211381i \(0.932204\pi\)
\(588\) 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 \(-0.656038\pi\)
−0.470810 + 0.882234i \(0.656038\pi\)
\(594\) 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 \(-0.454791\pi\)
0.141552 + 0.989931i \(0.454791\pi\)
\(600\) 0 0
\(601\) −9588.73 + 16608.2i −0.650803 + 1.12722i 0.332126 + 0.943235i \(0.392234\pi\)
−0.982928 + 0.183988i \(0.941099\pi\)
\(602\) 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 0.700877 0.713282i \(-0.252792\pi\)
−0.968159 + 0.250336i \(0.919459\pi\)
\(608\) 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 0.485490 + 0.874242i \(0.338641\pi\)
−0.999861 + 0.0166742i \(0.994692\pi\)
\(614\) 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 −0.966377 0.257128i \(-0.917224\pi\)
0.260509 0.965471i \(-0.416110\pi\)
\(618\) 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 0.783433 0.621476i \(-0.213467\pi\)
−0.929931 + 0.367735i \(0.880134\pi\)
\(632\) 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 \(-0.168176\pi\)
−0.868387 + 0.495887i \(0.834843\pi\)
\(642\) 0 0
\(643\) 4219.02 + 7307.56i 0.258759 + 0.448184i 0.965910 0.258879i \(-0.0833531\pi\)
−0.707151 + 0.707063i \(0.750020\pi\)
\(644\) −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 \(-0.839767\pi\)
0.855743 + 0.517401i \(0.173100\pi\)
\(648\) 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 −0.305805 0.952094i \(-0.598925\pi\)
0.977440 0.211213i \(-0.0677412\pi\)
\(654\) 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 0.944775 + 0.327721i \(0.106281\pi\)
−0.188572 + 0.982059i \(0.560386\pi\)
\(660\) 0 0
\(661\) 6658.75 11533.3i 0.391824 0.678658i −0.600866 0.799349i \(-0.705178\pi\)
0.992690 + 0.120691i \(0.0385110\pi\)
\(662\) −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 −0.971393 0.237479i \(-0.923679\pi\)
0.691359 + 0.722511i \(0.257012\pi\)
\(674\) −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 \(-0.385580\pi\)
0.351769 + 0.936087i \(0.385580\pi\)
\(678\) 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 0.999363 + 0.0356881i \(0.0113623\pi\)
−0.468775 + 0.883318i \(0.655304\pi\)
\(684\) 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 −0.0528645 + 0.998602i \(0.516835\pi\)
−0.838382 + 0.545083i \(0.816498\pi\)
\(692\) 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 \(-0.447694\pi\)
0.163587 + 0.986529i \(0.447694\pi\)
\(702\) 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 0.907515 0.420019i \(-0.137977\pi\)
−0.817505 + 0.575921i \(0.804643\pi\)
\(710\) 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 −0.948884 0.315626i \(-0.897786\pi\)
0.201102 0.979570i \(-0.435548\pi\)
\(720\) 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 −0.335251 0.942129i \(-0.608821\pi\)
0.983533 0.180728i \(-0.0578455\pi\)
\(740\) 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 \(-0.961902\pi\)
0.599829 + 0.800128i \(0.295235\pi\)
\(744\) 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 −0.891926 0.452182i \(-0.850646\pi\)
0.837564 + 0.546339i \(0.183979\pi\)
\(752\) 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 −0.902540 0.430606i \(-0.858300\pi\)
0.824186 + 0.566320i \(0.191633\pi\)
\(758\) 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 \(-0.152220\pi\)
−0.842449 + 0.538777i \(0.818887\pi\)
\(762\) 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 −0.903430 0.428736i \(-0.858959\pi\)
0.823011 + 0.568025i \(0.192292\pi\)
\(770\) −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 0.981367 + 0.192141i \(0.0615430\pi\)
−0.324285 + 0.945959i \(0.605124\pi\)
\(774\) 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 0.781180 0.624306i \(-0.214618\pi\)
−0.931255 + 0.364369i \(0.881285\pi\)
\(788\) −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 \(-0.0141128\pi\)
−0.537893 + 0.843013i \(0.680779\pi\)
\(798\) 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 \(-0.903094\pi\)
0.736606 + 0.676322i \(0.236427\pi\)
\(810\) 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 \(-0.812808\pi\)
0.896445 + 0.443155i \(0.146141\pi\)
\(822\) 0 0
\(823\) −15528.5 26896.2i −0.657704 1.13918i −0.981209 0.192950i \(-0.938195\pi\)
0.323505 0.946226i \(-0.395139\pi\)
\(824\) −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 \(-0.559028\pi\)
−0.184382 + 0.982855i \(0.559028\pi\)
\(828\) 0 0
\(829\) 19349.4 33514.2i 0.810656 1.40410i −0.101750 0.994810i \(-0.532444\pi\)
0.912406 0.409287i \(-0.134223\pi\)
\(830\) 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 \(-0.0131438\pi\)
−0.535324 + 0.844647i \(0.679810\pi\)
\(840\) 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 \(-0.294138\pi\)
0.602583 + 0.798056i \(0.294138\pi\)
\(858\) 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 \(-0.502552\pi\)
−0.00801723 + 0.999968i \(0.502552\pi\)
\(864\) 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 0.623733 0.781637i \(-0.285615\pi\)
−0.988784 + 0.149350i \(0.952282\pi\)
\(878\) 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 −0.400487 0.916303i \(-0.631159\pi\)
0.993785 0.111320i \(-0.0355078\pi\)
\(882\) 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 \(-0.822647\pi\)
0.882320 + 0.470651i \(0.155981\pi\)
\(888\) 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 −0.967200 0.254016i \(-0.918248\pi\)
0.703584 + 0.710612i \(0.251582\pi\)
\(908\) 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 \(-0.614294\pi\)
−0.351400 + 0.936226i \(0.614294\pi\)
\(912\) 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 0.648727 0.761021i \(-0.275302\pi\)
−0.983427 + 0.181304i \(0.941968\pi\)
\(920\) 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 \(-0.326951\pi\)
−0.999799 + 0.0200506i \(0.993617\pi\)
\(930\) 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 \(-0.909246\pi\)
−0.959630 + 0.281264i \(0.909246\pi\)
\(942\) 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 0.425883 + 0.904778i \(0.359963\pi\)
−0.996502 + 0.0835631i \(0.973370\pi\)
\(948\) 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 \(-0.190557\pi\)
−0.901078 + 0.433656i \(0.857223\pi\)
\(954\) 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 0.993074 + 0.117490i \(0.0374847\pi\)
−0.394788 + 0.918772i \(0.629182\pi\)
\(972\) 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 \(-0.760163\pi\)
0.957172 + 0.289522i \(0.0934962\pi\)
\(978\) 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 \(-0.570736\pi\)
−0.220398 + 0.975410i \(0.570736\pi\)
\(984\) 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 −0.857699 0.514153i \(-0.828107\pi\)
0.874119 + 0.485713i \(0.161440\pi\)
\(992\) −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 0.680700 0.732563i \(-0.261676\pi\)
−0.974768 + 0.223222i \(0.928343\pi\)
\(998\) 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.100.4 yes 16
3.2 odd 2 inner 117.4.g.f.100.5 yes 16
13.3 even 3 inner 117.4.g.f.55.4 16
13.4 even 6 1521.4.a.bd.1.4 8
13.9 even 3 1521.4.a.bc.1.5 8
39.17 odd 6 1521.4.a.bd.1.5 8
39.29 odd 6 inner 117.4.g.f.55.5 yes 16
39.35 odd 6 1521.4.a.bc.1.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.4.g.f.55.4 16 13.3 even 3 inner
117.4.g.f.55.5 yes 16 39.29 odd 6 inner
117.4.g.f.100.4 yes 16 1.1 even 1 trivial
117.4.g.f.100.5 yes 16 3.2 odd 2 inner
1521.4.a.bc.1.4 8 39.35 odd 6
1521.4.a.bc.1.5 8 13.9 even 3
1521.4.a.bd.1.4 8 13.4 even 6
1521.4.a.bd.1.5 8 39.17 odd 6