Properties

Label 162.3.f.a.125.2
Level $162$
Weight $3$
Character 162.125
Analytic conductor $4.414$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [162,3,Mod(17,162)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(162, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([11]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("162.17");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 162.f (of order \(18\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.41418028264\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 125.2
Character \(\chi\) \(=\) 162.125
Dual form 162.3.f.a.35.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.909039 - 1.08335i) q^{2} +(-0.347296 + 1.96962i) q^{4} +(-0.387127 - 1.06362i) q^{5} +(-0.332318 - 1.88467i) q^{7} +(2.44949 - 1.41421i) q^{8} +O(q^{10})\) \(q+(-0.909039 - 1.08335i) q^{2} +(-0.347296 + 1.96962i) q^{4} +(-0.387127 - 1.06362i) q^{5} +(-0.332318 - 1.88467i) q^{7} +(2.44949 - 1.41421i) q^{8} +(-0.800362 + 1.38627i) q^{10} +(6.05561 - 16.6376i) q^{11} +(-9.14397 - 7.67270i) q^{13} +(-1.73967 + 2.07326i) q^{14} +(-3.75877 - 1.36808i) q^{16} +(2.93931 + 1.69701i) q^{17} +(-10.2259 - 17.7118i) q^{19} +(2.22937 - 0.393099i) q^{20} +(-23.5292 + 8.56392i) q^{22} +(-0.678043 - 0.119557i) q^{23} +(18.1697 - 15.2462i) q^{25} +16.8809i q^{26} +3.82749 q^{28} +(-34.6788 - 41.3286i) q^{29} +(-7.33824 + 41.6172i) q^{31} +(1.93476 + 5.31570i) q^{32} +(-0.833488 - 4.72695i) q^{34} +(-1.87593 + 1.08307i) q^{35} +(8.24382 - 14.2787i) q^{37} +(-9.89233 + 27.1790i) q^{38} +(-2.45245 - 2.05785i) q^{40} +(-26.0070 + 30.9939i) q^{41} +(66.4698 + 24.1930i) q^{43} +(30.6667 + 17.7054i) q^{44} +(0.486845 + 0.843240i) q^{46} +(62.9822 - 11.1055i) q^{47} +(42.6034 - 15.5064i) q^{49} +(-33.0339 - 5.82477i) q^{50} +(18.2879 - 15.3454i) q^{52} +17.6375i q^{53} -20.0405 q^{55} +(-3.47934 - 4.14651i) q^{56} +(-13.2490 + 75.1385i) q^{58} +(19.1264 + 52.5494i) q^{59} +(11.5245 + 65.3586i) q^{61} +(51.7568 - 29.8818i) q^{62} +(4.00000 - 6.92820i) q^{64} +(-4.62098 + 12.6960i) q^{65} +(-17.2826 - 14.5018i) q^{67} +(-4.36327 + 5.19994i) q^{68} +(2.87864 + 1.04774i) q^{70} +(43.0775 + 24.8708i) q^{71} +(-45.2424 - 78.3622i) q^{73} +(-22.9628 + 4.04896i) q^{74} +(38.4369 - 13.9899i) q^{76} +(-33.3689 - 5.88383i) q^{77} +(-57.2341 + 48.0251i) q^{79} +4.52753i q^{80} +57.2187 q^{82} +(-8.15901 - 9.72353i) q^{83} +(0.667093 - 3.78327i) q^{85} +(-34.2141 - 94.0025i) q^{86} +(-8.69603 - 49.3177i) q^{88} +(-58.5070 + 33.7790i) q^{89} +(-11.4218 + 19.7832i) q^{91} +(0.470964 - 1.29396i) q^{92} +(-69.2844 - 58.1365i) q^{94} +(-14.8799 + 17.7332i) q^{95} +(-44.2956 - 16.1223i) q^{97} +(-55.5270 - 32.0585i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 18 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 18 q^{5} + 18 q^{11} + 36 q^{14} + 72 q^{20} + 36 q^{22} + 180 q^{23} + 18 q^{25} - 144 q^{29} - 90 q^{31} - 72 q^{34} - 486 q^{35} - 180 q^{38} + 90 q^{41} + 90 q^{43} + 378 q^{47} + 72 q^{49} + 72 q^{56} - 252 q^{59} - 144 q^{61} + 144 q^{64} - 18 q^{65} - 594 q^{67} + 180 q^{68} - 360 q^{70} + 648 q^{71} + 126 q^{73} + 504 q^{74} - 72 q^{76} + 342 q^{77} - 72 q^{79} - 594 q^{83} + 360 q^{85} - 540 q^{86} + 144 q^{88} - 648 q^{89} - 198 q^{91} - 396 q^{92} + 504 q^{94} - 252 q^{95} + 702 q^{97} - 648 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.909039 1.08335i −0.454519 0.541675i
\(3\) 0 0
\(4\) −0.347296 + 1.96962i −0.0868241 + 0.492404i
\(5\) −0.387127 1.06362i −0.0774254 0.212724i 0.894941 0.446184i \(-0.147217\pi\)
−0.972366 + 0.233460i \(0.924995\pi\)
\(6\) 0 0
\(7\) −0.332318 1.88467i −0.0474741 0.269239i 0.951826 0.306638i \(-0.0992039\pi\)
−0.999300 + 0.0373988i \(0.988093\pi\)
\(8\) 2.44949 1.41421i 0.306186 0.176777i
\(9\) 0 0
\(10\) −0.800362 + 1.38627i −0.0800362 + 0.138627i
\(11\) 6.05561 16.6376i 0.550510 1.51251i −0.282507 0.959265i \(-0.591166\pi\)
0.833017 0.553248i \(-0.186612\pi\)
\(12\) 0 0
\(13\) −9.14397 7.67270i −0.703382 0.590208i 0.219351 0.975646i \(-0.429606\pi\)
−0.922734 + 0.385438i \(0.874050\pi\)
\(14\) −1.73967 + 2.07326i −0.124262 + 0.148090i
\(15\) 0 0
\(16\) −3.75877 1.36808i −0.234923 0.0855050i
\(17\) 2.93931 + 1.69701i 0.172900 + 0.0998241i 0.583953 0.811788i \(-0.301505\pi\)
−0.411052 + 0.911612i \(0.634839\pi\)
\(18\) 0 0
\(19\) −10.2259 17.7118i −0.538206 0.932200i −0.999001 0.0446932i \(-0.985769\pi\)
0.460795 0.887507i \(-0.347564\pi\)
\(20\) 2.22937 0.393099i 0.111469 0.0196549i
\(21\) 0 0
\(22\) −23.5292 + 8.56392i −1.06951 + 0.389269i
\(23\) −0.678043 0.119557i −0.0294801 0.00519814i 0.158889 0.987297i \(-0.449209\pi\)
−0.188369 + 0.982098i \(0.560320\pi\)
\(24\) 0 0
\(25\) 18.1697 15.2462i 0.726787 0.609847i
\(26\) 16.8809i 0.649266i
\(27\) 0 0
\(28\) 3.82749 0.136696
\(29\) −34.6788 41.3286i −1.19582 1.42512i −0.879122 0.476596i \(-0.841870\pi\)
−0.316698 0.948527i \(-0.602574\pi\)
\(30\) 0 0
\(31\) −7.33824 + 41.6172i −0.236717 + 1.34249i 0.602249 + 0.798308i \(0.294271\pi\)
−0.838966 + 0.544183i \(0.816840\pi\)
\(32\) 1.93476 + 5.31570i 0.0604612 + 0.166116i
\(33\) 0 0
\(34\) −0.833488 4.72695i −0.0245144 0.139028i
\(35\) −1.87593 + 1.08307i −0.0535980 + 0.0309448i
\(36\) 0 0
\(37\) 8.24382 14.2787i 0.222806 0.385911i −0.732853 0.680387i \(-0.761812\pi\)
0.955659 + 0.294476i \(0.0951450\pi\)
\(38\) −9.89233 + 27.1790i −0.260325 + 0.715236i
\(39\) 0 0
\(40\) −2.45245 2.05785i −0.0613113 0.0514463i
\(41\) −26.0070 + 30.9939i −0.634317 + 0.755950i −0.983461 0.181119i \(-0.942028\pi\)
0.349144 + 0.937069i \(0.386472\pi\)
\(42\) 0 0
\(43\) 66.4698 + 24.1930i 1.54581 + 0.562628i 0.967430 0.253140i \(-0.0814632\pi\)
0.578379 + 0.815768i \(0.303685\pi\)
\(44\) 30.6667 + 17.7054i 0.696970 + 0.402396i
\(45\) 0 0
\(46\) 0.486845 + 0.843240i 0.0105836 + 0.0183313i
\(47\) 62.9822 11.1055i 1.34005 0.236286i 0.542760 0.839888i \(-0.317379\pi\)
0.797286 + 0.603601i \(0.206268\pi\)
\(48\) 0 0
\(49\) 42.6034 15.5064i 0.869457 0.316456i
\(50\) −33.0339 5.82477i −0.660678 0.116495i
\(51\) 0 0
\(52\) 18.2879 15.3454i 0.351691 0.295104i
\(53\) 17.6375i 0.332783i 0.986060 + 0.166392i \(0.0532116\pi\)
−0.986060 + 0.166392i \(0.946788\pi\)
\(54\) 0 0
\(55\) −20.0405 −0.364372
\(56\) −3.47934 4.14651i −0.0621310 0.0740449i
\(57\) 0 0
\(58\) −13.2490 + 75.1385i −0.228430 + 1.29549i
\(59\) 19.1264 + 52.5494i 0.324177 + 0.890668i 0.989554 + 0.144161i \(0.0460484\pi\)
−0.665377 + 0.746507i \(0.731729\pi\)
\(60\) 0 0
\(61\) 11.5245 + 65.3586i 0.188926 + 1.07145i 0.920807 + 0.390020i \(0.127532\pi\)
−0.731881 + 0.681433i \(0.761357\pi\)
\(62\) 51.7568 29.8818i 0.834787 0.481965i
\(63\) 0 0
\(64\) 4.00000 6.92820i 0.0625000 0.108253i
\(65\) −4.62098 + 12.6960i −0.0710920 + 0.195324i
\(66\) 0 0
\(67\) −17.2826 14.5018i −0.257949 0.216445i 0.504637 0.863331i \(-0.331626\pi\)
−0.762586 + 0.646887i \(0.776071\pi\)
\(68\) −4.36327 + 5.19994i −0.0641657 + 0.0764697i
\(69\) 0 0
\(70\) 2.87864 + 1.04774i 0.0411234 + 0.0149677i
\(71\) 43.0775 + 24.8708i 0.606726 + 0.350293i 0.771683 0.636007i \(-0.219415\pi\)
−0.164957 + 0.986301i \(0.552749\pi\)
\(72\) 0 0
\(73\) −45.2424 78.3622i −0.619759 1.07345i −0.989529 0.144331i \(-0.953897\pi\)
0.369770 0.929123i \(-0.379436\pi\)
\(74\) −22.9628 + 4.04896i −0.310308 + 0.0547157i
\(75\) 0 0
\(76\) 38.4369 13.9899i 0.505748 0.184077i
\(77\) −33.3689 5.88383i −0.433362 0.0764134i
\(78\) 0 0
\(79\) −57.2341 + 48.0251i −0.724482 + 0.607913i −0.928621 0.371029i \(-0.879005\pi\)
0.204139 + 0.978942i \(0.434561\pi\)
\(80\) 4.52753i 0.0565942i
\(81\) 0 0
\(82\) 57.2187 0.697789
\(83\) −8.15901 9.72353i −0.0983014 0.117151i 0.714651 0.699481i \(-0.246586\pi\)
−0.812952 + 0.582330i \(0.802141\pi\)
\(84\) 0 0
\(85\) 0.667093 3.78327i 0.00784815 0.0445091i
\(86\) −34.2141 94.0025i −0.397838 1.09305i
\(87\) 0 0
\(88\) −8.69603 49.3177i −0.0988186 0.560428i
\(89\) −58.5070 + 33.7790i −0.657382 + 0.379540i −0.791279 0.611455i \(-0.790584\pi\)
0.133897 + 0.990995i \(0.457251\pi\)
\(90\) 0 0
\(91\) −11.4218 + 19.7832i −0.125514 + 0.217397i
\(92\) 0.470964 1.29396i 0.00511917 0.0140648i
\(93\) 0 0
\(94\) −69.2844 58.1365i −0.737068 0.618473i
\(95\) −14.8799 + 17.7332i −0.156631 + 0.186665i
\(96\) 0 0
\(97\) −44.2956 16.1223i −0.456655 0.166209i 0.103442 0.994635i \(-0.467014\pi\)
−0.560098 + 0.828427i \(0.689236\pi\)
\(98\) −55.5270 32.0585i −0.566602 0.327128i
\(99\) 0 0
\(100\) 23.7188 + 41.0822i 0.237188 + 0.410822i
\(101\) 9.94227 1.75309i 0.0984383 0.0173573i −0.124212 0.992256i \(-0.539640\pi\)
0.222650 + 0.974898i \(0.428529\pi\)
\(102\) 0 0
\(103\) 121.488 44.2181i 1.17950 0.429301i 0.323472 0.946238i \(-0.395150\pi\)
0.856024 + 0.516936i \(0.172928\pi\)
\(104\) −33.2489 5.86268i −0.319701 0.0563719i
\(105\) 0 0
\(106\) 19.1076 16.0332i 0.180260 0.151257i
\(107\) 135.970i 1.27075i −0.772204 0.635375i \(-0.780846\pi\)
0.772204 0.635375i \(-0.219154\pi\)
\(108\) 0 0
\(109\) −182.307 −1.67254 −0.836269 0.548320i \(-0.815268\pi\)
−0.836269 + 0.548320i \(0.815268\pi\)
\(110\) 18.2176 + 21.7108i 0.165614 + 0.197371i
\(111\) 0 0
\(112\) −1.32927 + 7.53869i −0.0118685 + 0.0673097i
\(113\) −5.48933 15.0818i −0.0485781 0.133467i 0.913031 0.407890i \(-0.133735\pi\)
−0.961609 + 0.274423i \(0.911513\pi\)
\(114\) 0 0
\(115\) 0.135325 + 0.767465i 0.00117674 + 0.00667361i
\(116\) 93.4452 53.9506i 0.805562 0.465091i
\(117\) 0 0
\(118\) 39.5428 68.4901i 0.335108 0.580425i
\(119\) 2.22152 6.10358i 0.0186682 0.0512905i
\(120\) 0 0
\(121\) −147.449 123.725i −1.21859 1.02252i
\(122\) 60.3301 71.8986i 0.494509 0.589333i
\(123\) 0 0
\(124\) −79.4214 28.9070i −0.640495 0.233121i
\(125\) −47.7561 27.5720i −0.382049 0.220576i
\(126\) 0 0
\(127\) 81.7231 + 141.549i 0.643489 + 1.11456i 0.984648 + 0.174550i \(0.0558470\pi\)
−0.341160 + 0.940005i \(0.610820\pi\)
\(128\) −11.1418 + 1.96460i −0.0870455 + 0.0153485i
\(129\) 0 0
\(130\) 17.9549 6.53505i 0.138115 0.0502696i
\(131\) 194.629 + 34.3184i 1.48572 + 0.261972i 0.856861 0.515548i \(-0.172412\pi\)
0.628858 + 0.777520i \(0.283523\pi\)
\(132\) 0 0
\(133\) −29.9827 + 25.1584i −0.225434 + 0.189161i
\(134\) 31.9058i 0.238103i
\(135\) 0 0
\(136\) 9.59974 0.0705863
\(137\) 19.4564 + 23.1872i 0.142017 + 0.169250i 0.832364 0.554229i \(-0.186987\pi\)
−0.690347 + 0.723478i \(0.742542\pi\)
\(138\) 0 0
\(139\) −26.6334 + 151.046i −0.191607 + 1.08666i 0.725561 + 0.688158i \(0.241580\pi\)
−0.917168 + 0.398500i \(0.869531\pi\)
\(140\) −1.48172 4.07100i −0.0105837 0.0290786i
\(141\) 0 0
\(142\) −12.2153 69.2766i −0.0860235 0.487863i
\(143\) −183.028 + 105.671i −1.27992 + 0.738960i
\(144\) 0 0
\(145\) −30.5329 + 52.8845i −0.210572 + 0.364721i
\(146\) −43.7666 + 120.248i −0.299771 + 0.823614i
\(147\) 0 0
\(148\) 25.2605 + 21.1961i 0.170679 + 0.143217i
\(149\) 130.956 156.067i 0.878898 1.04743i −0.119610 0.992821i \(-0.538164\pi\)
0.998508 0.0546085i \(-0.0173911\pi\)
\(150\) 0 0
\(151\) −124.926 45.4693i −0.827324 0.301121i −0.106564 0.994306i \(-0.533985\pi\)
−0.720760 + 0.693184i \(0.756207\pi\)
\(152\) −50.0965 28.9232i −0.329582 0.190285i
\(153\) 0 0
\(154\) 23.9594 + 41.4988i 0.155580 + 0.269473i
\(155\) 47.1059 8.30603i 0.303909 0.0535873i
\(156\) 0 0
\(157\) 238.313 86.7387i 1.51791 0.552476i 0.557288 0.830319i \(-0.311842\pi\)
0.960626 + 0.277844i \(0.0896197\pi\)
\(158\) 104.056 + 18.3479i 0.658583 + 0.116126i
\(159\) 0 0
\(160\) 4.90490 4.11570i 0.0306557 0.0257231i
\(161\) 1.31762i 0.00818397i
\(162\) 0 0
\(163\) 261.536 1.60451 0.802257 0.596979i \(-0.203632\pi\)
0.802257 + 0.596979i \(0.203632\pi\)
\(164\) −52.0140 61.9879i −0.317159 0.377975i
\(165\) 0 0
\(166\) −3.11713 + 17.6781i −0.0187779 + 0.106495i
\(167\) 26.5485 + 72.9413i 0.158973 + 0.436774i 0.993450 0.114268i \(-0.0364523\pi\)
−0.834477 + 0.551043i \(0.814230\pi\)
\(168\) 0 0
\(169\) −4.60471 26.1146i −0.0272468 0.154524i
\(170\) −4.70502 + 2.71644i −0.0276766 + 0.0159791i
\(171\) 0 0
\(172\) −70.7357 + 122.518i −0.411254 + 0.712313i
\(173\) −36.6545 + 100.707i −0.211876 + 0.582123i −0.999417 0.0341382i \(-0.989131\pi\)
0.787542 + 0.616262i \(0.211354\pi\)
\(174\) 0 0
\(175\) −34.7722 29.1773i −0.198698 0.166727i
\(176\) −45.5233 + 54.2525i −0.258655 + 0.308253i
\(177\) 0 0
\(178\) 89.7797 + 32.6771i 0.504380 + 0.183579i
\(179\) −102.022 58.9024i −0.569955 0.329064i 0.187176 0.982326i \(-0.440066\pi\)
−0.757131 + 0.653263i \(0.773400\pi\)
\(180\) 0 0
\(181\) 59.7681 + 103.521i 0.330210 + 0.571941i 0.982553 0.185983i \(-0.0595470\pi\)
−0.652343 + 0.757924i \(0.726214\pi\)
\(182\) 31.8150 5.60984i 0.174808 0.0308233i
\(183\) 0 0
\(184\) −1.82994 + 0.666043i −0.00994532 + 0.00361980i
\(185\) −18.3786 3.24064i −0.0993436 0.0175170i
\(186\) 0 0
\(187\) 46.0335 38.6267i 0.246169 0.206560i
\(188\) 127.908i 0.680359i
\(189\) 0 0
\(190\) 32.7377 0.172304
\(191\) 146.062 + 174.070i 0.764722 + 0.911361i 0.998137 0.0610168i \(-0.0194343\pi\)
−0.233414 + 0.972377i \(0.574990\pi\)
\(192\) 0 0
\(193\) 12.7566 72.3465i 0.0660966 0.374853i −0.933760 0.357901i \(-0.883493\pi\)
0.999856 0.0169519i \(-0.00539623\pi\)
\(194\) 22.8003 + 62.6434i 0.117527 + 0.322904i
\(195\) 0 0
\(196\) 15.7456 + 89.2976i 0.0803346 + 0.455600i
\(197\) −80.0547 + 46.2196i −0.406369 + 0.234617i −0.689228 0.724544i \(-0.742050\pi\)
0.282859 + 0.959161i \(0.408717\pi\)
\(198\) 0 0
\(199\) 1.97251 3.41650i 0.00991214 0.0171683i −0.861027 0.508560i \(-0.830178\pi\)
0.870939 + 0.491391i \(0.163511\pi\)
\(200\) 22.9451 63.0412i 0.114726 0.315206i
\(201\) 0 0
\(202\) −10.9371 9.17733i −0.0541441 0.0454323i
\(203\) −66.3664 + 79.0923i −0.326928 + 0.389617i
\(204\) 0 0
\(205\) 43.0339 + 15.6630i 0.209921 + 0.0764051i
\(206\) −158.341 91.4183i −0.768646 0.443778i
\(207\) 0 0
\(208\) 23.8732 + 41.3496i 0.114775 + 0.198796i
\(209\) −356.607 + 62.8794i −1.70625 + 0.300858i
\(210\) 0 0
\(211\) 57.0834 20.7767i 0.270538 0.0984676i −0.203189 0.979139i \(-0.565131\pi\)
0.473727 + 0.880672i \(0.342908\pi\)
\(212\) −34.7391 6.12545i −0.163864 0.0288936i
\(213\) 0 0
\(214\) −147.303 + 123.602i −0.688334 + 0.577581i
\(215\) 80.0645i 0.372393i
\(216\) 0 0
\(217\) 80.8735 0.372689
\(218\) 165.724 + 197.502i 0.760201 + 0.905972i
\(219\) 0 0
\(220\) 6.95998 39.4720i 0.0316363 0.179418i
\(221\) −13.8563 38.0698i −0.0626981 0.172262i
\(222\) 0 0
\(223\) −28.2197 160.042i −0.126546 0.717678i −0.980378 0.197129i \(-0.936838\pi\)
0.853832 0.520549i \(-0.174273\pi\)
\(224\) 9.37540 5.41289i 0.0418545 0.0241647i
\(225\) 0 0
\(226\) −11.3489 + 19.6568i −0.0502162 + 0.0869771i
\(227\) 89.6325 246.263i 0.394857 1.08486i −0.569899 0.821715i \(-0.693018\pi\)
0.964756 0.263146i \(-0.0847601\pi\)
\(228\) 0 0
\(229\) −93.1242 78.1405i −0.406656 0.341225i 0.416404 0.909180i \(-0.363290\pi\)
−0.823060 + 0.567955i \(0.807735\pi\)
\(230\) 0.708418 0.844260i 0.00308008 0.00367070i
\(231\) 0 0
\(232\) −143.393 52.1907i −0.618072 0.224960i
\(233\) 362.949 + 209.549i 1.55772 + 0.899352i 0.997474 + 0.0710267i \(0.0226275\pi\)
0.560248 + 0.828325i \(0.310706\pi\)
\(234\) 0 0
\(235\) −36.1941 62.6900i −0.154017 0.266766i
\(236\) −110.145 + 19.4215i −0.466715 + 0.0822944i
\(237\) 0 0
\(238\) −8.63176 + 3.14170i −0.0362679 + 0.0132004i
\(239\) −102.988 18.1595i −0.430912 0.0759813i −0.0460143 0.998941i \(-0.514652\pi\)
−0.384897 + 0.922959i \(0.625763\pi\)
\(240\) 0 0
\(241\) 36.2898 30.4507i 0.150580 0.126352i −0.564385 0.825511i \(-0.690887\pi\)
0.714966 + 0.699160i \(0.246442\pi\)
\(242\) 272.210i 1.12483i
\(243\) 0 0
\(244\) −132.734 −0.543991
\(245\) −32.9858 39.3110i −0.134636 0.160453i
\(246\) 0 0
\(247\) −42.3919 + 240.417i −0.171627 + 0.973346i
\(248\) 40.8807 + 112.319i 0.164842 + 0.452899i
\(249\) 0 0
\(250\) 13.5420 + 76.8007i 0.0541681 + 0.307203i
\(251\) 147.898 85.3890i 0.589235 0.340195i −0.175560 0.984469i \(-0.556174\pi\)
0.764795 + 0.644274i \(0.222840\pi\)
\(252\) 0 0
\(253\) −6.09511 + 10.5570i −0.0240914 + 0.0417274i
\(254\) 79.0572 217.208i 0.311249 0.855149i
\(255\) 0 0
\(256\) 12.2567 + 10.2846i 0.0478778 + 0.0401742i
\(257\) 135.000 160.886i 0.525291 0.626017i −0.436533 0.899688i \(-0.643794\pi\)
0.961823 + 0.273671i \(0.0882381\pi\)
\(258\) 0 0
\(259\) −29.6503 10.7918i −0.114480 0.0416672i
\(260\) −23.4015 13.5108i −0.0900056 0.0519648i
\(261\) 0 0
\(262\) −139.747 242.048i −0.533384 0.923848i
\(263\) 87.0793 15.3544i 0.331100 0.0583818i −0.00562710 0.999984i \(-0.501791\pi\)
0.336727 + 0.941602i \(0.390680\pi\)
\(264\) 0 0
\(265\) 18.7597 6.82796i 0.0707912 0.0257659i
\(266\) 54.5108 + 9.61173i 0.204928 + 0.0361343i
\(267\) 0 0
\(268\) 34.5651 29.0036i 0.128974 0.108222i
\(269\) 417.890i 1.55350i −0.629812 0.776748i \(-0.716868\pi\)
0.629812 0.776748i \(-0.283132\pi\)
\(270\) 0 0
\(271\) 29.3344 0.108245 0.0541226 0.998534i \(-0.482764\pi\)
0.0541226 + 0.998534i \(0.482764\pi\)
\(272\) −8.72653 10.3999i −0.0320828 0.0382348i
\(273\) 0 0
\(274\) 7.43326 42.1561i 0.0271287 0.153854i
\(275\) −143.632 394.626i −0.522298 1.43500i
\(276\) 0 0
\(277\) 32.7591 + 185.786i 0.118264 + 0.670707i 0.985082 + 0.172083i \(0.0550499\pi\)
−0.866819 + 0.498624i \(0.833839\pi\)
\(278\) 187.846 108.453i 0.675705 0.390119i
\(279\) 0 0
\(280\) −3.06338 + 5.30593i −0.0109406 + 0.0189497i
\(281\) −16.2664 + 44.6916i −0.0578876 + 0.159045i −0.965266 0.261271i \(-0.915858\pi\)
0.907378 + 0.420316i \(0.138081\pi\)
\(282\) 0 0
\(283\) 58.5606 + 49.1382i 0.206928 + 0.173633i 0.740362 0.672209i \(-0.234654\pi\)
−0.533434 + 0.845842i \(0.679099\pi\)
\(284\) −63.9466 + 76.2086i −0.225164 + 0.268340i
\(285\) 0 0
\(286\) 280.859 + 102.224i 0.982023 + 0.357427i
\(287\) 67.0560 + 38.7148i 0.233645 + 0.134895i
\(288\) 0 0
\(289\) −138.740 240.305i −0.480070 0.831506i
\(290\) 85.0480 14.9963i 0.293269 0.0517113i
\(291\) 0 0
\(292\) 170.056 61.8953i 0.582383 0.211970i
\(293\) −321.453 56.6808i −1.09711 0.193450i −0.404339 0.914609i \(-0.632499\pi\)
−0.692770 + 0.721159i \(0.743610\pi\)
\(294\) 0 0
\(295\) 48.4884 40.6866i 0.164367 0.137921i
\(296\) 46.6341i 0.157548i
\(297\) 0 0
\(298\) −288.119 −0.966843
\(299\) 5.28268 + 6.29565i 0.0176678 + 0.0210557i
\(300\) 0 0
\(301\) 23.5068 133.314i 0.0780956 0.442902i
\(302\) 64.3034 + 176.672i 0.212925 + 0.585007i
\(303\) 0 0
\(304\) 14.2057 + 80.5645i 0.0467292 + 0.265015i
\(305\) 65.0554 37.5598i 0.213296 0.123147i
\(306\) 0 0
\(307\) 135.270 234.294i 0.440618 0.763172i −0.557118 0.830434i \(-0.688093\pi\)
0.997735 + 0.0672612i \(0.0214261\pi\)
\(308\) 23.1778 63.6804i 0.0752525 0.206755i
\(309\) 0 0
\(310\) −51.8194 43.4816i −0.167159 0.140263i
\(311\) −271.552 + 323.624i −0.873159 + 1.04059i 0.125663 + 0.992073i \(0.459894\pi\)
−0.998822 + 0.0485173i \(0.984550\pi\)
\(312\) 0 0
\(313\) 314.648 + 114.523i 1.00527 + 0.365887i 0.791613 0.611023i \(-0.209242\pi\)
0.213653 + 0.976910i \(0.431464\pi\)
\(314\) −310.604 179.327i −0.989184 0.571106i
\(315\) 0 0
\(316\) −74.7138 129.408i −0.236436 0.409519i
\(317\) −61.1385 + 10.7804i −0.192866 + 0.0340075i −0.269247 0.963071i \(-0.586775\pi\)
0.0763807 + 0.997079i \(0.475664\pi\)
\(318\) 0 0
\(319\) −897.611 + 326.704i −2.81383 + 1.02415i
\(320\) −8.91750 1.57240i −0.0278672 0.00491374i
\(321\) 0 0
\(322\) 1.42744 1.19777i 0.00443305 0.00371977i
\(323\) 69.4139i 0.214904i
\(324\) 0 0
\(325\) −283.122 −0.871146
\(326\) −237.746 283.335i −0.729283 0.869125i
\(327\) 0 0
\(328\) −19.8718 + 112.699i −0.0605849 + 0.343594i
\(329\) −41.8603 115.010i −0.127235 0.349575i
\(330\) 0 0
\(331\) −47.4950 269.357i −0.143489 0.813768i −0.968568 0.248750i \(-0.919980\pi\)
0.825078 0.565018i \(-0.191131\pi\)
\(332\) 21.9852 12.6932i 0.0662205 0.0382324i
\(333\) 0 0
\(334\) 54.8874 95.0678i 0.164334 0.284634i
\(335\) −8.73389 + 23.9962i −0.0260713 + 0.0716303i
\(336\) 0 0
\(337\) 420.078 + 352.488i 1.24652 + 1.04596i 0.996985 + 0.0775926i \(0.0247233\pi\)
0.249538 + 0.968365i \(0.419721\pi\)
\(338\) −24.1054 + 28.7277i −0.0713178 + 0.0849932i
\(339\) 0 0
\(340\) 7.21991 + 2.62783i 0.0212350 + 0.00772892i
\(341\) 647.975 + 374.109i 1.90022 + 1.09709i
\(342\) 0 0
\(343\) −90.2691 156.351i −0.263175 0.455833i
\(344\) 197.031 34.7419i 0.572765 0.100994i
\(345\) 0 0
\(346\) 142.422 51.8373i 0.411623 0.149819i
\(347\) −12.6788 2.23561i −0.0365382 0.00644267i 0.155349 0.987860i \(-0.450350\pi\)
−0.191887 + 0.981417i \(0.561461\pi\)
\(348\) 0 0
\(349\) 8.25639 6.92793i 0.0236573 0.0198508i −0.630882 0.775879i \(-0.717307\pi\)
0.654540 + 0.756028i \(0.272863\pi\)
\(350\) 64.1937i 0.183411i
\(351\) 0 0
\(352\) 100.157 0.284537
\(353\) −33.8253 40.3115i −0.0958225 0.114197i 0.716002 0.698098i \(-0.245970\pi\)
−0.811825 + 0.583901i \(0.801526\pi\)
\(354\) 0 0
\(355\) 9.77669 55.4464i 0.0275400 0.156187i
\(356\) −46.2125 126.968i −0.129810 0.356651i
\(357\) 0 0
\(358\) 28.9300 + 164.070i 0.0808100 + 0.458297i
\(359\) −85.6783 + 49.4664i −0.238658 + 0.137789i −0.614560 0.788870i \(-0.710666\pi\)
0.375902 + 0.926660i \(0.377333\pi\)
\(360\) 0 0
\(361\) −28.6385 + 49.6034i −0.0793311 + 0.137405i
\(362\) 57.8184 158.855i 0.159719 0.438825i
\(363\) 0 0
\(364\) −34.9985 29.3672i −0.0961496 0.0806791i
\(365\) −65.8332 + 78.4569i −0.180365 + 0.214951i
\(366\) 0 0
\(367\) −478.024 173.987i −1.30252 0.474078i −0.404702 0.914448i \(-0.632625\pi\)
−0.897816 + 0.440370i \(0.854847\pi\)
\(368\) 2.38504 + 1.37701i 0.00648110 + 0.00374186i
\(369\) 0 0
\(370\) 13.1961 + 22.8563i 0.0356651 + 0.0617738i
\(371\) 33.2409 5.86127i 0.0895982 0.0157986i
\(372\) 0 0
\(373\) −412.649 + 150.192i −1.10630 + 0.402660i −0.829634 0.558307i \(-0.811451\pi\)
−0.276664 + 0.960967i \(0.589229\pi\)
\(374\) −83.6925 14.7573i −0.223777 0.0394579i
\(375\) 0 0
\(376\) 138.569 116.273i 0.368534 0.309237i
\(377\) 643.987i 1.70819i
\(378\) 0 0
\(379\) 216.141 0.570293 0.285147 0.958484i \(-0.407958\pi\)
0.285147 + 0.958484i \(0.407958\pi\)
\(380\) −29.7599 35.4664i −0.0783155 0.0933327i
\(381\) 0 0
\(382\) 55.8027 316.473i 0.146080 0.828462i
\(383\) 224.513 + 616.845i 0.586197 + 1.61056i 0.777397 + 0.629011i \(0.216540\pi\)
−0.191200 + 0.981551i \(0.561238\pi\)
\(384\) 0 0
\(385\) 6.65981 + 37.7697i 0.0172982 + 0.0981031i
\(386\) −89.9729 + 51.9459i −0.233091 + 0.134575i
\(387\) 0 0
\(388\) 47.1384 81.6460i 0.121491 0.210428i
\(389\) −80.9652 + 222.450i −0.208137 + 0.571851i −0.999205 0.0398773i \(-0.987303\pi\)
0.791068 + 0.611729i \(0.209526\pi\)
\(390\) 0 0
\(391\) −1.79009 1.50206i −0.00457822 0.00384159i
\(392\) 82.4272 98.2330i 0.210274 0.250594i
\(393\) 0 0
\(394\) 122.845 + 44.7119i 0.311789 + 0.113482i
\(395\) 73.2374 + 42.2836i 0.185411 + 0.107047i
\(396\) 0 0
\(397\) 150.540 + 260.743i 0.379194 + 0.656783i 0.990945 0.134267i \(-0.0428680\pi\)
−0.611751 + 0.791050i \(0.709535\pi\)
\(398\) −5.49436 + 0.968803i −0.0138049 + 0.00243418i
\(399\) 0 0
\(400\) −89.1537 + 32.4493i −0.222884 + 0.0811232i
\(401\) −34.8014 6.13642i −0.0867864 0.0153028i 0.130086 0.991503i \(-0.458475\pi\)
−0.216873 + 0.976200i \(0.569586\pi\)
\(402\) 0 0
\(403\) 386.417 324.243i 0.958852 0.804572i
\(404\) 20.1913i 0.0499784i
\(405\) 0 0
\(406\) 146.014 0.359641
\(407\) −187.643 223.624i −0.461039 0.549445i
\(408\) 0 0
\(409\) −46.1552 + 261.759i −0.112849 + 0.639998i 0.874944 + 0.484224i \(0.160898\pi\)
−0.987793 + 0.155773i \(0.950213\pi\)
\(410\) −22.1509 60.8591i −0.0540266 0.148437i
\(411\) 0 0
\(412\) 44.9002 + 254.642i 0.108981 + 0.618062i
\(413\) 92.6823 53.5102i 0.224412 0.129565i
\(414\) 0 0
\(415\) −7.18359 + 12.4423i −0.0173099 + 0.0299816i
\(416\) 23.0944 63.4515i 0.0555155 0.152528i
\(417\) 0 0
\(418\) 392.290 + 329.170i 0.938492 + 0.787488i
\(419\) −297.132 + 354.108i −0.709145 + 0.845127i −0.993528 0.113584i \(-0.963767\pi\)
0.284383 + 0.958711i \(0.408211\pi\)
\(420\) 0 0
\(421\) 744.427 + 270.949i 1.76824 + 0.643585i 0.999994 + 0.00342601i \(0.00109054\pi\)
0.768242 + 0.640159i \(0.221132\pi\)
\(422\) −74.3995 42.9546i −0.176302 0.101788i
\(423\) 0 0
\(424\) 24.9432 + 43.2029i 0.0588283 + 0.101894i
\(425\) 79.2792 13.9791i 0.186539 0.0328919i
\(426\) 0 0
\(427\) 119.350 43.4397i 0.279508 0.101732i
\(428\) 267.809 + 47.2220i 0.625722 + 0.110332i
\(429\) 0 0
\(430\) −86.7379 + 72.7818i −0.201716 + 0.169260i
\(431\) 213.975i 0.496462i −0.968701 0.248231i \(-0.920151\pi\)
0.968701 0.248231i \(-0.0798492\pi\)
\(432\) 0 0
\(433\) 122.246 0.282323 0.141162 0.989987i \(-0.454916\pi\)
0.141162 + 0.989987i \(0.454916\pi\)
\(434\) −73.5171 87.6143i −0.169394 0.201876i
\(435\) 0 0
\(436\) 63.3144 359.074i 0.145217 0.823564i
\(437\) 4.81603 + 13.2319i 0.0110207 + 0.0302790i
\(438\) 0 0
\(439\) 23.1853 + 131.490i 0.0528139 + 0.299522i 0.999761 0.0218673i \(-0.00696114\pi\)
−0.946947 + 0.321390i \(0.895850\pi\)
\(440\) −49.0889 + 28.3415i −0.111566 + 0.0644125i
\(441\) 0 0
\(442\) −28.6471 + 49.6182i −0.0648124 + 0.112258i
\(443\) 48.3138 132.741i 0.109060 0.299641i −0.873142 0.487466i \(-0.837921\pi\)
0.982203 + 0.187825i \(0.0601437\pi\)
\(444\) 0 0
\(445\) 58.5778 + 49.1526i 0.131635 + 0.110455i
\(446\) −147.729 + 176.056i −0.331231 + 0.394745i
\(447\) 0 0
\(448\) −14.3867 5.23632i −0.0321131 0.0116882i
\(449\) 14.1480 + 8.16837i 0.0315101 + 0.0181924i 0.515672 0.856786i \(-0.327542\pi\)
−0.484162 + 0.874978i \(0.660876\pi\)
\(450\) 0 0
\(451\) 358.178 + 620.382i 0.794186 + 1.37557i
\(452\) 31.6118 5.57401i 0.0699376 0.0123319i
\(453\) 0 0
\(454\) −348.269 + 126.760i −0.767112 + 0.279206i
\(455\) 25.4635 + 4.48990i 0.0559637 + 0.00986792i
\(456\) 0 0
\(457\) −413.177 + 346.697i −0.904107 + 0.758636i −0.970989 0.239125i \(-0.923139\pi\)
0.0668816 + 0.997761i \(0.478695\pi\)
\(458\) 171.919i 0.375369i
\(459\) 0 0
\(460\) −1.55861 −0.00338828
\(461\) 232.751 + 277.382i 0.504882 + 0.601696i 0.956937 0.290295i \(-0.0937533\pi\)
−0.452055 + 0.891990i \(0.649309\pi\)
\(462\) 0 0
\(463\) 33.1055 187.751i 0.0715022 0.405509i −0.927959 0.372683i \(-0.878438\pi\)
0.999461 0.0328264i \(-0.0104508\pi\)
\(464\) 73.8088 + 202.788i 0.159071 + 0.437043i
\(465\) 0 0
\(466\) −102.920 583.689i −0.220859 1.25255i
\(467\) −617.016 + 356.234i −1.32123 + 0.762814i −0.983925 0.178580i \(-0.942850\pi\)
−0.337308 + 0.941394i \(0.609516\pi\)
\(468\) 0 0
\(469\) −21.5878 + 37.3912i −0.0460294 + 0.0797253i
\(470\) −35.0134 + 96.1986i −0.0744966 + 0.204678i
\(471\) 0 0
\(472\) 121.166 + 101.670i 0.256708 + 0.215403i
\(473\) 805.030 959.397i 1.70197 2.02832i
\(474\) 0 0
\(475\) −455.839 165.912i −0.959661 0.349288i
\(476\) 11.2502 + 6.49529i 0.0236348 + 0.0136456i
\(477\) 0 0
\(478\) 73.9468 + 128.080i 0.154700 + 0.267949i
\(479\) −224.974 + 39.6689i −0.469674 + 0.0828162i −0.403476 0.914990i \(-0.632198\pi\)
−0.0661981 + 0.997807i \(0.521087\pi\)
\(480\) 0 0
\(481\) −184.938 + 67.3118i −0.384486 + 0.139941i
\(482\) −65.9777 11.6336i −0.136883 0.0241362i
\(483\) 0 0
\(484\) 294.899 247.450i 0.609295 0.511259i
\(485\) 53.3551i 0.110011i
\(486\) 0 0
\(487\) 115.510 0.237188 0.118594 0.992943i \(-0.462161\pi\)
0.118594 + 0.992943i \(0.462161\pi\)
\(488\) 120.660 + 143.797i 0.247254 + 0.294666i
\(489\) 0 0
\(490\) −12.6022 + 71.4704i −0.0257187 + 0.145858i
\(491\) −150.903 414.604i −0.307339 0.844406i −0.993173 0.116649i \(-0.962785\pi\)
0.685834 0.727758i \(-0.259437\pi\)
\(492\) 0 0
\(493\) −31.7966 180.328i −0.0644962 0.365776i
\(494\) 298.991 172.623i 0.605245 0.349439i
\(495\) 0 0
\(496\) 84.5185 146.390i 0.170400 0.295142i
\(497\) 32.5579 89.4520i 0.0655088 0.179984i
\(498\) 0 0
\(499\) 216.247 + 181.453i 0.433361 + 0.363633i 0.833218 0.552945i \(-0.186496\pi\)
−0.399857 + 0.916577i \(0.630940\pi\)
\(500\) 70.8918 84.4856i 0.141784 0.168971i
\(501\) 0 0
\(502\) −226.951 82.6035i −0.452094 0.164549i
\(503\) −595.298 343.696i −1.18350 0.683291i −0.226675 0.973971i \(-0.572785\pi\)
−0.956821 + 0.290679i \(0.906119\pi\)
\(504\) 0 0
\(505\) −5.71354 9.89615i −0.0113139 0.0195963i
\(506\) 16.9777 2.99362i 0.0335527 0.00591625i
\(507\) 0 0
\(508\) −307.178 + 111.804i −0.604682 + 0.220086i
\(509\) 440.490 + 77.6702i 0.865402 + 0.152594i 0.588690 0.808359i \(-0.299644\pi\)
0.276712 + 0.960953i \(0.410755\pi\)
\(510\) 0 0
\(511\) −132.652 + 111.308i −0.259593 + 0.217824i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) −297.016 −0.577853
\(515\) −94.0626 112.099i −0.182646 0.217669i
\(516\) 0 0
\(517\) 196.627 1115.13i 0.380322 2.15692i
\(518\) 15.2619 + 41.9318i 0.0294632 + 0.0809494i
\(519\) 0 0
\(520\) 6.63587 + 37.6339i 0.0127613 + 0.0723728i
\(521\) 265.555 153.318i 0.509703 0.294277i −0.223008 0.974817i \(-0.571588\pi\)
0.732712 + 0.680539i \(0.238254\pi\)
\(522\) 0 0
\(523\) 185.369 321.068i 0.354434 0.613897i −0.632587 0.774489i \(-0.718007\pi\)
0.987021 + 0.160592i \(0.0513403\pi\)
\(524\) −135.188 + 371.426i −0.257992 + 0.708828i
\(525\) 0 0
\(526\) −95.7927 80.3796i −0.182115 0.152813i
\(527\) −92.1942 + 109.873i −0.174942 + 0.208487i
\(528\) 0 0
\(529\) −496.652 180.767i −0.938851 0.341714i
\(530\) −24.4503 14.1164i −0.0461327 0.0266347i
\(531\) 0 0
\(532\) −39.1396 67.7918i −0.0735707 0.127428i
\(533\) 475.615 83.8637i 0.892335 0.157343i
\(534\) 0 0
\(535\) −144.621 + 52.6377i −0.270320 + 0.0983883i
\(536\) −62.8421 11.0808i −0.117243 0.0206731i
\(537\) 0 0
\(538\) −452.722 + 379.879i −0.841490 + 0.706094i
\(539\) 802.720i 1.48928i
\(540\) 0 0
\(541\) −656.732 −1.21392 −0.606961 0.794732i \(-0.707612\pi\)
−0.606961 + 0.794732i \(0.707612\pi\)
\(542\) −26.6662 31.7795i −0.0491995 0.0586337i
\(543\) 0 0
\(544\) −3.33395 + 18.9078i −0.00612859 + 0.0347570i
\(545\) 70.5758 + 193.905i 0.129497 + 0.355790i
\(546\) 0 0
\(547\) −73.1807 415.029i −0.133786 0.758736i −0.975698 0.219121i \(-0.929681\pi\)
0.841912 0.539615i \(-0.181430\pi\)
\(548\) −52.4270 + 30.2687i −0.0956696 + 0.0552349i
\(549\) 0 0
\(550\) −296.951 + 514.334i −0.539910 + 0.935152i
\(551\) −377.381 + 1036.85i −0.684902 + 1.88175i
\(552\) 0 0
\(553\) 109.532 + 91.9078i 0.198068 + 0.166199i
\(554\) 171.492 204.376i 0.309552 0.368910i
\(555\) 0 0
\(556\) −288.252 104.915i −0.518439 0.188696i
\(557\) −412.640 238.238i −0.740825 0.427715i 0.0815442 0.996670i \(-0.474015\pi\)
−0.822369 + 0.568954i \(0.807348\pi\)
\(558\) 0 0
\(559\) −422.172 731.223i −0.755227 1.30809i
\(560\) 8.53291 1.50458i 0.0152373 0.00268675i
\(561\) 0 0
\(562\) 63.2035 23.0042i 0.112462 0.0409327i
\(563\) 206.039 + 36.3303i 0.365967 + 0.0645298i 0.353608 0.935394i \(-0.384955\pi\)
0.0123591 + 0.999924i \(0.496066\pi\)
\(564\) 0 0
\(565\) −13.9163 + 11.6771i −0.0246306 + 0.0206675i
\(566\) 108.110i 0.191007i
\(567\) 0 0
\(568\) 140.691 0.247695
\(569\) −569.179 678.321i −1.00031 1.19213i −0.981335 0.192308i \(-0.938403\pi\)
−0.0189794 0.999820i \(-0.506042\pi\)
\(570\) 0 0
\(571\) 127.475 722.948i 0.223249 1.26611i −0.642755 0.766072i \(-0.722209\pi\)
0.866004 0.500037i \(-0.166680\pi\)
\(572\) −144.567 397.194i −0.252739 0.694395i
\(573\) 0 0
\(574\) −19.0148 107.838i −0.0331269 0.187872i
\(575\) −14.1426 + 8.16524i −0.0245959 + 0.0142004i
\(576\) 0 0
\(577\) −349.289 + 604.986i −0.605353 + 1.04850i 0.386642 + 0.922230i \(0.373635\pi\)
−0.991996 + 0.126273i \(0.959699\pi\)
\(578\) −134.214 + 368.751i −0.232205 + 0.637978i
\(579\) 0 0
\(580\) −93.5582 78.5047i −0.161307 0.135353i
\(581\) −15.6143 + 18.6084i −0.0268748 + 0.0320282i
\(582\) 0 0
\(583\) 293.447 + 106.806i 0.503339 + 0.183200i
\(584\) −221.642 127.965i −0.379523 0.219118i
\(585\) 0 0
\(586\) 230.808 + 399.771i 0.393870 + 0.682204i
\(587\) 1118.40 197.205i 1.90529 0.335953i 0.908626 0.417610i \(-0.137132\pi\)
0.996660 + 0.0816570i \(0.0260212\pi\)
\(588\) 0 0
\(589\) 812.156 295.601i 1.37887 0.501869i
\(590\) −88.1557 15.5442i −0.149416 0.0263461i
\(591\) 0 0
\(592\) −50.5211 + 42.3922i −0.0853396 + 0.0716085i
\(593\) 463.710i 0.781973i −0.920396 0.390987i \(-0.872134\pi\)
0.920396 0.390987i \(-0.127866\pi\)
\(594\) 0 0
\(595\) −7.35191 −0.0123561
\(596\) 261.911 + 312.134i 0.439449 + 0.523715i
\(597\) 0 0
\(598\) 2.01823 11.4460i 0.00337497 0.0191404i
\(599\) −192.617 529.210i −0.321564 0.883489i −0.990170 0.139872i \(-0.955331\pi\)
0.668606 0.743617i \(-0.266891\pi\)
\(600\) 0 0
\(601\) 122.144 + 692.715i 0.203235 + 1.15260i 0.900193 + 0.435492i \(0.143425\pi\)
−0.696958 + 0.717112i \(0.745463\pi\)
\(602\) −165.794 + 95.7211i −0.275405 + 0.159005i
\(603\) 0 0
\(604\) 132.943 230.265i 0.220105 0.381233i
\(605\) −74.5148 + 204.728i −0.123165 + 0.338393i
\(606\) 0 0
\(607\) 313.569 + 263.116i 0.516589 + 0.433470i 0.863441 0.504450i \(-0.168305\pi\)
−0.346852 + 0.937920i \(0.612749\pi\)
\(608\) 74.3660 88.6260i 0.122313 0.145766i
\(609\) 0 0
\(610\) −99.8283 36.3345i −0.163653 0.0595648i
\(611\) −661.116 381.696i −1.08202 0.624706i
\(612\) 0 0
\(613\) 55.6369 + 96.3660i 0.0907617 + 0.157204i 0.907832 0.419334i \(-0.137737\pi\)
−0.817070 + 0.576538i \(0.804403\pi\)
\(614\) −376.788 + 66.4379i −0.613661 + 0.108205i
\(615\) 0 0
\(616\) −90.0577 + 32.7783i −0.146198 + 0.0532116i
\(617\) −438.710 77.3564i −0.711037 0.125375i −0.193581 0.981084i \(-0.562010\pi\)
−0.517457 + 0.855709i \(0.673121\pi\)
\(618\) 0 0
\(619\) −308.760 + 259.080i −0.498804 + 0.418546i −0.857169 0.515035i \(-0.827779\pi\)
0.358365 + 0.933582i \(0.383334\pi\)
\(620\) 95.6651i 0.154299i
\(621\) 0 0
\(622\) 597.449 0.960530
\(623\) 83.1054 + 99.0411i 0.133395 + 0.158975i
\(624\) 0 0
\(625\) 92.1298 522.494i 0.147408 0.835991i
\(626\) −161.959 444.980i −0.258721 0.710831i
\(627\) 0 0
\(628\) 88.0768 + 499.508i 0.140250 + 0.795395i
\(629\) 48.4622 27.9797i 0.0770465 0.0444828i
\(630\) 0 0
\(631\) −157.151 + 272.194i −0.249052 + 0.431370i −0.963263 0.268560i \(-0.913452\pi\)
0.714211 + 0.699930i \(0.246786\pi\)
\(632\) −72.2766 + 198.578i −0.114362 + 0.314206i
\(633\) 0 0
\(634\) 67.2562 + 56.4346i 0.106082 + 0.0890136i
\(635\) 118.917 141.720i 0.187271 0.223181i
\(636\) 0 0
\(637\) −508.540 185.093i −0.798336 0.290570i
\(638\) 1169.90 + 675.441i 1.83370 + 1.05868i
\(639\) 0 0
\(640\) 6.40290 + 11.0901i 0.0100045 + 0.0173284i
\(641\) −831.894 + 146.685i −1.29781 + 0.228838i −0.779525 0.626371i \(-0.784539\pi\)
−0.518282 + 0.855210i \(0.673428\pi\)
\(642\) 0 0
\(643\) 305.658 111.250i 0.475363 0.173018i −0.0932174 0.995646i \(-0.529715\pi\)
0.568580 + 0.822628i \(0.307493\pi\)
\(644\) −2.59520 0.457604i −0.00402982 0.000710566i
\(645\) 0 0
\(646\) −75.1995 + 63.0999i −0.116408 + 0.0976779i
\(647\) 1029.91i 1.59182i 0.605412 + 0.795912i \(0.293008\pi\)
−0.605412 + 0.795912i \(0.706992\pi\)
\(648\) 0 0
\(649\) 990.121 1.52561
\(650\) 257.369 + 306.721i 0.395953 + 0.471878i
\(651\) 0 0
\(652\) −90.8304 + 515.125i −0.139310 + 0.790069i
\(653\) 247.063 + 678.801i 0.378351 + 1.03951i 0.972040 + 0.234817i \(0.0754490\pi\)
−0.593688 + 0.804695i \(0.702329\pi\)
\(654\) 0 0
\(655\) −38.8444 220.297i −0.0593044 0.336332i
\(656\) 140.157 80.9194i 0.213653 0.123353i
\(657\) 0 0
\(658\) −86.5437 + 149.898i −0.131525 + 0.227809i
\(659\) 325.530 894.386i 0.493975 1.35719i −0.403038 0.915183i \(-0.632046\pi\)
0.897014 0.442003i \(-0.145732\pi\)
\(660\) 0 0
\(661\) 149.297 + 125.275i 0.225866 + 0.189524i 0.748697 0.662912i \(-0.230680\pi\)
−0.522831 + 0.852436i \(0.675124\pi\)
\(662\) −248.634 + 296.310i −0.375579 + 0.447598i
\(663\) 0 0
\(664\) −33.7366 12.2791i −0.0508081 0.0184926i
\(665\) 38.3662 + 22.1507i 0.0576935 + 0.0333094i
\(666\) 0 0
\(667\) 18.5726 + 32.1686i 0.0278449 + 0.0482288i
\(668\) −152.887 + 26.9580i −0.228872 + 0.0403563i
\(669\) 0 0
\(670\) 33.9357 12.3516i 0.0506503 0.0184352i
\(671\) 1157.20 + 204.046i 1.72459 + 0.304092i
\(672\) 0 0
\(673\) 268.446 225.253i 0.398880 0.334700i −0.421181 0.906977i \(-0.638384\pi\)
0.820060 + 0.572277i \(0.193940\pi\)
\(674\) 775.517i 1.15062i
\(675\) 0 0
\(676\) 53.0349 0.0784541
\(677\) 722.303 + 860.807i 1.06692 + 1.27150i 0.960828 + 0.277145i \(0.0893883\pi\)
0.106089 + 0.994357i \(0.466167\pi\)
\(678\) 0 0
\(679\) −15.6649 + 88.8403i −0.0230706 + 0.130840i
\(680\) −3.71632 10.2105i −0.00546517 0.0150154i
\(681\) 0 0
\(682\) −183.744 1042.06i −0.269419 1.52795i
\(683\) 132.500 76.4992i 0.193998 0.112005i −0.399855 0.916578i \(-0.630940\pi\)
0.593853 + 0.804574i \(0.297606\pi\)
\(684\) 0 0
\(685\) 17.1303 29.6706i 0.0250078 0.0433147i
\(686\) −87.3244 + 239.922i −0.127295 + 0.349740i
\(687\) 0 0
\(688\) −216.747 181.872i −0.315039 0.264349i
\(689\) 135.327 161.277i 0.196411 0.234074i
\(690\) 0 0
\(691\) 889.111 + 323.610i 1.28670 + 0.468321i 0.892643 0.450764i \(-0.148848\pi\)
0.394059 + 0.919085i \(0.371071\pi\)
\(692\) −185.625 107.171i −0.268244 0.154871i
\(693\) 0 0
\(694\) 9.10354 + 15.7678i 0.0131175 + 0.0227202i
\(695\) 170.966 30.1459i 0.245994 0.0433754i
\(696\) 0 0
\(697\) −129.040 + 46.9666i −0.185136 + 0.0673839i
\(698\) −15.0108 2.64680i −0.0215054 0.00379198i
\(699\) 0 0
\(700\) 69.5443 58.3546i 0.0993490 0.0833637i
\(701\) 250.910i 0.357932i 0.983855 + 0.178966i \(0.0572752\pi\)
−0.983855 + 0.178966i \(0.942725\pi\)
\(702\) 0 0
\(703\) −337.202 −0.479662
\(704\) −91.0465 108.505i −0.129327 0.154126i
\(705\) 0 0
\(706\) −12.9229 + 73.2894i −0.0183044 + 0.103809i
\(707\) −6.60800 18.1553i −0.00934653 0.0256794i
\(708\) 0 0
\(709\) 228.169 + 1294.01i 0.321818 + 1.82512i 0.531151 + 0.847277i \(0.321760\pi\)
−0.209333 + 0.977844i \(0.567129\pi\)
\(710\) −68.9553 + 39.8113i −0.0971201 + 0.0560723i
\(711\) 0 0
\(712\) −95.5416 + 165.483i −0.134188 + 0.232420i
\(713\) 9.95128 27.3409i 0.0139569 0.0383463i
\(714\) 0 0
\(715\) 183.249 + 153.764i 0.256293 + 0.215055i
\(716\) 151.447 180.487i 0.211518 0.252078i
\(717\) 0 0
\(718\) 131.474 + 47.8528i 0.183112 + 0.0666473i
\(719\) 503.280 + 290.569i 0.699972 + 0.404129i 0.807337 0.590091i \(-0.200908\pi\)
−0.107365 + 0.994220i \(0.534241\pi\)
\(720\) 0 0
\(721\) −123.709 214.271i −0.171580 0.297185i
\(722\) 79.7714 14.0658i 0.110487 0.0194818i
\(723\) 0 0
\(724\) −224.654 + 81.7675i −0.310296 + 0.112939i
\(725\) −1260.20 222.208i −1.73821 0.306494i
\(726\) 0 0
\(727\) −516.182 + 433.128i −0.710016 + 0.595774i −0.924604 0.380931i \(-0.875604\pi\)
0.214588 + 0.976705i \(0.431159\pi\)
\(728\) 64.6115i 0.0887521i
\(729\) 0 0
\(730\) 144.841 0.198413
\(731\) 154.319 + 183.911i 0.211107 + 0.251588i
\(732\) 0 0
\(733\) 43.1418 244.669i 0.0588565 0.333792i −0.941134 0.338032i \(-0.890239\pi\)
0.999991 + 0.00424043i \(0.00134977\pi\)
\(734\) 246.054 + 676.029i 0.335224 + 0.921020i
\(735\) 0 0
\(736\) −0.676318 3.83559i −0.000918910 0.00521140i
\(737\) −345.932 + 199.724i −0.469379 + 0.270996i
\(738\) 0 0
\(739\) −21.7967 + 37.7530i −0.0294949 + 0.0510866i −0.880396 0.474239i \(-0.842723\pi\)
0.850901 + 0.525326i \(0.176057\pi\)
\(740\) 12.7656 35.0732i 0.0172508 0.0473963i
\(741\) 0 0
\(742\) −36.5671 30.6834i −0.0492818 0.0413524i
\(743\) −805.304 + 959.724i −1.08385 + 1.29169i −0.129968 + 0.991518i \(0.541488\pi\)
−0.953886 + 0.300169i \(0.902957\pi\)
\(744\) 0 0
\(745\) −216.693 78.8697i −0.290863 0.105865i
\(746\) 537.825 + 310.513i 0.720945 + 0.416238i
\(747\) 0 0
\(748\) 60.0925 + 104.083i 0.0803376 + 0.139149i
\(749\) −256.259 + 45.1854i −0.342135 + 0.0603277i
\(750\) 0 0
\(751\) −81.7809 + 29.7658i −0.108896 + 0.0396349i −0.395894 0.918296i \(-0.629565\pi\)
0.286998 + 0.957931i \(0.407343\pi\)
\(752\) −251.929 44.4218i −0.335012 0.0590716i
\(753\) 0 0
\(754\) 697.664 585.409i 0.925283 0.776405i
\(755\) 150.476i 0.199307i
\(756\) 0 0
\(757\) −849.639 −1.12238 −0.561188 0.827688i \(-0.689656\pi\)
−0.561188 + 0.827688i \(0.689656\pi\)
\(758\) −196.481 234.157i −0.259209 0.308914i
\(759\) 0 0
\(760\) −11.3697 + 64.4807i −0.0149601 + 0.0848431i
\(761\) 218.959 + 601.584i 0.287725 + 0.790518i 0.996384 + 0.0849663i \(0.0270783\pi\)
−0.708659 + 0.705551i \(0.750700\pi\)
\(762\) 0 0
\(763\) 60.5838 + 343.588i 0.0794021 + 0.450312i
\(764\) −393.578 + 227.232i −0.515154 + 0.297424i
\(765\) 0 0
\(766\) 464.168 803.963i 0.605964 1.04956i
\(767\) 228.305 627.262i 0.297659 0.817812i
\(768\) 0 0
\(769\) −129.861 108.966i −0.168869 0.141698i 0.554436 0.832226i \(-0.312934\pi\)
−0.723306 + 0.690528i \(0.757378\pi\)
\(770\) 34.8638 41.5490i 0.0452776 0.0539598i
\(771\) 0 0
\(772\) 138.065 + 50.2514i 0.178840 + 0.0650925i
\(773\) −1141.45 659.019i −1.47666 0.852547i −0.477003 0.878902i \(-0.658277\pi\)
−0.999653 + 0.0263542i \(0.991610\pi\)
\(774\) 0 0
\(775\) 501.170 + 868.052i 0.646671 + 1.12007i
\(776\) −131.302 + 23.1521i −0.169203 + 0.0298351i
\(777\) 0 0
\(778\) 314.592 114.502i 0.404360 0.147175i
\(779\) 814.904 + 143.690i 1.04609 + 0.184454i
\(780\) 0 0
\(781\) 674.652 566.101i 0.863832 0.724841i
\(782\) 3.30472i 0.00422599i
\(783\) 0 0
\(784\) −181.350 −0.231314
\(785\) −184.514 219.896i −0.235050 0.280122i
\(786\) 0 0
\(787\) −199.680 + 1132.44i −0.253723 + 1.43893i 0.545608 + 0.838040i \(0.316299\pi\)
−0.799331 + 0.600891i \(0.794812\pi\)
\(788\) −63.2321 173.729i −0.0802438 0.220468i
\(789\) 0 0
\(790\) −20.7677 117.779i −0.0262882 0.149088i
\(791\) −26.6001 + 15.3575i −0.0336284 + 0.0194154i
\(792\) 0 0
\(793\) 396.098 686.061i 0.499492 0.865146i
\(794\) 145.629 400.113i 0.183412 0.503921i
\(795\) 0 0
\(796\) 6.04414 + 5.07163i 0.00759314 + 0.00637140i
\(797\) −97.8409 + 116.602i −0.122762 + 0.146301i −0.823925 0.566699i \(-0.808220\pi\)
0.701163 + 0.713001i \(0.252664\pi\)
\(798\) 0 0
\(799\) 203.970 + 74.2390i 0.255282 + 0.0929149i
\(800\) 116.198 + 67.0870i 0.145248 + 0.0838588i
\(801\) 0 0
\(802\) 24.9879 + 43.2803i 0.0311570 + 0.0539655i
\(803\) −1577.73 + 278.197i −1.96480 + 0.346447i
\(804\) 0 0
\(805\) 1.40145 0.510086i 0.00174093 0.000633647i
\(806\) −702.537 123.876i −0.871634 0.153693i
\(807\) 0 0
\(808\) 21.8742 18.3547i 0.0270721 0.0227162i
\(809\) 1046.40i 1.29345i 0.762725 + 0.646723i \(0.223861\pi\)
−0.762725 + 0.646723i \(0.776139\pi\)
\(810\) 0 0
\(811\) −360.583 −0.444615 −0.222308 0.974977i \(-0.571359\pi\)
−0.222308 + 0.974977i \(0.571359\pi\)
\(812\) −132.733 158.185i −0.163464 0.194809i
\(813\) 0 0
\(814\) −71.6885 + 406.566i −0.0880695 + 0.499467i
\(815\) −101.248 278.175i −0.124230 0.341319i
\(816\) 0 0
\(817\) −251.212 1424.70i −0.307481 1.74381i
\(818\) 325.534 187.947i 0.397963 0.229764i
\(819\) 0 0
\(820\) −45.7957 + 79.3204i −0.0558484 + 0.0967322i
\(821\) 519.549 1427.45i 0.632824 1.73867i −0.0403490 0.999186i \(-0.512847\pi\)
0.673173 0.739485i \(-0.264931\pi\)
\(822\) 0 0
\(823\) −647.973 543.714i −0.787331 0.660649i 0.157753 0.987479i \(-0.449575\pi\)
−0.945083 + 0.326830i \(0.894020\pi\)
\(824\) 235.050 280.122i 0.285255 0.339954i
\(825\) 0 0
\(826\) −142.222 51.7646i −0.172182 0.0626690i
\(827\) 939.412 + 542.370i 1.13593 + 0.655828i 0.945419 0.325858i \(-0.105653\pi\)
0.190508 + 0.981686i \(0.438986\pi\)
\(828\) 0 0
\(829\) −765.727 1326.28i −0.923675 1.59985i −0.793678 0.608338i \(-0.791836\pi\)
−0.129997 0.991514i \(-0.541497\pi\)
\(830\) 20.0096 3.52823i 0.0241079 0.00425088i
\(831\) 0 0
\(832\) −89.7339 + 32.6605i −0.107853 + 0.0392554i
\(833\) 151.539 + 26.7204i 0.181919 + 0.0320773i
\(834\) 0 0
\(835\) 67.3044 56.4751i 0.0806041 0.0676348i
\(836\) 724.216i 0.866287i
\(837\) 0 0
\(838\) 653.728 0.780105
\(839\) −83.5716 99.5967i −0.0996085 0.118709i 0.713937 0.700210i \(-0.246910\pi\)
−0.813546 + 0.581501i \(0.802466\pi\)
\(840\) 0 0
\(841\) −359.394 + 2038.22i −0.427341 + 2.42357i
\(842\) −383.180 1052.78i −0.455084 1.25033i
\(843\) 0 0
\(844\) 21.0972 + 119.648i 0.0249967 + 0.141763i
\(845\) −25.9935 + 15.0073i −0.0307615 + 0.0177602i
\(846\) 0 0
\(847\) −184.180 + 319.010i −0.217450 + 0.376635i
\(848\) 24.1295 66.2954i 0.0284547 0.0781785i
\(849\) 0 0
\(850\) −87.2121 73.1796i −0.102602 0.0860937i
\(851\) −7.29679 + 8.69597i −0.00857437 + 0.0102185i
\(852\) 0 0
\(853\) 440.159 + 160.205i 0.516012 + 0.187813i 0.586882 0.809672i \(-0.300355\pi\)
−0.0708696 + 0.997486i \(0.522577\pi\)
\(854\) −155.554 89.8091i −0.182148 0.105163i
\(855\) 0 0
\(856\) −192.291 333.058i −0.224639 0.389086i
\(857\) 871.104 153.599i 1.01646 0.179229i 0.359491 0.933149i \(-0.382950\pi\)
0.656967 + 0.753920i \(0.271839\pi\)
\(858\) 0 0
\(859\) −405.595 + 147.624i −0.472171 + 0.171856i −0.567135 0.823625i \(-0.691948\pi\)
0.0949648 + 0.995481i \(0.469726\pi\)
\(860\) 157.696 + 27.8061i 0.183368 + 0.0323327i
\(861\) 0 0
\(862\) −231.810 + 194.512i −0.268921 + 0.225652i
\(863\) 279.578i 0.323961i 0.986794 + 0.161980i \(0.0517881\pi\)
−0.986794 + 0.161980i \(0.948212\pi\)
\(864\) 0 0
\(865\) 121.305 0.140236
\(866\) −111.126 132.435i −0.128321 0.152927i
\(867\) 0 0
\(868\) −28.0871 + 159.290i −0.0323584 + 0.183513i
\(869\) 452.437 + 1243.06i 0.520641 + 1.43045i
\(870\) 0 0
\(871\) 46.7633 + 265.208i 0.0536892 + 0.304487i
\(872\) −446.558 + 257.820i −0.512108 + 0.295666i
\(873\) 0 0
\(874\) 9.95687 17.2458i 0.0113923 0.0197320i
\(875\) −36.0940 + 99.1673i −0.0412502 + 0.113334i
\(876\) 0 0
\(877\) −1227.88 1030.31i −1.40009 1.17482i −0.961058 0.276346i \(-0.910877\pi\)
−0.439033 0.898471i \(-0.644679\pi\)
\(878\) 121.374 144.648i 0.138239 0.164747i
\(879\) 0 0
\(880\) 75.3275 + 27.4170i 0.0855994 + 0.0311556i
\(881\) −37.7796 21.8121i −0.0428827 0.0247583i 0.478405 0.878139i \(-0.341215\pi\)
−0.521288 + 0.853381i \(0.674548\pi\)
\(882\) 0 0
\(883\) −460.205 797.099i −0.521184 0.902717i −0.999696 0.0246363i \(-0.992157\pi\)
0.478513 0.878081i \(-0.341176\pi\)
\(884\) 79.7952 14.0700i 0.0902660 0.0159163i
\(885\) 0 0
\(886\) −187.724 + 68.3260i −0.211878 + 0.0771174i
\(887\) 233.205 + 41.1203i 0.262914 + 0.0463588i 0.303551 0.952815i \(-0.401828\pi\)
−0.0406372 + 0.999174i \(0.512939\pi\)
\(888\) 0 0
\(889\) 239.614 201.060i 0.269533 0.226165i
\(890\) 108.142i 0.121508i
\(891\) 0 0
\(892\) 325.022 0.364374
\(893\) −840.748 1001.96i −0.941487 1.12202i
\(894\) 0 0
\(895\) −23.1545 + 131.316i −0.0258709 + 0.146721i
\(896\) 7.40527 + 20.3458i 0.00826481 + 0.0227074i
\(897\) 0 0
\(898\) −4.01190 22.7526i −0.00446760 0.0253370i
\(899\) 1974.46 1139.96i 2.19629 1.26803i
\(900\) 0 0
\(901\) −29.9310 + 51.8421i −0.0332198 + 0.0575384i
\(902\) 346.494 951.984i 0.384140 1.05541i
\(903\) 0 0
\(904\) −34.7750 29.1797i −0.0384679 0.0322784i
\(905\) 86.9698 103.647i 0.0960992 0.114527i
\(906\) 0 0
\(907\) 302.489 + 110.097i 0.333505 + 0.121386i 0.503345 0.864086i \(-0.332103\pi\)
−0.169839 + 0.985472i \(0.554325\pi\)
\(908\) 453.915 + 262.068i 0.499907 + 0.288621i
\(909\) 0 0
\(910\) −18.2832 31.6674i −0.0200914 0.0347993i
\(911\) 1105.64 194.955i 1.21366 0.214001i 0.470065 0.882632i \(-0.344230\pi\)
0.743595 + 0.668631i \(0.233119\pi\)
\(912\) 0 0
\(913\) −211.184 + 76.8648i −0.231308 + 0.0841893i
\(914\) 751.188 + 132.455i 0.821869 + 0.144918i
\(915\) 0 0
\(916\) 186.248 156.281i 0.203328 0.170612i
\(917\) 378.217i 0.412450i
\(918\) 0 0
\(919\) −486.580 −0.529467 −0.264734 0.964322i \(-0.585284\pi\)
−0.264734 + 0.964322i \(0.585284\pi\)
\(920\) 1.41684 + 1.68852i 0.00154004 + 0.00183535i
\(921\) 0 0
\(922\) 88.9219 504.301i 0.0964446 0.546965i
\(923\) −203.073 557.939i −0.220014 0.604484i
\(924\) 0 0
\(925\) −67.9082 385.127i −0.0734143 0.416353i
\(926\) −233.494 + 134.808i −0.252153 + 0.145581i
\(927\) 0 0
\(928\) 152.595 264.303i 0.164435 0.284809i
\(929\) −264.986 + 728.043i −0.285238 + 0.783684i 0.711478 + 0.702708i \(0.248026\pi\)
−0.996716 + 0.0809762i \(0.974196\pi\)
\(930\) 0 0
\(931\) −710.304 596.016i −0.762947 0.640189i
\(932\) −538.782 + 642.095i −0.578092 + 0.688943i
\(933\) 0 0
\(934\) 946.818 + 344.614i 1.01372 + 0.368965i
\(935\) −58.9050 34.0088i −0.0630000 0.0363731i
\(936\) 0 0
\(937\) 310.767 + 538.264i 0.331661 + 0.574454i 0.982838 0.184472i \(-0.0590575\pi\)
−0.651176 + 0.758926i \(0.725724\pi\)
\(938\) 60.1319 10.6029i 0.0641065 0.0113037i
\(939\) 0 0
\(940\) 136.045 49.5165i 0.144729 0.0526771i
\(941\) −1840.64 324.554i −1.95604 0.344903i −0.998372 0.0570327i \(-0.981836\pi\)
−0.957669 0.287870i \(-0.907053\pi\)
\(942\) 0 0
\(943\) 21.3394 17.9059i 0.0226293 0.0189882i
\(944\) 223.688i 0.236957i
\(945\) 0 0
\(946\) −1771.17 −1.87227
\(947\) 339.780 + 404.935i 0.358797 + 0.427597i 0.915003 0.403447i \(-0.132188\pi\)
−0.556206 + 0.831044i \(0.687744\pi\)
\(948\) 0 0
\(949\) −187.554 + 1063.67i −0.197634 + 1.12084i
\(950\) 234.635 + 644.653i 0.246984 + 0.678583i
\(951\) 0 0
\(952\) −3.19017 18.0923i −0.00335102 0.0190046i
\(953\) −226.233 + 130.616i −0.237391 + 0.137058i −0.613977 0.789324i \(-0.710431\pi\)
0.376586 + 0.926382i \(0.377098\pi\)
\(954\) 0 0
\(955\) 128.600 222.742i 0.134660 0.233238i
\(956\) 71.5346 196.540i 0.0748270 0.205585i
\(957\) 0 0
\(958\) 247.485 + 207.665i 0.258335 + 0.216769i
\(959\) 37.2345 44.3744i 0.0388264 0.0462715i
\(960\) 0 0
\(961\) −775.100 282.113i −0.806556 0.293562i
\(962\) 241.038 + 139.163i 0.250559 + 0.144660i
\(963\) 0 0
\(964\) 47.3730 + 82.0524i 0.0491421 + 0.0851166i
\(965\) −81.8878 + 14.4390i −0.0848579 + 0.0149627i
\(966\) 0 0
\(967\) 1645.56 598.934i 1.70172 0.619374i 0.705696 0.708515i \(-0.250634\pi\)
0.996019 + 0.0891408i \(0.0284121\pi\)
\(968\) −536.149 94.5375i −0.553873 0.0976628i
\(969\) 0 0
\(970\) 57.8023 48.5019i 0.0595900 0.0500019i
\(971\) 718.037i 0.739482i 0.929135 + 0.369741i \(0.120554\pi\)
−0.929135 + 0.369741i \(0.879446\pi\)
\(972\) 0 0
\(973\) 293.522 0.301667
\(974\) −105.004 125.138i −0.107807 0.128479i
\(975\) 0 0
\(976\) 46.0979 261.434i 0.0472315 0.267863i
\(977\) −359.573 987.919i −0.368038 1.01118i −0.976107 0.217291i \(-0.930278\pi\)
0.608069 0.793884i \(-0.291944\pi\)
\(978\) 0 0
\(979\) 207.708 + 1177.97i 0.212164 + 1.20324i
\(980\) 88.8834 51.3168i 0.0906973 0.0523641i
\(981\) 0 0
\(982\) −311.984 + 540.372i −0.317703 + 0.550277i
\(983\) 280.070 769.486i 0.284913 0.782793i −0.711845 0.702337i \(-0.752140\pi\)
0.996758 0.0804562i \(-0.0256377\pi\)
\(984\) 0 0
\(985\) 80.1515 + 67.2551i 0.0813721 + 0.0682793i
\(986\) −166.454 + 198.372i −0.168817 + 0.201188i
\(987\) 0 0
\(988\) −458.806 166.992i −0.464378 0.169020i
\(989\) −42.1769 24.3509i −0.0426460 0.0246217i
\(990\) 0 0
\(991\) 433.521 + 750.880i 0.437458 + 0.757699i 0.997493 0.0707698i \(-0.0225456\pi\)
−0.560035 + 0.828469i \(0.689212\pi\)
\(992\) −235.423 + 41.5114i −0.237321 + 0.0418461i
\(993\) 0 0
\(994\) −126.504 + 46.0438i −0.127268 + 0.0463217i
\(995\) −4.39747 0.775393i −0.00441957 0.000779290i
\(996\) 0 0
\(997\) −502.010 + 421.237i −0.503521 + 0.422504i −0.858842 0.512240i \(-0.828816\pi\)
0.355321 + 0.934744i \(0.384371\pi\)
\(998\) 399.219i 0.400019i
\(999\) 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 162.3.f.a.125.2 36
3.2 odd 2 54.3.f.a.5.6 36
12.11 even 2 432.3.bc.c.113.2 36
27.4 even 9 1458.3.b.c.1457.11 36
27.11 odd 18 inner 162.3.f.a.35.2 36
27.16 even 9 54.3.f.a.11.6 yes 36
27.23 odd 18 1458.3.b.c.1457.26 36
108.43 odd 18 432.3.bc.c.65.2 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.3.f.a.5.6 36 3.2 odd 2
54.3.f.a.11.6 yes 36 27.16 even 9
162.3.f.a.35.2 36 27.11 odd 18 inner
162.3.f.a.125.2 36 1.1 even 1 trivial
432.3.bc.c.65.2 36 108.43 odd 18
432.3.bc.c.113.2 36 12.11 even 2
1458.3.b.c.1457.11 36 27.4 even 9
1458.3.b.c.1457.26 36 27.23 odd 18