Properties

Label 162.3.f.a.71.1
Level $162$
Weight $3$
Character 162.71
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 71.1
Character \(\chi\) \(=\) 162.71
Dual form 162.3.f.a.89.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.39273 + 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} +(-1.85971 + 2.21631i) q^{5} +(2.17427 + 0.791369i) q^{7} +(-2.44949 + 1.41421i) q^{8} +O(q^{10})\) \(q+(-1.39273 + 0.245576i) q^{2} +(1.87939 - 0.684040i) q^{4} +(-1.85971 + 2.21631i) q^{5} +(2.17427 + 0.791369i) q^{7} +(-2.44949 + 1.41421i) q^{8} +(2.04580 - 3.54342i) q^{10} +(0.401092 + 0.478003i) q^{11} +(-4.06850 + 23.0736i) q^{13} +(-3.22251 - 0.568215i) q^{14} +(3.06418 - 2.57115i) q^{16} +(-2.71755 - 1.56898i) q^{17} +(2.04119 + 3.53544i) q^{19} +(-1.97906 + 5.43742i) q^{20} +(-0.675999 - 0.567230i) q^{22} +(15.5068 + 42.6045i) q^{23} +(2.88767 + 16.3768i) q^{25} -33.1344i q^{26} +4.62762 q^{28} +(-19.6570 + 3.46606i) q^{29} +(-42.6238 + 15.5138i) q^{31} +(-3.63616 + 4.33340i) q^{32} +(4.17011 + 1.51780i) q^{34} +(-5.79743 + 3.34715i) q^{35} +(18.7730 - 32.5159i) q^{37} +(-3.71104 - 4.42264i) q^{38} +(1.42100 - 8.05886i) q^{40} +(45.6993 + 8.05802i) q^{41} +(46.3885 - 38.9246i) q^{43} +(1.08078 + 0.623989i) q^{44} +(-32.0594 - 55.5285i) q^{46} +(-1.06082 + 2.91457i) q^{47} +(-33.4350 - 28.0553i) q^{49} +(-8.04348 - 22.0993i) q^{50} +(8.13700 + 46.1472i) q^{52} -79.9023i q^{53} -1.80532 q^{55} +(-6.44501 + 1.13643i) q^{56} +(26.5257 - 9.65457i) q^{58} +(41.9763 - 50.0254i) q^{59} +(-33.1902 - 12.0803i) q^{61} +(55.5536 - 32.0739i) q^{62} +(4.00000 - 6.92820i) q^{64} +(-43.5721 - 51.9272i) q^{65} +(-4.92896 + 27.9535i) q^{67} +(-6.18056 - 1.08980i) q^{68} +(7.25227 - 6.08537i) q^{70} +(70.7261 + 40.8337i) q^{71} +(-12.6048 - 21.8321i) q^{73} +(-18.1606 + 49.8960i) q^{74} +(6.25456 + 5.24820i) q^{76} +(0.493805 + 1.35672i) q^{77} +(11.5555 + 65.5347i) q^{79} +11.5728i q^{80} -65.6256 q^{82} +(-49.1681 + 8.66967i) q^{83} +(8.53120 - 3.10510i) q^{85} +(-55.0476 + 65.6032i) q^{86} +(-1.65847 - 0.603634i) q^{88} +(-111.133 + 64.1626i) q^{89} +(-27.1057 + 46.9485i) q^{91} +(58.2864 + 69.4631i) q^{92} +(0.761683 - 4.31972i) q^{94} +(-11.6317 - 2.05097i) q^{95} +(107.970 - 90.5977i) q^{97} +(53.4556 + 30.8626i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 18 q^{5}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).

\(n\) \(83\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.39273 + 0.245576i −0.696364 + 0.122788i
\(3\) 0 0
\(4\) 1.87939 0.684040i 0.469846 0.171010i
\(5\) −1.85971 + 2.21631i −0.371942 + 0.443263i −0.919254 0.393666i \(-0.871207\pi\)
0.547312 + 0.836929i \(0.315651\pi\)
\(6\) 0 0
\(7\) 2.17427 + 0.791369i 0.310610 + 0.113053i 0.492622 0.870244i \(-0.336039\pi\)
−0.182012 + 0.983296i \(0.558261\pi\)
\(8\) −2.44949 + 1.41421i −0.306186 + 0.176777i
\(9\) 0 0
\(10\) 2.04580 3.54342i 0.204580 0.354342i
\(11\) 0.401092 + 0.478003i 0.0364629 + 0.0434548i 0.783968 0.620802i \(-0.213193\pi\)
−0.747505 + 0.664256i \(0.768748\pi\)
\(12\) 0 0
\(13\) −4.06850 + 23.0736i −0.312961 + 1.77489i 0.270469 + 0.962729i \(0.412821\pi\)
−0.583430 + 0.812163i \(0.698290\pi\)
\(14\) −3.22251 0.568215i −0.230179 0.0405868i
\(15\) 0 0
\(16\) 3.06418 2.57115i 0.191511 0.160697i
\(17\) −2.71755 1.56898i −0.159856 0.0922928i 0.417938 0.908476i \(-0.362753\pi\)
−0.577794 + 0.816183i \(0.696086\pi\)
\(18\) 0 0
\(19\) 2.04119 + 3.53544i 0.107431 + 0.186076i 0.914729 0.404068i \(-0.132404\pi\)
−0.807298 + 0.590144i \(0.799071\pi\)
\(20\) −1.97906 + 5.43742i −0.0989530 + 0.271871i
\(21\) 0 0
\(22\) −0.675999 0.567230i −0.0307272 0.0257832i
\(23\) 15.5068 + 42.6045i 0.674208 + 1.85237i 0.495857 + 0.868404i \(0.334854\pi\)
0.178351 + 0.983967i \(0.442924\pi\)
\(24\) 0 0
\(25\) 2.88767 + 16.3768i 0.115507 + 0.655072i
\(26\) 33.1344i 1.27440i
\(27\) 0 0
\(28\) 4.62762 0.165272
\(29\) −19.6570 + 3.46606i −0.677828 + 0.119519i −0.501955 0.864894i \(-0.667386\pi\)
−0.175873 + 0.984413i \(0.556275\pi\)
\(30\) 0 0
\(31\) −42.6238 + 15.5138i −1.37496 + 0.500445i −0.920647 0.390395i \(-0.872338\pi\)
−0.454315 + 0.890841i \(0.650116\pi\)
\(32\) −3.63616 + 4.33340i −0.113630 + 0.135419i
\(33\) 0 0
\(34\) 4.17011 + 1.51780i 0.122650 + 0.0446411i
\(35\) −5.79743 + 3.34715i −0.165641 + 0.0956328i
\(36\) 0 0
\(37\) 18.7730 32.5159i 0.507379 0.878807i −0.492584 0.870265i \(-0.663948\pi\)
0.999964 0.00854213i \(-0.00271908\pi\)
\(38\) −3.71104 4.42264i −0.0976588 0.116385i
\(39\) 0 0
\(40\) 1.42100 8.05886i 0.0355249 0.201472i
\(41\) 45.6993 + 8.05802i 1.11462 + 0.196537i 0.700477 0.713675i \(-0.252971\pi\)
0.414141 + 0.910213i \(0.364082\pi\)
\(42\) 0 0
\(43\) 46.3885 38.9246i 1.07880 0.905222i 0.0829811 0.996551i \(-0.473556\pi\)
0.995821 + 0.0913289i \(0.0291115\pi\)
\(44\) 1.08078 + 0.623989i 0.0245632 + 0.0141816i
\(45\) 0 0
\(46\) −32.0594 55.5285i −0.696943 1.20714i
\(47\) −1.06082 + 2.91457i −0.0225706 + 0.0620122i −0.950466 0.310828i \(-0.899394\pi\)
0.927896 + 0.372840i \(0.121616\pi\)
\(48\) 0 0
\(49\) −33.4350 28.0553i −0.682347 0.572557i
\(50\) −8.04348 22.0993i −0.160870 0.441986i
\(51\) 0 0
\(52\) 8.13700 + 46.1472i 0.156481 + 0.887446i
\(53\) 79.9023i 1.50759i −0.657109 0.753795i \(-0.728221\pi\)
0.657109 0.753795i \(-0.271779\pi\)
\(54\) 0 0
\(55\) −1.80532 −0.0328240
\(56\) −6.44501 + 1.13643i −0.115090 + 0.0202934i
\(57\) 0 0
\(58\) 26.5257 9.65457i 0.457340 0.166458i
\(59\) 41.9763 50.0254i 0.711463 0.847888i −0.282309 0.959323i \(-0.591100\pi\)
0.993772 + 0.111435i \(0.0355448\pi\)
\(60\) 0 0
\(61\) −33.1902 12.0803i −0.544102 0.198037i 0.0553219 0.998469i \(-0.482382\pi\)
−0.599424 + 0.800432i \(0.704604\pi\)
\(62\) 55.5536 32.0739i 0.896026 0.517321i
\(63\) 0 0
\(64\) 4.00000 6.92820i 0.0625000 0.108253i
\(65\) −43.5721 51.9272i −0.670340 0.798881i
\(66\) 0 0
\(67\) −4.92896 + 27.9535i −0.0735666 + 0.417217i 0.925676 + 0.378316i \(0.123497\pi\)
−0.999243 + 0.0389009i \(0.987614\pi\)
\(68\) −6.18056 1.08980i −0.0908907 0.0160265i
\(69\) 0 0
\(70\) 7.25227 6.08537i 0.103604 0.0869339i
\(71\) 70.7261 + 40.8337i 0.996142 + 0.575123i 0.907105 0.420905i \(-0.138287\pi\)
0.0890378 + 0.996028i \(0.471621\pi\)
\(72\) 0 0
\(73\) −12.6048 21.8321i −0.172668 0.299070i 0.766684 0.642025i \(-0.221905\pi\)
−0.939352 + 0.342955i \(0.888572\pi\)
\(74\) −18.1606 + 49.8960i −0.245414 + 0.674270i
\(75\) 0 0
\(76\) 6.25456 + 5.24820i 0.0822968 + 0.0690552i
\(77\) 0.493805 + 1.35672i 0.00641306 + 0.0176197i
\(78\) 0 0
\(79\) 11.5555 + 65.5347i 0.146273 + 0.829553i 0.966337 + 0.257281i \(0.0828267\pi\)
−0.820064 + 0.572272i \(0.806062\pi\)
\(80\) 11.5728i 0.144660i
\(81\) 0 0
\(82\) −65.6256 −0.800312
\(83\) −49.1681 + 8.66967i −0.592387 + 0.104454i −0.461802 0.886983i \(-0.652797\pi\)
−0.130585 + 0.991437i \(0.541686\pi\)
\(84\) 0 0
\(85\) 8.53120 3.10510i 0.100367 0.0365306i
\(86\) −55.0476 + 65.6032i −0.640089 + 0.762828i
\(87\) 0 0
\(88\) −1.65847 0.603634i −0.0188463 0.00685947i
\(89\) −111.133 + 64.1626i −1.24868 + 0.720928i −0.970847 0.239700i \(-0.922951\pi\)
−0.277838 + 0.960628i \(0.589618\pi\)
\(90\) 0 0
\(91\) −27.1057 + 46.9485i −0.297865 + 0.515918i
\(92\) 58.2864 + 69.4631i 0.633548 + 0.755033i
\(93\) 0 0
\(94\) 0.761683 4.31972i 0.00810301 0.0459544i
\(95\) −11.6317 2.05097i −0.122438 0.0215892i
\(96\) 0 0
\(97\) 107.970 90.5977i 1.11309 0.933997i 0.114859 0.993382i \(-0.463358\pi\)
0.998235 + 0.0593849i \(0.0189139\pi\)
\(98\) 53.4556 + 30.8626i 0.545465 + 0.314924i
\(99\) 0 0
\(100\) 16.6294 + 28.8030i 0.166294 + 0.288030i
\(101\) 13.5909 37.3408i 0.134564 0.369710i −0.854049 0.520192i \(-0.825860\pi\)
0.988613 + 0.150482i \(0.0480825\pi\)
\(102\) 0 0
\(103\) 35.6457 + 29.9103i 0.346074 + 0.290391i 0.799211 0.601050i \(-0.205251\pi\)
−0.453137 + 0.891441i \(0.649695\pi\)
\(104\) −22.6653 62.2723i −0.217935 0.598772i
\(105\) 0 0
\(106\) 19.6221 + 111.282i 0.185114 + 1.04983i
\(107\) 107.937i 1.00876i 0.863482 + 0.504379i \(0.168279\pi\)
−0.863482 + 0.504379i \(0.831721\pi\)
\(108\) 0 0
\(109\) 61.3938 0.563246 0.281623 0.959525i \(-0.409127\pi\)
0.281623 + 0.959525i \(0.409127\pi\)
\(110\) 2.51432 0.443343i 0.0228575 0.00403039i
\(111\) 0 0
\(112\) 8.69707 3.16548i 0.0776525 0.0282632i
\(113\) −26.3026 + 31.3463i −0.232767 + 0.277401i −0.869767 0.493463i \(-0.835731\pi\)
0.637000 + 0.770864i \(0.280175\pi\)
\(114\) 0 0
\(115\) −123.263 44.8641i −1.07185 0.390123i
\(116\) −34.5722 + 19.9603i −0.298036 + 0.172071i
\(117\) 0 0
\(118\) −46.1766 + 79.9801i −0.391327 + 0.677798i
\(119\) −4.66704 5.56196i −0.0392188 0.0467392i
\(120\) 0 0
\(121\) 20.9438 118.778i 0.173089 0.981639i
\(122\) 49.1916 + 8.67381i 0.403210 + 0.0710968i
\(123\) 0 0
\(124\) −69.4945 + 58.3128i −0.560440 + 0.470265i
\(125\) −104.306 60.2210i −0.834447 0.481768i
\(126\) 0 0
\(127\) 106.842 + 185.055i 0.841272 + 1.45713i 0.888820 + 0.458256i \(0.151526\pi\)
−0.0475484 + 0.998869i \(0.515141\pi\)
\(128\) −3.86952 + 10.6314i −0.0302306 + 0.0830579i
\(129\) 0 0
\(130\) 73.4362 + 61.6203i 0.564894 + 0.474002i
\(131\) 5.01372 + 13.7751i 0.0382727 + 0.105153i 0.957357 0.288908i \(-0.0932921\pi\)
−0.919084 + 0.394061i \(0.871070\pi\)
\(132\) 0 0
\(133\) 1.64025 + 9.30232i 0.0123327 + 0.0699423i
\(134\) 40.1421i 0.299568i
\(135\) 0 0
\(136\) 8.87548 0.0652609
\(137\) 133.156 23.4789i 0.971938 0.171379i 0.334936 0.942241i \(-0.391285\pi\)
0.637002 + 0.770862i \(0.280174\pi\)
\(138\) 0 0
\(139\) −70.1461 + 25.5311i −0.504648 + 0.183677i −0.581783 0.813344i \(-0.697645\pi\)
0.0771354 + 0.997021i \(0.475423\pi\)
\(140\) −8.60602 + 10.2563i −0.0614716 + 0.0732590i
\(141\) 0 0
\(142\) −108.530 39.5017i −0.764296 0.278181i
\(143\) −12.6611 + 7.30989i −0.0885391 + 0.0511181i
\(144\) 0 0
\(145\) 28.8744 50.0120i 0.199134 0.344910i
\(146\) 22.9164 + 27.3107i 0.156962 + 0.187060i
\(147\) 0 0
\(148\) 13.0396 73.9513i 0.0881055 0.499671i
\(149\) −216.356 38.1494i −1.45205 0.256036i −0.608702 0.793399i \(-0.708309\pi\)
−0.843351 + 0.537363i \(0.819420\pi\)
\(150\) 0 0
\(151\) 92.8259 77.8901i 0.614741 0.515829i −0.281405 0.959589i \(-0.590800\pi\)
0.896145 + 0.443760i \(0.146356\pi\)
\(152\) −9.99973 5.77335i −0.0657877 0.0379825i
\(153\) 0 0
\(154\) −1.02091 1.76828i −0.00662931 0.0114823i
\(155\) 44.8844 123.319i 0.289577 0.795606i
\(156\) 0 0
\(157\) 53.3237 + 44.7439i 0.339641 + 0.284993i 0.796615 0.604487i \(-0.206622\pi\)
−0.456973 + 0.889480i \(0.651066\pi\)
\(158\) −32.1874 88.4343i −0.203718 0.559711i
\(159\) 0 0
\(160\) −2.84199 16.1177i −0.0177624 0.100736i
\(161\) 104.905i 0.651586i
\(162\) 0 0
\(163\) 67.8167 0.416054 0.208027 0.978123i \(-0.433296\pi\)
0.208027 + 0.978123i \(0.433296\pi\)
\(164\) 91.3987 16.1160i 0.557309 0.0982686i
\(165\) 0 0
\(166\) 66.3488 24.1490i 0.399692 0.145476i
\(167\) 150.446 179.295i 0.900875 1.07362i −0.0960587 0.995376i \(-0.530624\pi\)
0.996934 0.0782459i \(-0.0249319\pi\)
\(168\) 0 0
\(169\) −357.030 129.948i −2.11260 0.768925i
\(170\) −11.1191 + 6.41962i −0.0654065 + 0.0377625i
\(171\) 0 0
\(172\) 60.5559 104.886i 0.352069 0.609801i
\(173\) 34.4431 + 41.0477i 0.199093 + 0.237270i 0.856349 0.516398i \(-0.172727\pi\)
−0.657256 + 0.753667i \(0.728283\pi\)
\(174\) 0 0
\(175\) −6.68152 + 37.8928i −0.0381801 + 0.216530i
\(176\) 2.45804 + 0.433418i 0.0139661 + 0.00246260i
\(177\) 0 0
\(178\) 139.021 116.653i 0.781018 0.655352i
\(179\) 8.59027 + 4.95959i 0.0479903 + 0.0277072i 0.523803 0.851839i \(-0.324513\pi\)
−0.475813 + 0.879547i \(0.657846\pi\)
\(180\) 0 0
\(181\) −54.1558 93.8006i −0.299203 0.518235i 0.676751 0.736212i \(-0.263388\pi\)
−0.975954 + 0.217977i \(0.930054\pi\)
\(182\) 26.2215 72.0430i 0.144074 0.395841i
\(183\) 0 0
\(184\) −98.2356 82.4295i −0.533889 0.447986i
\(185\) 37.1530 + 102.077i 0.200827 + 0.551767i
\(186\) 0 0
\(187\) −0.340012 1.92830i −0.00181824 0.0103118i
\(188\) 6.20324i 0.0329960i
\(189\) 0 0
\(190\) 16.7034 0.0879127
\(191\) 153.674 27.0970i 0.804578 0.141869i 0.243790 0.969828i \(-0.421609\pi\)
0.560788 + 0.827959i \(0.310498\pi\)
\(192\) 0 0
\(193\) 247.481 90.0756i 1.28228 0.466713i 0.391097 0.920350i \(-0.372096\pi\)
0.891187 + 0.453636i \(0.149874\pi\)
\(194\) −128.124 + 152.693i −0.660436 + 0.787076i
\(195\) 0 0
\(196\) −82.0282 29.8558i −0.418511 0.152326i
\(197\) 124.915 72.1196i 0.634085 0.366089i −0.148247 0.988950i \(-0.547363\pi\)
0.782332 + 0.622861i \(0.214030\pi\)
\(198\) 0 0
\(199\) −133.137 + 230.600i −0.669030 + 1.15879i 0.309146 + 0.951015i \(0.399957\pi\)
−0.978176 + 0.207779i \(0.933376\pi\)
\(200\) −30.2336 36.0310i −0.151168 0.180155i
\(201\) 0 0
\(202\) −9.75849 + 55.3431i −0.0483093 + 0.273976i
\(203\) −45.4826 8.01980i −0.224052 0.0395064i
\(204\) 0 0
\(205\) −102.847 + 86.2985i −0.501690 + 0.420968i
\(206\) −56.9900 32.9032i −0.276650 0.159724i
\(207\) 0 0
\(208\) 46.8591 + 81.1623i 0.225284 + 0.390203i
\(209\) −0.871247 + 2.39373i −0.00416864 + 0.0114533i
\(210\) 0 0
\(211\) −156.280 131.134i −0.740663 0.621490i 0.192352 0.981326i \(-0.438388\pi\)
−0.933016 + 0.359836i \(0.882833\pi\)
\(212\) −54.6564 150.167i −0.257813 0.708336i
\(213\) 0 0
\(214\) −26.5067 150.327i −0.123863 0.702463i
\(215\) 175.200i 0.814883i
\(216\) 0 0
\(217\) −104.953 −0.483654
\(218\) −85.5049 + 15.0768i −0.392224 + 0.0691597i
\(219\) 0 0
\(220\) −3.39289 + 1.23491i −0.0154222 + 0.00561323i
\(221\) 47.2583 56.3202i 0.213838 0.254843i
\(222\) 0 0
\(223\) 16.9442 + 6.16717i 0.0759828 + 0.0276555i 0.379732 0.925097i \(-0.376016\pi\)
−0.303749 + 0.952752i \(0.598238\pi\)
\(224\) −11.3353 + 6.54444i −0.0506040 + 0.0292162i
\(225\) 0 0
\(226\) 28.9346 50.1161i 0.128029 0.221753i
\(227\) 69.1464 + 82.4054i 0.304610 + 0.363020i 0.896535 0.442973i \(-0.146076\pi\)
−0.591925 + 0.805993i \(0.701632\pi\)
\(228\) 0 0
\(229\) −24.1988 + 137.238i −0.105672 + 0.599294i 0.885278 + 0.465062i \(0.153968\pi\)
−0.990950 + 0.134232i \(0.957143\pi\)
\(230\) 182.690 + 32.2131i 0.794303 + 0.140057i
\(231\) 0 0
\(232\) 43.2479 36.2893i 0.186413 0.156419i
\(233\) −56.5488 32.6485i −0.242699 0.140122i 0.373718 0.927542i \(-0.378083\pi\)
−0.616416 + 0.787420i \(0.711416\pi\)
\(234\) 0 0
\(235\) −4.48680 7.77136i −0.0190927 0.0330696i
\(236\) 44.6702 122.730i 0.189281 0.520044i
\(237\) 0 0
\(238\) 7.86580 + 6.60019i 0.0330496 + 0.0277319i
\(239\) 27.3384 + 75.1116i 0.114387 + 0.314274i 0.983654 0.180067i \(-0.0576315\pi\)
−0.869268 + 0.494341i \(0.835409\pi\)
\(240\) 0 0
\(241\) 42.1583 + 239.092i 0.174931 + 0.992082i 0.938224 + 0.346029i \(0.112470\pi\)
−0.763293 + 0.646053i \(0.776419\pi\)
\(242\) 170.569i 0.704831i
\(243\) 0 0
\(244\) −70.6406 −0.289511
\(245\) 124.359 21.9278i 0.507587 0.0895012i
\(246\) 0 0
\(247\) −89.8798 + 32.7136i −0.363886 + 0.132444i
\(248\) 82.4668 98.2801i 0.332528 0.396291i
\(249\) 0 0
\(250\) 160.058 + 58.2565i 0.640234 + 0.233026i
\(251\) 110.677 63.8992i 0.440943 0.254579i −0.263055 0.964781i \(-0.584730\pi\)
0.703998 + 0.710202i \(0.251397\pi\)
\(252\) 0 0
\(253\) −14.1455 + 24.5006i −0.0559109 + 0.0968405i
\(254\) −194.246 231.494i −0.764749 0.911392i
\(255\) 0 0
\(256\) 2.77837 15.7569i 0.0108530 0.0615505i
\(257\) −305.230 53.8203i −1.18767 0.209418i −0.455306 0.890335i \(-0.650470\pi\)
−0.732360 + 0.680918i \(0.761581\pi\)
\(258\) 0 0
\(259\) 66.5497 55.8418i 0.256949 0.215605i
\(260\) −117.409 67.7862i −0.451574 0.260716i
\(261\) 0 0
\(262\) −10.3656 17.9537i −0.0395633 0.0685256i
\(263\) −128.767 + 353.785i −0.489609 + 1.34519i 0.411427 + 0.911443i \(0.365031\pi\)
−0.901035 + 0.433746i \(0.857192\pi\)
\(264\) 0 0
\(265\) 177.089 + 148.595i 0.668259 + 0.560736i
\(266\) −4.56885 12.5528i −0.0171761 0.0471910i
\(267\) 0 0
\(268\) 9.85793 + 55.9071i 0.0367833 + 0.208609i
\(269\) 265.016i 0.985188i −0.870259 0.492594i \(-0.836049\pi\)
0.870259 0.492594i \(-0.163951\pi\)
\(270\) 0 0
\(271\) 32.4939 0.119904 0.0599518 0.998201i \(-0.480905\pi\)
0.0599518 + 0.998201i \(0.480905\pi\)
\(272\) −12.3611 + 2.17960i −0.0454453 + 0.00801324i
\(273\) 0 0
\(274\) −179.684 + 65.3995i −0.655780 + 0.238684i
\(275\) −6.66994 + 7.94892i −0.0242543 + 0.0289052i
\(276\) 0 0
\(277\) 439.202 + 159.857i 1.58557 + 0.577099i 0.976405 0.215946i \(-0.0692836\pi\)
0.609162 + 0.793046i \(0.291506\pi\)
\(278\) 91.4246 52.7840i 0.328866 0.189871i
\(279\) 0 0
\(280\) 9.46716 16.3976i 0.0338113 0.0585629i
\(281\) 77.3744 + 92.2112i 0.275354 + 0.328154i 0.885943 0.463793i \(-0.153512\pi\)
−0.610590 + 0.791947i \(0.709068\pi\)
\(282\) 0 0
\(283\) 55.5870 315.249i 0.196420 1.11396i −0.713961 0.700185i \(-0.753101\pi\)
0.910382 0.413770i \(-0.135788\pi\)
\(284\) 160.854 + 28.3628i 0.566386 + 0.0998691i
\(285\) 0 0
\(286\) 15.8383 13.2899i 0.0553788 0.0464683i
\(287\) 92.9857 + 53.6853i 0.323992 + 0.187057i
\(288\) 0 0
\(289\) −139.577 241.754i −0.482964 0.836518i
\(290\) −27.9325 + 76.7440i −0.0963191 + 0.264634i
\(291\) 0 0
\(292\) −38.6232 32.4087i −0.132271 0.110989i
\(293\) 128.007 + 351.696i 0.436883 + 1.20033i 0.941509 + 0.336988i \(0.109408\pi\)
−0.504626 + 0.863338i \(0.668370\pi\)
\(294\) 0 0
\(295\) 32.8083 + 186.065i 0.111215 + 0.630730i
\(296\) 106.196i 0.358771i
\(297\) 0 0
\(298\) 310.693 1.04260
\(299\) −1046.13 + 184.461i −3.49876 + 0.616926i
\(300\) 0 0
\(301\) 131.665 47.9220i 0.437424 0.159209i
\(302\) −110.153 + 131.276i −0.364746 + 0.434687i
\(303\) 0 0
\(304\) 15.3447 + 5.58501i 0.0504760 + 0.0183718i
\(305\) 88.4978 51.0942i 0.290157 0.167522i
\(306\) 0 0
\(307\) 164.444 284.826i 0.535650 0.927773i −0.463482 0.886106i \(-0.653400\pi\)
0.999132 0.0416662i \(-0.0132666\pi\)
\(308\) 1.85610 + 2.21202i 0.00602630 + 0.00718187i
\(309\) 0 0
\(310\) −32.2277 + 182.772i −0.103960 + 0.589588i
\(311\) 115.437 + 20.3546i 0.371180 + 0.0654490i 0.356127 0.934438i \(-0.384097\pi\)
0.0150531 + 0.999887i \(0.495208\pi\)
\(312\) 0 0
\(313\) −286.451 + 240.361i −0.915178 + 0.767926i −0.973097 0.230396i \(-0.925998\pi\)
0.0579189 + 0.998321i \(0.481554\pi\)
\(314\) −85.2535 49.2211i −0.271508 0.156755i
\(315\) 0 0
\(316\) 66.5457 + 115.260i 0.210588 + 0.364748i
\(317\) −63.7546 + 175.164i −0.201118 + 0.552568i −0.998718 0.0506189i \(-0.983881\pi\)
0.797600 + 0.603187i \(0.206103\pi\)
\(318\) 0 0
\(319\) −9.54107 8.00590i −0.0299093 0.0250969i
\(320\) 7.91624 + 21.7497i 0.0247383 + 0.0679678i
\(321\) 0 0
\(322\) −25.7622 146.105i −0.0800068 0.453741i
\(323\) 12.8103i 0.0396604i
\(324\) 0 0
\(325\) −389.620 −1.19883
\(326\) −94.4503 + 16.6541i −0.289725 + 0.0510863i
\(327\) 0 0
\(328\) −123.336 + 44.8906i −0.376024 + 0.136861i
\(329\) −4.61300 + 5.49756i −0.0140213 + 0.0167099i
\(330\) 0 0
\(331\) 437.065 + 159.079i 1.32044 + 0.480600i 0.903598 0.428381i \(-0.140916\pi\)
0.416839 + 0.908980i \(0.363138\pi\)
\(332\) −86.4755 + 49.9266i −0.260468 + 0.150381i
\(333\) 0 0
\(334\) −165.500 + 286.655i −0.495510 + 0.858248i
\(335\) −52.7874 62.9096i −0.157574 0.187790i
\(336\) 0 0
\(337\) −77.3110 + 438.452i −0.229409 + 1.30105i 0.624664 + 0.780893i \(0.285236\pi\)
−0.854074 + 0.520152i \(0.825875\pi\)
\(338\) 529.158 + 93.3049i 1.56556 + 0.276050i
\(339\) 0 0
\(340\) 13.9094 11.6714i 0.0409100 0.0343275i
\(341\) −24.5117 14.1519i −0.0718819 0.0415011i
\(342\) 0 0
\(343\) −107.183 185.646i −0.312487 0.541243i
\(344\) −58.5805 + 160.949i −0.170292 + 0.467874i
\(345\) 0 0
\(346\) −58.0502 48.7099i −0.167775 0.140780i
\(347\) −165.942 455.923i −0.478220 1.31390i −0.911003 0.412401i \(-0.864690\pi\)
0.432782 0.901498i \(-0.357532\pi\)
\(348\) 0 0
\(349\) 41.3173 + 234.322i 0.118388 + 0.671409i 0.985017 + 0.172457i \(0.0551706\pi\)
−0.866629 + 0.498952i \(0.833718\pi\)
\(350\) 54.4152i 0.155472i
\(351\) 0 0
\(352\) −3.52981 −0.0100279
\(353\) 500.675 88.2825i 1.41834 0.250092i 0.588684 0.808363i \(-0.299646\pi\)
0.829659 + 0.558271i \(0.188535\pi\)
\(354\) 0 0
\(355\) −222.030 + 80.8124i −0.625438 + 0.227641i
\(356\) −164.972 + 196.606i −0.463404 + 0.552263i
\(357\) 0 0
\(358\) −13.1819 4.79781i −0.0368209 0.0134017i
\(359\) 439.887 253.969i 1.22531 0.707435i 0.259267 0.965806i \(-0.416519\pi\)
0.966046 + 0.258371i \(0.0831857\pi\)
\(360\) 0 0
\(361\) 172.167 298.202i 0.476917 0.826045i
\(362\) 98.4595 + 117.339i 0.271987 + 0.324142i
\(363\) 0 0
\(364\) −18.8274 + 106.776i −0.0517238 + 0.293340i
\(365\) 71.8279 + 12.6652i 0.196789 + 0.0346992i
\(366\) 0 0
\(367\) 70.1493 58.8623i 0.191143 0.160388i −0.542194 0.840253i \(-0.682406\pi\)
0.733337 + 0.679866i \(0.237962\pi\)
\(368\) 157.058 + 90.6776i 0.426789 + 0.246407i
\(369\) 0 0
\(370\) −76.8116 133.042i −0.207599 0.359572i
\(371\) 63.2322 173.729i 0.170437 0.468273i
\(372\) 0 0
\(373\) −175.435 147.207i −0.470335 0.394658i 0.376582 0.926383i \(-0.377099\pi\)
−0.846917 + 0.531725i \(0.821544\pi\)
\(374\) 0.947088 + 2.60210i 0.00253232 + 0.00695749i
\(375\) 0 0
\(376\) −1.52337 8.63943i −0.00405150 0.0229772i
\(377\) 467.660i 1.24048i
\(378\) 0 0
\(379\) −143.466 −0.378539 −0.189269 0.981925i \(-0.560612\pi\)
−0.189269 + 0.981925i \(0.560612\pi\)
\(380\) −23.2633 + 4.10195i −0.0612192 + 0.0107946i
\(381\) 0 0
\(382\) −207.372 + 75.4774i −0.542860 + 0.197585i
\(383\) 101.565 121.040i 0.265183 0.316032i −0.616979 0.786980i \(-0.711643\pi\)
0.882161 + 0.470948i \(0.156088\pi\)
\(384\) 0 0
\(385\) −3.92525 1.42867i −0.0101955 0.00371084i
\(386\) −322.553 + 186.226i −0.835630 + 0.482451i
\(387\) 0 0
\(388\) 140.945 244.124i 0.363260 0.629185i
\(389\) −141.000 168.037i −0.362468 0.431972i 0.553732 0.832695i \(-0.313203\pi\)
−0.916199 + 0.400723i \(0.868759\pi\)
\(390\) 0 0
\(391\) 24.7051 140.110i 0.0631844 0.358337i
\(392\) 121.575 + 21.4369i 0.310140 + 0.0546860i
\(393\) 0 0
\(394\) −156.262 + 131.119i −0.396603 + 0.332789i
\(395\) −166.735 96.2647i −0.422115 0.243708i
\(396\) 0 0
\(397\) −39.9845 69.2553i −0.100717 0.174447i 0.811263 0.584681i \(-0.198780\pi\)
−0.911980 + 0.410234i \(0.865447\pi\)
\(398\) 128.794 353.858i 0.323603 0.889091i
\(399\) 0 0
\(400\) 50.9555 + 42.7568i 0.127389 + 0.106892i
\(401\) 204.847 + 562.811i 0.510839 + 1.40352i 0.880364 + 0.474299i \(0.157298\pi\)
−0.369525 + 0.929221i \(0.620479\pi\)
\(402\) 0 0
\(403\) −184.544 1046.60i −0.457927 2.59703i
\(404\) 79.4744i 0.196719i
\(405\) 0 0
\(406\) 65.3143 0.160873
\(407\) 23.0724 4.06829i 0.0566890 0.00999579i
\(408\) 0 0
\(409\) 88.1001 32.0658i 0.215404 0.0784005i −0.232064 0.972700i \(-0.574548\pi\)
0.447468 + 0.894300i \(0.352326\pi\)
\(410\) 122.045 145.447i 0.297670 0.354749i
\(411\) 0 0
\(412\) 87.4518 + 31.8298i 0.212262 + 0.0772569i
\(413\) 130.856 75.5499i 0.316843 0.182930i
\(414\) 0 0
\(415\) 72.2237 125.095i 0.174033 0.301434i
\(416\) −85.1935 101.530i −0.204792 0.244062i
\(417\) 0 0
\(418\) 0.625568 3.54777i 0.00149657 0.00848750i
\(419\) −473.542 83.4983i −1.13017 0.199280i −0.422870 0.906191i \(-0.638977\pi\)
−0.707303 + 0.706911i \(0.750088\pi\)
\(420\) 0 0
\(421\) −160.713 + 134.854i −0.381742 + 0.320319i −0.813386 0.581725i \(-0.802378\pi\)
0.431644 + 0.902044i \(0.357934\pi\)
\(422\) 249.859 + 144.256i 0.592083 + 0.341839i
\(423\) 0 0
\(424\) 112.999 + 195.720i 0.266507 + 0.461604i
\(425\) 17.8474 49.0354i 0.0419940 0.115377i
\(426\) 0 0
\(427\) −62.6046 52.5315i −0.146615 0.123024i
\(428\) 73.8333 + 202.855i 0.172508 + 0.473961i
\(429\) 0 0
\(430\) −43.0248 244.006i −0.100058 0.567455i
\(431\) 323.120i 0.749698i −0.927086 0.374849i \(-0.877695\pi\)
0.927086 0.374849i \(-0.122305\pi\)
\(432\) 0 0
\(433\) 382.089 0.882422 0.441211 0.897403i \(-0.354549\pi\)
0.441211 + 0.897403i \(0.354549\pi\)
\(434\) 146.171 25.7739i 0.336799 0.0593868i
\(435\) 0 0
\(436\) 115.383 41.9958i 0.264639 0.0963207i
\(437\) −118.973 + 141.787i −0.272250 + 0.324456i
\(438\) 0 0
\(439\) 263.667 + 95.9670i 0.600609 + 0.218604i 0.624389 0.781114i \(-0.285348\pi\)
−0.0237804 + 0.999717i \(0.507570\pi\)
\(440\) 4.42211 2.55311i 0.0100503 0.00580252i
\(441\) 0 0
\(442\) −51.9871 + 90.0443i −0.117618 + 0.203720i
\(443\) 58.0355 + 69.1641i 0.131006 + 0.156127i 0.827559 0.561378i \(-0.189729\pi\)
−0.696554 + 0.717505i \(0.745284\pi\)
\(444\) 0 0
\(445\) 64.4703 365.629i 0.144877 0.821639i
\(446\) −25.1131 4.42812i −0.0563075 0.00992853i
\(447\) 0 0
\(448\) 14.1798 11.8983i 0.0316514 0.0265587i
\(449\) −327.853 189.286i −0.730186 0.421573i 0.0883044 0.996094i \(-0.471855\pi\)
−0.818490 + 0.574521i \(0.805188\pi\)
\(450\) 0 0
\(451\) 14.4779 + 25.0764i 0.0321017 + 0.0556019i
\(452\) −27.9907 + 76.9038i −0.0619263 + 0.170141i
\(453\) 0 0
\(454\) −116.539 97.7877i −0.256694 0.215391i
\(455\) −53.6439 147.385i −0.117899 0.323924i
\(456\) 0 0
\(457\) −69.0721 391.727i −0.151142 0.857171i −0.962228 0.272244i \(-0.912234\pi\)
0.811086 0.584927i \(-0.198877\pi\)
\(458\) 197.079i 0.430302i
\(459\) 0 0
\(460\) −262.348 −0.570321
\(461\) 395.858 69.8004i 0.858694 0.151411i 0.273070 0.961994i \(-0.411961\pi\)
0.585624 + 0.810583i \(0.300850\pi\)
\(462\) 0 0
\(463\) −179.095 + 65.1851i −0.386814 + 0.140789i −0.528104 0.849180i \(-0.677097\pi\)
0.141291 + 0.989968i \(0.454875\pi\)
\(464\) −51.3208 + 61.1618i −0.110605 + 0.131814i
\(465\) 0 0
\(466\) 86.7748 + 31.5834i 0.186212 + 0.0677756i
\(467\) −746.239 + 430.841i −1.59794 + 0.922572i −0.606058 + 0.795420i \(0.707250\pi\)
−0.991883 + 0.127151i \(0.959417\pi\)
\(468\) 0 0
\(469\) −32.8385 + 56.8779i −0.0700180 + 0.121275i
\(470\) 8.15734 + 9.72154i 0.0173561 + 0.0206841i
\(471\) 0 0
\(472\) −32.0739 + 181.900i −0.0679532 + 0.385382i
\(473\) 37.2121 + 6.56150i 0.0786726 + 0.0138721i
\(474\) 0 0
\(475\) −52.0049 + 43.6373i −0.109484 + 0.0918679i
\(476\) −12.5758 7.26063i −0.0264197 0.0152534i
\(477\) 0 0
\(478\) −56.5205 97.8964i −0.118244 0.204804i
\(479\) 162.154 445.513i 0.338525 0.930090i −0.647288 0.762245i \(-0.724097\pi\)
0.985813 0.167845i \(-0.0536808\pi\)
\(480\) 0 0
\(481\) 673.880 + 565.452i 1.40100 + 1.17558i
\(482\) −117.430 322.637i −0.243631 0.669371i
\(483\) 0 0
\(484\) −41.8876 237.557i −0.0865447 0.490819i
\(485\) 407.781i 0.840786i
\(486\) 0 0
\(487\) 118.562 0.243454 0.121727 0.992564i \(-0.461157\pi\)
0.121727 + 0.992564i \(0.461157\pi\)
\(488\) 98.3832 17.3476i 0.201605 0.0355484i
\(489\) 0 0
\(490\) −167.813 + 61.0789i −0.342475 + 0.124651i
\(491\) 251.435 299.648i 0.512087 0.610282i −0.446604 0.894732i \(-0.647367\pi\)
0.958691 + 0.284450i \(0.0918111\pi\)
\(492\) 0 0
\(493\) 58.8571 + 21.4222i 0.119386 + 0.0434528i
\(494\) 117.145 67.6334i 0.237135 0.136910i
\(495\) 0 0
\(496\) −90.7187 + 157.129i −0.182901 + 0.316793i
\(497\) 121.463 + 144.754i 0.244392 + 0.291256i
\(498\) 0 0
\(499\) 32.0248 181.622i 0.0641779 0.363971i −0.935758 0.352643i \(-0.885283\pi\)
0.999936 0.0113281i \(-0.00360592\pi\)
\(500\) −237.224 41.8291i −0.474449 0.0836581i
\(501\) 0 0
\(502\) −138.451 + 116.174i −0.275798 + 0.231422i
\(503\) 758.479 + 437.908i 1.50791 + 0.870593i 0.999958 + 0.00920825i \(0.00293112\pi\)
0.507953 + 0.861385i \(0.330402\pi\)
\(504\) 0 0
\(505\) 57.4837 + 99.5647i 0.113829 + 0.197158i
\(506\) 13.6840 37.5965i 0.0270435 0.0743014i
\(507\) 0 0
\(508\) 327.381 + 274.706i 0.644451 + 0.540759i
\(509\) −21.7815 59.8443i −0.0427928 0.117572i 0.916456 0.400136i \(-0.131037\pi\)
−0.959248 + 0.282564i \(0.908815\pi\)
\(510\) 0 0
\(511\) −10.1289 57.4438i −0.0198217 0.112415i
\(512\) 22.6274i 0.0441942i
\(513\) 0 0
\(514\) 438.320 0.852762
\(515\) −132.581 + 23.3776i −0.257439 + 0.0453935i
\(516\) 0 0
\(517\) −1.81866 + 0.661938i −0.00351772 + 0.00128034i
\(518\) −78.9722 + 94.1155i −0.152456 + 0.181690i
\(519\) 0 0
\(520\) 180.166 + 65.5749i 0.346472 + 0.126106i
\(521\) −418.613 + 241.686i −0.803479 + 0.463889i −0.844686 0.535262i \(-0.820213\pi\)
0.0412070 + 0.999151i \(0.486880\pi\)
\(522\) 0 0
\(523\) −353.459 + 612.209i −0.675830 + 1.17057i 0.300396 + 0.953815i \(0.402881\pi\)
−0.976226 + 0.216757i \(0.930452\pi\)
\(524\) 18.8454 + 22.4591i 0.0359646 + 0.0428609i
\(525\) 0 0
\(526\) 92.4567 524.348i 0.175773 0.996859i
\(527\) 140.173 + 24.7163i 0.265983 + 0.0469000i
\(528\) 0 0
\(529\) −1169.45 + 981.284i −2.21068 + 1.85498i
\(530\) −283.128 163.464i −0.534203 0.308422i
\(531\) 0 0
\(532\) 9.44583 + 16.3607i 0.0177553 + 0.0307531i
\(533\) −371.855 + 1021.66i −0.697665 + 1.91682i
\(534\) 0 0
\(535\) −239.223 200.732i −0.447145 0.375199i
\(536\) −27.4588 75.4425i −0.0512292 0.140751i
\(537\) 0 0
\(538\) 65.0814 + 369.095i 0.120969 + 0.686050i
\(539\) 27.2348i 0.0505284i
\(540\) 0 0
\(541\) −64.3040 −0.118861 −0.0594307 0.998232i \(-0.518929\pi\)
−0.0594307 + 0.998232i \(0.518929\pi\)
\(542\) −45.2552 + 7.97971i −0.0834966 + 0.0147227i
\(543\) 0 0
\(544\) 16.6804 6.07118i 0.0306626 0.0111603i
\(545\) −114.175 + 136.068i −0.209495 + 0.249666i
\(546\) 0 0
\(547\) −162.501 59.1454i −0.297076 0.108127i 0.189182 0.981942i \(-0.439416\pi\)
−0.486258 + 0.873815i \(0.661639\pi\)
\(548\) 234.190 135.210i 0.427354 0.246733i
\(549\) 0 0
\(550\) 7.33735 12.7087i 0.0133406 0.0231067i
\(551\) −52.3777 62.4213i −0.0950593 0.113287i
\(552\) 0 0
\(553\) −26.7373 + 151.635i −0.0483495 + 0.274204i
\(554\) −650.946 114.779i −1.17499 0.207183i
\(555\) 0 0
\(556\) −114.367 + 95.9655i −0.205696 + 0.172600i
\(557\) 575.226 + 332.107i 1.03272 + 0.596242i 0.917763 0.397128i \(-0.129993\pi\)
0.114958 + 0.993370i \(0.463327\pi\)
\(558\) 0 0
\(559\) 709.398 + 1228.71i 1.26905 + 2.19806i
\(560\) −9.15833 + 25.1623i −0.0163542 + 0.0449327i
\(561\) 0 0
\(562\) −130.406 109.424i −0.232040 0.194704i
\(563\) 106.367 + 292.240i 0.188929 + 0.519077i 0.997604 0.0691777i \(-0.0220376\pi\)
−0.808676 + 0.588255i \(0.799815\pi\)
\(564\) 0 0
\(565\) −20.5579 116.590i −0.0363857 0.206354i
\(566\) 452.707i 0.799837i
\(567\) 0 0
\(568\) −230.991 −0.406673
\(569\) 322.708 56.9022i 0.567150 0.100004i 0.117282 0.993099i \(-0.462582\pi\)
0.449869 + 0.893095i \(0.351471\pi\)
\(570\) 0 0
\(571\) 557.293 202.838i 0.975995 0.355233i 0.195713 0.980661i \(-0.437298\pi\)
0.780282 + 0.625428i \(0.215076\pi\)
\(572\) −18.7948 + 22.3988i −0.0328581 + 0.0391587i
\(573\) 0 0
\(574\) −142.688 51.9341i −0.248585 0.0904775i
\(575\) −652.947 + 376.979i −1.13556 + 0.655616i
\(576\) 0 0
\(577\) −87.0488 + 150.773i −0.150864 + 0.261305i −0.931546 0.363625i \(-0.881539\pi\)
0.780681 + 0.624930i \(0.214872\pi\)
\(578\) 253.761 + 302.421i 0.439033 + 0.523219i
\(579\) 0 0
\(580\) 20.0560 113.743i 0.0345793 0.196109i
\(581\) −113.766 20.0599i −0.195810 0.0345266i
\(582\) 0 0
\(583\) 38.1936 32.0482i 0.0655121 0.0549712i
\(584\) 61.7505 + 35.6516i 0.105737 + 0.0610473i
\(585\) 0 0
\(586\) −264.647 458.381i −0.451615 0.782220i
\(587\) 214.475 589.265i 0.365375 1.00386i −0.611724 0.791071i \(-0.709524\pi\)
0.977099 0.212787i \(-0.0682541\pi\)
\(588\) 0 0
\(589\) −141.851 119.027i −0.240834 0.202084i
\(590\) −91.3862 251.082i −0.154892 0.425562i
\(591\) 0 0
\(592\) −26.0792 147.903i −0.0440528 0.249836i
\(593\) 495.118i 0.834938i 0.908691 + 0.417469i \(0.137083\pi\)
−0.908691 + 0.417469i \(0.862917\pi\)
\(594\) 0 0
\(595\) 21.0064 0.0353049
\(596\) −432.712 + 76.2987i −0.726026 + 0.128018i
\(597\) 0 0
\(598\) 1411.67 513.808i 2.36066 0.859210i
\(599\) 109.105 130.026i 0.182145 0.217072i −0.667244 0.744839i \(-0.732526\pi\)
0.849389 + 0.527767i \(0.176971\pi\)
\(600\) 0 0
\(601\) 317.677 + 115.625i 0.528581 + 0.192388i 0.592505 0.805567i \(-0.298139\pi\)
−0.0639237 + 0.997955i \(0.520361\pi\)
\(602\) −171.605 + 99.0760i −0.285058 + 0.164578i
\(603\) 0 0
\(604\) 121.176 209.882i 0.200622 0.347487i
\(605\) 224.301 + 267.311i 0.370745 + 0.441837i
\(606\) 0 0
\(607\) −160.570 + 910.637i −0.264530 + 1.50023i 0.505839 + 0.862628i \(0.331183\pi\)
−0.770369 + 0.637598i \(0.779928\pi\)
\(608\) −22.7425 4.01012i −0.0374055 0.00659560i
\(609\) 0 0
\(610\) −110.706 + 92.8933i −0.181485 + 0.152284i
\(611\) −62.9337 36.3348i −0.103001 0.0594677i
\(612\) 0 0
\(613\) 56.5416 + 97.9329i 0.0922375 + 0.159760i 0.908452 0.417989i \(-0.137265\pi\)
−0.816215 + 0.577748i \(0.803931\pi\)
\(614\) −159.080 + 437.069i −0.259088 + 0.711839i
\(615\) 0 0
\(616\) −3.12826 2.62492i −0.00507835 0.00426124i
\(617\) −309.177 849.458i −0.501098 1.37675i −0.890204 0.455562i \(-0.849438\pi\)
0.389106 0.921193i \(-0.372784\pi\)
\(618\) 0 0
\(619\) −57.2390 324.618i −0.0924700 0.524424i −0.995493 0.0948320i \(-0.969769\pi\)
0.903023 0.429592i \(-0.141343\pi\)
\(620\) 262.467i 0.423333i
\(621\) 0 0
\(622\) −165.771 −0.266513
\(623\) −292.409 + 51.5596i −0.469357 + 0.0827602i
\(624\) 0 0
\(625\) −63.2168 + 23.0090i −0.101147 + 0.0368145i
\(626\) 339.921 405.103i 0.543005 0.647129i
\(627\) 0 0
\(628\) 130.822 + 47.6155i 0.208316 + 0.0758208i
\(629\) −102.033 + 58.9090i −0.162215 + 0.0936549i
\(630\) 0 0
\(631\) −291.993 + 505.746i −0.462746 + 0.801500i −0.999097 0.0424954i \(-0.986469\pi\)
0.536350 + 0.843995i \(0.319803\pi\)
\(632\) −120.985 144.185i −0.191432 0.228140i
\(633\) 0 0
\(634\) 45.7767 259.613i 0.0722030 0.409484i
\(635\) −608.834 107.354i −0.958794 0.169061i
\(636\) 0 0
\(637\) 783.367 657.323i 1.22978 1.03190i
\(638\) 15.2542 + 8.80700i 0.0239094 + 0.0138041i
\(639\) 0 0
\(640\) −16.3664 28.3474i −0.0255725 0.0442928i
\(641\) 302.004 829.750i 0.471146 1.29446i −0.445687 0.895189i \(-0.647040\pi\)
0.916832 0.399273i \(-0.130737\pi\)
\(642\) 0 0
\(643\) −488.473 409.878i −0.759679 0.637446i 0.178365 0.983964i \(-0.442919\pi\)
−0.938043 + 0.346518i \(0.887364\pi\)
\(644\) 71.7594 + 197.157i 0.111428 + 0.306145i
\(645\) 0 0
\(646\) 3.14590 + 17.8413i 0.00486981 + 0.0276181i
\(647\) 950.774i 1.46951i 0.678332 + 0.734756i \(0.262703\pi\)
−0.678332 + 0.734756i \(0.737297\pi\)
\(648\) 0 0
\(649\) 40.7487 0.0627868
\(650\) 542.635 95.6812i 0.834823 0.147202i
\(651\) 0 0
\(652\) 127.454 46.3894i 0.195481 0.0711493i
\(653\) −86.4460 + 103.022i −0.132383 + 0.157768i −0.828163 0.560487i \(-0.810614\pi\)
0.695781 + 0.718254i \(0.255059\pi\)
\(654\) 0 0
\(655\) −39.8540 14.5057i −0.0608458 0.0221461i
\(656\) 160.749 92.8086i 0.245045 0.141477i
\(657\) 0 0
\(658\) 5.07459 8.78945i 0.00771215 0.0133578i
\(659\) 46.3613 + 55.2513i 0.0703510 + 0.0838411i 0.800072 0.599904i \(-0.204795\pi\)
−0.729721 + 0.683745i \(0.760350\pi\)
\(660\) 0 0
\(661\) 118.446 671.739i 0.179192 1.01625i −0.754002 0.656872i \(-0.771879\pi\)
0.933194 0.359374i \(-0.117010\pi\)
\(662\) −647.778 114.221i −0.978517 0.172539i
\(663\) 0 0
\(664\) 108.176 90.7705i 0.162916 0.136703i
\(665\) −23.6673 13.6643i −0.0355899 0.0205478i
\(666\) 0 0
\(667\) −452.487 783.731i −0.678391 1.17501i
\(668\) 160.101 439.875i 0.239673 0.658496i
\(669\) 0 0
\(670\) 88.9676 + 74.6527i 0.132787 + 0.111422i
\(671\) −7.53795 20.7103i −0.0112339 0.0308649i
\(672\) 0 0
\(673\) −57.0789 323.710i −0.0848126 0.480996i −0.997397 0.0721075i \(-0.977028\pi\)
0.912584 0.408889i \(-0.134084\pi\)
\(674\) 629.631i 0.934170i
\(675\) 0 0
\(676\) −759.887 −1.12409
\(677\) 485.025 85.5230i 0.716433 0.126326i 0.196463 0.980511i \(-0.437054\pi\)
0.519970 + 0.854185i \(0.325943\pi\)
\(678\) 0 0
\(679\) 306.452 111.540i 0.451329 0.164270i
\(680\) −16.5058 + 19.6708i −0.0242732 + 0.0289277i
\(681\) 0 0
\(682\) 37.6136 + 13.6902i 0.0551518 + 0.0200736i
\(683\) 725.236 418.715i 1.06184 0.613053i 0.135899 0.990723i \(-0.456608\pi\)
0.925940 + 0.377669i \(0.123274\pi\)
\(684\) 0 0
\(685\) −195.594 + 338.778i −0.285538 + 0.494567i
\(686\) 194.867 + 232.233i 0.284062 + 0.338532i
\(687\) 0 0
\(688\) 42.0617 238.544i 0.0611361 0.346720i
\(689\) 1843.63 + 325.082i 2.67581 + 0.471818i
\(690\) 0 0
\(691\) −125.334 + 105.168i −0.181381 + 0.152197i −0.728958 0.684559i \(-0.759995\pi\)
0.547577 + 0.836756i \(0.315551\pi\)
\(692\) 92.8101 + 53.5839i 0.134119 + 0.0774334i
\(693\) 0 0
\(694\) 343.076 + 594.226i 0.494346 + 0.856233i
\(695\) 73.8663 202.946i 0.106283 0.292009i
\(696\) 0 0
\(697\) −111.547 93.5993i −0.160039 0.134289i
\(698\) −115.087 316.200i −0.164882 0.453009i
\(699\) 0 0
\(700\) 13.3630 + 75.7855i 0.0190900 + 0.108265i
\(701\) 730.990i 1.04278i −0.853318 0.521391i \(-0.825413\pi\)
0.853318 0.521391i \(-0.174587\pi\)
\(702\) 0 0
\(703\) 153.277 0.218033
\(704\) 4.91607 0.866836i 0.00698306 0.00123130i
\(705\) 0 0
\(706\) −675.624 + 245.907i −0.956975 + 0.348310i
\(707\) 59.1006 70.4334i 0.0835935 0.0996229i
\(708\) 0 0
\(709\) −752.159 273.764i −1.06087 0.386126i −0.248117 0.968730i \(-0.579812\pi\)
−0.812756 + 0.582604i \(0.802034\pi\)
\(710\) 289.382 167.075i 0.407581 0.235317i
\(711\) 0 0
\(712\) 181.479 314.331i 0.254887 0.441477i
\(713\) −1321.92 1575.40i −1.85402 2.20954i
\(714\) 0 0
\(715\) 7.34494 41.6552i 0.0102726 0.0582591i
\(716\) 19.5370 + 3.44490i 0.0272863 + 0.00481131i
\(717\) 0 0
\(718\) −550.275 + 461.735i −0.766400 + 0.643086i
\(719\) −103.412 59.7052i −0.143828 0.0830392i 0.426359 0.904554i \(-0.359796\pi\)
−0.570187 + 0.821515i \(0.693129\pi\)
\(720\) 0 0
\(721\) 53.8332 + 93.2418i 0.0746646 + 0.129323i
\(722\) −166.551 + 457.595i −0.230680 + 0.633788i
\(723\) 0 0
\(724\) −165.943 139.243i −0.229203 0.192324i
\(725\) −113.526 311.910i −0.156588 0.430221i
\(726\) 0 0
\(727\) −23.5632 133.634i −0.0324116 0.183815i 0.964304 0.264798i \(-0.0853052\pi\)
−0.996716 + 0.0809827i \(0.974194\pi\)
\(728\) 153.333i 0.210623i
\(729\) 0 0
\(730\) −103.147 −0.141297
\(731\) −187.135 + 32.9969i −0.255998 + 0.0451394i
\(732\) 0 0
\(733\) −706.692 + 257.215i −0.964110 + 0.350907i −0.775643 0.631172i \(-0.782574\pi\)
−0.188467 + 0.982080i \(0.560352\pi\)
\(734\) −83.2438 + 99.2061i −0.113411 + 0.135158i
\(735\) 0 0
\(736\) −241.008 87.7196i −0.327456 0.119184i
\(737\) −15.3389 + 8.85589i −0.0208126 + 0.0120161i
\(738\) 0 0
\(739\) 568.765 985.130i 0.769642 1.33306i −0.168116 0.985767i \(-0.553768\pi\)
0.937757 0.347291i \(-0.112898\pi\)
\(740\) 139.650 + 166.428i 0.188716 + 0.224902i
\(741\) 0 0
\(742\) −45.4017 + 257.486i −0.0611883 + 0.347016i
\(743\) 707.445 + 124.742i 0.952147 + 0.167889i 0.628083 0.778146i \(-0.283840\pi\)
0.324064 + 0.946035i \(0.394951\pi\)
\(744\) 0 0
\(745\) 486.910 408.566i 0.653570 0.548411i
\(746\) 280.484 + 161.937i 0.375984 + 0.217074i
\(747\) 0 0
\(748\) −1.95805 3.39144i −0.00261771 0.00453401i
\(749\) −85.4181 + 234.684i −0.114043 + 0.313330i
\(750\) 0 0
\(751\) 481.188 + 403.765i 0.640730 + 0.537636i 0.904242 0.427020i \(-0.140436\pi\)
−0.263512 + 0.964656i \(0.584881\pi\)
\(752\) 4.24327 + 11.6583i 0.00564264 + 0.0155030i
\(753\) 0 0
\(754\) 114.846 + 651.323i 0.152315 + 0.863824i
\(755\) 350.584i 0.464350i
\(756\) 0 0
\(757\) 393.374 0.519648 0.259824 0.965656i \(-0.416335\pi\)
0.259824 + 0.965656i \(0.416335\pi\)
\(758\) 199.809 35.2318i 0.263601 0.0464799i
\(759\) 0 0
\(760\) 31.3921 11.4258i 0.0413054 0.0150339i
\(761\) −519.995 + 619.706i −0.683305 + 0.814331i −0.990529 0.137306i \(-0.956155\pi\)
0.307224 + 0.951637i \(0.400600\pi\)
\(762\) 0 0
\(763\) 133.487 + 48.5852i 0.174950 + 0.0636765i
\(764\) 270.278 156.045i 0.353767 0.204248i
\(765\) 0 0
\(766\) −111.728 + 193.518i −0.145859 + 0.252635i
\(767\) 983.485 + 1172.07i 1.28225 + 1.52813i
\(768\) 0 0
\(769\) 15.5452 88.1614i 0.0202149 0.114644i −0.973031 0.230676i \(-0.925906\pi\)
0.993246 + 0.116032i \(0.0370174\pi\)
\(770\) 5.81766 + 1.02581i 0.00755540 + 0.00133222i
\(771\) 0 0
\(772\) 403.496 338.574i 0.522664 0.438567i
\(773\) −1053.61 608.304i −1.36302 0.786939i −0.372994 0.927834i \(-0.621669\pi\)
−0.990025 + 0.140894i \(0.955002\pi\)
\(774\) 0 0
\(775\) −377.150 653.243i −0.486645 0.842894i
\(776\) −136.347 + 374.611i −0.175705 + 0.482746i
\(777\) 0 0
\(778\) 237.640 + 199.404i 0.305450 + 0.256303i
\(779\) 64.7922 + 178.015i 0.0831735 + 0.228517i
\(780\) 0 0
\(781\) 8.84904 + 50.1854i 0.0113304 + 0.0642579i
\(782\) 201.202i 0.257291i
\(783\) 0 0
\(784\) −174.585 −0.222685
\(785\) −198.333 + 34.9715i −0.252654 + 0.0445497i
\(786\) 0 0
\(787\) −771.120 + 280.665i −0.979822 + 0.356626i −0.781771 0.623566i \(-0.785683\pi\)
−0.198051 + 0.980192i \(0.563461\pi\)
\(788\) 185.430 220.987i 0.235318 0.280441i
\(789\) 0 0
\(790\) 255.857 + 93.1245i 0.323870 + 0.117879i
\(791\) −81.9955 + 47.3401i −0.103661 + 0.0598484i
\(792\) 0 0
\(793\) 413.769 716.670i 0.521777 0.903745i
\(794\) 72.6950 + 86.6346i 0.0915554 + 0.109112i
\(795\) 0 0
\(796\) −92.4760 + 524.457i −0.116176 + 0.658866i
\(797\) −942.932 166.264i −1.18310 0.208613i −0.452720 0.891653i \(-0.649546\pi\)
−0.730381 + 0.683040i \(0.760658\pi\)
\(798\) 0 0
\(799\) 7.45572 6.25609i 0.00933131 0.00782990i
\(800\) −81.4673 47.0351i −0.101834 0.0587939i
\(801\) 0 0
\(802\) −423.508 733.538i −0.528065 0.914636i
\(803\) 5.38013 14.7818i 0.00670004 0.0184082i
\(804\) 0 0
\(805\) −232.503 195.093i −0.288824 0.242352i
\(806\) 514.040 + 1412.31i 0.637767 + 1.75225i
\(807\) 0 0
\(808\) 19.5170 + 110.686i 0.0241547 + 0.136988i
\(809\) 180.576i 0.223209i 0.993753 + 0.111605i \(0.0355990\pi\)
−0.993753 + 0.111605i \(0.964401\pi\)
\(810\) 0 0
\(811\) 518.424 0.639240 0.319620 0.947546i \(-0.396445\pi\)
0.319620 + 0.947546i \(0.396445\pi\)
\(812\) −90.9651 + 16.0396i −0.112026 + 0.0197532i
\(813\) 0 0
\(814\) −31.1345 + 11.3320i −0.0382488 + 0.0139214i
\(815\) −126.119 + 150.303i −0.154748 + 0.184421i
\(816\) 0 0
\(817\) 232.303 + 84.5513i 0.284336 + 0.103490i
\(818\) −114.825 + 66.2942i −0.140373 + 0.0810443i
\(819\) 0 0
\(820\) −134.257 + 232.539i −0.163728 + 0.283585i
\(821\) −176.439 210.271i −0.214907 0.256116i 0.647812 0.761801i \(-0.275684\pi\)
−0.862718 + 0.505685i \(0.831240\pi\)
\(822\) 0 0
\(823\) −107.367 + 608.911i −0.130459 + 0.739867i 0.847457 + 0.530865i \(0.178133\pi\)
−0.977915 + 0.209002i \(0.932978\pi\)
\(824\) −129.613 22.8543i −0.157298 0.0277358i
\(825\) 0 0
\(826\) −163.694 + 137.356i −0.198177 + 0.166290i
\(827\) −672.492 388.263i −0.813170 0.469484i 0.0348852 0.999391i \(-0.488893\pi\)
−0.848056 + 0.529907i \(0.822227\pi\)
\(828\) 0 0
\(829\) 265.258 + 459.440i 0.319973 + 0.554209i 0.980482 0.196609i \(-0.0629928\pi\)
−0.660509 + 0.750818i \(0.729660\pi\)
\(830\) −69.8677 + 191.960i −0.0841779 + 0.231277i
\(831\) 0 0
\(832\) 143.585 + 120.482i 0.172578 + 0.144810i
\(833\) 46.8431 + 128.700i 0.0562342 + 0.154502i
\(834\) 0 0
\(835\) 117.588 + 666.872i 0.140823 + 0.798649i
\(836\) 5.09471i 0.00609415i
\(837\) 0 0
\(838\) 680.021 0.811481
\(839\) −992.570 + 175.017i −1.18304 + 0.208602i −0.730354 0.683069i \(-0.760645\pi\)
−0.452685 + 0.891670i \(0.649534\pi\)
\(840\) 0 0
\(841\) −415.897 + 151.374i −0.494527 + 0.179993i
\(842\) 190.713 227.283i 0.226500 0.269932i
\(843\) 0 0
\(844\) −383.411 139.550i −0.454279 0.165344i
\(845\) 951.978 549.625i 1.12660 0.650444i
\(846\) 0 0
\(847\) 139.535 241.682i 0.164740 0.285338i
\(848\) −205.441 244.835i −0.242265 0.288720i
\(849\) 0 0
\(850\) −12.8147 + 72.6759i −0.0150762 + 0.0855011i
\(851\) 1676.43 + 295.600i 1.96996 + 0.347356i
\(852\) 0 0
\(853\) 668.076 560.582i 0.783207 0.657189i −0.160847 0.986979i \(-0.551423\pi\)
0.944054 + 0.329791i \(0.106978\pi\)
\(854\) 100.092 + 57.7879i 0.117203 + 0.0676673i
\(855\) 0 0
\(856\) −152.646 264.391i −0.178325 0.308868i
\(857\) −285.540 + 784.514i −0.333185 + 0.915419i 0.654093 + 0.756414i \(0.273051\pi\)
−0.987278 + 0.159004i \(0.949172\pi\)
\(858\) 0 0
\(859\) −51.8826 43.5347i −0.0603989 0.0506807i 0.612088 0.790789i \(-0.290330\pi\)
−0.672487 + 0.740109i \(0.734774\pi\)
\(860\) 119.844 + 329.268i 0.139353 + 0.382870i
\(861\) 0 0
\(862\) 79.3504 + 450.018i 0.0920538 + 0.522063i
\(863\) 1191.58i 1.38074i −0.723456 0.690370i \(-0.757448\pi\)
0.723456 0.690370i \(-0.242552\pi\)
\(864\) 0 0
\(865\) −155.029 −0.179224
\(866\) −532.146 + 93.8317i −0.614487 + 0.108351i
\(867\) 0 0
\(868\) −197.247 + 71.7920i −0.227243 + 0.0827096i
\(869\) −26.6910 + 31.8090i −0.0307146 + 0.0366042i
\(870\) 0 0
\(871\) −624.935 227.458i −0.717492 0.261146i
\(872\) −150.384 + 86.8240i −0.172458 + 0.0995688i
\(873\) 0 0
\(874\) 130.878 226.688i 0.149746 0.259368i
\(875\) −179.132 213.481i −0.204722 0.243978i
\(876\) 0 0
\(877\) −127.873 + 725.202i −0.145807 + 0.826912i 0.820909 + 0.571059i \(0.193467\pi\)
−0.966716 + 0.255853i \(0.917644\pi\)
\(878\) −390.784 68.9058i −0.445084 0.0784804i
\(879\) 0 0
\(880\) −5.53182 + 4.64175i −0.00628616 + 0.00527472i
\(881\) −1028.88 594.025i −1.16786 0.674263i −0.214683 0.976684i \(-0.568872\pi\)
−0.953174 + 0.302421i \(0.902205\pi\)
\(882\) 0 0
\(883\) 509.485 + 882.454i 0.576993 + 0.999382i 0.995822 + 0.0913164i \(0.0291075\pi\)
−0.418829 + 0.908065i \(0.637559\pi\)
\(884\) 50.2912 138.174i 0.0568905 0.156305i
\(885\) 0 0
\(886\) −97.8128 82.0747i −0.110398 0.0926351i
\(887\) 267.381 + 734.624i 0.301445 + 0.828212i 0.994250 + 0.107087i \(0.0341524\pi\)
−0.692805 + 0.721125i \(0.743625\pi\)
\(888\) 0 0
\(889\) 85.8554 + 486.910i 0.0965752 + 0.547705i
\(890\) 525.055i 0.589949i
\(891\) 0 0
\(892\) 36.0632 0.0404296
\(893\) −12.4696 + 2.19873i −0.0139637 + 0.00246218i
\(894\) 0 0
\(895\) −26.9674 + 9.81534i −0.0301312 + 0.0109669i
\(896\) −16.8267 + 20.0533i −0.0187798 + 0.0223809i
\(897\) 0 0
\(898\) 503.095 + 183.112i 0.560239 + 0.203910i
\(899\) 784.086 452.692i 0.872175 0.503551i
\(900\) 0 0
\(901\) −125.365 + 217.138i −0.139140 + 0.240997i
\(902\) −26.3219 31.3692i −0.0291817 0.0347774i
\(903\) 0 0
\(904\) 20.0977 113.980i 0.0222320 0.126084i
\(905\) 308.606 + 54.4155i 0.341001 + 0.0601276i
\(906\) 0 0
\(907\) 367.436 308.315i 0.405111 0.339929i −0.417354 0.908744i \(-0.637042\pi\)
0.822465 + 0.568815i \(0.192598\pi\)
\(908\) 186.321 + 107.573i 0.205200 + 0.118472i
\(909\) 0 0
\(910\) 110.906 + 192.094i 0.121874 + 0.211093i
\(911\) 218.659 600.761i 0.240021 0.659452i −0.759934 0.650000i \(-0.774769\pi\)
0.999955 0.00945235i \(-0.00300882\pi\)
\(912\) 0 0
\(913\) −23.8651 20.0252i −0.0261392 0.0219334i
\(914\) 192.397 + 528.607i 0.210500 + 0.578345i
\(915\) 0 0
\(916\) 48.3977 + 274.477i 0.0528359 + 0.299647i
\(917\) 33.9184i 0.0369885i
\(918\) 0 0
\(919\) −14.7768 −0.0160792 −0.00803959 0.999968i \(-0.502559\pi\)
−0.00803959 + 0.999968i \(0.502559\pi\)
\(920\) 365.379 64.4262i 0.397151 0.0700285i
\(921\) 0 0
\(922\) −534.181 + 194.426i −0.579372 + 0.210874i
\(923\) −1229.93 + 1465.77i −1.33254 + 1.58805i
\(924\) 0 0
\(925\) 586.716 + 213.547i 0.634288 + 0.230862i
\(926\) 233.422 134.766i 0.252076 0.145536i
\(927\) 0 0
\(928\) 56.4561 97.7849i 0.0608363 0.105372i
\(929\) −795.223 947.710i −0.855999 1.02014i −0.999535 0.0304949i \(-0.990292\pi\)
0.143536 0.989645i \(-0.454153\pi\)
\(930\) 0 0
\(931\) 30.9407 175.473i 0.0332338 0.188478i
\(932\) −128.610 22.6774i −0.137993 0.0243320i
\(933\) 0 0
\(934\) 933.504 783.303i 0.999469 0.838654i
\(935\) 4.90605 + 2.83251i 0.00524711 + 0.00302942i
\(936\) 0 0
\(937\) −764.046 1323.37i −0.815418 1.41234i −0.909028 0.416736i \(-0.863174\pi\)
0.0936099 0.995609i \(-0.470159\pi\)
\(938\) 31.7672 87.2798i 0.0338670 0.0930488i
\(939\) 0 0
\(940\) −13.7483 11.5362i −0.0146259 0.0122726i
\(941\) −352.183 967.616i −0.374265 1.02828i −0.973695 0.227857i \(-0.926828\pi\)
0.599430 0.800427i \(-0.295394\pi\)
\(942\) 0 0
\(943\) 365.341 + 2071.95i 0.387424 + 2.19719i
\(944\) 261.214i 0.276710i
\(945\) 0 0
\(946\) −53.4377 −0.0564881
\(947\) −129.208 + 22.7828i −0.136439 + 0.0240579i −0.241451 0.970413i \(-0.577623\pi\)
0.105011 + 0.994471i \(0.466512\pi\)
\(948\) 0 0
\(949\) 555.027 202.013i 0.584855 0.212870i
\(950\) 61.7124 73.5460i 0.0649604 0.0774168i
\(951\) 0 0
\(952\) 19.2977 + 7.02378i 0.0202707 + 0.00737792i
\(953\) −1223.02 + 706.112i −1.28334 + 0.740936i −0.977457 0.211133i \(-0.932285\pi\)
−0.305882 + 0.952069i \(0.598951\pi\)
\(954\) 0 0
\(955\) −225.734 + 390.983i −0.236371 + 0.409407i
\(956\) 102.759 + 122.463i 0.107488 + 0.128099i
\(957\) 0 0
\(958\) −116.429 + 660.300i −0.121533 + 0.689249i
\(959\) 308.096 + 54.3257i 0.321268 + 0.0566483i
\(960\) 0 0
\(961\) 839.945 704.797i 0.874032 0.733400i
\(962\) −1077.39 622.033i −1.11995 0.646604i
\(963\) 0 0
\(964\) 242.780 + 420.508i 0.251847 + 0.436211i
\(965\) −260.606 + 716.010i −0.270058 + 0.741979i
\(966\) 0 0
\(967\) 445.513 + 373.830i 0.460717 + 0.386587i 0.843395 0.537295i \(-0.180554\pi\)
−0.382678 + 0.923882i \(0.624998\pi\)
\(968\) 116.676 + 320.565i 0.120533 + 0.331162i
\(969\) 0 0
\(970\) −100.141 567.928i −0.103238 0.585493i
\(971\) 208.668i 0.214900i 0.994210 + 0.107450i \(0.0342686\pi\)
−0.994210 + 0.107450i \(0.965731\pi\)
\(972\) 0 0
\(973\) −172.721 −0.177514
\(974\) −165.125 + 29.1159i −0.169533 + 0.0298932i
\(975\) 0 0
\(976\) −132.761 + 48.3210i −0.136026 + 0.0495093i
\(977\) 1130.45 1347.21i 1.15706 1.37893i 0.244667 0.969607i \(-0.421321\pi\)
0.912391 0.409320i \(-0.134234\pi\)
\(978\) 0 0
\(979\) −75.2445 27.3868i −0.0768585 0.0279742i
\(980\) 218.718 126.277i 0.223182 0.128854i
\(981\) 0 0
\(982\) −276.594 + 479.075i −0.281664 + 0.487856i
\(983\) 795.222 + 947.708i 0.808974 + 0.964098i 0.999847 0.0175168i \(-0.00557606\pi\)
−0.190872 + 0.981615i \(0.561132\pi\)
\(984\) 0 0
\(985\) −72.4654 + 410.972i −0.0735690 + 0.417230i
\(986\) −87.2327 15.3815i −0.0884713 0.0155999i
\(987\) 0 0
\(988\) −146.541 + 122.963i −0.148321 + 0.124456i
\(989\) 2377.70 + 1372.76i 2.40414 + 1.38803i
\(990\) 0 0
\(991\) −384.670 666.268i −0.388163 0.672319i 0.604039 0.796955i \(-0.293557\pi\)
−0.992203 + 0.124636i \(0.960224\pi\)
\(992\) 87.7594 241.117i 0.0884671 0.243061i
\(993\) 0 0
\(994\) −204.713 171.775i −0.205949 0.172812i
\(995\) −263.486 723.922i −0.264810 0.727560i
\(996\) 0 0
\(997\) −15.4474 87.6066i −0.0154939 0.0878702i 0.976080 0.217410i \(-0.0697610\pi\)
−0.991574 + 0.129540i \(0.958650\pi\)
\(998\) 260.814i 0.261337i
\(999\) 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.71.1 36
3.2 odd 2 54.3.f.a.41.4 yes 36
12.11 even 2 432.3.bc.c.257.4 36
27.2 odd 18 inner 162.3.f.a.89.1 36
27.5 odd 18 1458.3.b.c.1457.6 36
27.22 even 9 1458.3.b.c.1457.31 36
27.25 even 9 54.3.f.a.29.4 36
108.79 odd 18 432.3.bc.c.353.4 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.3.f.a.29.4 36 27.25 even 9
54.3.f.a.41.4 yes 36 3.2 odd 2
162.3.f.a.71.1 36 1.1 even 1 trivial
162.3.f.a.89.1 36 27.2 odd 18 inner
432.3.bc.c.257.4 36 12.11 even 2
432.3.bc.c.353.4 36 108.79 odd 18
1458.3.b.c.1457.6 36 27.5 odd 18
1458.3.b.c.1457.31 36 27.22 even 9