Properties

Label 441.2.w.a.188.6
Level $441$
Weight $2$
Character 441.188
Analytic conductor $3.521$
Analytic rank $0$
Dimension $120$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(62,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([7, 11]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.62");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.w (of order \(14\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(120\)
Relative dimension: \(20\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 188.6
Character \(\chi\) \(=\) 441.188
Dual form 441.2.w.a.251.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.16155 + 0.926303i) q^{2} +(0.0461133 - 0.202036i) q^{4} +(2.75921 - 1.32877i) q^{5} +(-2.64574 - 0.00862187i) q^{7} +(-1.15564 - 2.39971i) q^{8} +O(q^{10})\) \(q+(-1.16155 + 0.926303i) q^{2} +(0.0461133 - 0.202036i) q^{4} +(2.75921 - 1.32877i) q^{5} +(-2.64574 - 0.00862187i) q^{7} +(-1.15564 - 2.39971i) q^{8} +(-1.97412 + 4.09929i) q^{10} +(4.38394 - 3.49607i) q^{11} +(-0.126413 + 0.100811i) q^{13} +(3.08114 - 2.44074i) q^{14} +(3.93860 + 1.89673i) q^{16} +(-0.351332 - 1.53929i) q^{17} -5.64561i q^{19} +(-0.141222 - 0.618733i) q^{20} +(-1.85373 + 8.12172i) q^{22} +(-4.97667 - 1.13589i) q^{23} +(2.73018 - 3.42354i) q^{25} +(0.0534533 - 0.234194i) q^{26} +(-0.123746 + 0.534136i) q^{28} +(3.45359 - 0.788260i) q^{29} +0.856946i q^{31} +(-1.13844 + 0.259840i) q^{32} +(1.83393 + 1.46251i) q^{34} +(-7.31161 + 3.49178i) q^{35} +(0.520922 + 2.28231i) q^{37} +(5.22954 + 6.55764i) q^{38} +(-6.37730 - 5.08572i) q^{40} +(10.3963 - 5.00660i) q^{41} +(10.9288 + 5.26303i) q^{43} +(-0.504174 - 1.04693i) q^{44} +(6.83282 - 3.29051i) q^{46} +(6.32346 + 7.92937i) q^{47} +(6.99985 + 0.0456224i) q^{49} +6.50558i q^{50} +(0.0145381 + 0.0301888i) q^{52} +(-6.39600 - 1.45985i) q^{53} +(7.45075 - 15.4716i) q^{55} +(3.03682 + 6.35895i) q^{56} +(-3.28135 + 4.11468i) q^{58} +(-8.14279 - 3.92136i) q^{59} +(-0.616348 + 0.140677i) q^{61} +(-0.793792 - 0.995384i) q^{62} +(-4.36954 + 5.47923i) q^{64} +(-0.214847 + 0.446134i) q^{65} -10.8925 q^{67} -0.327192 q^{68} +(5.25833 - 10.8286i) q^{70} +(-4.40071 - 1.00443i) q^{71} +(5.53256 + 4.41207i) q^{73} +(-2.71918 - 2.16848i) q^{74} +(-1.14061 - 0.260338i) q^{76} +(-11.6289 + 9.21190i) q^{77} -9.69282 q^{79} +13.3877 q^{80} +(-7.43819 + 15.4456i) q^{82} +(4.61146 - 5.78259i) q^{83} +(-3.01475 - 3.78038i) q^{85} +(-17.5695 + 4.01012i) q^{86} +(-13.4558 - 6.47997i) q^{88} +(1.71125 - 2.14584i) q^{89} +(0.335326 - 0.265630i) q^{91} +(-0.458982 + 0.953086i) q^{92} +(-14.6900 - 3.35290i) q^{94} +(-7.50169 - 15.5774i) q^{95} +6.81046i q^{97} +(-8.17292 + 6.43099i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 120 q + 24 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{14}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.16155 + 0.926303i −0.821338 + 0.654995i −0.941221 0.337793i \(-0.890320\pi\)
0.119882 + 0.992788i \(0.461748\pi\)
\(3\) 0 0
\(4\) 0.0461133 0.202036i 0.0230567 0.101018i
\(5\) 2.75921 1.32877i 1.23396 0.594242i 0.300792 0.953690i \(-0.402749\pi\)
0.933165 + 0.359448i \(0.117035\pi\)
\(6\) 0 0
\(7\) −2.64574 0.00862187i −0.999995 0.00325876i
\(8\) −1.15564 2.39971i −0.408579 0.848424i
\(9\) 0 0
\(10\) −1.97412 + 4.09929i −0.624270 + 1.29631i
\(11\) 4.38394 3.49607i 1.32181 1.05411i 0.327805 0.944745i \(-0.393691\pi\)
0.994002 0.109361i \(-0.0348804\pi\)
\(12\) 0 0
\(13\) −0.126413 + 0.100811i −0.0350608 + 0.0279600i −0.640863 0.767655i \(-0.721424\pi\)
0.605803 + 0.795615i \(0.292852\pi\)
\(14\) 3.08114 2.44074i 0.823468 0.652315i
\(15\) 0 0
\(16\) 3.93860 + 1.89673i 0.984650 + 0.474183i
\(17\) −0.351332 1.53929i −0.0852105 0.373331i 0.914286 0.405070i \(-0.132753\pi\)
−0.999496 + 0.0317384i \(0.989896\pi\)
\(18\) 0 0
\(19\) 5.64561i 1.29519i −0.761984 0.647595i \(-0.775775\pi\)
0.761984 0.647595i \(-0.224225\pi\)
\(20\) −0.141222 0.618733i −0.0315781 0.138353i
\(21\) 0 0
\(22\) −1.85373 + 8.12172i −0.395216 + 1.73156i
\(23\) −4.97667 1.13589i −1.03771 0.236850i −0.330463 0.943819i \(-0.607205\pi\)
−0.707245 + 0.706969i \(0.750062\pi\)
\(24\) 0 0
\(25\) 2.73018 3.42354i 0.546036 0.684707i
\(26\) 0.0534533 0.234194i 0.0104831 0.0459293i
\(27\) 0 0
\(28\) −0.123746 + 0.534136i −0.0233857 + 0.100942i
\(29\) 3.45359 0.788260i 0.641316 0.146376i 0.110518 0.993874i \(-0.464749\pi\)
0.530799 + 0.847498i \(0.321892\pi\)
\(30\) 0 0
\(31\) 0.856946i 0.153912i 0.997034 + 0.0769561i \(0.0245201\pi\)
−0.997034 + 0.0769561i \(0.975480\pi\)
\(32\) −1.13844 + 0.259840i −0.201249 + 0.0459337i
\(33\) 0 0
\(34\) 1.83393 + 1.46251i 0.314517 + 0.250819i
\(35\) −7.31161 + 3.49178i −1.23589 + 0.590218i
\(36\) 0 0
\(37\) 0.520922 + 2.28231i 0.0856390 + 0.375209i 0.999527 0.0307578i \(-0.00979205\pi\)
−0.913888 + 0.405967i \(0.866935\pi\)
\(38\) 5.22954 + 6.55764i 0.848344 + 1.06379i
\(39\) 0 0
\(40\) −6.37730 5.08572i −1.00834 0.804123i
\(41\) 10.3963 5.00660i 1.62363 0.781900i 0.623632 0.781718i \(-0.285656\pi\)
1.00000 0.000182349i \(-5.80435e-5\pi\)
\(42\) 0 0
\(43\) 10.9288 + 5.26303i 1.66662 + 0.802604i 0.998272 + 0.0587591i \(0.0187144\pi\)
0.668352 + 0.743845i \(0.267000\pi\)
\(44\) −0.504174 1.04693i −0.0760071 0.157830i
\(45\) 0 0
\(46\) 6.83282 3.29051i 1.00745 0.485160i
\(47\) 6.32346 + 7.92937i 0.922372 + 1.15662i 0.987322 + 0.158730i \(0.0507398\pi\)
−0.0649500 + 0.997889i \(0.520689\pi\)
\(48\) 0 0
\(49\) 6.99985 + 0.0456224i 0.999979 + 0.00651749i
\(50\) 6.50558i 0.920027i
\(51\) 0 0
\(52\) 0.0145381 + 0.0301888i 0.00201608 + 0.00418643i
\(53\) −6.39600 1.45985i −0.878558 0.200525i −0.240626 0.970618i \(-0.577353\pi\)
−0.637932 + 0.770093i \(0.720210\pi\)
\(54\) 0 0
\(55\) 7.45075 15.4716i 1.00466 2.08620i
\(56\) 3.03682 + 6.35895i 0.405812 + 0.849751i
\(57\) 0 0
\(58\) −3.28135 + 4.11468i −0.430862 + 0.540284i
\(59\) −8.14279 3.92136i −1.06010 0.510518i −0.179198 0.983813i \(-0.557350\pi\)
−0.880904 + 0.473295i \(0.843064\pi\)
\(60\) 0 0
\(61\) −0.616348 + 0.140677i −0.0789153 + 0.0180119i −0.261796 0.965123i \(-0.584315\pi\)
0.182881 + 0.983135i \(0.441458\pi\)
\(62\) −0.793792 0.995384i −0.100812 0.126414i
\(63\) 0 0
\(64\) −4.36954 + 5.47923i −0.546192 + 0.684903i
\(65\) −0.214847 + 0.446134i −0.0266484 + 0.0553361i
\(66\) 0 0
\(67\) −10.8925 −1.33073 −0.665367 0.746516i \(-0.731725\pi\)
−0.665367 + 0.746516i \(0.731725\pi\)
\(68\) −0.327192 −0.0396778
\(69\) 0 0
\(70\) 5.25833 10.8286i 0.628491 1.29427i
\(71\) −4.40071 1.00443i −0.522268 0.119204i −0.0467436 0.998907i \(-0.514884\pi\)
−0.475524 + 0.879703i \(0.657742\pi\)
\(72\) 0 0
\(73\) 5.53256 + 4.41207i 0.647537 + 0.516394i 0.891284 0.453445i \(-0.149805\pi\)
−0.243747 + 0.969839i \(0.578377\pi\)
\(74\) −2.71918 2.16848i −0.316099 0.252080i
\(75\) 0 0
\(76\) −1.14061 0.260338i −0.130837 0.0298628i
\(77\) −11.6289 + 9.21190i −1.32524 + 1.04979i
\(78\) 0 0
\(79\) −9.69282 −1.09053 −0.545263 0.838265i \(-0.683570\pi\)
−0.545263 + 0.838265i \(0.683570\pi\)
\(80\) 13.3877 1.49680
\(81\) 0 0
\(82\) −7.43819 + 15.4456i −0.821410 + 1.70568i
\(83\) 4.61146 5.78259i 0.506173 0.634721i −0.461436 0.887173i \(-0.652666\pi\)
0.967609 + 0.252452i \(0.0812371\pi\)
\(84\) 0 0
\(85\) −3.01475 3.78038i −0.326995 0.410039i
\(86\) −17.5695 + 4.01012i −1.89456 + 0.432422i
\(87\) 0 0
\(88\) −13.4558 6.47997i −1.43439 0.690767i
\(89\) 1.71125 2.14584i 0.181392 0.227459i −0.682819 0.730587i \(-0.739246\pi\)
0.864212 + 0.503129i \(0.167818\pi\)
\(90\) 0 0
\(91\) 0.335326 0.265630i 0.0351517 0.0278456i
\(92\) −0.458982 + 0.953086i −0.0478522 + 0.0993660i
\(93\) 0 0
\(94\) −14.6900 3.35290i −1.51516 0.345825i
\(95\) −7.50169 15.5774i −0.769657 1.59821i
\(96\) 0 0
\(97\) 6.81046i 0.691497i 0.938327 + 0.345749i \(0.112375\pi\)
−0.938327 + 0.345749i \(0.887625\pi\)
\(98\) −8.17292 + 6.43099i −0.825590 + 0.649628i
\(99\) 0 0
\(100\) −0.565779 0.709464i −0.0565779 0.0709464i
\(101\) −0.859158 + 0.413749i −0.0854894 + 0.0411695i −0.476140 0.879370i \(-0.657964\pi\)
0.390650 + 0.920539i \(0.372250\pi\)
\(102\) 0 0
\(103\) −6.04953 12.5620i −0.596078 1.23777i −0.952812 0.303562i \(-0.901824\pi\)
0.356734 0.934206i \(-0.383890\pi\)
\(104\) 0.388006 + 0.186854i 0.0380471 + 0.0183225i
\(105\) 0 0
\(106\) 8.78152 4.22896i 0.852936 0.410753i
\(107\) −6.41385 5.11488i −0.620051 0.494474i 0.262350 0.964973i \(-0.415503\pi\)
−0.882401 + 0.470499i \(0.844074\pi\)
\(108\) 0 0
\(109\) 6.71224 + 8.41689i 0.642916 + 0.806191i 0.991364 0.131137i \(-0.0418627\pi\)
−0.348448 + 0.937328i \(0.613291\pi\)
\(110\) 5.67703 + 24.8727i 0.541284 + 2.37152i
\(111\) 0 0
\(112\) −10.4042 5.05221i −0.983100 0.477389i
\(113\) 10.4348 + 8.32149i 0.981625 + 0.782820i 0.976135 0.217165i \(-0.0696810\pi\)
0.00549020 + 0.999985i \(0.498252\pi\)
\(114\) 0 0
\(115\) −15.2410 + 3.47867i −1.42123 + 0.324387i
\(116\) 0.734099i 0.0681593i
\(117\) 0 0
\(118\) 13.0906 2.98785i 1.20509 0.275054i
\(119\) 0.916260 + 4.07557i 0.0839934 + 0.373607i
\(120\) 0 0
\(121\) 4.54865 19.9290i 0.413514 1.81172i
\(122\) 0.585608 0.734329i 0.0530184 0.0664830i
\(123\) 0 0
\(124\) 0.173134 + 0.0395166i 0.0155479 + 0.00354870i
\(125\) −0.423282 + 1.85452i −0.0378595 + 0.165873i
\(126\) 0 0
\(127\) −1.30691 5.72596i −0.115970 0.508097i −0.999231 0.0392151i \(-0.987514\pi\)
0.883261 0.468882i \(-0.155343\pi\)
\(128\) 12.7473i 1.12672i
\(129\) 0 0
\(130\) −0.163701 0.717219i −0.0143575 0.0629042i
\(131\) −13.5262 6.51387i −1.18179 0.569120i −0.263357 0.964698i \(-0.584830\pi\)
−0.918432 + 0.395579i \(0.870544\pi\)
\(132\) 0 0
\(133\) −0.0486757 + 14.9368i −0.00422072 + 1.29518i
\(134\) 12.6522 10.0898i 1.09298 0.871625i
\(135\) 0 0
\(136\) −3.28782 + 2.62195i −0.281928 + 0.224830i
\(137\) 5.11747 10.6265i 0.437215 0.907886i −0.559648 0.828731i \(-0.689064\pi\)
0.996862 0.0791550i \(-0.0252222\pi\)
\(138\) 0 0
\(139\) 7.48155 + 15.5356i 0.634577 + 1.31771i 0.931823 + 0.362912i \(0.118217\pi\)
−0.297246 + 0.954801i \(0.596068\pi\)
\(140\) 0.368301 + 1.63822i 0.0311271 + 0.138455i
\(141\) 0 0
\(142\) 6.04204 2.90969i 0.507037 0.244176i
\(143\) −0.201745 + 0.883902i −0.0168707 + 0.0739156i
\(144\) 0 0
\(145\) 8.48178 6.76400i 0.704374 0.561719i
\(146\) −10.5133 −0.870083
\(147\) 0 0
\(148\) 0.485129 0.0398773
\(149\) −7.35855 + 5.86825i −0.602836 + 0.480746i −0.876710 0.481020i \(-0.840266\pi\)
0.273874 + 0.961766i \(0.411695\pi\)
\(150\) 0 0
\(151\) 1.36982 6.00156i 0.111474 0.488400i −0.888112 0.459627i \(-0.847983\pi\)
0.999586 0.0287726i \(-0.00915988\pi\)
\(152\) −13.5478 + 6.52427i −1.09887 + 0.529188i
\(153\) 0 0
\(154\) 4.97450 21.4719i 0.400857 1.73026i
\(155\) 1.13868 + 2.36450i 0.0914611 + 0.189921i
\(156\) 0 0
\(157\) −8.06690 + 16.7511i −0.643808 + 1.33688i 0.282191 + 0.959358i \(0.408939\pi\)
−0.926000 + 0.377524i \(0.876776\pi\)
\(158\) 11.2587 8.97849i 0.895692 0.714290i
\(159\) 0 0
\(160\) −2.79592 + 2.22967i −0.221037 + 0.176271i
\(161\) 13.1572 + 3.04818i 1.03693 + 0.240230i
\(162\) 0 0
\(163\) −6.64838 3.20169i −0.520742 0.250776i 0.155000 0.987914i \(-0.450462\pi\)
−0.675742 + 0.737139i \(0.736177\pi\)
\(164\) −0.532104 2.33130i −0.0415503 0.182044i
\(165\) 0 0
\(166\) 10.9884i 0.852862i
\(167\) 2.94816 + 12.9167i 0.228136 + 0.999528i 0.951158 + 0.308703i \(0.0998950\pi\)
−0.723023 + 0.690824i \(0.757248\pi\)
\(168\) 0 0
\(169\) −2.88695 + 12.6486i −0.222073 + 0.972967i
\(170\) 7.00355 + 1.59851i 0.537148 + 0.122600i
\(171\) 0 0
\(172\) 1.56728 1.96531i 0.119504 0.149853i
\(173\) 0.268273 1.17538i 0.0203964 0.0893625i −0.963705 0.266968i \(-0.913978\pi\)
0.984102 + 0.177606i \(0.0568352\pi\)
\(174\) 0 0
\(175\) −7.25285 + 9.03424i −0.548264 + 0.682924i
\(176\) 23.8977 5.45449i 1.80136 0.411148i
\(177\) 0 0
\(178\) 4.07763i 0.305632i
\(179\) −17.1681 + 3.91850i −1.28320 + 0.292882i −0.809143 0.587612i \(-0.800068\pi\)
−0.474057 + 0.880494i \(0.657211\pi\)
\(180\) 0 0
\(181\) −1.88800 1.50563i −0.140334 0.111913i 0.550807 0.834633i \(-0.314320\pi\)
−0.691141 + 0.722720i \(0.742892\pi\)
\(182\) −0.143443 + 0.619156i −0.0106327 + 0.0458949i
\(183\) 0 0
\(184\) 3.02542 + 13.2552i 0.223037 + 0.977188i
\(185\) 4.46998 + 5.60518i 0.328640 + 0.412101i
\(186\) 0 0
\(187\) −6.92167 5.51985i −0.506163 0.403651i
\(188\) 1.89361 0.911916i 0.138106 0.0665083i
\(189\) 0 0
\(190\) 23.1430 + 11.1451i 1.67897 + 0.808549i
\(191\) 3.51849 + 7.30622i 0.254589 + 0.528659i 0.988616 0.150461i \(-0.0480758\pi\)
−0.734027 + 0.679120i \(0.762361\pi\)
\(192\) 0 0
\(193\) 0.856581 0.412508i 0.0616580 0.0296930i −0.402801 0.915288i \(-0.631963\pi\)
0.464459 + 0.885595i \(0.346249\pi\)
\(194\) −6.30855 7.91067i −0.452928 0.567953i
\(195\) 0 0
\(196\) 0.332004 1.41212i 0.0237146 0.100865i
\(197\) 14.5833i 1.03902i −0.854465 0.519509i \(-0.826115\pi\)
0.854465 0.519509i \(-0.173885\pi\)
\(198\) 0 0
\(199\) −1.27445 2.64642i −0.0903433 0.187600i 0.850901 0.525326i \(-0.176057\pi\)
−0.941244 + 0.337726i \(0.890342\pi\)
\(200\) −11.3706 2.59526i −0.804021 0.183513i
\(201\) 0 0
\(202\) 0.614696 1.27643i 0.0432499 0.0898093i
\(203\) −9.14410 + 2.05575i −0.641790 + 0.144286i
\(204\) 0 0
\(205\) 22.0330 27.6286i 1.53885 1.92966i
\(206\) 18.6630 + 8.98763i 1.30031 + 0.626198i
\(207\) 0 0
\(208\) −0.689104 + 0.157283i −0.0477808 + 0.0109056i
\(209\) −19.7375 24.7500i −1.36527 1.71199i
\(210\) 0 0
\(211\) 7.50330 9.40884i 0.516548 0.647731i −0.453324 0.891346i \(-0.649762\pi\)
0.969872 + 0.243615i \(0.0783332\pi\)
\(212\) −0.589882 + 1.22490i −0.0405132 + 0.0841266i
\(213\) 0 0
\(214\) 12.1879 0.833150
\(215\) 37.1482 2.53348
\(216\) 0 0
\(217\) 0.00738848 2.26726i 0.000501563 0.153911i
\(218\) −15.5932 3.55904i −1.05610 0.241049i
\(219\) 0 0
\(220\) −2.78224 2.21877i −0.187579 0.149589i
\(221\) 0.199590 + 0.159168i 0.0134259 + 0.0107068i
\(222\) 0 0
\(223\) 28.5534 + 6.51713i 1.91208 + 0.436420i 0.999629 + 0.0272313i \(0.00866905\pi\)
0.912450 + 0.409188i \(0.134188\pi\)
\(224\) 3.01424 0.677654i 0.201397 0.0452777i
\(225\) 0 0
\(226\) −19.8288 −1.31899
\(227\) 0.395985 0.0262824 0.0131412 0.999914i \(-0.495817\pi\)
0.0131412 + 0.999914i \(0.495817\pi\)
\(228\) 0 0
\(229\) −9.94649 + 20.6541i −0.657282 + 1.36486i 0.259605 + 0.965715i \(0.416408\pi\)
−0.916887 + 0.399146i \(0.869307\pi\)
\(230\) 14.4809 18.1585i 0.954841 1.19733i
\(231\) 0 0
\(232\) −5.88270 7.37667i −0.386218 0.484302i
\(233\) −5.08467 + 1.16054i −0.333108 + 0.0760297i −0.385804 0.922581i \(-0.626076\pi\)
0.0526958 + 0.998611i \(0.483219\pi\)
\(234\) 0 0
\(235\) 27.9841 + 13.4764i 1.82548 + 0.879104i
\(236\) −1.16775 + 1.46431i −0.0760138 + 0.0953183i
\(237\) 0 0
\(238\) −4.83950 3.88524i −0.313698 0.251843i
\(239\) −2.07368 + 4.30604i −0.134135 + 0.278535i −0.957208 0.289401i \(-0.906544\pi\)
0.823072 + 0.567936i \(0.192258\pi\)
\(240\) 0 0
\(241\) 21.2200 + 4.84332i 1.36690 + 0.311986i 0.842137 0.539264i \(-0.181297\pi\)
0.524762 + 0.851249i \(0.324154\pi\)
\(242\) 13.1768 + 27.3619i 0.847035 + 1.75889i
\(243\) 0 0
\(244\) 0.131011i 0.00838714i
\(245\) 19.3747 9.17528i 1.23780 0.586187i
\(246\) 0 0
\(247\) 0.569141 + 0.713680i 0.0362136 + 0.0454104i
\(248\) 2.05642 0.990319i 0.130583 0.0628853i
\(249\) 0 0
\(250\) −1.22619 2.54620i −0.0775509 0.161036i
\(251\) 13.1197 + 6.31813i 0.828110 + 0.398797i 0.799406 0.600791i \(-0.205148\pi\)
0.0287041 + 0.999588i \(0.490862\pi\)
\(252\) 0 0
\(253\) −25.7886 + 12.4191i −1.62132 + 0.780784i
\(254\) 6.82202 + 5.44038i 0.428051 + 0.341360i
\(255\) 0 0
\(256\) 3.06882 + 3.84817i 0.191801 + 0.240511i
\(257\) 2.56465 + 11.2365i 0.159978 + 0.700911i 0.989750 + 0.142809i \(0.0456133\pi\)
−0.829772 + 0.558103i \(0.811530\pi\)
\(258\) 0 0
\(259\) −1.35854 6.04287i −0.0844158 0.375486i
\(260\) 0.0802276 + 0.0639794i 0.00497551 + 0.00396783i
\(261\) 0 0
\(262\) 21.7451 4.96319i 1.34342 0.306627i
\(263\) 0.202684i 0.0124980i −0.999980 0.00624902i \(-0.998011\pi\)
0.999980 0.00624902i \(-0.00198914\pi\)
\(264\) 0 0
\(265\) −19.5877 + 4.47077i −1.20326 + 0.274637i
\(266\) −13.7795 17.3949i −0.844873 1.06655i
\(267\) 0 0
\(268\) −0.502291 + 2.20068i −0.0306823 + 0.134428i
\(269\) 10.0208 12.5657i 0.610978 0.766143i −0.376066 0.926593i \(-0.622723\pi\)
0.987044 + 0.160451i \(0.0512947\pi\)
\(270\) 0 0
\(271\) 10.5944 + 2.41809i 0.643562 + 0.146889i 0.531832 0.846850i \(-0.321504\pi\)
0.111730 + 0.993739i \(0.464361\pi\)
\(272\) 1.53585 6.72901i 0.0931248 0.408006i
\(273\) 0 0
\(274\) 3.89921 + 17.0835i 0.235560 + 1.03205i
\(275\) 24.5535i 1.48063i
\(276\) 0 0
\(277\) 1.59759 + 6.99950i 0.0959899 + 0.420559i 0.999975 0.00700363i \(-0.00222934\pi\)
−0.903986 + 0.427563i \(0.859372\pi\)
\(278\) −23.0809 11.1152i −1.38430 0.666643i
\(279\) 0 0
\(280\) 16.8288 + 13.5105i 1.00571 + 0.807405i
\(281\) −4.28527 + 3.41739i −0.255638 + 0.203864i −0.742920 0.669380i \(-0.766560\pi\)
0.487282 + 0.873245i \(0.337988\pi\)
\(282\) 0 0
\(283\) 13.3207 10.6229i 0.791834 0.631467i −0.141718 0.989907i \(-0.545263\pi\)
0.933553 + 0.358440i \(0.116691\pi\)
\(284\) −0.405862 + 0.842782i −0.0240835 + 0.0500099i
\(285\) 0 0
\(286\) −0.584425 1.21357i −0.0345578 0.0717599i
\(287\) −27.5491 + 13.1565i −1.62617 + 0.776605i
\(288\) 0 0
\(289\) 13.0705 6.29442i 0.768853 0.370260i
\(290\) −3.58648 + 15.7134i −0.210606 + 0.922723i
\(291\) 0 0
\(292\) 1.14652 0.914320i 0.0670950 0.0535065i
\(293\) 26.8491 1.56854 0.784270 0.620420i \(-0.213038\pi\)
0.784270 + 0.620420i \(0.213038\pi\)
\(294\) 0 0
\(295\) −27.6783 −1.61149
\(296\) 4.87487 3.88758i 0.283346 0.225961i
\(297\) 0 0
\(298\) 3.11153 13.6325i 0.180246 0.789710i
\(299\) 0.743629 0.358113i 0.0430052 0.0207102i
\(300\) 0 0
\(301\) −28.8693 14.0188i −1.66400 0.808031i
\(302\) 3.96816 + 8.23996i 0.228342 + 0.474157i
\(303\) 0 0
\(304\) 10.7082 22.2358i 0.614157 1.27531i
\(305\) −1.51371 + 1.20714i −0.0866746 + 0.0691207i
\(306\) 0 0
\(307\) −19.9681 + 15.9241i −1.13964 + 0.908834i −0.996722 0.0809003i \(-0.974220\pi\)
−0.142920 + 0.989734i \(0.545649\pi\)
\(308\) 1.32488 + 2.77424i 0.0754923 + 0.158077i
\(309\) 0 0
\(310\) −3.51287 1.69171i −0.199518 0.0960827i
\(311\) 4.68552 + 20.5286i 0.265691 + 1.16407i 0.914971 + 0.403520i \(0.132213\pi\)
−0.649280 + 0.760550i \(0.724929\pi\)
\(312\) 0 0
\(313\) 24.0859i 1.36142i 0.732555 + 0.680708i \(0.238328\pi\)
−0.732555 + 0.680708i \(0.761672\pi\)
\(314\) −6.14650 26.9296i −0.346867 1.51972i
\(315\) 0 0
\(316\) −0.446968 + 1.95829i −0.0251439 + 0.110163i
\(317\) 17.9501 + 4.09700i 1.00818 + 0.230110i 0.694557 0.719438i \(-0.255600\pi\)
0.313622 + 0.949548i \(0.398458\pi\)
\(318\) 0 0
\(319\) 12.3845 15.5297i 0.693401 0.869497i
\(320\) −4.77587 + 20.9244i −0.266979 + 1.16971i
\(321\) 0 0
\(322\) −18.1062 + 8.64693i −1.00902 + 0.481874i
\(323\) −8.69020 + 1.98348i −0.483535 + 0.110364i
\(324\) 0 0
\(325\) 0.708014i 0.0392735i
\(326\) 10.6882 2.43950i 0.591962 0.135111i
\(327\) 0 0
\(328\) −24.0287 19.1623i −1.32677 1.05806i
\(329\) −16.6619 21.0336i −0.918598 1.15962i
\(330\) 0 0
\(331\) 3.71516 + 16.2772i 0.204203 + 0.894674i 0.968343 + 0.249623i \(0.0803067\pi\)
−0.764140 + 0.645051i \(0.776836\pi\)
\(332\) −0.955639 1.19833i −0.0524475 0.0657671i
\(333\) 0 0
\(334\) −15.3893 12.2725i −0.842063 0.671523i
\(335\) −30.0548 + 14.4736i −1.64207 + 0.790778i
\(336\) 0 0
\(337\) −30.9969 14.9273i −1.68851 0.813144i −0.995762 0.0919653i \(-0.970685\pi\)
−0.692749 0.721179i \(-0.743601\pi\)
\(338\) −8.36308 17.3661i −0.454892 0.944592i
\(339\) 0 0
\(340\) −0.902791 + 0.434761i −0.0489607 + 0.0235782i
\(341\) 2.99595 + 3.75680i 0.162240 + 0.203442i
\(342\) 0 0
\(343\) −18.5194 0.181057i −0.999952 0.00977615i
\(344\) 32.3080i 1.74193i
\(345\) 0 0
\(346\) 0.777147 + 1.61376i 0.0417797 + 0.0867564i
\(347\) −12.3329 2.81490i −0.662064 0.151112i −0.121731 0.992563i \(-0.538845\pi\)
−0.540333 + 0.841451i \(0.681702\pi\)
\(348\) 0 0
\(349\) −1.27642 + 2.65052i −0.0683254 + 0.141879i −0.932334 0.361597i \(-0.882232\pi\)
0.864009 + 0.503476i \(0.167946\pi\)
\(350\) 0.0560903 17.2120i 0.00299815 0.920022i
\(351\) 0 0
\(352\) −4.08241 + 5.11918i −0.217593 + 0.272853i
\(353\) −18.8308 9.06845i −1.00226 0.482665i −0.140557 0.990073i \(-0.544889\pi\)
−0.861706 + 0.507408i \(0.830604\pi\)
\(354\) 0 0
\(355\) −13.4771 + 3.07607i −0.715292 + 0.163261i
\(356\) −0.354625 0.444686i −0.0187951 0.0235683i
\(357\) 0 0
\(358\) 16.3118 20.4543i 0.862105 1.08105i
\(359\) −11.4770 + 23.8322i −0.605732 + 1.25781i 0.342286 + 0.939596i \(0.388799\pi\)
−0.948017 + 0.318219i \(0.896915\pi\)
\(360\) 0 0
\(361\) −12.8729 −0.677519
\(362\) 3.58768 0.188564
\(363\) 0 0
\(364\) −0.0382038 0.0799969i −0.00200242 0.00419298i
\(365\) 21.1281 + 4.82236i 1.10590 + 0.252414i
\(366\) 0 0
\(367\) 4.39923 + 3.50827i 0.229638 + 0.183130i 0.731548 0.681789i \(-0.238798\pi\)
−0.501911 + 0.864919i \(0.667369\pi\)
\(368\) −17.4466 13.9132i −0.909469 0.725278i
\(369\) 0 0
\(370\) −10.3842 2.37013i −0.539849 0.123217i
\(371\) 16.9095 + 3.91751i 0.877900 + 0.203387i
\(372\) 0 0
\(373\) −16.4267 −0.850540 −0.425270 0.905067i \(-0.639821\pi\)
−0.425270 + 0.905067i \(0.639821\pi\)
\(374\) 13.1529 0.680121
\(375\) 0 0
\(376\) 11.7205 24.3379i 0.604440 1.25513i
\(377\) −0.357115 + 0.447808i −0.0183924 + 0.0230633i
\(378\) 0 0
\(379\) 9.13137 + 11.4504i 0.469047 + 0.588166i 0.958937 0.283618i \(-0.0915347\pi\)
−0.489891 + 0.871784i \(0.662963\pi\)
\(380\) −3.49312 + 0.797282i −0.179193 + 0.0408997i
\(381\) 0 0
\(382\) −10.8547 5.22733i −0.555373 0.267454i
\(383\) 10.1270 12.6989i 0.517466 0.648881i −0.452603 0.891712i \(-0.649505\pi\)
0.970069 + 0.242831i \(0.0780760\pi\)
\(384\) 0 0
\(385\) −19.8461 + 40.8697i −1.01145 + 2.08291i
\(386\) −0.612852 + 1.27260i −0.0311934 + 0.0647737i
\(387\) 0 0
\(388\) 1.37596 + 0.314053i 0.0698535 + 0.0159436i
\(389\) 2.22663 + 4.62365i 0.112895 + 0.234429i 0.949759 0.312982i \(-0.101328\pi\)
−0.836864 + 0.547410i \(0.815614\pi\)
\(390\) 0 0
\(391\) 8.05959i 0.407591i
\(392\) −7.97981 16.8503i −0.403041 0.851069i
\(393\) 0 0
\(394\) 13.5086 + 16.9392i 0.680553 + 0.853386i
\(395\) −26.7445 + 12.8795i −1.34566 + 0.648037i
\(396\) 0 0
\(397\) 2.39913 + 4.98184i 0.120409 + 0.250031i 0.952458 0.304671i \(-0.0985465\pi\)
−0.832049 + 0.554702i \(0.812832\pi\)
\(398\) 3.93172 + 1.89342i 0.197079 + 0.0949085i
\(399\) 0 0
\(400\) 17.2466 8.30553i 0.862331 0.415277i
\(401\) 16.6316 + 13.2632i 0.830541 + 0.662335i 0.943539 0.331261i \(-0.107474\pi\)
−0.112998 + 0.993595i \(0.536045\pi\)
\(402\) 0 0
\(403\) −0.0863899 0.108330i −0.00430339 0.00539628i
\(404\) 0.0439734 + 0.192660i 0.00218776 + 0.00958519i
\(405\) 0 0
\(406\) 8.71706 10.8581i 0.432620 0.538877i
\(407\) 10.2628 + 8.18431i 0.508708 + 0.405681i
\(408\) 0 0
\(409\) 16.8749 3.85158i 0.834408 0.190448i 0.216087 0.976374i \(-0.430670\pi\)
0.618321 + 0.785926i \(0.287813\pi\)
\(410\) 52.5012i 2.59285i
\(411\) 0 0
\(412\) −2.81693 + 0.642946i −0.138780 + 0.0316757i
\(413\) 21.5099 + 10.4451i 1.05843 + 0.513970i
\(414\) 0 0
\(415\) 5.04028 22.0829i 0.247418 1.08401i
\(416\) 0.117719 0.147614i 0.00577163 0.00723740i
\(417\) 0 0
\(418\) 45.8520 + 10.4654i 2.24269 + 0.511880i
\(419\) −5.31551 + 23.2888i −0.259679 + 1.13773i 0.661916 + 0.749578i \(0.269744\pi\)
−0.921595 + 0.388152i \(0.873114\pi\)
\(420\) 0 0
\(421\) −7.28529 31.9189i −0.355063 1.55563i −0.765312 0.643660i \(-0.777415\pi\)
0.410248 0.911974i \(-0.365442\pi\)
\(422\) 17.8791i 0.870343i
\(423\) 0 0
\(424\) 3.88826 + 17.0356i 0.188830 + 0.827320i
\(425\) −6.22900 2.99973i −0.302151 0.145508i
\(426\) 0 0
\(427\) 1.63191 0.366881i 0.0789735 0.0177546i
\(428\) −1.32915 + 1.05996i −0.0642470 + 0.0512353i
\(429\) 0 0
\(430\) −43.1494 + 34.4105i −2.08085 + 1.65942i
\(431\) −5.17869 + 10.7537i −0.249449 + 0.517986i −0.987666 0.156578i \(-0.949954\pi\)
0.738217 + 0.674564i \(0.235668\pi\)
\(432\) 0 0
\(433\) −2.55898 5.31377i −0.122977 0.255364i 0.830387 0.557186i \(-0.188119\pi\)
−0.953364 + 0.301823i \(0.902405\pi\)
\(434\) 2.09158 + 2.64037i 0.100399 + 0.126742i
\(435\) 0 0
\(436\) 2.01003 0.967982i 0.0962632 0.0463579i
\(437\) −6.41280 + 28.0963i −0.306766 + 1.34403i
\(438\) 0 0
\(439\) 30.0294 23.9476i 1.43322 1.14296i 0.467310 0.884094i \(-0.345223\pi\)
0.965914 0.258864i \(-0.0833481\pi\)
\(440\) −45.7377 −2.18046
\(441\) 0 0
\(442\) −0.379272 −0.0180401
\(443\) −20.7453 + 16.5438i −0.985640 + 0.786022i −0.976847 0.213940i \(-0.931370\pi\)
−0.00879328 + 0.999961i \(0.502799\pi\)
\(444\) 0 0
\(445\) 1.87038 8.19468i 0.0886646 0.388465i
\(446\) −39.2030 + 18.8792i −1.85632 + 0.893955i
\(447\) 0 0
\(448\) 11.6079 14.4589i 0.548421 0.683120i
\(449\) −4.72913 9.82014i −0.223181 0.463441i 0.759070 0.651009i \(-0.225654\pi\)
−0.982252 + 0.187568i \(0.939940\pi\)
\(450\) 0 0
\(451\) 28.0734 58.2950i 1.32192 2.74500i
\(452\) 2.16242 1.72447i 0.101712 0.0811124i
\(453\) 0 0
\(454\) −0.459955 + 0.366802i −0.0215868 + 0.0172149i
\(455\) 0.572274 1.17850i 0.0268286 0.0552489i
\(456\) 0 0
\(457\) −5.20275 2.50551i −0.243374 0.117203i 0.308221 0.951315i \(-0.400266\pi\)
−0.551595 + 0.834112i \(0.685981\pi\)
\(458\) −7.57864 33.2042i −0.354126 1.55153i
\(459\) 0 0
\(460\) 3.23964i 0.151049i
\(461\) −0.522508 2.28926i −0.0243356 0.106621i 0.961301 0.275499i \(-0.0888430\pi\)
−0.985637 + 0.168877i \(0.945986\pi\)
\(462\) 0 0
\(463\) 4.73786 20.7579i 0.220187 0.964702i −0.737150 0.675729i \(-0.763829\pi\)
0.957337 0.288973i \(-0.0933139\pi\)
\(464\) 15.0975 + 3.44589i 0.700882 + 0.159972i
\(465\) 0 0
\(466\) 4.83107 6.05797i 0.223795 0.280630i
\(467\) 5.44149 23.8407i 0.251802 1.10322i −0.677972 0.735087i \(-0.737141\pi\)
0.929774 0.368130i \(-0.120002\pi\)
\(468\) 0 0
\(469\) 28.8188 + 0.0939140i 1.33073 + 0.00433655i
\(470\) −44.9881 + 10.2682i −2.07515 + 0.473638i
\(471\) 0 0
\(472\) 24.0720i 1.10800i
\(473\) 66.3111 15.1351i 3.04899 0.695911i
\(474\) 0 0
\(475\) −19.3279 15.4135i −0.886826 0.707221i
\(476\) 0.865663 + 0.00282100i 0.0396776 + 0.000129301i
\(477\) 0 0
\(478\) −1.58002 6.92253i −0.0722686 0.316629i
\(479\) 13.9399 + 17.4801i 0.636930 + 0.798685i 0.990615 0.136680i \(-0.0436432\pi\)
−0.353686 + 0.935364i \(0.615072\pi\)
\(480\) 0 0
\(481\) −0.295934 0.235999i −0.0134934 0.0107606i
\(482\) −29.1344 + 14.0304i −1.32704 + 0.639067i
\(483\) 0 0
\(484\) −3.81661 1.83798i −0.173482 0.0835446i
\(485\) 9.04951 + 18.7915i 0.410917 + 0.853278i
\(486\) 0 0
\(487\) −35.9295 + 17.3027i −1.62812 + 0.784062i −0.628139 + 0.778101i \(0.716183\pi\)
−0.999982 + 0.00596062i \(0.998103\pi\)
\(488\) 1.04986 + 1.31648i 0.0475249 + 0.0595943i
\(489\) 0 0
\(490\) −14.0055 + 28.6044i −0.632705 + 1.29221i
\(491\) 0.0942791i 0.00425476i 0.999998 + 0.00212738i \(0.000677166\pi\)
−0.999998 + 0.00212738i \(0.999323\pi\)
\(492\) 0 0
\(493\) −2.42672 5.03913i −0.109294 0.226951i
\(494\) −1.32217 0.301776i −0.0594872 0.0135776i
\(495\) 0 0
\(496\) −1.62540 + 3.37517i −0.0729825 + 0.151550i
\(497\) 11.6345 + 2.69541i 0.521876 + 0.120905i
\(498\) 0 0
\(499\) 6.29351 7.89181i 0.281736 0.353286i −0.620747 0.784011i \(-0.713171\pi\)
0.902483 + 0.430725i \(0.141742\pi\)
\(500\) 0.355161 + 0.171036i 0.0158833 + 0.00764898i
\(501\) 0 0
\(502\) −21.0917 + 4.81404i −0.941369 + 0.214861i
\(503\) 18.8923 + 23.6903i 0.842368 + 1.05630i 0.997656 + 0.0684268i \(0.0217980\pi\)
−0.155288 + 0.987869i \(0.549631\pi\)
\(504\) 0 0
\(505\) −1.82082 + 2.28324i −0.0810256 + 0.101603i
\(506\) 18.4508 38.3135i 0.820238 1.70324i
\(507\) 0 0
\(508\) −1.21711 −0.0540007
\(509\) −19.1471 −0.848679 −0.424340 0.905503i \(-0.639494\pi\)
−0.424340 + 0.905503i \(0.639494\pi\)
\(510\) 0 0
\(511\) −14.5997 11.7209i −0.645851 0.518501i
\(512\) 17.7263 + 4.04591i 0.783399 + 0.178806i
\(513\) 0 0
\(514\) −13.3873 10.6760i −0.590490 0.470900i
\(515\) −33.3838 26.6227i −1.47107 1.17314i
\(516\) 0 0
\(517\) 55.4434 + 12.6546i 2.43840 + 0.556548i
\(518\) 7.17555 + 5.76066i 0.315276 + 0.253109i
\(519\) 0 0
\(520\) 1.31887 0.0578365
\(521\) −6.27022 −0.274703 −0.137352 0.990522i \(-0.543859\pi\)
−0.137352 + 0.990522i \(0.543859\pi\)
\(522\) 0 0
\(523\) −12.3641 + 25.6744i −0.540645 + 1.12266i 0.434413 + 0.900714i \(0.356956\pi\)
−0.975059 + 0.221948i \(0.928759\pi\)
\(524\) −1.93977 + 2.43240i −0.0847393 + 0.106260i
\(525\) 0 0
\(526\) 0.187747 + 0.235428i 0.00818617 + 0.0102651i
\(527\) 1.31908 0.301073i 0.0574602 0.0131149i
\(528\) 0 0
\(529\) 2.75473 + 1.32661i 0.119771 + 0.0576787i
\(530\) 18.6108 23.3372i 0.808400 1.01370i
\(531\) 0 0
\(532\) 3.01552 + 0.698619i 0.130739 + 0.0302890i
\(533\) −0.809512 + 1.68097i −0.0350639 + 0.0728108i
\(534\) 0 0
\(535\) −24.4937 5.59052i −1.05895 0.241699i
\(536\) 12.5878 + 26.1389i 0.543711 + 1.12903i
\(537\) 0 0
\(538\) 23.8779i 1.02945i
\(539\) 30.8464 24.2720i 1.32865 1.04547i
\(540\) 0 0
\(541\) −5.53360 6.93892i −0.237908 0.298327i 0.648516 0.761201i \(-0.275390\pi\)
−0.886424 + 0.462873i \(0.846818\pi\)
\(542\) −14.5457 + 7.00486i −0.624793 + 0.300885i
\(543\) 0 0
\(544\) 0.799937 + 1.66109i 0.0342970 + 0.0712185i
\(545\) 29.7046 + 14.3050i 1.27240 + 0.612757i
\(546\) 0 0
\(547\) −6.39834 + 3.08128i −0.273573 + 0.131746i −0.565641 0.824652i \(-0.691371\pi\)
0.292067 + 0.956398i \(0.405657\pi\)
\(548\) −1.91095 1.52394i −0.0816319 0.0650993i
\(549\) 0 0
\(550\) 22.7440 + 28.5200i 0.969807 + 1.21610i
\(551\) −4.45021 19.4976i −0.189585 0.830627i
\(552\) 0 0
\(553\) 25.6446 + 0.0835702i 1.09052 + 0.00355377i
\(554\) −8.33934 6.65040i −0.354305 0.282549i
\(555\) 0 0
\(556\) 3.48375 0.795142i 0.147744 0.0337215i
\(557\) 8.93590i 0.378626i 0.981917 + 0.189313i \(0.0606261\pi\)
−0.981917 + 0.189313i \(0.939374\pi\)
\(558\) 0 0
\(559\) −1.91212 + 0.436428i −0.0808740 + 0.0184590i
\(560\) −35.4205 0.115427i −1.49679 0.00487770i
\(561\) 0 0
\(562\) 1.81201 7.93892i 0.0764349 0.334883i
\(563\) 14.6444 18.3635i 0.617189 0.773930i −0.370757 0.928730i \(-0.620902\pi\)
0.987946 + 0.154800i \(0.0494732\pi\)
\(564\) 0 0
\(565\) 39.8492 + 9.09532i 1.67647 + 0.382643i
\(566\) −5.63260 + 24.6780i −0.236756 + 1.03730i
\(567\) 0 0
\(568\) 2.67528 + 11.7212i 0.112252 + 0.491809i
\(569\) 22.9316i 0.961342i −0.876901 0.480671i \(-0.840393\pi\)
0.876901 0.480671i \(-0.159607\pi\)
\(570\) 0 0
\(571\) 3.34250 + 14.6444i 0.139879 + 0.612851i 0.995460 + 0.0951815i \(0.0303431\pi\)
−0.855581 + 0.517669i \(0.826800\pi\)
\(572\) 0.169277 + 0.0815193i 0.00707781 + 0.00340849i
\(573\) 0 0
\(574\) 19.8127 40.8008i 0.826964 1.70299i
\(575\) −17.4760 + 13.9366i −0.728799 + 0.581198i
\(576\) 0 0
\(577\) 5.54341 4.42072i 0.230775 0.184037i −0.501274 0.865288i \(-0.667135\pi\)
0.732050 + 0.681251i \(0.238564\pi\)
\(578\) −9.35147 + 19.4185i −0.388970 + 0.807704i
\(579\) 0 0
\(580\) −0.975445 2.02553i −0.0405032 0.0841057i
\(581\) −12.2506 + 15.2594i −0.508239 + 0.633068i
\(582\) 0 0
\(583\) −33.1434 + 15.9610i −1.37266 + 0.661038i
\(584\) 4.19404 18.3753i 0.173550 0.760374i
\(585\) 0 0
\(586\) −31.1865 + 24.8704i −1.28830 + 1.02739i
\(587\) 16.8193 0.694206 0.347103 0.937827i \(-0.387165\pi\)
0.347103 + 0.937827i \(0.387165\pi\)
\(588\) 0 0
\(589\) 4.83798 0.199346
\(590\) 32.1496 25.6385i 1.32358 1.05552i
\(591\) 0 0
\(592\) −2.27722 + 9.97714i −0.0935931 + 0.410058i
\(593\) −9.27765 + 4.46788i −0.380987 + 0.183474i −0.614568 0.788864i \(-0.710670\pi\)
0.233581 + 0.972337i \(0.424956\pi\)
\(594\) 0 0
\(595\) 7.94364 + 10.0279i 0.325657 + 0.411103i
\(596\) 0.846268 + 1.75729i 0.0346645 + 0.0719816i
\(597\) 0 0
\(598\) −0.532040 + 1.10479i −0.0217567 + 0.0451783i
\(599\) 17.7390 14.1464i 0.724798 0.578007i −0.190065 0.981771i \(-0.560870\pi\)
0.914863 + 0.403765i \(0.132299\pi\)
\(600\) 0 0
\(601\) −7.17003 + 5.71790i −0.292471 + 0.233238i −0.758722 0.651414i \(-0.774176\pi\)
0.466251 + 0.884653i \(0.345604\pi\)
\(602\) 46.5188 10.4582i 1.89596 0.426246i
\(603\) 0 0
\(604\) −1.14936 0.553504i −0.0467669 0.0225217i
\(605\) −13.9302 61.0323i −0.566344 2.48132i
\(606\) 0 0
\(607\) 26.9406i 1.09348i −0.837301 0.546742i \(-0.815868\pi\)
0.837301 0.546742i \(-0.184132\pi\)
\(608\) 1.46696 + 6.42716i 0.0594929 + 0.260656i
\(609\) 0 0
\(610\) 0.640064 2.80430i 0.0259154 0.113543i
\(611\) −1.59874 0.364902i −0.0646782 0.0147624i
\(612\) 0 0
\(613\) 2.23951 2.80826i 0.0904532 0.113425i −0.734545 0.678560i \(-0.762604\pi\)
0.824998 + 0.565135i \(0.191176\pi\)
\(614\) 8.44344 36.9931i 0.340749 1.49292i
\(615\) 0 0
\(616\) 35.5446 + 17.2603i 1.43213 + 0.695438i
\(617\) −14.0559 + 3.20816i −0.565868 + 0.129156i −0.495878 0.868392i \(-0.665154\pi\)
−0.0699898 + 0.997548i \(0.522297\pi\)
\(618\) 0 0
\(619\) 0.980947i 0.0394276i 0.999806 + 0.0197138i \(0.00627550\pi\)
−0.999806 + 0.0197138i \(0.993725\pi\)
\(620\) 0.530221 0.121019i 0.0212942 0.00486026i
\(621\) 0 0
\(622\) −24.4582 19.5047i −0.980683 0.782069i
\(623\) −4.54602 + 5.66258i −0.182133 + 0.226866i
\(624\) 0 0
\(625\) 6.16825 + 27.0249i 0.246730 + 1.08099i
\(626\) −22.3109 27.9769i −0.891721 1.11818i
\(627\) 0 0
\(628\) 3.01232 + 2.40225i 0.120205 + 0.0958602i
\(629\) 3.33010 1.60369i 0.132780 0.0639434i
\(630\) 0 0
\(631\) −13.1070 6.31199i −0.521781 0.251276i 0.154405 0.988008i \(-0.450654\pi\)
−0.676186 + 0.736731i \(0.736368\pi\)
\(632\) 11.2014 + 23.2599i 0.445567 + 0.925229i
\(633\) 0 0
\(634\) −24.6450 + 11.8684i −0.978777 + 0.471354i
\(635\) −11.2145 14.0625i −0.445034 0.558055i
\(636\) 0 0
\(637\) −0.889474 + 0.699897i −0.0352423 + 0.0277309i
\(638\) 29.5103i 1.16833i
\(639\) 0 0
\(640\) −16.9382 35.1726i −0.669542 1.39032i
\(641\) −15.3622 3.50631i −0.606769 0.138491i −0.0919120 0.995767i \(-0.529298\pi\)
−0.514857 + 0.857276i \(0.672155\pi\)
\(642\) 0 0
\(643\) 7.33780 15.2371i 0.289375 0.600892i −0.704711 0.709495i \(-0.748923\pi\)
0.994085 + 0.108602i \(0.0346375\pi\)
\(644\) 1.22256 2.51766i 0.0481757 0.0992096i
\(645\) 0 0
\(646\) 8.25677 10.3537i 0.324858 0.407360i
\(647\) −29.3155 14.1176i −1.15251 0.555020i −0.242724 0.970096i \(-0.578041\pi\)
−0.909787 + 0.415076i \(0.863755\pi\)
\(648\) 0 0
\(649\) −49.4069 + 11.2768i −1.93939 + 0.442653i
\(650\) −0.655836 0.822392i −0.0257240 0.0322569i
\(651\) 0 0
\(652\) −0.953435 + 1.19557i −0.0373394 + 0.0468221i
\(653\) 16.6651 34.6055i 0.652157 1.35422i −0.268286 0.963339i \(-0.586457\pi\)
0.920443 0.390878i \(-0.127829\pi\)
\(654\) 0 0
\(655\) −45.9770 −1.79647
\(656\) 50.4431 1.96947
\(657\) 0 0
\(658\) 38.8370 + 8.99755i 1.51402 + 0.350761i
\(659\) −14.1684 3.23384i −0.551922 0.125973i −0.0625406 0.998042i \(-0.519920\pi\)
−0.489381 + 0.872070i \(0.662777\pi\)
\(660\) 0 0
\(661\) 28.9366 + 23.0762i 1.12550 + 0.897558i 0.995575 0.0939653i \(-0.0299543\pi\)
0.129927 + 0.991524i \(0.458526\pi\)
\(662\) −19.3929 15.4653i −0.753727 0.601078i
\(663\) 0 0
\(664\) −19.2057 4.38357i −0.745325 0.170115i
\(665\) 19.7132 + 41.2784i 0.764445 + 1.60071i
\(666\) 0 0
\(667\) −18.0828 −0.700168
\(668\) 2.74559 0.106230
\(669\) 0 0
\(670\) 21.5031 44.6517i 0.830737 1.72504i
\(671\) −2.21021 + 2.77152i −0.0853243 + 0.106993i
\(672\) 0 0
\(673\) 10.8518 + 13.6078i 0.418308 + 0.524542i 0.945683 0.325091i \(-0.105395\pi\)
−0.527375 + 0.849633i \(0.676824\pi\)
\(674\) 49.8317 11.3738i 1.91944 0.438101i
\(675\) 0 0
\(676\) 2.42234 + 1.16654i 0.0931668 + 0.0448668i
\(677\) −1.30490 + 1.63630i −0.0501514 + 0.0628879i −0.806275 0.591541i \(-0.798520\pi\)
0.756123 + 0.654429i \(0.227091\pi\)
\(678\) 0 0
\(679\) 0.0587189 18.0187i 0.00225342 0.691494i
\(680\) −5.58783 + 11.6033i −0.214284 + 0.444964i
\(681\) 0 0
\(682\) −6.95988 1.58855i −0.266507 0.0608286i
\(683\) 1.08682 + 2.25680i 0.0415860 + 0.0863542i 0.920727 0.390208i \(-0.127597\pi\)
−0.879141 + 0.476562i \(0.841883\pi\)
\(684\) 0 0
\(685\) 36.1208i 1.38010i
\(686\) 21.6789 16.9443i 0.827702 0.646935i
\(687\) 0 0
\(688\) 33.0616 + 41.4579i 1.26046 + 1.58057i
\(689\) 0.955709 0.460245i 0.0364096 0.0175339i
\(690\) 0 0
\(691\) 18.1168 + 37.6199i 0.689195 + 1.43113i 0.892058 + 0.451921i \(0.149261\pi\)
−0.202863 + 0.979207i \(0.565025\pi\)
\(692\) −0.225098 0.108401i −0.00855694 0.00412080i
\(693\) 0 0
\(694\) 16.9327 8.15435i 0.642756 0.309535i
\(695\) 41.2864 + 32.9248i 1.56608 + 1.24891i
\(696\) 0 0
\(697\) −11.3591 14.2439i −0.430258 0.539527i
\(698\) −0.972560 4.26107i −0.0368120 0.161284i
\(699\) 0 0
\(700\) 1.49079 + 1.88193i 0.0563464 + 0.0711304i
\(701\) −24.0216 19.1566i −0.907282 0.723533i 0.0541625 0.998532i \(-0.482751\pi\)
−0.961445 + 0.274999i \(0.911323\pi\)
\(702\) 0 0
\(703\) 12.8850 2.94092i 0.485967 0.110919i
\(704\) 39.2968i 1.48105i
\(705\) 0 0
\(706\) 30.2730 6.90962i 1.13934 0.260047i
\(707\) 2.27667 1.08726i 0.0856231 0.0408907i
\(708\) 0 0
\(709\) −9.65247 + 42.2902i −0.362506 + 1.58824i 0.384305 + 0.923206i \(0.374441\pi\)
−0.746811 + 0.665036i \(0.768416\pi\)
\(710\) 12.8050 16.0569i 0.480562 0.602605i
\(711\) 0 0
\(712\) −7.12697 1.62668i −0.267095 0.0609626i
\(713\) 0.973400 4.26474i 0.0364541 0.159716i
\(714\) 0 0
\(715\) 0.617842 + 2.70694i 0.0231060 + 0.101234i
\(716\) 3.64925i 0.136379i
\(717\) 0 0
\(718\) −8.74478 38.3134i −0.326352 1.42984i
\(719\) −5.29463 2.54976i −0.197457 0.0950900i 0.332543 0.943088i \(-0.392093\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(720\) 0 0
\(721\) 15.8972 + 33.2878i 0.592041 + 1.23970i
\(722\) 14.9524 11.9242i 0.556472 0.443772i
\(723\) 0 0
\(724\) −0.391254 + 0.312014i −0.0145408 + 0.0115959i
\(725\) 6.73029 13.9756i 0.249957 0.519041i
\(726\) 0 0
\(727\) 21.0355 + 43.6807i 0.780163 + 1.62003i 0.784574 + 0.620036i \(0.212882\pi\)
−0.00441016 + 0.999990i \(0.501404\pi\)
\(728\) −1.02495 0.497711i −0.0379872 0.0184464i
\(729\) 0 0
\(730\) −29.0083 + 13.9697i −1.07364 + 0.517040i
\(731\) 4.26167 18.6716i 0.157623 0.690594i
\(732\) 0 0
\(733\) 20.5255 16.3685i 0.758125 0.604585i −0.166244 0.986085i \(-0.553164\pi\)
0.924369 + 0.381500i \(0.124592\pi\)
\(734\) −8.35963 −0.308560
\(735\) 0 0
\(736\) 5.96077 0.219717
\(737\) −47.7522 + 38.0811i −1.75897 + 1.40273i
\(738\) 0 0
\(739\) 5.33449 23.3719i 0.196232 0.859751i −0.776922 0.629597i \(-0.783220\pi\)
0.973154 0.230154i \(-0.0739228\pi\)
\(740\) 1.33857 0.644623i 0.0492069 0.0236968i
\(741\) 0 0
\(742\) −23.2701 + 11.1130i −0.854270 + 0.407971i
\(743\) −1.67693 3.48217i −0.0615205 0.127749i 0.867942 0.496666i \(-0.165443\pi\)
−0.929462 + 0.368918i \(0.879728\pi\)
\(744\) 0 0
\(745\) −12.5063 + 25.9695i −0.458194 + 0.951450i
\(746\) 19.0803 15.2161i 0.698581 0.557100i
\(747\) 0 0
\(748\) −1.43439 + 1.14389i −0.0524464 + 0.0418246i
\(749\) 16.9253 + 13.5879i 0.618436 + 0.496492i
\(750\) 0 0
\(751\) 5.76201 + 2.77484i 0.210259 + 0.101255i 0.536049 0.844187i \(-0.319916\pi\)
−0.325791 + 0.945442i \(0.605630\pi\)
\(752\) 9.86572 + 43.2246i 0.359766 + 1.57624i
\(753\) 0 0
\(754\) 0.850948i 0.0309897i
\(755\) −4.19506 18.3797i −0.152674 0.668907i
\(756\) 0 0
\(757\) 0.101990 0.446847i 0.00370689 0.0162409i −0.973041 0.230634i \(-0.925920\pi\)
0.976748 + 0.214393i \(0.0687772\pi\)
\(758\) −21.2130 4.84174i −0.770492 0.175860i
\(759\) 0 0
\(760\) −28.7120 + 36.0037i −1.04149 + 1.30599i
\(761\) 8.93457 39.1449i 0.323878 1.41900i −0.506711 0.862116i \(-0.669139\pi\)
0.830589 0.556886i \(-0.188004\pi\)
\(762\) 0 0
\(763\) −17.6863 22.3267i −0.640286 0.808282i
\(764\) 1.63837 0.373946i 0.0592740 0.0135289i
\(765\) 0 0
\(766\) 24.1310i 0.871889i
\(767\) 1.42468 0.325173i 0.0514421 0.0117413i
\(768\) 0 0
\(769\) −2.13350 1.70141i −0.0769358 0.0613543i 0.584267 0.811562i \(-0.301382\pi\)
−0.661203 + 0.750207i \(0.729954\pi\)
\(770\) −14.8055 65.8556i −0.533553 2.37327i
\(771\) 0 0
\(772\) −0.0438415 0.192082i −0.00157789 0.00691318i
\(773\) −14.4004 18.0575i −0.517946 0.649483i 0.452226 0.891904i \(-0.350630\pi\)
−0.970171 + 0.242420i \(0.922059\pi\)
\(774\) 0 0
\(775\) 2.93379 + 2.33962i 0.105385 + 0.0840415i
\(776\) 16.3431 7.87042i 0.586683 0.282532i
\(777\) 0 0
\(778\) −6.86925 3.30806i −0.246274 0.118600i
\(779\) −28.2653 58.6935i −1.01271 2.10291i
\(780\) 0 0
\(781\) −22.8040 + 10.9818i −0.815991 + 0.392961i
\(782\) −7.46563 9.36160i −0.266970 0.334770i
\(783\) 0 0
\(784\) 27.4831 + 13.4565i 0.981539 + 0.480590i
\(785\) 56.9388i 2.03223i
\(786\) 0 0
\(787\) −7.42263 15.4133i −0.264588 0.549423i 0.725773 0.687935i \(-0.241482\pi\)
−0.990361 + 0.138512i \(0.955768\pi\)
\(788\) −2.94635 0.672485i −0.104959 0.0239563i
\(789\) 0 0
\(790\) 19.1347 39.7337i 0.680783 1.41366i
\(791\) −27.5360 22.1064i −0.979069 0.786015i
\(792\) 0 0
\(793\) 0.0637328 0.0799184i 0.00226322 0.00283798i
\(794\) −7.40140 3.56432i −0.262666 0.126493i
\(795\) 0 0
\(796\) −0.593441 + 0.135449i −0.0210339 + 0.00480086i
\(797\) 8.00799 + 10.0417i 0.283658 + 0.355695i 0.903164 0.429296i \(-0.141238\pi\)
−0.619506 + 0.784992i \(0.712667\pi\)
\(798\) 0 0
\(799\) 9.98393 12.5195i 0.353206 0.442907i
\(800\) −2.21856 + 4.60689i −0.0784379 + 0.162878i
\(801\) 0 0
\(802\) −31.6042 −1.11598
\(803\) 39.6793 1.40025
\(804\) 0 0
\(805\) 40.3537 9.07223i 1.42228 0.319754i
\(806\) 0.200692 + 0.0458066i 0.00706908 + 0.00161347i
\(807\) 0 0
\(808\) 1.98575 + 1.58358i 0.0698585 + 0.0557103i
\(809\) 42.2041 + 33.6567i 1.48382 + 1.18330i 0.938599 + 0.345011i \(0.112125\pi\)
0.545219 + 0.838294i \(0.316447\pi\)
\(810\) 0 0
\(811\) −13.2223 3.01790i −0.464298 0.105973i −0.0160286 0.999872i \(-0.505102\pi\)
−0.448269 + 0.893899i \(0.647959\pi\)
\(812\) −0.00632931 + 1.94223i −0.000222115 + 0.0681590i
\(813\) 0 0
\(814\) −19.5019 −0.683541
\(815\) −22.5986 −0.791594
\(816\) 0 0
\(817\) 29.7130 61.6996i 1.03953 2.15860i
\(818\) −16.0332 + 20.1050i −0.560589 + 0.702956i
\(819\) 0 0
\(820\) −4.56594 5.72550i −0.159449 0.199943i
\(821\) −54.4258 + 12.4223i −1.89947 + 0.433542i −0.999994 0.00342203i \(-0.998911\pi\)
−0.899479 + 0.436964i \(0.856054\pi\)
\(822\) 0 0
\(823\) 22.6670 + 10.9159i 0.790122 + 0.380503i 0.785009 0.619484i \(-0.212658\pi\)
0.00511310 + 0.999987i \(0.498372\pi\)
\(824\) −23.1540 + 29.0342i −0.806607 + 1.01145i
\(825\) 0 0
\(826\) −34.6601 + 7.79220i −1.20598 + 0.271125i
\(827\) 2.87253 5.96486i 0.0998876 0.207419i −0.845036 0.534709i \(-0.820421\pi\)
0.944924 + 0.327290i \(0.106136\pi\)
\(828\) 0 0
\(829\) −23.7815 5.42798i −0.825967 0.188522i −0.211414 0.977397i \(-0.567807\pi\)
−0.614554 + 0.788875i \(0.710664\pi\)
\(830\) 14.6010 + 30.3192i 0.506807 + 1.05239i
\(831\) 0 0
\(832\) 1.13315i 0.0392848i
\(833\) −2.38904 10.7908i −0.0827755 0.373879i
\(834\) 0 0
\(835\) 25.2979 + 31.7226i 0.875471 + 1.09781i
\(836\) −5.91054 + 2.84637i −0.204420 + 0.0984436i
\(837\) 0 0
\(838\) −15.3982 31.9748i −0.531923 1.10455i
\(839\) 18.5319 + 8.92451i 0.639793 + 0.308108i 0.725510 0.688211i \(-0.241604\pi\)
−0.0857169 + 0.996320i \(0.527318\pi\)
\(840\) 0 0
\(841\) −14.8221 + 7.13796i −0.511108 + 0.246137i
\(842\) 38.0288 + 30.3270i 1.31056 + 1.04514i
\(843\) 0 0
\(844\) −1.55492 1.94981i −0.0535225 0.0671151i
\(845\) 8.84128 + 38.7362i 0.304149 + 1.33257i
\(846\) 0 0
\(847\) −12.2064 + 52.6876i −0.419416 + 1.81037i
\(848\) −22.4224 17.8812i −0.769987 0.614044i
\(849\) 0 0
\(850\) 10.0139 2.28562i 0.343475 0.0783960i
\(851\) 11.9500i 0.409641i
\(852\) 0 0
\(853\) −22.8710 + 5.22016i −0.783089 + 0.178735i −0.595331 0.803480i \(-0.702979\pi\)
−0.187758 + 0.982215i \(0.560122\pi\)
\(854\) −1.55570 + 1.93779i −0.0532348 + 0.0663099i
\(855\) 0 0
\(856\) −4.86211 + 21.3023i −0.166184 + 0.728098i
\(857\) −14.9678 + 18.7690i −0.511289 + 0.641136i −0.968734 0.248102i \(-0.920193\pi\)
0.457445 + 0.889238i \(0.348765\pi\)
\(858\) 0 0
\(859\) 40.5766 + 9.26135i 1.38446 + 0.315993i 0.848921 0.528520i \(-0.177253\pi\)
0.535535 + 0.844513i \(0.320110\pi\)
\(860\) 1.71303 7.50525i 0.0584137 0.255927i
\(861\) 0 0
\(862\) −3.94586 17.2879i −0.134396 0.588830i
\(863\) 5.32102i 0.181130i 0.995891 + 0.0905649i \(0.0288673\pi\)
−0.995891 + 0.0905649i \(0.971133\pi\)
\(864\) 0 0
\(865\) −0.821584 3.59960i −0.0279347 0.122390i
\(866\) 7.89454 + 3.80181i 0.268267 + 0.129191i
\(867\) 0 0
\(868\) −0.457726 0.106043i −0.0155362 0.00359935i
\(869\) −42.4927 + 33.8868i −1.44147 + 1.14953i
\(870\) 0 0
\(871\) 1.37696 1.09809i 0.0466566 0.0372074i
\(872\) 12.4411 25.8343i 0.421310 0.874859i
\(873\) 0 0
\(874\) −18.5769 38.5754i −0.628375 1.30483i
\(875\) 1.13588 4.90293i 0.0383999 0.165749i
\(876\) 0 0
\(877\) 36.1086 17.3890i 1.21930 0.587184i 0.290184 0.956971i \(-0.406283\pi\)
0.929117 + 0.369787i \(0.120569\pi\)
\(878\) −12.6978 + 55.6326i −0.428529 + 1.87751i
\(879\) 0 0
\(880\) 58.6911 46.8046i 1.97848 1.57778i
\(881\) −12.4143 −0.418250 −0.209125 0.977889i \(-0.567062\pi\)
−0.209125 + 0.977889i \(0.567062\pi\)
\(882\) 0 0
\(883\) 50.9904 1.71596 0.857981 0.513681i \(-0.171718\pi\)
0.857981 + 0.513681i \(0.171718\pi\)
\(884\) 0.0413614 0.0329846i 0.00139113 0.00110939i
\(885\) 0 0
\(886\) 8.77207 38.4329i 0.294703 1.29118i
\(887\) −9.96564 + 4.79920i −0.334613 + 0.161141i −0.593644 0.804728i \(-0.702311\pi\)
0.259031 + 0.965869i \(0.416597\pi\)
\(888\) 0 0
\(889\) 3.40838 + 15.1607i 0.114313 + 0.508472i
\(890\) 5.41822 + 11.2511i 0.181619 + 0.377136i
\(891\) 0 0
\(892\) 2.63339 5.46828i 0.0881723 0.183092i
\(893\) 44.7661 35.6998i 1.49804 1.19465i
\(894\) 0 0
\(895\) −42.1635 + 33.6243i −1.40937 + 1.12394i
\(896\) −0.109906 + 33.7261i −0.00367170 + 1.12671i
\(897\) 0 0
\(898\) 14.5895 + 7.02595i 0.486859 + 0.234459i
\(899\) 0.675497 + 2.95955i 0.0225291 + 0.0987064i
\(900\) 0 0
\(901\) 10.3582i 0.345080i
\(902\) 21.3903 + 93.7168i 0.712218 + 3.12043i
\(903\) 0 0
\(904\) 7.91026 34.6571i 0.263091 1.15268i
\(905\) −7.21004 1.64564i −0.239670 0.0547031i
\(906\) 0 0
\(907\) 23.5926 29.5842i 0.783381 0.982328i −0.216601 0.976260i \(-0.569497\pi\)
0.999982 0.00606799i \(-0.00193151\pi\)
\(908\) 0.0182602 0.0800031i 0.000605985 0.00265500i
\(909\) 0 0
\(910\) 0.426925 + 1.89898i 0.0141524 + 0.0629507i
\(911\) 7.84963 1.79163i 0.260070 0.0593593i −0.0904978 0.995897i \(-0.528846\pi\)
0.350568 + 0.936537i \(0.385989\pi\)
\(912\) 0 0
\(913\) 41.4725i 1.37254i
\(914\) 8.36410 1.90905i 0.276660 0.0631458i
\(915\) 0 0
\(916\) 3.71420 + 2.96197i 0.122721 + 0.0978664i
\(917\) 35.7306 + 17.3506i 1.17993 + 0.572968i
\(918\) 0 0
\(919\) 5.49391 + 24.0704i 0.181227 + 0.794008i 0.981047 + 0.193768i \(0.0620711\pi\)
−0.799820 + 0.600240i \(0.795072\pi\)
\(920\) 25.9609 + 32.5539i 0.855905 + 1.07327i
\(921\) 0 0
\(922\) 2.72747 + 2.17508i 0.0898243 + 0.0716325i
\(923\) 0.657566 0.316667i 0.0216441 0.0104232i
\(924\) 0 0
\(925\) 9.23577 + 4.44771i 0.303670 + 0.146240i
\(926\) 13.7249 + 28.5000i 0.451028 + 0.936569i
\(927\) 0 0
\(928\) −3.72687 + 1.79477i −0.122341 + 0.0589161i
\(929\) −33.0461 41.4385i −1.08421 1.35955i −0.928322 0.371776i \(-0.878749\pi\)
−0.155884 0.987775i \(-0.549823\pi\)
\(930\) 0 0
\(931\) 0.257566 39.5184i 0.00844139 1.29516i
\(932\) 1.08080i 0.0354028i
\(933\) 0 0
\(934\) 15.7632 + 32.7326i 0.515788 + 1.07104i
\(935\) −26.4329 6.03315i −0.864450 0.197305i
\(936\) 0 0
\(937\) 18.5050 38.4261i 0.604533 1.25533i −0.344096 0.938935i \(-0.611814\pi\)
0.948629 0.316391i \(-0.102471\pi\)
\(938\) −33.5614 + 26.5858i −1.09582 + 0.868058i
\(939\) 0 0
\(940\) 4.01315 5.03234i 0.130895 0.164137i
\(941\) −50.9216 24.5225i −1.66000 0.799412i −0.998789 0.0492076i \(-0.984330\pi\)
−0.661207 0.750204i \(-0.729955\pi\)
\(942\) 0 0
\(943\) −57.4260 + 13.1071i −1.87005 + 0.426827i
\(944\) −24.6335 30.8894i −0.801751 1.00536i
\(945\) 0 0
\(946\) −63.0038 + 79.0043i −2.04843 + 2.56865i
\(947\) −11.9160 + 24.7438i −0.387218 + 0.804066i 0.612688 + 0.790325i \(0.290088\pi\)
−0.999906 + 0.0137411i \(0.995626\pi\)
\(948\) 0 0
\(949\) −1.14418 −0.0371416
\(950\) 36.7279 1.19161
\(951\) 0 0
\(952\) 8.72131 6.90864i 0.282659 0.223910i
\(953\) −37.7015 8.60512i −1.22127 0.278747i −0.437170 0.899379i \(-0.644019\pi\)
−0.784102 + 0.620632i \(0.786876\pi\)
\(954\) 0 0
\(955\) 19.4165 + 15.4841i 0.628303 + 0.501055i
\(956\) 0.774350 + 0.617524i 0.0250443 + 0.0199721i
\(957\) 0 0
\(958\) −32.3837 7.39137i −1.04627 0.238804i
\(959\) −13.6311 + 28.0709i −0.440171 + 0.906456i
\(960\) 0 0
\(961\) 30.2656 0.976311
\(962\) 0.562348 0.0181308
\(963\) 0 0
\(964\) 1.95705 4.06385i 0.0630322 0.130888i
\(965\) 1.81536 2.27639i 0.0584386 0.0732796i
\(966\) 0 0
\(967\) −2.11785 2.65570i −0.0681055 0.0854016i 0.746612 0.665260i \(-0.231679\pi\)
−0.814717 + 0.579858i \(0.803108\pi\)
\(968\) −53.0802 + 12.1152i −1.70606 + 0.389398i
\(969\) 0 0
\(970\) −27.9181 13.4446i −0.896395 0.431681i
\(971\) 20.7106 25.9702i 0.664634 0.833424i −0.329205 0.944258i \(-0.606781\pi\)
0.993839 + 0.110834i \(0.0353522\pi\)
\(972\) 0 0
\(973\) −19.6603 41.1676i −0.630280 1.31977i
\(974\) 25.7062 53.3796i 0.823681 1.71039i
\(975\) 0 0
\(976\) −2.69438 0.614974i −0.0862449 0.0196848i
\(977\) −10.9659 22.7709i −0.350830 0.728506i 0.648639 0.761096i \(-0.275339\pi\)
−0.999469 + 0.0325905i \(0.989624\pi\)
\(978\) 0 0
\(979\) 15.3899i 0.491863i
\(980\) −0.960303 4.33748i −0.0306758 0.138556i
\(981\) 0 0
\(982\) −0.0873310 0.109510i −0.00278685 0.00349459i
\(983\) 11.8859 5.72393i 0.379100 0.182565i −0.234623 0.972086i \(-0.575386\pi\)
0.613723 + 0.789522i \(0.289671\pi\)
\(984\) 0 0
\(985\) −19.3778 40.2385i −0.617429 1.28210i
\(986\) 7.48651 + 3.60531i 0.238419 + 0.114816i
\(987\) 0 0
\(988\) 0.170434 0.0820766i 0.00542222 0.00261120i
\(989\) −48.4108 38.6063i −1.53937 1.22761i
\(990\) 0 0
\(991\) 22.1327 + 27.7536i 0.703070 + 0.881622i 0.997249 0.0741288i \(-0.0236176\pi\)
−0.294179 + 0.955750i \(0.595046\pi\)
\(992\) −0.222669 0.975578i −0.00706976 0.0309746i
\(993\) 0 0
\(994\) −16.0107 + 7.64619i −0.507830 + 0.242522i
\(995\) −7.03295 5.60859i −0.222960 0.177804i
\(996\) 0 0
\(997\) −4.60452 + 1.05095i −0.145827 + 0.0332840i −0.294811 0.955556i \(-0.595257\pi\)
0.148984 + 0.988840i \(0.452400\pi\)
\(998\) 14.9964i 0.474703i
\(999\) 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 441.2.w.a.188.6 120
3.2 odd 2 inner 441.2.w.a.188.15 yes 120
49.6 odd 14 inner 441.2.w.a.251.15 yes 120
147.104 even 14 inner 441.2.w.a.251.6 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.w.a.188.6 120 1.1 even 1 trivial
441.2.w.a.188.15 yes 120 3.2 odd 2 inner
441.2.w.a.251.6 yes 120 147.104 even 14 inner
441.2.w.a.251.15 yes 120 49.6 odd 14 inner