Properties

Label 441.2.w.a.188.15
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 188.15
Character \(\chi\) \(=\) 441.188
Dual form 441.2.w.a.251.15

$q$-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 −0.119882 0.992788i \(-0.538252\pi\)
0.941221 + 0.337793i \(0.109680\pi\)
\(3\) 0 0
\(4\) 0.0461133 0.202036i 0.0230567 0.101018i
\(5\) −2.75921 + 1.32877i −1.23396 + 0.594242i −0.933165 0.359448i \(-0.882965\pi\)
−0.300792 + 0.953690i \(0.597251\pi\)
\(6\) 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 \(0.606309\pi\)
−0.994002 + 0.109361i \(0.965120\pi\)
\(12\) 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 0.999496 0.0317384i \(-0.0101043\pi\)
−0.914286 + 0.405070i \(0.867247\pi\)
\(18\) 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 0.707245 0.706969i \(-0.249938\pi\)
0.330463 + 0.943819i \(0.392795\pi\)
\(24\) 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 −0.530799 0.847498i \(-0.678108\pi\)
−0.110518 + 0.993874i \(0.535251\pi\)
\(30\) 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 \(0.714344\pi\)
−1.00000 0.000182349i \(0.999942\pi\)
\(42\) 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 \(-0.949260\pi\)
0.0649500 0.997889i \(-0.479311\pi\)
\(48\) 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 0.637932 0.770093i \(-0.279790\pi\)
0.240626 + 0.970618i \(0.422647\pi\)
\(54\) 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 0.880904 0.473295i \(-0.156936\pi\)
0.179198 + 0.983813i \(0.442650\pi\)
\(60\) 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 0.475524 0.879703i \(-0.342258\pi\)
0.0467436 + 0.998907i \(0.485116\pi\)
\(72\) 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 −0.967609 0.252452i \(-0.918763\pi\)
0.461436 + 0.887173i \(0.347334\pi\)
\(84\) 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 −0.864212 0.503129i \(-0.832182\pi\)
0.682819 + 0.730587i \(0.260754\pi\)
\(90\) 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 −0.390650 0.920539i \(-0.627750\pi\)
0.476140 + 0.879370i \(0.342036\pi\)
\(102\) 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 0.882401 0.470499i \(-0.155926\pi\)
−0.262350 + 0.964973i \(0.584497\pi\)
\(108\) 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 −0.00549020 0.999985i \(-0.501748\pi\)
−0.976135 + 0.217165i \(0.930319\pi\)
\(114\) 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 0.918432 0.395579i \(-0.129456\pi\)
0.263357 + 0.964698i \(0.415170\pi\)
\(132\) 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 \(0.310936\pi\)
−0.996862 + 0.0791550i \(0.974778\pi\)
\(138\) 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 −0.273874 0.961766i \(-0.588305\pi\)
0.876710 + 0.481020i \(0.159734\pi\)
\(150\) 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 \(-0.900105\pi\)
0.723023 0.690824i \(-0.242752\pi\)
\(168\) 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 −0.984102 0.177606i \(-0.943165\pi\)
0.963705 + 0.266968i \(0.0860219\pi\)
\(174\) 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 0.474057 0.880494i \(-0.342789\pi\)
0.809143 + 0.587612i \(0.199932\pi\)
\(180\) 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 0.734027 0.679120i \(-0.237639\pi\)
−0.988616 + 0.150461i \(0.951924\pi\)
\(192\) 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 \(0.173885\pi\)
−0.854465 + 0.519509i \(0.826115\pi\)
\(198\) 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 \(-0.504183\pi\)
−0.0131412 + 0.999914i \(0.504183\pi\)
\(228\) 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 −0.0526958 0.998611i \(-0.516781\pi\)
0.385804 + 0.922581i \(0.373924\pi\)
\(234\) 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 −0.823072 0.567936i \(-0.807742\pi\)
0.957208 + 0.289401i \(0.0934563\pi\)
\(240\) 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 −0.0287041 0.999588i \(-0.509138\pi\)
−0.799406 + 0.600791i \(0.794852\pi\)
\(252\) 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 \(-0.954387\pi\)
0.829772 0.558103i \(-0.188470\pi\)
\(258\) 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 \(0.00198914\pi\)
−0.999980 + 0.00624902i \(0.998011\pi\)
\(264\) 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 −0.987044 0.160451i \(-0.948705\pi\)
0.376066 + 0.926593i \(0.377277\pi\)
\(270\) 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 −0.487282 0.873245i \(-0.662012\pi\)
0.742920 + 0.669380i \(0.233440\pi\)
\(282\) 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 \(-0.786962\pi\)
−0.784270 + 0.620420i \(0.786962\pi\)
\(294\) 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 \(-0.867787\pi\)
0.649280 0.760550i \(-0.275071\pi\)
\(312\) 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 −0.313622 0.949548i \(-0.601542\pi\)
−0.694557 + 0.719438i \(0.744400\pi\)
\(318\) 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 0.540333 0.841451i \(-0.318298\pi\)
0.121731 + 0.992563i \(0.461155\pi\)
\(348\) 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 0.861706 0.507408i \(-0.169396\pi\)
0.140557 + 0.990073i \(0.455111\pi\)
\(354\) 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 \(-0.611201\pi\)
0.948017 0.318219i \(-0.103085\pi\)
\(360\) 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 −0.970069 0.242831i \(-0.921924\pi\)
0.452603 + 0.891712i \(0.350495\pi\)
\(384\) 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 0.836864 0.547410i \(-0.184386\pi\)
−0.949759 + 0.312982i \(0.898672\pi\)
\(390\) 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 0.112998 0.993595i \(-0.463955\pi\)
−0.943539 + 0.331261i \(0.892526\pi\)
\(402\) 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 \(-0.730256\pi\)
0.921595 0.388152i \(-0.126886\pi\)
\(420\) 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 −0.738217 0.674564i \(-0.764332\pi\)
0.987666 + 0.156578i \(0.0500461\pi\)
\(432\) 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 0.00879328 0.999961i \(-0.497201\pi\)
0.976847 + 0.213940i \(0.0686295\pi\)
\(444\) 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 0.982252 0.187568i \(-0.0600604\pi\)
−0.759070 + 0.651009i \(0.774346\pi\)
\(450\) 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 0.985637 0.168877i \(-0.0540142\pi\)
−0.961301 + 0.275499i \(0.911157\pi\)
\(462\) 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 \(0.262859\pi\)
−0.929774 + 0.368130i \(0.879998\pi\)
\(468\) 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 0.353686 0.935364i \(-0.384928\pi\)
−0.990615 + 0.136680i \(0.956357\pi\)
\(480\) 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 \(-0.999323\pi\)
0.999998 0.00212738i \(-0.000677166\pi\)
\(492\) 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 \(-0.978202\pi\)
0.155288 0.987869i \(-0.450369\pi\)
\(504\) 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 \(-0.360506\pi\)
0.424340 + 0.905503i \(0.360506\pi\)
\(510\) 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 \(-0.456141\pi\)
0.137352 + 0.990522i \(0.456141\pi\)
\(522\) 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 \(-0.939374\pi\)
0.981917 0.189313i \(-0.0606261\pi\)
\(558\) 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 −0.987946 0.154800i \(-0.950527\pi\)
0.370757 + 0.928730i \(0.379098\pi\)
\(564\) 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 \(0.159607\pi\)
−0.876901 + 0.480671i \(0.840393\pi\)
\(570\) 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 \(-0.612835\pi\)
−0.347103 + 0.937827i \(0.612835\pi\)
\(588\) 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 −0.233581 0.972337i \(-0.575044\pi\)
0.614568 + 0.788864i \(0.289330\pi\)
\(594\) 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 −0.914863 0.403765i \(-0.867701\pi\)
0.190065 + 0.981771i \(0.439130\pi\)
\(600\) 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 0.0699898 0.997548i \(-0.477703\pi\)
0.495878 + 0.868392i \(0.334846\pi\)
\(618\) 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 0.514857 0.857276i \(-0.327845\pi\)
0.0919120 + 0.995767i \(0.470702\pi\)
\(642\) 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 0.909787 0.415076i \(-0.136245\pi\)
0.242724 + 0.970096i \(0.421959\pi\)
\(648\) 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 \(0.413543\pi\)
−0.920443 + 0.390878i \(0.872171\pi\)
\(654\) 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 0.489381 0.872070i \(-0.337223\pi\)
0.0625406 + 0.998042i \(0.480080\pi\)
\(660\) 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 −0.756123 0.654429i \(-0.772909\pi\)
0.806275 + 0.591541i \(0.201480\pi\)
\(678\) 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 0.879141 0.476562i \(-0.158117\pi\)
−0.920727 + 0.390208i \(0.872403\pi\)
\(684\) 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 0.961445 0.274999i \(-0.0886775\pi\)
−0.0541625 + 0.998532i \(0.517249\pi\)
\(702\) 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 0.529999 0.847998i \(-0.322192\pi\)
−0.332543 + 0.943088i \(0.607907\pi\)
\(720\) 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 0.929462 0.368918i \(-0.120272\pi\)
−0.867942 + 0.496666i \(0.834557\pi\)
\(744\) 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 \(0.330861\pi\)
−0.830589 + 0.556886i \(0.811996\pi\)
\(762\) 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 0.970171 0.242420i \(-0.0779413\pi\)
−0.452226 + 0.891904i \(0.649370\pi\)
\(774\) 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 0.619506 0.784992i \(-0.287333\pi\)
−0.903164 + 0.429296i \(0.858762\pi\)
\(798\) 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 \(-0.887875\pi\)
−0.545219 0.838294i \(-0.683553\pi\)
\(810\) 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 0.899479 0.436964i \(-0.143946\pi\)
0.999994 + 0.00342203i \(0.00108927\pi\)
\(822\) 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 −0.944924 0.327290i \(-0.893864\pi\)
0.845036 + 0.534709i \(0.179579\pi\)
\(828\) 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 0.0857169 0.996320i \(-0.472682\pi\)
−0.725510 + 0.688211i \(0.758396\pi\)
\(840\) 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 −0.457445 0.889238i \(-0.651235\pi\)
0.968734 + 0.248102i \(0.0798068\pi\)
\(858\) 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 \(-0.971133\pi\)
0.995891 0.0905649i \(-0.0288673\pi\)
\(864\) 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 \(-0.432938\pi\)
0.209125 + 0.977889i \(0.432938\pi\)
\(882\) 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 −0.259031 0.965869i \(-0.583403\pi\)
0.593644 + 0.804728i \(0.297689\pi\)
\(888\) 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 −0.350568 0.936537i \(-0.614011\pi\)
0.0904978 + 0.995897i \(0.471154\pi\)
\(912\) 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 \(0.121251\pi\)
0.155884 + 0.987775i \(0.450177\pi\)
\(930\) 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 \(0.0156696\pi\)
0.661207 + 0.750204i \(0.270045\pi\)
\(942\) 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 \(-0.709912\pi\)
0.999906 0.0137411i \(-0.00437408\pi\)
\(948\) 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 0.784102 0.620632i \(-0.213124\pi\)
0.437170 + 0.899379i \(0.355981\pi\)
\(954\) 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 −0.993839 0.110834i \(-0.964648\pi\)
0.329205 + 0.944258i \(0.393219\pi\)
\(972\) 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 0.999469 0.0325905i \(-0.0103757\pi\)
−0.648639 + 0.761096i \(0.724661\pi\)
\(978\) 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 −0.613723 0.789522i \(-0.710329\pi\)
0.234623 + 0.972086i \(0.424614\pi\)
\(984\) 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.188.15 yes 120
3.2 odd 2 inner 441.2.w.a.188.6 120
49.6 odd 14 inner 441.2.w.a.251.6 yes 120
147.104 even 14 inner 441.2.w.a.251.15 yes 120
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.w.a.188.6 120 3.2 odd 2 inner
441.2.w.a.188.15 yes 120 1.1 even 1 trivial
441.2.w.a.251.6 yes 120 49.6 odd 14 inner
441.2.w.a.251.15 yes 120 147.104 even 14 inner