Properties

Label 810.2.s.a.773.7
Level $810$
Weight $2$
Character 810.773
Analytic conductor $6.468$
Analytic rank $0$
Dimension $216$
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] = [810,2,Mod(17,810)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(810, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([22, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("810.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 810.s (of order \(36\), degree \(12\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.46788256372\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(18\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 270)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 773.7
Character \(\chi\) \(=\) 810.773
Dual form 810.2.s.a.197.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(1.39703 - 1.74594i) q^{5} +(0.564372 + 0.395177i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})\) \(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(1.39703 - 1.74594i) q^{5} +(0.564372 + 0.395177i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-1.54388 + 1.61754i) q^{10} +(-1.76146 + 4.83957i) q^{11} +(0.446561 + 5.10422i) q^{13} +(-0.527782 - 0.442862i) q^{14} +(0.939693 + 0.342020i) q^{16} +(-0.221302 + 0.0592977i) q^{17} +(-6.21536 + 3.58844i) q^{19} +(1.67899 - 1.47682i) q^{20} +(2.17655 - 4.66763i) q^{22} +(4.94460 + 7.06162i) q^{23} +(-1.09660 - 4.87826i) q^{25} -5.12371i q^{26} +(0.487176 + 0.487176i) q^{28} +(3.94345 - 3.30895i) q^{29} +(0.210869 - 1.19590i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(0.225628 - 0.0397843i) q^{34} +(1.47840 - 0.433282i) q^{35} +(2.11922 + 7.90903i) q^{37} +(6.50446 - 3.03308i) q^{38} +(-1.80131 + 1.32487i) q^{40} +(5.46868 - 6.51731i) q^{41} +(-0.185563 - 0.397941i) q^{43} +(-2.57508 + 4.46017i) q^{44} +(-4.31032 - 7.46569i) q^{46} +(2.03954 - 2.91277i) q^{47} +(-2.23179 - 6.13179i) q^{49} +(0.667259 + 4.95528i) q^{50} +(-0.446561 + 5.10422i) q^{52} +(-8.07298 + 8.07298i) q^{53} +(5.98878 + 9.83644i) q^{55} +(-0.442862 - 0.527782i) q^{56} +(-4.21684 + 2.95266i) q^{58} +(-2.64552 + 0.962890i) q^{59} +(-0.117426 - 0.665953i) q^{61} +(-0.314295 + 1.17297i) q^{62} +(0.866025 + 0.500000i) q^{64} +(9.53550 + 6.35109i) q^{65} +(9.55113 - 0.835616i) q^{67} +(-0.228237 + 0.0199681i) q^{68} +(-1.51054 + 0.302783i) q^{70} +(0.366992 + 0.211883i) q^{71} +(-1.47394 + 5.50083i) q^{73} +(-1.42184 - 8.06363i) q^{74} +(-6.74406 + 2.45464i) q^{76} +(-2.90661 + 2.03523i) q^{77} +(3.26214 + 3.88766i) q^{79} +(1.90993 - 1.16283i) q^{80} +(-6.01589 + 6.01589i) q^{82} +(-0.605842 + 6.92481i) q^{83} +(-0.205636 + 0.469221i) q^{85} +(0.150174 + 0.412600i) q^{86} +(2.95401 - 4.21877i) q^{88} +(-0.102987 - 0.178379i) q^{89} +(-1.76504 + 3.05714i) q^{91} +(3.64324 + 7.81295i) q^{92} +(-2.28565 + 2.72393i) q^{94} +(-2.41787 + 15.8648i) q^{95} +(12.2584 - 5.71617i) q^{97} +(1.68888 + 6.30297i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216 q+O(q^{10}) \) Copy content Toggle raw display \( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.996195 0.0871557i −0.704416 0.0616284i
\(3\) 0 0
\(4\) 0.984808 + 0.173648i 0.492404 + 0.0868241i
\(5\) 1.39703 1.74594i 0.624772 0.780807i
\(6\) 0 0
\(7\) 0.564372 + 0.395177i 0.213312 + 0.149363i 0.675350 0.737497i \(-0.263993\pi\)
−0.462038 + 0.886860i \(0.652881\pi\)
\(8\) −0.965926 0.258819i −0.341506 0.0915064i
\(9\) 0 0
\(10\) −1.54388 + 1.61754i −0.488219 + 0.511509i
\(11\) −1.76146 + 4.83957i −0.531100 + 1.45919i 0.326663 + 0.945141i \(0.394076\pi\)
−0.857763 + 0.514045i \(0.828147\pi\)
\(12\) 0 0
\(13\) 0.446561 + 5.10422i 0.123854 + 1.41565i 0.762915 + 0.646499i \(0.223767\pi\)
−0.639061 + 0.769156i \(0.720677\pi\)
\(14\) −0.527782 0.442862i −0.141056 0.118360i
\(15\) 0 0
\(16\) 0.939693 + 0.342020i 0.234923 + 0.0855050i
\(17\) −0.221302 + 0.0592977i −0.0536736 + 0.0143818i −0.285556 0.958362i \(-0.592178\pi\)
0.231882 + 0.972744i \(0.425512\pi\)
\(18\) 0 0
\(19\) −6.21536 + 3.58844i −1.42590 + 0.823245i −0.996794 0.0800089i \(-0.974505\pi\)
−0.429107 + 0.903253i \(0.641172\pi\)
\(20\) 1.67899 1.47682i 0.375433 0.330227i
\(21\) 0 0
\(22\) 2.17655 4.66763i 0.464043 0.995143i
\(23\) 4.94460 + 7.06162i 1.03102 + 1.47245i 0.874653 + 0.484749i \(0.161089\pi\)
0.156366 + 0.987699i \(0.450022\pi\)
\(24\) 0 0
\(25\) −1.09660 4.87826i −0.219320 0.975653i
\(26\) 5.12371i 1.00484i
\(27\) 0 0
\(28\) 0.487176 + 0.487176i 0.0920675 + 0.0920675i
\(29\) 3.94345 3.30895i 0.732281 0.614457i −0.198471 0.980107i \(-0.563598\pi\)
0.930752 + 0.365650i \(0.119153\pi\)
\(30\) 0 0
\(31\) 0.210869 1.19590i 0.0378731 0.214789i −0.959998 0.280007i \(-0.909663\pi\)
0.997871 + 0.0652179i \(0.0207743\pi\)
\(32\) −0.906308 0.422618i −0.160214 0.0747091i
\(33\) 0 0
\(34\) 0.225628 0.0397843i 0.0386949 0.00682295i
\(35\) 1.47840 0.433282i 0.249895 0.0732381i
\(36\) 0 0
\(37\) 2.11922 + 7.90903i 0.348397 + 1.30024i 0.888593 + 0.458697i \(0.151684\pi\)
−0.540196 + 0.841539i \(0.681650\pi\)
\(38\) 6.50446 3.03308i 1.05516 0.492031i
\(39\) 0 0
\(40\) −1.80131 + 1.32487i −0.284812 + 0.209480i
\(41\) 5.46868 6.51731i 0.854064 1.01783i −0.145531 0.989354i \(-0.546489\pi\)
0.999594 0.0284797i \(-0.00906659\pi\)
\(42\) 0 0
\(43\) −0.185563 0.397941i −0.0282981 0.0606854i 0.891651 0.452724i \(-0.149548\pi\)
−0.919949 + 0.392039i \(0.871770\pi\)
\(44\) −2.57508 + 4.46017i −0.388208 + 0.672396i
\(45\) 0 0
\(46\) −4.31032 7.46569i −0.635522 1.10076i
\(47\) 2.03954 2.91277i 0.297498 0.424871i −0.642377 0.766388i \(-0.722052\pi\)
0.939876 + 0.341517i \(0.110941\pi\)
\(48\) 0 0
\(49\) −2.23179 6.13179i −0.318827 0.875971i
\(50\) 0.667259 + 4.95528i 0.0943647 + 0.700782i
\(51\) 0 0
\(52\) −0.446561 + 5.10422i −0.0619269 + 0.707827i
\(53\) −8.07298 + 8.07298i −1.10891 + 1.10891i −0.115615 + 0.993294i \(0.536884\pi\)
−0.993294 + 0.115615i \(0.963116\pi\)
\(54\) 0 0
\(55\) 5.98878 + 9.83644i 0.807526 + 1.32634i
\(56\) −0.442862 0.527782i −0.0591799 0.0705278i
\(57\) 0 0
\(58\) −4.21684 + 2.95266i −0.553698 + 0.387704i
\(59\) −2.64552 + 0.962890i −0.344417 + 0.125358i −0.508436 0.861100i \(-0.669776\pi\)
0.164019 + 0.986457i \(0.447554\pi\)
\(60\) 0 0
\(61\) −0.117426 0.665953i −0.0150348 0.0852666i 0.976367 0.216119i \(-0.0693398\pi\)
−0.991402 + 0.130852i \(0.958229\pi\)
\(62\) −0.314295 + 1.17297i −0.0399156 + 0.148967i
\(63\) 0 0
\(64\) 0.866025 + 0.500000i 0.108253 + 0.0625000i
\(65\) 9.53550 + 6.35109i 1.18273 + 0.787755i
\(66\) 0 0
\(67\) 9.55113 0.835616i 1.16686 0.102087i 0.512783 0.858518i \(-0.328614\pi\)
0.654073 + 0.756431i \(0.273059\pi\)
\(68\) −0.228237 + 0.0199681i −0.0276778 + 0.00242149i
\(69\) 0 0
\(70\) −1.51054 + 0.302783i −0.180544 + 0.0361894i
\(71\) 0.366992 + 0.211883i 0.0435540 + 0.0251459i 0.521619 0.853179i \(-0.325328\pi\)
−0.478065 + 0.878325i \(0.658662\pi\)
\(72\) 0 0
\(73\) −1.47394 + 5.50083i −0.172512 + 0.643823i 0.824450 + 0.565934i \(0.191484\pi\)
−0.996962 + 0.0778885i \(0.975182\pi\)
\(74\) −1.42184 8.06363i −0.165285 0.937378i
\(75\) 0 0
\(76\) −6.74406 + 2.45464i −0.773597 + 0.281566i
\(77\) −2.90661 + 2.03523i −0.331238 + 0.231936i
\(78\) 0 0
\(79\) 3.26214 + 3.88766i 0.367019 + 0.437396i 0.917672 0.397338i \(-0.130066\pi\)
−0.550653 + 0.834734i \(0.685621\pi\)
\(80\) 1.90993 1.16283i 0.213536 0.130009i
\(81\) 0 0
\(82\) −6.01589 + 6.01589i −0.664344 + 0.664344i
\(83\) −0.605842 + 6.92481i −0.0664998 + 0.760096i 0.887601 + 0.460612i \(0.152370\pi\)
−0.954101 + 0.299484i \(0.903185\pi\)
\(84\) 0 0
\(85\) −0.205636 + 0.469221i −0.0223044 + 0.0508941i
\(86\) 0.150174 + 0.412600i 0.0161937 + 0.0444918i
\(87\) 0 0
\(88\) 2.95401 4.21877i 0.314899 0.449722i
\(89\) −0.102987 0.178379i −0.0109166 0.0189081i 0.860515 0.509424i \(-0.170142\pi\)
−0.871432 + 0.490516i \(0.836808\pi\)
\(90\) 0 0
\(91\) −1.76504 + 3.05714i −0.185027 + 0.320476i
\(92\) 3.64324 + 7.81295i 0.379834 + 0.814557i
\(93\) 0 0
\(94\) −2.28565 + 2.72393i −0.235747 + 0.280952i
\(95\) −2.41787 + 15.8648i −0.248068 + 1.62769i
\(96\) 0 0
\(97\) 12.2584 5.71617i 1.24465 0.580389i 0.315090 0.949062i \(-0.397965\pi\)
0.929559 + 0.368672i \(0.120188\pi\)
\(98\) 1.68888 + 6.30297i 0.170602 + 0.636697i
\(99\) 0 0
\(100\) −0.232839 4.99458i −0.0232839 0.499458i
\(101\) 7.78401 1.37253i 0.774538 0.136572i 0.227611 0.973752i \(-0.426909\pi\)
0.546927 + 0.837180i \(0.315797\pi\)
\(102\) 0 0
\(103\) 0.200790 + 0.0936298i 0.0197844 + 0.00922562i 0.432485 0.901641i \(-0.357637\pi\)
−0.412701 + 0.910867i \(0.635415\pi\)
\(104\) 0.889723 5.04587i 0.0872445 0.494788i
\(105\) 0 0
\(106\) 8.74587 7.33865i 0.849474 0.712793i
\(107\) −6.83610 6.83610i −0.660871 0.660871i 0.294714 0.955585i \(-0.404775\pi\)
−0.955585 + 0.294714i \(0.904775\pi\)
\(108\) 0 0
\(109\) 1.60043i 0.153293i 0.997058 + 0.0766466i \(0.0244213\pi\)
−0.997058 + 0.0766466i \(0.975579\pi\)
\(110\) −5.10868 10.3210i −0.487094 0.984065i
\(111\) 0 0
\(112\) 0.395177 + 0.564372i 0.0373407 + 0.0533281i
\(113\) 1.85991 3.98858i 0.174965 0.375215i −0.799195 0.601072i \(-0.794741\pi\)
0.974160 + 0.225857i \(0.0725183\pi\)
\(114\) 0 0
\(115\) 19.2369 + 1.23235i 1.79385 + 0.114917i
\(116\) 4.45814 2.57391i 0.413928 0.238981i
\(117\) 0 0
\(118\) 2.71937 0.728654i 0.250339 0.0670780i
\(119\) −0.148330 0.0539876i −0.0135974 0.00494903i
\(120\) 0 0
\(121\) −11.8922 9.97875i −1.08111 0.907160i
\(122\) 0.0589371 + 0.673654i 0.00533591 + 0.0609897i
\(123\) 0 0
\(124\) 0.415330 1.14111i 0.0372978 0.102475i
\(125\) −10.0491 4.90050i −0.898822 0.438314i
\(126\) 0 0
\(127\) 6.09265 + 1.63252i 0.540635 + 0.144863i 0.518795 0.854899i \(-0.326381\pi\)
0.0218403 + 0.999761i \(0.493047\pi\)
\(128\) −0.819152 0.573576i −0.0724035 0.0506975i
\(129\) 0 0
\(130\) −8.94569 7.15799i −0.784589 0.627797i
\(131\) −10.6165 1.87197i −0.927564 0.163555i −0.310595 0.950542i \(-0.600528\pi\)
−0.616969 + 0.786988i \(0.711639\pi\)
\(132\) 0 0
\(133\) −4.92584 0.430955i −0.427125 0.0373686i
\(134\) −9.58761 −0.828244
\(135\) 0 0
\(136\) 0.229109 0.0196459
\(137\) 2.92252 + 0.255687i 0.249687 + 0.0218448i 0.211312 0.977419i \(-0.432226\pi\)
0.0383751 + 0.999263i \(0.487782\pi\)
\(138\) 0 0
\(139\) −1.01355 0.178717i −0.0859686 0.0151586i 0.130498 0.991449i \(-0.458342\pi\)
−0.216467 + 0.976290i \(0.569453\pi\)
\(140\) 1.53118 0.169978i 0.129408 0.0143658i
\(141\) 0 0
\(142\) −0.347129 0.243062i −0.0291304 0.0203973i
\(143\) −25.4888 6.82971i −2.13148 0.571129i
\(144\) 0 0
\(145\) −0.268091 11.5077i −0.0222637 0.955666i
\(146\) 1.94776 5.35143i 0.161198 0.442888i
\(147\) 0 0
\(148\) 0.713634 + 8.15687i 0.0586603 + 0.670491i
\(149\) 5.53064 + 4.64076i 0.453087 + 0.380186i 0.840580 0.541687i \(-0.182214\pi\)
−0.387493 + 0.921873i \(0.626659\pi\)
\(150\) 0 0
\(151\) −11.6383 4.23600i −0.947113 0.344721i −0.178142 0.984005i \(-0.557009\pi\)
−0.768971 + 0.639284i \(0.779231\pi\)
\(152\) 6.93233 1.85751i 0.562287 0.150664i
\(153\) 0 0
\(154\) 3.07293 1.77416i 0.247624 0.142966i
\(155\) −1.79337 2.03887i −0.144047 0.163766i
\(156\) 0 0
\(157\) 3.34167 7.16624i 0.266695 0.571929i −0.726663 0.686994i \(-0.758930\pi\)
0.993358 + 0.115065i \(0.0367077\pi\)
\(158\) −2.91089 4.15718i −0.231578 0.330728i
\(159\) 0 0
\(160\) −2.00401 + 0.991946i −0.158431 + 0.0784202i
\(161\) 5.93937i 0.468088i
\(162\) 0 0
\(163\) 12.4778 + 12.4778i 0.977336 + 0.977336i 0.999749 0.0224123i \(-0.00713466\pi\)
−0.0224123 + 0.999749i \(0.507135\pi\)
\(164\) 6.51731 5.46868i 0.508917 0.427032i
\(165\) 0 0
\(166\) 1.20707 6.84565i 0.0936871 0.531326i
\(167\) −3.11445 1.45229i −0.241003 0.112382i 0.298364 0.954452i \(-0.403559\pi\)
−0.539368 + 0.842070i \(0.681337\pi\)
\(168\) 0 0
\(169\) −13.0511 + 2.30126i −1.00393 + 0.177020i
\(170\) 0.245749 0.449513i 0.0188481 0.0344761i
\(171\) 0 0
\(172\) −0.113642 0.424118i −0.00866513 0.0323387i
\(173\) −13.4689 + 6.28066i −1.02402 + 0.477510i −0.860727 0.509067i \(-0.829990\pi\)
−0.163296 + 0.986577i \(0.552213\pi\)
\(174\) 0 0
\(175\) 1.30889 3.18651i 0.0989427 0.240877i
\(176\) −3.31046 + 3.94525i −0.249535 + 0.297385i
\(177\) 0 0
\(178\) 0.0870485 + 0.186676i 0.00652456 + 0.0139920i
\(179\) 1.61541 2.79798i 0.120742 0.209131i −0.799319 0.600907i \(-0.794806\pi\)
0.920060 + 0.391777i \(0.128139\pi\)
\(180\) 0 0
\(181\) −8.58566 14.8708i −0.638167 1.10534i −0.985835 0.167720i \(-0.946360\pi\)
0.347668 0.937618i \(-0.386974\pi\)
\(182\) 2.02477 2.89168i 0.150086 0.214345i
\(183\) 0 0
\(184\) −2.94843 8.10075i −0.217361 0.597195i
\(185\) 16.7693 + 7.34914i 1.23290 + 0.540320i
\(186\) 0 0
\(187\) 0.102839 1.17546i 0.00752035 0.0859580i
\(188\) 2.51436 2.51436i 0.183378 0.183378i
\(189\) 0 0
\(190\) 3.79137 15.5937i 0.275055 1.13129i
\(191\) −11.2591 13.4180i −0.814678 0.970895i 0.185253 0.982691i \(-0.440690\pi\)
−0.999930 + 0.0117957i \(0.996245\pi\)
\(192\) 0 0
\(193\) −4.88801 + 3.42262i −0.351847 + 0.246366i −0.736116 0.676855i \(-0.763342\pi\)
0.384269 + 0.923221i \(0.374453\pi\)
\(194\) −12.7099 + 4.62603i −0.912519 + 0.332130i
\(195\) 0 0
\(196\) −1.13311 6.42619i −0.0809364 0.459013i
\(197\) 2.16270 8.07130i 0.154086 0.575057i −0.845096 0.534615i \(-0.820457\pi\)
0.999182 0.0404419i \(-0.0128766\pi\)
\(198\) 0 0
\(199\) 11.6465 + 6.72410i 0.825598 + 0.476659i 0.852343 0.522983i \(-0.175181\pi\)
−0.0267452 + 0.999642i \(0.508514\pi\)
\(200\) −0.203353 + 4.99586i −0.0143792 + 0.353261i
\(201\) 0 0
\(202\) −7.87401 + 0.688887i −0.554014 + 0.0484699i
\(203\) 3.53319 0.309114i 0.247982 0.0216956i
\(204\) 0 0
\(205\) −3.73891 18.6529i −0.261137 1.30277i
\(206\) −0.191865 0.110773i −0.0133679 0.00771795i
\(207\) 0 0
\(208\) −1.32611 + 4.94913i −0.0919495 + 0.343160i
\(209\) −6.41840 36.4006i −0.443970 2.51788i
\(210\) 0 0
\(211\) 3.60818 1.31327i 0.248397 0.0904092i −0.214821 0.976653i \(-0.568917\pi\)
0.463218 + 0.886244i \(0.346695\pi\)
\(212\) −9.35219 + 6.54848i −0.642311 + 0.449751i
\(213\) 0 0
\(214\) 6.21428 + 7.40590i 0.424800 + 0.506257i
\(215\) −0.954018 0.231955i −0.0650635 0.0158192i
\(216\) 0 0
\(217\) 0.591599 0.591599i 0.0401604 0.0401604i
\(218\) 0.139486 1.59434i 0.00944721 0.107982i
\(219\) 0 0
\(220\) 4.18971 + 10.7269i 0.282470 + 0.723210i
\(221\) −0.401493 1.10309i −0.0270074 0.0742021i
\(222\) 0 0
\(223\) 6.34138 9.05643i 0.424650 0.606464i −0.548635 0.836062i \(-0.684852\pi\)
0.973285 + 0.229598i \(0.0737413\pi\)
\(224\) −0.344485 0.596666i −0.0230169 0.0398664i
\(225\) 0 0
\(226\) −2.20046 + 3.81131i −0.146372 + 0.253524i
\(227\) 9.15998 + 19.6436i 0.607969 + 1.30379i 0.933607 + 0.358300i \(0.116643\pi\)
−0.325637 + 0.945495i \(0.605579\pi\)
\(228\) 0 0
\(229\) 9.61516 11.4589i 0.635387 0.757225i −0.348247 0.937403i \(-0.613223\pi\)
0.983634 + 0.180178i \(0.0576673\pi\)
\(230\) −19.0563 2.90426i −1.25653 0.191501i
\(231\) 0 0
\(232\) −4.66550 + 2.17556i −0.306305 + 0.142832i
\(233\) −6.09991 22.7652i −0.399618 1.49140i −0.813770 0.581188i \(-0.802588\pi\)
0.414151 0.910208i \(-0.364078\pi\)
\(234\) 0 0
\(235\) −2.23621 7.63015i −0.145874 0.497736i
\(236\) −2.77253 + 0.488872i −0.180476 + 0.0318229i
\(237\) 0 0
\(238\) 0.143060 + 0.0667099i 0.00927320 + 0.00432416i
\(239\) −1.97913 + 11.2242i −0.128019 + 0.726032i 0.851450 + 0.524436i \(0.175724\pi\)
−0.979469 + 0.201596i \(0.935387\pi\)
\(240\) 0 0
\(241\) −16.7492 + 14.0543i −1.07891 + 0.905316i −0.995830 0.0912265i \(-0.970921\pi\)
−0.0830836 + 0.996543i \(0.526477\pi\)
\(242\) 10.9773 + 10.9773i 0.705645 + 0.705645i
\(243\) 0 0
\(244\) 0.676227i 0.0432910i
\(245\) −13.8236 4.66975i −0.883159 0.298339i
\(246\) 0 0
\(247\) −21.0917 30.1221i −1.34203 1.91662i
\(248\) −0.513204 + 1.10057i −0.0325885 + 0.0698863i
\(249\) 0 0
\(250\) 9.58379 + 5.75769i 0.606132 + 0.364148i
\(251\) 16.5931 9.58004i 1.04735 0.604687i 0.125443 0.992101i \(-0.459965\pi\)
0.921906 + 0.387414i \(0.126632\pi\)
\(252\) 0 0
\(253\) −42.8849 + 11.4910i −2.69615 + 0.722431i
\(254\) −5.92718 2.15732i −0.371904 0.135362i
\(255\) 0 0
\(256\) 0.766044 + 0.642788i 0.0478778 + 0.0401742i
\(257\) 0.0985374 + 1.12629i 0.00614659 + 0.0702559i 0.998648 0.0519736i \(-0.0165512\pi\)
−0.992502 + 0.122229i \(0.960996\pi\)
\(258\) 0 0
\(259\) −1.92944 + 5.30110i −0.119890 + 0.329394i
\(260\) 8.28778 + 7.91042i 0.513987 + 0.490584i
\(261\) 0 0
\(262\) 10.4129 + 2.79013i 0.643311 + 0.172375i
\(263\) 20.7388 + 14.5214i 1.27881 + 0.895431i 0.997930 0.0643126i \(-0.0204855\pi\)
0.280878 + 0.959743i \(0.409374\pi\)
\(264\) 0 0
\(265\) 2.81671 + 25.3731i 0.173029 + 1.55866i
\(266\) 4.86954 + 0.858631i 0.298571 + 0.0526460i
\(267\) 0 0
\(268\) 9.55113 + 0.835616i 0.583428 + 0.0510433i
\(269\) −1.62150 −0.0988645 −0.0494322 0.998777i \(-0.515741\pi\)
−0.0494322 + 0.998777i \(0.515741\pi\)
\(270\) 0 0
\(271\) −5.67196 −0.344547 −0.172274 0.985049i \(-0.555111\pi\)
−0.172274 + 0.985049i \(0.555111\pi\)
\(272\) −0.228237 0.0199681i −0.0138389 0.00121075i
\(273\) 0 0
\(274\) −2.88911 0.509428i −0.174538 0.0307757i
\(275\) 25.5403 + 3.28579i 1.54014 + 0.198141i
\(276\) 0 0
\(277\) 2.32366 + 1.62704i 0.139615 + 0.0977595i 0.641297 0.767292i \(-0.278396\pi\)
−0.501682 + 0.865052i \(0.667285\pi\)
\(278\) 0.994121 + 0.266374i 0.0596234 + 0.0159761i
\(279\) 0 0
\(280\) −1.54017 + 0.0358806i −0.0920426 + 0.00214428i
\(281\) −3.09754 + 8.51042i −0.184784 + 0.507689i −0.997149 0.0754602i \(-0.975957\pi\)
0.812365 + 0.583149i \(0.198180\pi\)
\(282\) 0 0
\(283\) −1.24677 14.2507i −0.0741130 0.847116i −0.938723 0.344672i \(-0.887990\pi\)
0.864610 0.502443i \(-0.167566\pi\)
\(284\) 0.324624 + 0.272392i 0.0192629 + 0.0161635i
\(285\) 0 0
\(286\) 24.7966 + 9.02521i 1.46625 + 0.533672i
\(287\) 5.66186 1.51709i 0.334209 0.0895510i
\(288\) 0 0
\(289\) −14.6770 + 8.47375i −0.863351 + 0.498456i
\(290\) −0.735895 + 11.4873i −0.0432132 + 0.674558i
\(291\) 0 0
\(292\) −2.40676 + 5.16131i −0.140845 + 0.302043i
\(293\) −11.0424 15.7702i −0.645104 0.921305i 0.354803 0.934941i \(-0.384548\pi\)
−0.999907 + 0.0136366i \(0.995659\pi\)
\(294\) 0 0
\(295\) −2.01473 + 5.96410i −0.117302 + 0.347243i
\(296\) 8.18803i 0.475919i
\(297\) 0 0
\(298\) −5.10512 5.10512i −0.295732 0.295732i
\(299\) −33.8359 + 28.3917i −1.95678 + 1.64194i
\(300\) 0 0
\(301\) 0.0525308 0.297917i 0.00302782 0.0171716i
\(302\) 11.2248 + 5.23423i 0.645917 + 0.301196i
\(303\) 0 0
\(304\) −7.06785 + 1.24625i −0.405369 + 0.0714775i
\(305\) −1.32676 0.725341i −0.0759701 0.0415329i
\(306\) 0 0
\(307\) 3.85267 + 14.3784i 0.219883 + 0.820616i 0.984390 + 0.176000i \(0.0563160\pi\)
−0.764507 + 0.644616i \(0.777017\pi\)
\(308\) −3.21586 + 1.49958i −0.183241 + 0.0854465i
\(309\) 0 0
\(310\) 1.60885 + 2.18741i 0.0913763 + 0.124237i
\(311\) 19.2921 22.9914i 1.09395 1.30372i 0.144608 0.989489i \(-0.453808\pi\)
0.949345 0.314234i \(-0.101748\pi\)
\(312\) 0 0
\(313\) −4.80579 10.3061i −0.271639 0.582533i 0.722410 0.691465i \(-0.243035\pi\)
−0.994049 + 0.108933i \(0.965257\pi\)
\(314\) −3.95354 + 6.84773i −0.223111 + 0.386440i
\(315\) 0 0
\(316\) 2.53749 + 4.39507i 0.142745 + 0.247242i
\(317\) 17.9510 25.6367i 1.00823 1.43990i 0.113370 0.993553i \(-0.463835\pi\)
0.894859 0.446348i \(-0.147276\pi\)
\(318\) 0 0
\(319\) 9.06767 + 24.9132i 0.507692 + 1.39487i
\(320\) 2.08283 0.813511i 0.116434 0.0454766i
\(321\) 0 0
\(322\) 0.517650 5.91676i 0.0288475 0.329728i
\(323\) 1.16269 1.16269i 0.0646936 0.0646936i
\(324\) 0 0
\(325\) 24.4100 7.77573i 1.35402 0.431320i
\(326\) −11.3428 13.5178i −0.628220 0.748683i
\(327\) 0 0
\(328\) −6.96914 + 4.87984i −0.384806 + 0.269444i
\(329\) 2.30212 0.837904i 0.126920 0.0461951i
\(330\) 0 0
\(331\) 1.57325 + 8.92236i 0.0864738 + 0.490417i 0.997029 + 0.0770294i \(0.0245435\pi\)
−0.910555 + 0.413388i \(0.864345\pi\)
\(332\) −1.79912 + 6.71440i −0.0987394 + 0.368501i
\(333\) 0 0
\(334\) 2.97602 + 1.71821i 0.162841 + 0.0940161i
\(335\) 11.8843 17.8431i 0.649309 0.974871i
\(336\) 0 0
\(337\) 0.305409 0.0267198i 0.0166367 0.00145552i −0.0788344 0.996888i \(-0.525120\pi\)
0.0954711 + 0.995432i \(0.469564\pi\)
\(338\) 13.2020 1.15503i 0.718094 0.0628251i
\(339\) 0 0
\(340\) −0.283991 + 0.426384i −0.0154016 + 0.0231239i
\(341\) 5.41619 + 3.12704i 0.293303 + 0.169339i
\(342\) 0 0
\(343\) 2.41182 9.00102i 0.130226 0.486010i
\(344\) 0.0762453 + 0.432409i 0.00411087 + 0.0233139i
\(345\) 0 0
\(346\) 13.9651 5.08287i 0.750767 0.273257i
\(347\) −0.0616536 + 0.0431703i −0.00330974 + 0.00231750i −0.575230 0.817992i \(-0.695088\pi\)
0.571920 + 0.820309i \(0.306199\pi\)
\(348\) 0 0
\(349\) −2.42419 2.88904i −0.129764 0.154647i 0.697250 0.716828i \(-0.254407\pi\)
−0.827014 + 0.562181i \(0.809962\pi\)
\(350\) −1.58163 + 3.06030i −0.0845417 + 0.163580i
\(351\) 0 0
\(352\) 3.64172 3.64172i 0.194104 0.194104i
\(353\) −1.39040 + 15.8923i −0.0740035 + 0.845864i 0.864958 + 0.501844i \(0.167345\pi\)
−0.938962 + 0.344021i \(0.888211\pi\)
\(354\) 0 0
\(355\) 0.882635 0.344738i 0.0468454 0.0182968i
\(356\) −0.0704474 0.193553i −0.00373370 0.0102583i
\(357\) 0 0
\(358\) −1.85313 + 2.64654i −0.0979408 + 0.139874i
\(359\) 13.3476 + 23.1187i 0.704458 + 1.22016i 0.966887 + 0.255205i \(0.0821431\pi\)
−0.262429 + 0.964951i \(0.584524\pi\)
\(360\) 0 0
\(361\) 16.2538 28.1524i 0.855463 1.48171i
\(362\) 7.25691 + 15.5625i 0.381415 + 0.817947i
\(363\) 0 0
\(364\) −2.26910 + 2.70420i −0.118933 + 0.141739i
\(365\) 7.54496 + 10.2582i 0.394921 + 0.536941i
\(366\) 0 0
\(367\) −28.7115 + 13.3884i −1.49873 + 0.698869i −0.987066 0.160317i \(-0.948748\pi\)
−0.511664 + 0.859186i \(0.670971\pi\)
\(368\) 2.23119 + 8.32690i 0.116309 + 0.434070i
\(369\) 0 0
\(370\) −16.0650 8.78272i −0.835177 0.456592i
\(371\) −7.74642 + 1.36590i −0.402174 + 0.0709141i
\(372\) 0 0
\(373\) 30.8236 + 14.3733i 1.59598 + 0.744220i 0.998343 0.0575432i \(-0.0183267\pi\)
0.597642 + 0.801763i \(0.296104\pi\)
\(374\) −0.204896 + 1.16202i −0.0105949 + 0.0600867i
\(375\) 0 0
\(376\) −2.72393 + 2.28565i −0.140476 + 0.117873i
\(377\) 18.6506 + 18.6506i 0.960554 + 0.960554i
\(378\) 0 0
\(379\) 25.5086i 1.31029i −0.755503 0.655145i \(-0.772607\pi\)
0.755503 0.655145i \(-0.227393\pi\)
\(380\) −5.13603 + 15.2039i −0.263473 + 0.779945i
\(381\) 0 0
\(382\) 10.0468 + 14.3483i 0.514037 + 0.734121i
\(383\) 1.95650 4.19573i 0.0999725 0.214392i −0.849960 0.526848i \(-0.823374\pi\)
0.949932 + 0.312456i \(0.101152\pi\)
\(384\) 0 0
\(385\) −0.507241 + 7.91803i −0.0258514 + 0.403540i
\(386\) 5.16771 2.98358i 0.263030 0.151860i
\(387\) 0 0
\(388\) 13.0647 3.50069i 0.663262 0.177720i
\(389\) 26.6358 + 9.69465i 1.35049 + 0.491538i 0.913101 0.407734i \(-0.133681\pi\)
0.437389 + 0.899272i \(0.355903\pi\)
\(390\) 0 0
\(391\) −1.51299 1.26955i −0.0765150 0.0642037i
\(392\) 0.568719 + 6.50049i 0.0287247 + 0.328324i
\(393\) 0 0
\(394\) −2.85793 + 7.85210i −0.143980 + 0.395583i
\(395\) 11.3449 0.264298i 0.570826 0.0132983i
\(396\) 0 0
\(397\) −3.47803 0.931934i −0.174557 0.0467725i 0.170482 0.985361i \(-0.445468\pi\)
−0.345039 + 0.938588i \(0.612134\pi\)
\(398\) −11.0161 7.71358i −0.552189 0.386647i
\(399\) 0 0
\(400\) 0.637997 4.95913i 0.0318998 0.247956i
\(401\) −1.73265 0.305513i −0.0865245 0.0152566i 0.130218 0.991485i \(-0.458432\pi\)
−0.216743 + 0.976229i \(0.569543\pi\)
\(402\) 0 0
\(403\) 6.19828 + 0.542279i 0.308758 + 0.0270128i
\(404\) 7.90409 0.393243
\(405\) 0 0
\(406\) −3.54669 −0.176019
\(407\) −42.0092 3.67533i −2.08232 0.182179i
\(408\) 0 0
\(409\) 6.33540 + 1.11710i 0.313266 + 0.0552372i 0.328071 0.944653i \(-0.393602\pi\)
−0.0148050 + 0.999890i \(0.504713\pi\)
\(410\) 2.09898 + 18.9078i 0.103661 + 0.933788i
\(411\) 0 0
\(412\) 0.181481 + 0.127074i 0.00894091 + 0.00626049i
\(413\) −1.87357 0.502021i −0.0921922 0.0247028i
\(414\) 0 0
\(415\) 11.2439 + 10.7319i 0.551942 + 0.526810i
\(416\) 1.75241 4.81471i 0.0859191 0.236061i
\(417\) 0 0
\(418\) 3.22146 + 36.8215i 0.157567 + 1.80100i
\(419\) −16.4788 13.8273i −0.805041 0.675510i 0.144377 0.989523i \(-0.453882\pi\)
−0.949419 + 0.314013i \(0.898327\pi\)
\(420\) 0 0
\(421\) 30.3048 + 11.0300i 1.47696 + 0.537571i 0.949982 0.312305i \(-0.101101\pi\)
0.526982 + 0.849876i \(0.323323\pi\)
\(422\) −3.70891 + 0.993799i −0.180547 + 0.0483774i
\(423\) 0 0
\(424\) 9.88734 5.70846i 0.480172 0.277227i
\(425\) 0.531950 + 1.01454i 0.0258034 + 0.0492126i
\(426\) 0 0
\(427\) 0.196898 0.422249i 0.00952856 0.0204341i
\(428\) −5.54517 7.91932i −0.268036 0.382795i
\(429\) 0 0
\(430\) 0.930172 + 0.314221i 0.0448569 + 0.0151531i
\(431\) 18.6983i 0.900664i −0.892861 0.450332i \(-0.851306\pi\)
0.892861 0.450332i \(-0.148694\pi\)
\(432\) 0 0
\(433\) −0.223161 0.223161i −0.0107244 0.0107244i 0.701724 0.712449i \(-0.252414\pi\)
−0.712449 + 0.701724i \(0.752414\pi\)
\(434\) −0.640909 + 0.537787i −0.0307646 + 0.0258146i
\(435\) 0 0
\(436\) −0.277911 + 1.57611i −0.0133095 + 0.0754821i
\(437\) −56.0726 26.1471i −2.68232 1.25079i
\(438\) 0 0
\(439\) −38.6067 + 6.80740i −1.84260 + 0.324900i −0.982648 0.185480i \(-0.940616\pi\)
−0.859949 + 0.510380i \(0.829505\pi\)
\(440\) −3.23886 11.0513i −0.154406 0.526849i
\(441\) 0 0
\(442\) 0.303824 + 1.13389i 0.0144515 + 0.0539336i
\(443\) 2.98350 1.39123i 0.141750 0.0660993i −0.350449 0.936582i \(-0.613971\pi\)
0.492199 + 0.870483i \(0.336193\pi\)
\(444\) 0 0
\(445\) −0.455315 0.0693920i −0.0215840 0.00328950i
\(446\) −7.10657 + 8.46928i −0.336506 + 0.401032i
\(447\) 0 0
\(448\) 0.291171 + 0.624419i 0.0137566 + 0.0295010i
\(449\) −8.26235 + 14.3108i −0.389924 + 0.675369i −0.992439 0.122739i \(-0.960832\pi\)
0.602515 + 0.798108i \(0.294166\pi\)
\(450\) 0 0
\(451\) 21.9081 + 37.9460i 1.03161 + 1.78681i
\(452\) 2.52426 3.60502i 0.118731 0.169566i
\(453\) 0 0
\(454\) −7.41307 20.3672i −0.347913 0.955882i
\(455\) 2.87176 + 7.35259i 0.134630 + 0.344695i
\(456\) 0 0
\(457\) 2.45349 28.0435i 0.114769 1.31182i −0.692406 0.721508i \(-0.743449\pi\)
0.807175 0.590312i \(-0.200995\pi\)
\(458\) −10.5773 + 10.5773i −0.494244 + 0.494244i
\(459\) 0 0
\(460\) 18.7307 + 4.55408i 0.873321 + 0.212335i
\(461\) 1.24335 + 1.48177i 0.0579086 + 0.0690128i 0.794221 0.607629i \(-0.207879\pi\)
−0.736313 + 0.676642i \(0.763435\pi\)
\(462\) 0 0
\(463\) 3.25355 2.27816i 0.151205 0.105875i −0.495526 0.868593i \(-0.665025\pi\)
0.646731 + 0.762718i \(0.276136\pi\)
\(464\) 4.83736 1.76066i 0.224569 0.0817364i
\(465\) 0 0
\(466\) 4.09258 + 23.2102i 0.189585 + 1.07519i
\(467\) −6.84432 + 25.5434i −0.316718 + 1.18201i 0.605662 + 0.795722i \(0.292908\pi\)
−0.922380 + 0.386284i \(0.873758\pi\)
\(468\) 0 0
\(469\) 5.72060 + 3.30279i 0.264153 + 0.152509i
\(470\) 1.56269 + 7.79602i 0.0720814 + 0.359603i
\(471\) 0 0
\(472\) 2.80459 0.245370i 0.129092 0.0112941i
\(473\) 2.25273 0.197088i 0.103580 0.00906211i
\(474\) 0 0
\(475\) 24.3211 + 26.3851i 1.11593 + 1.21063i
\(476\) −0.136701 0.0789246i −0.00626570 0.00361750i
\(477\) 0 0
\(478\) 2.94985 11.0090i 0.134923 0.503539i
\(479\) 2.29891 + 13.0378i 0.105040 + 0.595711i 0.991204 + 0.132340i \(0.0422491\pi\)
−0.886164 + 0.463371i \(0.846640\pi\)
\(480\) 0 0
\(481\) −39.4230 + 14.3488i −1.79753 + 0.654249i
\(482\) 17.9104 12.5410i 0.815797 0.571227i
\(483\) 0 0
\(484\) −9.97875 11.8922i −0.453580 0.540555i
\(485\) 7.14526 29.3880i 0.324449 1.33444i
\(486\) 0 0
\(487\) −9.21014 + 9.21014i −0.417351 + 0.417351i −0.884290 0.466938i \(-0.845357\pi\)
0.466938 + 0.884290i \(0.345357\pi\)
\(488\) −0.0589371 + 0.673654i −0.00266796 + 0.0304949i
\(489\) 0 0
\(490\) 13.3640 + 5.85679i 0.603725 + 0.264583i
\(491\) 9.62552 + 26.4459i 0.434394 + 1.19349i 0.943089 + 0.332540i \(0.107906\pi\)
−0.508695 + 0.860947i \(0.669872\pi\)
\(492\) 0 0
\(493\) −0.676481 + 0.966115i −0.0304672 + 0.0435116i
\(494\) 18.3861 + 31.8457i 0.827231 + 1.43281i
\(495\) 0 0
\(496\) 0.607172 1.05165i 0.0272628 0.0472206i
\(497\) 0.123389 + 0.264608i 0.00553474 + 0.0118693i
\(498\) 0 0
\(499\) 18.9190 22.5467i 0.846929 1.00933i −0.152849 0.988250i \(-0.548845\pi\)
0.999778 0.0210808i \(-0.00671072\pi\)
\(500\) −9.04550 6.57106i −0.404527 0.293867i
\(501\) 0 0
\(502\) −17.3649 + 8.09740i −0.775035 + 0.361405i
\(503\) 3.45662 + 12.9003i 0.154123 + 0.575195i 0.999179 + 0.0405171i \(0.0129005\pi\)
−0.845056 + 0.534678i \(0.820433\pi\)
\(504\) 0 0
\(505\) 8.47816 15.5079i 0.377273 0.690091i
\(506\) 43.7232 7.70958i 1.94373 0.342733i
\(507\) 0 0
\(508\) 5.71660 + 2.66570i 0.253633 + 0.118271i
\(509\) 5.74935 32.6062i 0.254835 1.44524i −0.541660 0.840598i \(-0.682204\pi\)
0.796495 0.604645i \(-0.206685\pi\)
\(510\) 0 0
\(511\) −3.00565 + 2.52204i −0.132962 + 0.111569i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0 0
\(514\) 1.13059i 0.0498682i
\(515\) 0.443982 0.219763i 0.0195642 0.00968390i
\(516\) 0 0
\(517\) 10.5040 + 15.0012i 0.461965 + 0.659754i
\(518\) 2.38412 5.11276i 0.104752 0.224642i
\(519\) 0 0
\(520\) −7.56681 8.60265i −0.331826 0.377251i
\(521\) −14.1900 + 8.19259i −0.621675 + 0.358924i −0.777521 0.628857i \(-0.783523\pi\)
0.155846 + 0.987781i \(0.450190\pi\)
\(522\) 0 0
\(523\) −23.4942 + 6.29526i −1.02733 + 0.275273i −0.732854 0.680386i \(-0.761812\pi\)
−0.294477 + 0.955658i \(0.595146\pi\)
\(524\) −10.1301 3.68706i −0.442536 0.161070i
\(525\) 0 0
\(526\) −19.3942 16.2737i −0.845629 0.709567i
\(527\) 0.0242482 + 0.277158i 0.00105627 + 0.0120732i
\(528\) 0 0
\(529\) −17.5509 + 48.2207i −0.763083 + 2.09655i
\(530\) −0.594577 25.5221i −0.0258268 1.10861i
\(531\) 0 0
\(532\) −4.77617 1.27977i −0.207073 0.0554851i
\(533\) 35.7079 + 25.0029i 1.54668 + 1.08300i
\(534\) 0 0
\(535\) −21.4857 + 2.38516i −0.928907 + 0.103119i
\(536\) −9.44196 1.66487i −0.407830 0.0719115i
\(537\) 0 0
\(538\) 1.61533 + 0.141323i 0.0696417 + 0.00609286i
\(539\) 33.6065 1.44753
\(540\) 0 0
\(541\) −28.4120 −1.22153 −0.610763 0.791814i \(-0.709137\pi\)
−0.610763 + 0.791814i \(0.709137\pi\)
\(542\) 5.65038 + 0.494344i 0.242705 + 0.0212339i
\(543\) 0 0
\(544\) 0.225628 + 0.0397843i 0.00967373 + 0.00170574i
\(545\) 2.79425 + 2.23585i 0.119692 + 0.0957732i
\(546\) 0 0
\(547\) −17.1447 12.0048i −0.733055 0.513290i 0.146428 0.989221i \(-0.453222\pi\)
−0.879483 + 0.475931i \(0.842111\pi\)
\(548\) 2.83372 + 0.759292i 0.121050 + 0.0324354i
\(549\) 0 0
\(550\) −25.1568 5.49927i −1.07269 0.234490i
\(551\) −12.6360 + 34.7172i −0.538312 + 1.47900i
\(552\) 0 0
\(553\) 0.304741 + 3.48321i 0.0129589 + 0.148121i
\(554\) −2.17301 1.82337i −0.0923223 0.0774676i
\(555\) 0 0
\(556\) −0.967123 0.352004i −0.0410151 0.0149283i
\(557\) −8.75390 + 2.34560i −0.370915 + 0.0993863i −0.439461 0.898262i \(-0.644831\pi\)
0.0685465 + 0.997648i \(0.478164\pi\)
\(558\) 0 0
\(559\) 1.94831 1.12486i 0.0824048 0.0475764i
\(560\) 1.53743 + 0.0984903i 0.0649684 + 0.00416198i
\(561\) 0 0
\(562\) 3.82748 8.20806i 0.161453 0.346236i
\(563\) −14.6995 20.9930i −0.619510 0.884751i 0.379675 0.925120i \(-0.376036\pi\)
−0.999185 + 0.0403685i \(0.987147\pi\)
\(564\) 0 0
\(565\) −4.36547 8.81947i −0.183657 0.371038i
\(566\) 14.3051i 0.601289i
\(567\) 0 0
\(568\) −0.299648 0.299648i −0.0125730 0.0125730i
\(569\) 10.3461 8.68139i 0.433730 0.363943i −0.399627 0.916678i \(-0.630860\pi\)
0.833357 + 0.552735i \(0.186416\pi\)
\(570\) 0 0
\(571\) −2.92996 + 16.6166i −0.122615 + 0.695385i 0.860081 + 0.510158i \(0.170413\pi\)
−0.982696 + 0.185227i \(0.940698\pi\)
\(572\) −23.9156 11.1520i −0.999962 0.466290i
\(573\) 0 0
\(574\) −5.77254 + 1.01785i −0.240941 + 0.0424844i
\(575\) 29.0262 31.8648i 1.21048 1.32885i
\(576\) 0 0
\(577\) −8.48749 31.6757i −0.353339 1.31868i −0.882562 0.470196i \(-0.844183\pi\)
0.529223 0.848483i \(-0.322483\pi\)
\(578\) 15.3597 7.16233i 0.638878 0.297914i
\(579\) 0 0
\(580\) 1.73428 11.3795i 0.0720120 0.472506i
\(581\) −3.07845 + 3.66875i −0.127715 + 0.152205i
\(582\) 0 0
\(583\) −24.8495 53.2900i −1.02916 2.20705i
\(584\) 2.84744 4.93191i 0.117828 0.204084i
\(585\) 0 0
\(586\) 9.62593 + 16.6726i 0.397643 + 0.688739i
\(587\) 7.86411 11.2311i 0.324587 0.463558i −0.623384 0.781916i \(-0.714243\pi\)
0.947970 + 0.318358i \(0.103131\pi\)
\(588\) 0 0
\(589\) 2.98078 + 8.18961i 0.122821 + 0.337447i
\(590\) 2.52687 5.76581i 0.104030 0.237375i
\(591\) 0 0
\(592\) −0.713634 + 8.15687i −0.0293302 + 0.335245i
\(593\) 3.68940 3.68940i 0.151506 0.151506i −0.627285 0.778790i \(-0.715834\pi\)
0.778790 + 0.627285i \(0.215834\pi\)
\(594\) 0 0
\(595\) −0.301480 + 0.183552i −0.0123595 + 0.00752490i
\(596\) 4.64076 + 5.53064i 0.190093 + 0.226544i
\(597\) 0 0
\(598\) 36.1817 25.3347i 1.47958 1.03601i
\(599\) 12.8843 4.68951i 0.526439 0.191608i −0.0651086 0.997878i \(-0.520739\pi\)
0.591548 + 0.806270i \(0.298517\pi\)
\(600\) 0 0
\(601\) −7.38092 41.8593i −0.301074 1.70748i −0.641432 0.767180i \(-0.721659\pi\)
0.340357 0.940296i \(-0.389452\pi\)
\(602\) −0.0782961 + 0.292205i −0.00319111 + 0.0119094i
\(603\) 0 0
\(604\) −10.7259 6.19262i −0.436432 0.251974i
\(605\) −34.0361 + 6.82243i −1.38376 + 0.277371i
\(606\) 0 0
\(607\) 24.6112 2.15320i 0.998939 0.0873958i 0.424060 0.905634i \(-0.360605\pi\)
0.574879 + 0.818238i \(0.305049\pi\)
\(608\) 7.14957 0.625506i 0.289953 0.0253676i
\(609\) 0 0
\(610\) 1.25849 + 0.838216i 0.0509550 + 0.0339384i
\(611\) 15.7782 + 9.10954i 0.638317 + 0.368533i
\(612\) 0 0
\(613\) −0.844110 + 3.15026i −0.0340933 + 0.127238i −0.980875 0.194638i \(-0.937647\pi\)
0.946782 + 0.321876i \(0.104313\pi\)
\(614\) −2.58485 14.6594i −0.104316 0.591606i
\(615\) 0 0
\(616\) 3.33432 1.21359i 0.134344 0.0488971i
\(617\) 37.8538 26.5055i 1.52394 1.06707i 0.551424 0.834225i \(-0.314085\pi\)
0.972513 0.232847i \(-0.0748042\pi\)
\(618\) 0 0
\(619\) 7.87169 + 9.38112i 0.316390 + 0.377059i 0.900678 0.434488i \(-0.143071\pi\)
−0.584288 + 0.811547i \(0.698626\pi\)
\(620\) −1.41208 2.31931i −0.0567104 0.0931457i
\(621\) 0 0
\(622\) −21.2225 + 21.2225i −0.850945 + 0.850945i
\(623\) 0.0123683 0.141370i 0.000495525 0.00566388i
\(624\) 0 0
\(625\) −22.5949 + 10.6990i −0.903797 + 0.427961i
\(626\) 3.88927 + 10.6857i 0.155447 + 0.427086i
\(627\) 0 0
\(628\) 4.53531 6.47710i 0.180979 0.258464i
\(629\) −0.937974 1.62462i −0.0373995 0.0647778i
\(630\) 0 0
\(631\) 15.4263 26.7191i 0.614110 1.06367i −0.376430 0.926445i \(-0.622848\pi\)
0.990540 0.137225i \(-0.0438183\pi\)
\(632\) −2.14478 4.59950i −0.0853148 0.182958i
\(633\) 0 0
\(634\) −20.1171 + 23.9746i −0.798952 + 0.952154i
\(635\) 11.3619 8.35671i 0.450884 0.331626i
\(636\) 0 0
\(637\) 30.3014 14.1298i 1.20058 0.559841i
\(638\) −6.86183 25.6087i −0.271662 1.01386i
\(639\) 0 0
\(640\) −2.14581 + 0.628884i −0.0848206 + 0.0248588i
\(641\) −41.4855 + 7.31502i −1.63858 + 0.288926i −0.915644 0.401990i \(-0.868319\pi\)
−0.722936 + 0.690915i \(0.757208\pi\)
\(642\) 0 0
\(643\) 35.7659 + 16.6779i 1.41047 + 0.657713i 0.970678 0.240385i \(-0.0772738\pi\)
0.439794 + 0.898099i \(0.355052\pi\)
\(644\) −1.03136 + 5.84913i −0.0406413 + 0.230488i
\(645\) 0 0
\(646\) −1.25960 + 1.05693i −0.0495582 + 0.0415842i
\(647\) −12.3552 12.3552i −0.485732 0.485732i 0.421224 0.906956i \(-0.361601\pi\)
−0.906956 + 0.421224i \(0.861601\pi\)
\(648\) 0 0
\(649\) 14.4993i 0.569146i
\(650\) −24.9948 + 5.61867i −0.980378 + 0.220382i
\(651\) 0 0
\(652\) 10.1215 + 14.4550i 0.396388 + 0.566101i
\(653\) −3.52950 + 7.56905i −0.138120 + 0.296200i −0.963185 0.268838i \(-0.913360\pi\)
0.825065 + 0.565037i \(0.191138\pi\)
\(654\) 0 0
\(655\) −18.0999 + 15.9205i −0.707220 + 0.622064i
\(656\) 7.36793 4.25387i 0.287669 0.166086i
\(657\) 0 0
\(658\) −2.36639 + 0.634072i −0.0922514 + 0.0247187i
\(659\) −19.9965 7.27814i −0.778954 0.283516i −0.0782177 0.996936i \(-0.524923\pi\)
−0.700737 + 0.713420i \(0.747145\pi\)
\(660\) 0 0
\(661\) 14.8137 + 12.4302i 0.576186 + 0.483477i 0.883692 0.468069i \(-0.155050\pi\)
−0.307506 + 0.951546i \(0.599494\pi\)
\(662\) −0.789631 9.02553i −0.0306899 0.350787i
\(663\) 0 0
\(664\) 2.37747 6.53205i 0.0922637 0.253493i
\(665\) −7.63398 + 7.99816i −0.296033 + 0.310155i
\(666\) 0 0
\(667\) 42.8653 + 11.4857i 1.65975 + 0.444729i
\(668\) −2.81495 1.97105i −0.108914 0.0762621i
\(669\) 0 0
\(670\) −13.3942 + 16.7394i −0.517463 + 0.646699i
\(671\) 3.42977 + 0.604761i 0.132405 + 0.0233465i
\(672\) 0 0
\(673\) −1.05962 0.0927051i −0.0408455 0.00357352i 0.0667147 0.997772i \(-0.478748\pi\)
−0.107560 + 0.994199i \(0.534304\pi\)
\(674\) −0.306576 −0.0118089
\(675\) 0 0
\(676\) −13.2524 −0.509709
\(677\) 23.1826 + 2.02822i 0.890980 + 0.0779507i 0.523446 0.852059i \(-0.324646\pi\)
0.367535 + 0.930010i \(0.380202\pi\)
\(678\) 0 0
\(679\) 9.17718 + 1.61818i 0.352188 + 0.0621002i
\(680\) 0.320072 0.400010i 0.0122742 0.0153397i
\(681\) 0 0
\(682\) −5.12304 3.58719i −0.196171 0.137361i
\(683\) −34.5505 9.25778i −1.32204 0.354239i −0.472297 0.881439i \(-0.656575\pi\)
−0.849741 + 0.527200i \(0.823242\pi\)
\(684\) 0 0
\(685\) 4.52926 4.74533i 0.173054 0.181310i
\(686\) −3.18713 + 8.75657i −0.121685 + 0.334327i
\(687\) 0 0
\(688\) −0.0382683 0.437409i −0.00145896 0.0166760i
\(689\) −44.8113 37.6012i −1.70718 1.43249i
\(690\) 0 0
\(691\) −23.6754 8.61714i −0.900655 0.327812i −0.150140 0.988665i \(-0.547972\pi\)
−0.750515 + 0.660853i \(0.770195\pi\)
\(692\) −14.3549 + 3.84639i −0.545692 + 0.146218i
\(693\) 0 0
\(694\) 0.0651815 0.0376325i 0.00247426 0.00142851i
\(695\) −1.72800 + 1.51993i −0.0655467 + 0.0576542i
\(696\) 0 0
\(697\) −0.823767 + 1.76658i −0.0312024 + 0.0669138i
\(698\) 2.16317 + 3.08933i 0.0818773 + 0.116933i
\(699\) 0 0
\(700\) 1.84233 2.91081i 0.0696337 0.110018i
\(701\) 16.3602i 0.617918i 0.951075 + 0.308959i \(0.0999806\pi\)
−0.951075 + 0.308959i \(0.900019\pi\)
\(702\) 0 0
\(703\) −41.5528 41.5528i −1.56719 1.56719i
\(704\) −3.94525 + 3.31046i −0.148692 + 0.124768i
\(705\) 0 0
\(706\) 2.77022 15.7107i 0.104259 0.591280i
\(707\) 4.93547 + 2.30145i 0.185617 + 0.0865548i
\(708\) 0 0
\(709\) 25.5907 4.51233i 0.961078 0.169464i 0.328967 0.944341i \(-0.393300\pi\)
0.632112 + 0.774877i \(0.282188\pi\)
\(710\) −0.909322 + 0.266500i −0.0341263 + 0.0100016i
\(711\) 0 0
\(712\) 0.0533101 + 0.198956i 0.00199788 + 0.00745619i
\(713\) 9.48762 4.42415i 0.355314 0.165686i
\(714\) 0 0
\(715\) −47.5329 + 34.9606i −1.77763 + 1.30745i
\(716\) 2.07674 2.47496i 0.0776113 0.0924936i
\(717\) 0 0
\(718\) −11.2819 24.1940i −0.421035 0.902913i
\(719\) 4.17596 7.23298i 0.155737 0.269745i −0.777590 0.628772i \(-0.783558\pi\)
0.933327 + 0.359027i \(0.116891\pi\)
\(720\) 0 0
\(721\) 0.0763196 + 0.132189i 0.00284229 + 0.00492299i
\(722\) −18.6456 + 26.6287i −0.693917 + 0.991017i
\(723\) 0 0
\(724\) −5.87294 16.1358i −0.218266 0.599681i
\(725\) −20.4663 15.6086i −0.760100 0.579689i
\(726\) 0 0
\(727\) 1.90761 21.8041i 0.0707494 0.808670i −0.875074 0.483989i \(-0.839188\pi\)
0.945824 0.324681i \(-0.105257\pi\)
\(728\) 2.49615 2.49615i 0.0925134 0.0925134i
\(729\) 0 0
\(730\) −6.62218 10.8768i −0.245098 0.402568i
\(731\) 0.0646625 + 0.0770617i 0.00239163 + 0.00285023i
\(732\) 0 0
\(733\) 14.6982 10.2918i 0.542889 0.380135i −0.269725 0.962937i \(-0.586933\pi\)
0.812614 + 0.582802i \(0.198044\pi\)
\(734\) 29.7691 10.8351i 1.09880 0.399930i
\(735\) 0 0
\(736\) −1.49696 8.48967i −0.0551786 0.312934i
\(737\) −12.7799 + 47.6953i −0.470754 + 1.75688i
\(738\) 0 0
\(739\) 27.1154 + 15.6551i 0.997457 + 0.575882i 0.907495 0.420063i \(-0.137992\pi\)
0.0899618 + 0.995945i \(0.471325\pi\)
\(740\) 15.2384 + 10.1495i 0.560173 + 0.373101i
\(741\) 0 0
\(742\) 7.83599 0.685560i 0.287668 0.0251677i
\(743\) −0.503855 + 0.0440816i −0.0184847 + 0.00161720i −0.0963943 0.995343i \(-0.530731\pi\)
0.0779097 + 0.996960i \(0.475175\pi\)
\(744\) 0 0
\(745\) 15.8290 3.17287i 0.579928 0.116245i
\(746\) −29.4536 17.0050i −1.07837 0.622599i
\(747\) 0 0
\(748\) 0.305393 1.13974i 0.0111663 0.0416731i
\(749\) −1.15663 6.55957i −0.0422623 0.239682i
\(750\) 0 0
\(751\) 35.9421 13.0819i 1.31155 0.477364i 0.410807 0.911722i \(-0.365247\pi\)
0.900740 + 0.434358i \(0.143025\pi\)
\(752\) 2.91277 2.03954i 0.106218 0.0743745i
\(753\) 0 0
\(754\) −16.9541 20.2051i −0.617432 0.735827i
\(755\) −23.6549 + 14.4020i −0.860890 + 0.524141i
\(756\) 0 0
\(757\) −19.5892 + 19.5892i −0.711983 + 0.711983i −0.966950 0.254967i \(-0.917935\pi\)
0.254967 + 0.966950i \(0.417935\pi\)
\(758\) −2.22322 + 25.4116i −0.0807511 + 0.922990i
\(759\) 0 0
\(760\) 6.44159 14.6984i 0.233661 0.533168i
\(761\) 0.568233 + 1.56121i 0.0205984 + 0.0565937i 0.949566 0.313568i \(-0.101524\pi\)
−0.928967 + 0.370162i \(0.879302\pi\)
\(762\) 0 0
\(763\) −0.632452 + 0.903235i −0.0228963 + 0.0326993i
\(764\) −8.75800 15.1693i −0.316853 0.548806i
\(765\) 0 0
\(766\) −2.31474 + 4.00924i −0.0836348 + 0.144860i
\(767\) −6.09618 13.0733i −0.220120 0.472050i
\(768\) 0 0
\(769\) 31.6759 37.7499i 1.14226 1.36129i 0.219644 0.975580i \(-0.429511\pi\)
0.922618 0.385715i \(-0.126045\pi\)
\(770\) 1.19541 7.84369i 0.0430797 0.282667i
\(771\) 0 0
\(772\) −5.40808 + 2.52183i −0.194641 + 0.0907627i
\(773\) −5.87742 21.9348i −0.211396 0.788941i −0.987404 0.158218i \(-0.949425\pi\)
0.776008 0.630723i \(-0.217241\pi\)
\(774\) 0 0
\(775\) −6.06514 + 0.282747i −0.217866 + 0.0101566i
\(776\) −13.3201 + 2.34870i −0.478165 + 0.0843134i
\(777\) 0 0
\(778\) −25.6895 11.9792i −0.921014 0.429476i
\(779\) −10.6028 + 60.1315i −0.379885 + 2.15443i
\(780\) 0 0
\(781\) −1.67187 + 1.40286i −0.0598241 + 0.0501984i
\(782\) 1.39658 + 1.39658i 0.0499416 + 0.0499416i
\(783\) 0 0
\(784\) 6.52532i 0.233047i
\(785\) −7.84339 15.8458i −0.279943 0.565562i
\(786\) 0 0
\(787\) −2.61309 3.73187i −0.0931464 0.133027i 0.769874 0.638196i \(-0.220319\pi\)
−0.863020 + 0.505169i \(0.831430\pi\)
\(788\) 3.53141 7.57313i 0.125801 0.269782i
\(789\) 0 0
\(790\) −11.3248 0.725484i −0.402918 0.0258116i
\(791\) 2.62588 1.51605i 0.0933654 0.0539046i
\(792\) 0 0
\(793\) 3.34673 0.896754i 0.118846 0.0318447i
\(794\) 3.38357 + 1.23152i 0.120078 + 0.0437049i
\(795\) 0 0
\(796\) 10.3019 + 8.64434i 0.365142 + 0.306391i
\(797\) −0.226051 2.58378i −0.00800715 0.0915221i 0.991140 0.132825i \(-0.0424048\pi\)
−0.999147 + 0.0413027i \(0.986849\pi\)
\(798\) 0 0
\(799\) −0.278635 + 0.765543i −0.00985739 + 0.0270829i
\(800\) −1.06779 + 4.88465i −0.0377519 + 0.172699i
\(801\) 0 0
\(802\) 1.69943 + 0.455361i 0.0600090 + 0.0160794i
\(803\) −24.0254 16.8227i −0.847836 0.593661i
\(804\) 0 0
\(805\) 10.3698 + 8.29749i 0.365486 + 0.292448i
\(806\) −6.12743 1.08043i −0.215829 0.0380565i
\(807\) 0 0
\(808\) −7.87401 0.688887i −0.277007 0.0242350i
\(809\) 41.9996 1.47663 0.738313 0.674458i \(-0.235623\pi\)
0.738313 + 0.674458i \(0.235623\pi\)
\(810\) 0 0
\(811\) 14.1219 0.495888 0.247944 0.968774i \(-0.420245\pi\)
0.247944 + 0.968774i \(0.420245\pi\)
\(812\) 3.53319 + 0.309114i 0.123991 + 0.0108478i
\(813\) 0 0
\(814\) 41.5290 + 7.32269i 1.45559 + 0.256660i
\(815\) 39.2173 4.35358i 1.37372 0.152499i
\(816\) 0 0
\(817\) 2.58133 + 1.80747i 0.0903093 + 0.0632352i
\(818\) −6.21393 1.66502i −0.217265 0.0582160i
\(819\) 0 0
\(820\) −0.443071 19.0187i −0.0154727 0.664163i
\(821\) −0.466036 + 1.28042i −0.0162648 + 0.0446871i −0.947559 0.319580i \(-0.896458\pi\)
0.931295 + 0.364267i \(0.118680\pi\)
\(822\) 0 0
\(823\) −1.36351 15.5850i −0.0475290 0.543258i −0.982212 0.187776i \(-0.939872\pi\)
0.934683 0.355482i \(-0.115683\pi\)
\(824\) −0.169715 0.142408i −0.00591230 0.00496100i
\(825\) 0 0
\(826\) 1.82268 + 0.663403i 0.0634193 + 0.0230827i
\(827\) −27.0219 + 7.24049i −0.939643 + 0.251777i −0.695962 0.718079i \(-0.745022\pi\)
−0.243681 + 0.969855i \(0.578355\pi\)
\(828\) 0 0
\(829\) −10.8695 + 6.27552i −0.377514 + 0.217958i −0.676736 0.736226i \(-0.736606\pi\)
0.299222 + 0.954183i \(0.403273\pi\)
\(830\) −10.2658 11.6711i −0.356330 0.405109i
\(831\) 0 0
\(832\) −2.16537 + 4.64366i −0.0750709 + 0.160990i
\(833\) 0.857501 + 1.22464i 0.0297107 + 0.0424312i
\(834\) 0 0
\(835\) −6.88660 + 3.40874i −0.238320 + 0.117964i
\(836\) 36.9621i 1.27836i
\(837\) 0 0
\(838\) 15.2109 + 15.2109i 0.525453 + 0.525453i
\(839\) 28.6334 24.0263i 0.988536 0.829480i 0.00318115 0.999995i \(-0.498987\pi\)
0.985355 + 0.170514i \(0.0545430\pi\)
\(840\) 0 0
\(841\) −0.434124 + 2.46204i −0.0149698 + 0.0848980i
\(842\) −29.2281 13.6293i −1.00727 0.469697i
\(843\) 0 0
\(844\) 3.78141 0.666764i 0.130161 0.0229510i
\(845\) −14.2149 + 26.0013i −0.489009 + 0.894473i
\(846\) 0 0
\(847\) −2.76825 10.3313i −0.0951183 0.354986i
\(848\) −10.3472 + 4.82500i −0.355326 + 0.165691i
\(849\) 0 0
\(850\) −0.441502 1.05705i −0.0151434 0.0362564i
\(851\) −45.3718 + 54.0720i −1.55533 + 1.85357i
\(852\) 0 0
\(853\) 12.9401 + 27.7501i 0.443060 + 0.950144i 0.993346 + 0.115168i \(0.0367407\pi\)
−0.550286 + 0.834976i \(0.685481\pi\)
\(854\) −0.232950 + 0.403482i −0.00797139 + 0.0138069i
\(855\) 0 0
\(856\) 4.83385 + 8.37248i 0.165218 + 0.286166i
\(857\) 6.00801 8.58033i 0.205230 0.293099i −0.703321 0.710872i \(-0.748301\pi\)
0.908551 + 0.417773i \(0.137189\pi\)
\(858\) 0 0
\(859\) −15.7634 43.3095i −0.537839 1.47770i −0.849542 0.527521i \(-0.823122\pi\)
0.311703 0.950180i \(-0.399101\pi\)
\(860\) −0.899246 0.394095i −0.0306640 0.0134385i
\(861\) 0 0
\(862\) −1.62966 + 18.6271i −0.0555065 + 0.634442i
\(863\) −1.44969 + 1.44969i −0.0493480 + 0.0493480i −0.731350 0.682002i \(-0.761109\pi\)
0.682002 + 0.731350i \(0.261109\pi\)
\(864\) 0 0
\(865\) −7.85087 + 32.2902i −0.266938 + 1.09790i
\(866\) 0.202862 + 0.241762i 0.00689353 + 0.00821539i
\(867\) 0 0
\(868\) 0.685341 0.479881i 0.0232620 0.0162882i
\(869\) −24.5608 + 8.93938i −0.833166 + 0.303248i
\(870\) 0 0
\(871\) 8.53032 + 48.3779i 0.289039 + 1.63922i
\(872\) 0.414221 1.54589i 0.0140273 0.0523506i
\(873\) 0 0
\(874\) 53.5804 + 30.9347i 1.81238 + 1.04638i
\(875\) −3.73488 6.73689i −0.126262 0.227748i
\(876\) 0 0
\(877\) −16.5614 + 1.44894i −0.559239 + 0.0489271i −0.363272 0.931683i \(-0.618340\pi\)
−0.195968 + 0.980610i \(0.562785\pi\)
\(878\) 39.0531 3.41670i 1.31798 0.115308i
\(879\) 0 0
\(880\) 2.26335 + 11.2915i 0.0762975 + 0.380637i
\(881\) 43.5164 + 25.1242i 1.46610 + 0.846455i 0.999282 0.0378966i \(-0.0120657\pi\)
0.466821 + 0.884352i \(0.345399\pi\)
\(882\) 0 0
\(883\) 3.51384 13.1138i 0.118250 0.441316i −0.881259 0.472633i \(-0.843304\pi\)
0.999509 + 0.0313172i \(0.00997020\pi\)
\(884\) −0.203843 1.15605i −0.00685600 0.0388823i
\(885\) 0 0
\(886\) −3.09340 + 1.12591i −0.103925 + 0.0378255i
\(887\) −10.1382 + 7.09887i −0.340409 + 0.238357i −0.731263 0.682096i \(-0.761069\pi\)
0.390854 + 0.920453i \(0.372180\pi\)
\(888\) 0 0
\(889\) 2.79338 + 3.32902i 0.0936871 + 0.111652i
\(890\) 0.447535 + 0.108811i 0.0150014 + 0.00364736i
\(891\) 0 0
\(892\) 7.81768 7.81768i 0.261755 0.261755i
\(893\) −2.22420 + 25.4227i −0.0744300 + 0.850738i
\(894\) 0 0
\(895\) −2.62831 6.72928i −0.0878549 0.224935i
\(896\) −0.235642 0.647420i −0.00787224 0.0216288i
\(897\) 0 0
\(898\) 9.47818 13.5362i 0.316291 0.451710i
\(899\) −3.12561 5.41371i −0.104245 0.180557i
\(900\) 0 0
\(901\) 1.30786 2.26528i 0.0435711 0.0754673i
\(902\) −18.5176 39.7111i −0.616568 1.32223i
\(903\) 0 0
\(904\) −2.82885 + 3.37130i −0.0940863 + 0.112128i
\(905\) −37.9579 5.78495i −1.26176 0.192298i
\(906\) 0 0
\(907\) −41.8937 + 19.5353i −1.39106 + 0.648660i −0.966482 0.256733i \(-0.917354\pi\)
−0.424574 + 0.905393i \(0.639576\pi\)
\(908\) 5.60974 + 20.9358i 0.186166 + 0.694780i
\(909\) 0 0
\(910\) −2.22001 7.57490i −0.0735928 0.251105i
\(911\) −23.7870 + 4.19429i −0.788098 + 0.138963i −0.553191 0.833055i \(-0.686590\pi\)
−0.234908 + 0.972018i \(0.575479\pi\)
\(912\) 0 0
\(913\) −32.4459 15.1298i −1.07380 0.500723i
\(914\) −4.88831 + 27.7230i −0.161691 + 0.916994i
\(915\) 0 0
\(916\) 11.4589 9.61516i 0.378613 0.317694i
\(917\) −5.25186 5.25186i −0.173432 0.173432i
\(918\) 0 0
\(919\) 26.6607i 0.879455i −0.898131 0.439727i \(-0.855075\pi\)
0.898131 0.439727i \(-0.144925\pi\)
\(920\) −18.2625 6.16923i −0.602096 0.203394i
\(921\) 0 0
\(922\) −1.10947 1.58449i −0.0365386 0.0521825i
\(923\) −0.917613 + 1.96783i −0.0302036 + 0.0647718i
\(924\) 0 0
\(925\) 36.2584 19.0111i 1.19217 0.625083i
\(926\) −3.43972 + 1.98593i −0.113036 + 0.0652616i
\(927\) 0 0
\(928\) −4.97241 + 1.33235i −0.163227 + 0.0437366i
\(929\) 40.2501 + 14.6498i 1.32056 + 0.480645i 0.903638 0.428296i \(-0.140886\pi\)
0.416924 + 0.908941i \(0.363108\pi\)
\(930\) 0 0
\(931\) 35.8750 + 30.1027i 1.17575 + 0.986575i
\(932\) −2.05411 23.4786i −0.0672845 0.769065i
\(933\) 0 0
\(934\) 9.04453 24.8496i 0.295946 0.813105i
\(935\) −1.90861 1.82170i −0.0624181 0.0595761i
\(936\) 0 0
\(937\) 31.8122 + 8.52406i 1.03926 + 0.278469i 0.737807 0.675012i \(-0.235862\pi\)
0.301453 + 0.953481i \(0.402528\pi\)
\(938\) −5.41098 3.78881i −0.176675 0.123709i
\(939\) 0 0
\(940\) −0.877274 7.90255i −0.0286135 0.257753i
\(941\) 15.6178 + 2.75384i 0.509125 + 0.0897725i 0.422309 0.906452i \(-0.361220\pi\)
0.0868161 + 0.996224i \(0.472331\pi\)
\(942\) 0 0
\(943\) 73.0632 + 6.39220i 2.37926 + 0.208159i
\(944\) −2.81530 −0.0916303
\(945\) 0 0
\(946\) −2.26133 −0.0735222
\(947\) 22.5639 + 1.97409i 0.733228 + 0.0641492i 0.447653 0.894207i \(-0.352260\pi\)
0.285575 + 0.958356i \(0.407815\pi\)
\(948\) 0 0
\(949\) −28.7356 5.06686i −0.932797 0.164477i
\(950\) −21.9290 28.4044i −0.711470 0.921561i
\(951\) 0 0
\(952\) 0.129302 + 0.0905386i 0.00419072 + 0.00293437i
\(953\) 54.3042 + 14.5508i 1.75909 + 0.471346i 0.986527 0.163596i \(-0.0523094\pi\)
0.772560 + 0.634942i \(0.218976\pi\)
\(954\) 0 0
\(955\) −39.1564 + 0.912209i −1.26707 + 0.0295184i
\(956\) −3.89812 + 10.7100i −0.126074 + 0.346386i
\(957\) 0 0
\(958\) −1.15385 13.1885i −0.0372791 0.426102i
\(959\) 1.54834 + 1.29921i 0.0499986 + 0.0419538i
\(960\) 0 0
\(961\) 27.7448 + 10.0983i 0.894993 + 0.325751i
\(962\) 40.5236 10.8583i 1.30653 0.350084i
\(963\) 0 0
\(964\) −18.9353 + 10.9323i −0.609865 + 0.352105i
\(965\) −0.853023 + 13.3157i −0.0274598 + 0.428647i
\(966\) 0 0
\(967\) 6.52300 13.9886i 0.209765 0.449844i −0.773072 0.634319i \(-0.781281\pi\)
0.982837 + 0.184475i \(0.0590585\pi\)
\(968\) 8.90431 + 12.7167i 0.286195 + 0.408729i
\(969\) 0 0
\(970\) −9.67941 + 28.6535i −0.310787 + 0.920007i
\(971\) 47.8033i 1.53408i 0.641599 + 0.767040i \(0.278271\pi\)
−0.641599 + 0.767040i \(0.721729\pi\)
\(972\) 0 0
\(973\) −0.501396 0.501396i −0.0160740 0.0160740i
\(974\) 9.97781 8.37238i 0.319710 0.268268i
\(975\) 0 0
\(976\) 0.117426 0.665953i 0.00375870 0.0213167i
\(977\) 2.12391 + 0.990393i 0.0679498 + 0.0316855i 0.456296 0.889828i \(-0.349176\pi\)
−0.388346 + 0.921513i \(0.626954\pi\)
\(978\) 0 0
\(979\) 1.04469 0.184206i 0.0333883 0.00588726i
\(980\) −12.8027 6.99925i −0.408968 0.223583i
\(981\) 0 0
\(982\) −7.28398 27.1842i −0.232441 0.867482i
\(983\) 13.4725 6.28233i 0.429706 0.200375i −0.195718 0.980660i \(-0.562704\pi\)
0.625424 + 0.780285i \(0.284926\pi\)
\(984\) 0 0
\(985\) −11.0706 15.0518i −0.352740 0.479591i
\(986\) 0.758110 0.903480i 0.0241431 0.0287727i
\(987\) 0 0
\(988\) −15.5406 33.3270i −0.494413 1.06027i
\(989\) 1.89257 3.27803i 0.0601803 0.104235i
\(990\) 0 0
\(991\) −16.8966 29.2658i −0.536739 0.929659i −0.999077 0.0429551i \(-0.986323\pi\)
0.462338 0.886704i \(-0.347011\pi\)
\(992\) −0.696519 + 0.994733i −0.0221145 + 0.0315828i
\(993\) 0 0
\(994\) −0.0998570 0.274355i −0.00316727 0.00870201i
\(995\) 28.0104 10.9403i 0.887989 0.346830i
\(996\) 0 0
\(997\) −3.63234 + 41.5179i −0.115037 + 1.31488i 0.690929 + 0.722923i \(0.257202\pi\)
−0.805966 + 0.591961i \(0.798354\pi\)
\(998\) −20.8120 + 20.8120i −0.658794 + 0.658794i
\(999\) 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 810.2.s.a.773.7 216
3.2 odd 2 270.2.r.a.113.18 216
5.2 odd 4 inner 810.2.s.a.287.10 216
15.2 even 4 270.2.r.a.167.5 yes 216
27.11 odd 18 inner 810.2.s.a.683.10 216
27.16 even 9 270.2.r.a.173.5 yes 216
135.92 even 36 inner 810.2.s.a.197.7 216
135.97 odd 36 270.2.r.a.227.18 yes 216
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
270.2.r.a.113.18 216 3.2 odd 2
270.2.r.a.167.5 yes 216 15.2 even 4
270.2.r.a.173.5 yes 216 27.16 even 9
270.2.r.a.227.18 yes 216 135.97 odd 36
810.2.s.a.197.7 216 135.92 even 36 inner
810.2.s.a.287.10 216 5.2 odd 4 inner
810.2.s.a.683.10 216 27.11 odd 18 inner
810.2.s.a.773.7 216 1.1 even 1 trivial