Properties

Label 567.2.s.f.458.5
Level $567$
Weight $2$
Character 567.458
Analytic conductor $4.528$
Analytic rank $0$
Dimension $12$
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] = [567,2,Mod(26,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{4} \)
Twist minimal: no (minimal twist has level 189)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 458.5
Root \(1.90412 + 1.09935i\) of defining polynomial
Character \(\chi\) \(=\) 567.458
Dual form 567.2.s.f.26.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.58850 + 0.917122i) q^{2} +(0.682224 + 1.18165i) q^{4} -3.80824 q^{5} +(-2.43359 - 1.03810i) q^{7} -1.16576i q^{8} +O(q^{10})\) \(q+(1.58850 + 0.917122i) q^{2} +(0.682224 + 1.18165i) q^{4} -3.80824 q^{5} +(-2.43359 - 1.03810i) q^{7} -1.16576i q^{8} +(-6.04940 - 3.49262i) q^{10} +1.16576i q^{11} +(-4.79804 - 2.77015i) q^{13} +(-2.91370 - 3.88092i) q^{14} +(2.43359 - 4.21510i) q^{16} +(-1.58850 + 2.75136i) q^{17} +(-0.546672 + 0.315621i) q^{19} +(-2.59808 - 4.50000i) q^{20} +(-1.06914 + 1.85181i) q^{22} +1.76183i q^{23} +9.50273 q^{25} +(-5.08112 - 8.80077i) q^{26} +(-0.433589 - 3.58386i) q^{28} +(-4.18658 + 2.41712i) q^{29} +(3.70469 - 2.13891i) q^{31} +(5.71237 - 3.29804i) q^{32} +(-5.04667 + 2.91370i) q^{34} +(9.26770 + 3.95333i) q^{35} +(-2.11581 - 3.66470i) q^{37} -1.15785 q^{38} +4.43949i q^{40} +(-2.28245 + 3.95333i) q^{41} +(-3.61581 - 6.26277i) q^{43} +(-1.37751 + 0.795307i) q^{44} +(-1.61581 + 2.79867i) q^{46} +(1.27288 - 2.20469i) q^{47} +(4.84471 + 5.05260i) q^{49} +(15.0951 + 8.71516i) q^{50} -7.55945i q^{52} +(-0.0627112 - 0.0362063i) q^{53} -4.43949i q^{55} +(-1.21017 + 2.83697i) q^{56} -8.86718 q^{58} +(3.49262 + 6.04940i) q^{59} +(-7.00273 - 4.04303i) q^{61} +7.84655 q^{62} +2.36445 q^{64} +(18.2721 + 10.5494i) q^{65} +(-2.54940 - 4.41569i) q^{67} -4.33485 q^{68} +(11.0961 + 14.7795i) q^{70} +4.76183i q^{71} +(4.84744 + 2.79867i) q^{73} -7.76183i q^{74} +(-0.745906 - 0.430649i) q^{76} +(1.21017 - 2.83697i) q^{77} +(-8.54940 + 14.8080i) q^{79} +(-9.26770 + 16.0521i) q^{80} +(-7.25136 + 4.18658i) q^{82} +(-5.08112 - 8.80077i) q^{83} +(6.04940 - 10.4779i) q^{85} -13.2646i q^{86} +1.35899 q^{88} +(-5.77508 - 10.0027i) q^{89} +(8.80077 + 11.7222i) q^{91} +(-2.08186 + 1.20196i) q^{92} +(4.04394 - 2.33477i) q^{94} +(2.08186 - 1.20196i) q^{95} +(0.596074 - 0.344143i) q^{97} +(3.06197 + 12.4693i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 8 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 8 q^{4} + 4 q^{7} - 6 q^{10} - 24 q^{13} - 4 q^{16} - 6 q^{19} + 20 q^{22} + 48 q^{25} + 28 q^{28} + 12 q^{31} - 60 q^{34} + 8 q^{37} - 10 q^{43} + 14 q^{46} + 24 q^{49} - 40 q^{58} - 18 q^{61} + 28 q^{64} + 36 q^{67} + 66 q^{70} - 42 q^{73} - 108 q^{76} - 36 q^{79} - 54 q^{82} + 6 q^{85} + 148 q^{88} + 6 q^{91} + 114 q^{94} - 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.58850 + 0.917122i 1.12324 + 0.648503i 0.942226 0.334978i \(-0.108729\pi\)
0.181014 + 0.983481i \(0.442062\pi\)
\(3\) 0 0
\(4\) 0.682224 + 1.18165i 0.341112 + 0.590823i
\(5\) −3.80824 −1.70310 −0.851549 0.524274i \(-0.824337\pi\)
−0.851549 + 0.524274i \(0.824337\pi\)
\(6\) 0 0
\(7\) −2.43359 1.03810i −0.919810 0.392364i
\(8\) 1.16576i 0.412157i
\(9\) 0 0
\(10\) −6.04940 3.49262i −1.91299 1.10446i
\(11\) 1.16576i 0.351489i 0.984436 + 0.175744i \(0.0562332\pi\)
−0.984436 + 0.175744i \(0.943767\pi\)
\(12\) 0 0
\(13\) −4.79804 2.77015i −1.33074 0.768301i −0.345324 0.938484i \(-0.612231\pi\)
−0.985412 + 0.170183i \(0.945564\pi\)
\(14\) −2.91370 3.88092i −0.778718 1.03722i
\(15\) 0 0
\(16\) 2.43359 4.21510i 0.608397 1.05377i
\(17\) −1.58850 + 2.75136i −0.385268 + 0.667304i −0.991806 0.127750i \(-0.959224\pi\)
0.606538 + 0.795054i \(0.292558\pi\)
\(18\) 0 0
\(19\) −0.546672 + 0.315621i −0.125415 + 0.0724085i −0.561395 0.827548i \(-0.689735\pi\)
0.435980 + 0.899956i \(0.356402\pi\)
\(20\) −2.59808 4.50000i −0.580948 1.00623i
\(21\) 0 0
\(22\) −1.06914 + 1.85181i −0.227942 + 0.394806i
\(23\) 1.76183i 0.367367i 0.982985 + 0.183684i \(0.0588022\pi\)
−0.982985 + 0.183684i \(0.941198\pi\)
\(24\) 0 0
\(25\) 9.50273 1.90055
\(26\) −5.08112 8.80077i −0.996491 1.72597i
\(27\) 0 0
\(28\) −0.433589 3.58386i −0.0819406 0.677285i
\(29\) −4.18658 + 2.41712i −0.777428 + 0.448848i −0.835518 0.549463i \(-0.814832\pi\)
0.0580901 + 0.998311i \(0.481499\pi\)
\(30\) 0 0
\(31\) 3.70469 2.13891i 0.665382 0.384159i −0.128942 0.991652i \(-0.541158\pi\)
0.794325 + 0.607493i \(0.207825\pi\)
\(32\) 5.71237 3.29804i 1.00981 0.583016i
\(33\) 0 0
\(34\) −5.04667 + 2.91370i −0.865497 + 0.499695i
\(35\) 9.26770 + 3.95333i 1.56653 + 0.668234i
\(36\) 0 0
\(37\) −2.11581 3.66470i −0.347837 0.602472i 0.638028 0.770014i \(-0.279751\pi\)
−0.985865 + 0.167541i \(0.946417\pi\)
\(38\) −1.15785 −0.187828
\(39\) 0 0
\(40\) 4.43949i 0.701945i
\(41\) −2.28245 + 3.95333i −0.356460 + 0.617406i −0.987367 0.158452i \(-0.949350\pi\)
0.630907 + 0.775858i \(0.282683\pi\)
\(42\) 0 0
\(43\) −3.61581 6.26277i −0.551406 0.955064i −0.998173 0.0604134i \(-0.980758\pi\)
0.446767 0.894650i \(-0.352575\pi\)
\(44\) −1.37751 + 0.795307i −0.207668 + 0.119897i
\(45\) 0 0
\(46\) −1.61581 + 2.79867i −0.238239 + 0.412641i
\(47\) 1.27288 2.20469i 0.185669 0.321587i −0.758133 0.652100i \(-0.773888\pi\)
0.943802 + 0.330512i \(0.107222\pi\)
\(48\) 0 0
\(49\) 4.84471 + 5.05260i 0.692101 + 0.721800i
\(50\) 15.0951 + 8.71516i 2.13477 + 1.23251i
\(51\) 0 0
\(52\) 7.55945i 1.04831i
\(53\) −0.0627112 0.0362063i −0.00861404 0.00497332i 0.495687 0.868501i \(-0.334916\pi\)
−0.504301 + 0.863528i \(0.668250\pi\)
\(54\) 0 0
\(55\) 4.43949i 0.598620i
\(56\) −1.21017 + 2.83697i −0.161716 + 0.379106i
\(57\) 0 0
\(58\) −8.86718 −1.16432
\(59\) 3.49262 + 6.04940i 0.454701 + 0.787565i 0.998671 0.0515396i \(-0.0164128\pi\)
−0.543970 + 0.839105i \(0.683080\pi\)
\(60\) 0 0
\(61\) −7.00273 4.04303i −0.896608 0.517657i −0.0205096 0.999790i \(-0.506529\pi\)
−0.876098 + 0.482133i \(0.839862\pi\)
\(62\) 7.84655 0.996512
\(63\) 0 0
\(64\) 2.36445 0.295556
\(65\) 18.2721 + 10.5494i 2.26638 + 1.30849i
\(66\) 0 0
\(67\) −2.54940 4.41569i −0.311459 0.539463i 0.667219 0.744861i \(-0.267484\pi\)
−0.978678 + 0.205398i \(0.934151\pi\)
\(68\) −4.33485 −0.525678
\(69\) 0 0
\(70\) 11.0961 + 14.7795i 1.32623 + 1.76649i
\(71\) 4.76183i 0.565125i 0.959249 + 0.282563i \(0.0911845\pi\)
−0.959249 + 0.282563i \(0.908815\pi\)
\(72\) 0 0
\(73\) 4.84744 + 2.79867i 0.567350 + 0.327560i 0.756090 0.654467i \(-0.227107\pi\)
−0.188740 + 0.982027i \(0.560440\pi\)
\(74\) 7.76183i 0.902294i
\(75\) 0 0
\(76\) −0.745906 0.430649i −0.0855612 0.0493988i
\(77\) 1.21017 2.83697i 0.137912 0.323303i
\(78\) 0 0
\(79\) −8.54940 + 14.8080i −0.961883 + 1.66603i −0.244116 + 0.969746i \(0.578498\pi\)
−0.717766 + 0.696284i \(0.754835\pi\)
\(80\) −9.26770 + 16.0521i −1.03616 + 1.79468i
\(81\) 0 0
\(82\) −7.25136 + 4.18658i −0.800779 + 0.462330i
\(83\) −5.08112 8.80077i −0.557726 0.966010i −0.997686 0.0679922i \(-0.978341\pi\)
0.439960 0.898017i \(-0.354993\pi\)
\(84\) 0 0
\(85\) 6.04940 10.4779i 0.656150 1.13648i
\(86\) 13.2646i 1.43035i
\(87\) 0 0
\(88\) 1.35899 0.144869
\(89\) −5.77508 10.0027i −0.612157 1.06029i −0.990876 0.134776i \(-0.956969\pi\)
0.378719 0.925512i \(-0.376365\pi\)
\(90\) 0 0
\(91\) 8.80077 + 11.7222i 0.922571 + 1.22882i
\(92\) −2.08186 + 1.20196i −0.217049 + 0.125313i
\(93\) 0 0
\(94\) 4.04394 2.33477i 0.417101 0.240813i
\(95\) 2.08186 1.20196i 0.213594 0.123319i
\(96\) 0 0
\(97\) 0.596074 0.344143i 0.0605221 0.0349425i −0.469434 0.882968i \(-0.655542\pi\)
0.529956 + 0.848025i \(0.322209\pi\)
\(98\) 3.06197 + 12.4693i 0.309306 + 1.25958i
\(99\) 0 0
\(100\) 6.48299 + 11.2289i 0.648299 + 1.12289i
\(101\) −6.58406 −0.655138 −0.327569 0.944827i \(-0.606229\pi\)
−0.327569 + 0.944827i \(0.606229\pi\)
\(102\) 0 0
\(103\) 9.34854i 0.921139i −0.887624 0.460570i \(-0.847645\pi\)
0.887624 0.460570i \(-0.152355\pi\)
\(104\) −3.22932 + 5.59334i −0.316661 + 0.548473i
\(105\) 0 0
\(106\) −0.0664112 0.115028i −0.00645043 0.0111725i
\(107\) 13.6549 7.88364i 1.32007 0.762141i 0.336328 0.941745i \(-0.390815\pi\)
0.983739 + 0.179604i \(0.0574818\pi\)
\(108\) 0 0
\(109\) 7.23163 12.5255i 0.692664 1.19973i −0.278298 0.960495i \(-0.589770\pi\)
0.970962 0.239235i \(-0.0768965\pi\)
\(110\) 4.07155 7.05213i 0.388207 0.672394i
\(111\) 0 0
\(112\) −10.2980 + 7.73152i −0.973073 + 0.730560i
\(113\) −17.1998 9.93032i −1.61802 0.934166i −0.987431 0.158051i \(-0.949479\pi\)
−0.630591 0.776115i \(-0.717188\pi\)
\(114\) 0 0
\(115\) 6.70948i 0.625662i
\(116\) −5.71237 3.29804i −0.530380 0.306215i
\(117\) 0 0
\(118\) 12.8126i 1.17950i
\(119\) 6.72194 5.04667i 0.616199 0.462628i
\(120\) 0 0
\(121\) 9.64101 0.876456
\(122\) −7.41590 12.8447i −0.671404 1.16291i
\(123\) 0 0
\(124\) 5.05486 + 2.91843i 0.453940 + 0.262082i
\(125\) −17.1475 −1.53372
\(126\) 0 0
\(127\) −8.90666 −0.790338 −0.395169 0.918608i \(-0.629314\pi\)
−0.395169 + 0.918608i \(0.629314\pi\)
\(128\) −7.66881 4.42759i −0.677833 0.391347i
\(129\) 0 0
\(130\) 19.3502 + 33.5155i 1.69712 + 2.93950i
\(131\) 6.75519 0.590204 0.295102 0.955466i \(-0.404646\pi\)
0.295102 + 0.955466i \(0.404646\pi\)
\(132\) 0 0
\(133\) 1.65802 0.200594i 0.143769 0.0173937i
\(134\) 9.35245i 0.807928i
\(135\) 0 0
\(136\) 3.20742 + 1.85181i 0.275034 + 0.158791i
\(137\) 16.8606i 1.44050i 0.693714 + 0.720251i \(0.255973\pi\)
−0.693714 + 0.720251i \(0.744027\pi\)
\(138\) 0 0
\(139\) −0.704693 0.406855i −0.0597713 0.0345089i 0.469817 0.882764i \(-0.344320\pi\)
−0.529588 + 0.848255i \(0.677653\pi\)
\(140\) 1.65121 + 13.6482i 0.139553 + 1.15348i
\(141\) 0 0
\(142\) −4.36718 + 7.56417i −0.366485 + 0.634771i
\(143\) 3.22932 5.59334i 0.270049 0.467739i
\(144\) 0 0
\(145\) 15.9435 9.20499i 1.32404 0.764433i
\(146\) 5.13344 + 8.89138i 0.424847 + 0.735856i
\(147\) 0 0
\(148\) 2.88692 5.00029i 0.237303 0.411021i
\(149\) 8.43032i 0.690638i −0.938485 0.345319i \(-0.887771\pi\)
0.938485 0.345319i \(-0.112229\pi\)
\(150\) 0 0
\(151\) 3.03948 0.247349 0.123675 0.992323i \(-0.460532\pi\)
0.123675 + 0.992323i \(0.460532\pi\)
\(152\) 0.367938 + 0.637287i 0.0298437 + 0.0516908i
\(153\) 0 0
\(154\) 4.52420 3.39666i 0.364571 0.273711i
\(155\) −14.1084 + 8.14548i −1.13321 + 0.654260i
\(156\) 0 0
\(157\) 3.29804 1.90412i 0.263212 0.151966i −0.362587 0.931950i \(-0.618106\pi\)
0.625799 + 0.779984i \(0.284773\pi\)
\(158\) −27.1615 + 15.6817i −2.16085 + 1.24757i
\(159\) 0 0
\(160\) −21.7541 + 12.5597i −1.71981 + 0.992934i
\(161\) 1.82895 4.28757i 0.144142 0.337908i
\(162\) 0 0
\(163\) 5.54667 + 9.60712i 0.434449 + 0.752488i 0.997250 0.0741045i \(-0.0236098\pi\)
−0.562802 + 0.826592i \(0.690276\pi\)
\(164\) −6.22858 −0.486371
\(165\) 0 0
\(166\) 18.6400i 1.44675i
\(167\) −1.85181 + 3.20742i −0.143297 + 0.248198i −0.928736 0.370741i \(-0.879104\pi\)
0.785439 + 0.618939i \(0.212437\pi\)
\(168\) 0 0
\(169\) 8.84744 + 15.3242i 0.680572 + 1.17879i
\(170\) 19.2190 11.0961i 1.47403 0.851030i
\(171\) 0 0
\(172\) 4.93359 8.54523i 0.376183 0.651567i
\(173\) 4.81782 8.34471i 0.366292 0.634436i −0.622691 0.782468i \(-0.713960\pi\)
0.988983 + 0.148032i \(0.0472938\pi\)
\(174\) 0 0
\(175\) −23.1257 9.86476i −1.74814 0.745705i
\(176\) 4.91378 + 2.83697i 0.370390 + 0.213845i
\(177\) 0 0
\(178\) 21.1858i 1.58794i
\(179\) −15.9792 9.22562i −1.19435 0.689556i −0.235056 0.971982i \(-0.575527\pi\)
−0.959289 + 0.282426i \(0.908861\pi\)
\(180\) 0 0
\(181\) 16.6209i 1.23542i 0.786406 + 0.617710i \(0.211940\pi\)
−0.786406 + 0.617710i \(0.788060\pi\)
\(182\) 3.22932 + 26.6921i 0.239373 + 1.97855i
\(183\) 0 0
\(184\) 2.05387 0.151413
\(185\) 8.05753 + 13.9561i 0.592402 + 1.02607i
\(186\) 0 0
\(187\) −3.20742 1.85181i −0.234550 0.135417i
\(188\) 3.47356 0.253335
\(189\) 0 0
\(190\) 4.40939 0.319890
\(191\) −6.20573 3.58288i −0.449031 0.259248i 0.258390 0.966041i \(-0.416808\pi\)
−0.707421 + 0.706793i \(0.750141\pi\)
\(192\) 0 0
\(193\) 1.58888 + 2.75202i 0.114370 + 0.198095i 0.917528 0.397672i \(-0.130182\pi\)
−0.803158 + 0.595766i \(0.796848\pi\)
\(194\) 1.26249 0.0906411
\(195\) 0 0
\(196\) −2.66521 + 9.17174i −0.190372 + 0.655124i
\(197\) 1.93305i 0.137724i −0.997626 0.0688619i \(-0.978063\pi\)
0.997626 0.0688619i \(-0.0219368\pi\)
\(198\) 0 0
\(199\) −7.50000 4.33013i −0.531661 0.306955i 0.210032 0.977695i \(-0.432643\pi\)
−0.741693 + 0.670740i \(0.765977\pi\)
\(200\) 11.0779i 0.783324i
\(201\) 0 0
\(202\) −10.4588 6.03838i −0.735878 0.424859i
\(203\) 12.6976 1.53621i 0.891198 0.107821i
\(204\) 0 0
\(205\) 8.69215 15.0552i 0.607086 1.05150i
\(206\) 8.57375 14.8502i 0.597361 1.03466i
\(207\) 0 0
\(208\) −23.3529 + 13.4828i −1.61923 + 0.934864i
\(209\) −0.367938 0.637287i −0.0254508 0.0440820i
\(210\) 0 0
\(211\) −6.20916 + 10.7546i −0.427456 + 0.740376i −0.996646 0.0818303i \(-0.973923\pi\)
0.569190 + 0.822206i \(0.307257\pi\)
\(212\) 0.0988033i 0.00678584i
\(213\) 0 0
\(214\) 28.9210 1.97700
\(215\) 13.7699 + 23.8502i 0.939099 + 1.62657i
\(216\) 0 0
\(217\) −11.2361 + 1.35939i −0.762755 + 0.0922811i
\(218\) 22.9749 13.2646i 1.55606 0.898389i
\(219\) 0 0
\(220\) 5.24591 3.02873i 0.353679 0.204197i
\(221\) 15.2434 8.80077i 1.02538 0.592004i
\(222\) 0 0
\(223\) −16.3996 + 9.46830i −1.09820 + 0.634044i −0.935747 0.352673i \(-0.885273\pi\)
−0.162450 + 0.986717i \(0.551940\pi\)
\(224\) −17.3252 + 2.09607i −1.15759 + 0.140050i
\(225\) 0 0
\(226\) −18.2146 31.5486i −1.21162 2.09858i
\(227\) −5.72276 −0.379833 −0.189917 0.981800i \(-0.560822\pi\)
−0.189917 + 0.981800i \(0.560822\pi\)
\(228\) 0 0
\(229\) 11.1376i 0.735996i 0.929827 + 0.367998i \(0.119957\pi\)
−0.929827 + 0.367998i \(0.880043\pi\)
\(230\) 6.15341 10.6580i 0.405744 0.702769i
\(231\) 0 0
\(232\) 2.81778 + 4.88053i 0.184996 + 0.320423i
\(233\) −8.95208 + 5.16849i −0.586470 + 0.338599i −0.763701 0.645571i \(-0.776620\pi\)
0.177230 + 0.984169i \(0.443286\pi\)
\(234\) 0 0
\(235\) −4.84744 + 8.39601i −0.316212 + 0.547695i
\(236\) −4.76550 + 8.25409i −0.310208 + 0.537296i
\(237\) 0 0
\(238\) 15.3062 1.85181i 0.992155 0.120035i
\(239\) −14.3592 8.29030i −0.928821 0.536255i −0.0423824 0.999101i \(-0.513495\pi\)
−0.886438 + 0.462846i \(0.846828\pi\)
\(240\) 0 0
\(241\) 23.8932i 1.53910i −0.638587 0.769549i \(-0.720481\pi\)
0.638587 0.769549i \(-0.279519\pi\)
\(242\) 15.3148 + 8.84198i 0.984470 + 0.568384i
\(243\) 0 0
\(244\) 11.0330i 0.706316i
\(245\) −18.4498 19.2415i −1.17872 1.22930i
\(246\) 0 0
\(247\) 3.49727 0.222526
\(248\) −2.49344 4.31877i −0.158334 0.274242i
\(249\) 0 0
\(250\) −27.2388 15.7263i −1.72273 0.994621i
\(251\) −19.9233 −1.25755 −0.628774 0.777588i \(-0.716443\pi\)
−0.628774 + 0.777588i \(0.716443\pi\)
\(252\) 0 0
\(253\) −2.05387 −0.129125
\(254\) −14.1482 8.16849i −0.887739 0.512536i
\(255\) 0 0
\(256\) −10.4857 18.1618i −0.655358 1.13511i
\(257\) 23.2049 1.44748 0.723742 0.690070i \(-0.242420\pi\)
0.723742 + 0.690070i \(0.242420\pi\)
\(258\) 0 0
\(259\) 1.34471 + 11.1148i 0.0835561 + 0.690639i
\(260\) 28.7882i 1.78537i
\(261\) 0 0
\(262\) 10.7306 + 6.19533i 0.662941 + 0.382749i
\(263\) 9.62246i 0.593347i −0.954979 0.296673i \(-0.904123\pi\)
0.954979 0.296673i \(-0.0958772\pi\)
\(264\) 0 0
\(265\) 0.238820 + 0.137883i 0.0146706 + 0.00847006i
\(266\) 2.81774 + 1.20196i 0.172767 + 0.0736971i
\(267\) 0 0
\(268\) 3.47853 6.02498i 0.212485 0.368034i
\(269\) −10.4152 + 18.0396i −0.635024 + 1.09989i 0.351487 + 0.936193i \(0.385676\pi\)
−0.986510 + 0.163700i \(0.947657\pi\)
\(270\) 0 0
\(271\) 17.0467 9.84190i 1.03551 0.597853i 0.116953 0.993137i \(-0.462687\pi\)
0.918559 + 0.395285i \(0.129354\pi\)
\(272\) 7.73152 + 13.3914i 0.468792 + 0.811972i
\(273\) 0 0
\(274\) −15.4633 + 26.7831i −0.934169 + 1.61803i
\(275\) 11.0779i 0.668021i
\(276\) 0 0
\(277\) 8.31604 0.499662 0.249831 0.968289i \(-0.419625\pi\)
0.249831 + 0.968289i \(0.419625\pi\)
\(278\) −0.746270 1.29258i −0.0447583 0.0775237i
\(279\) 0 0
\(280\) 4.60862 10.8039i 0.275418 0.645656i
\(281\) 19.7123 11.3809i 1.17594 0.678928i 0.220867 0.975304i \(-0.429111\pi\)
0.955072 + 0.296375i \(0.0957780\pi\)
\(282\) 0 0
\(283\) 14.7514 8.51670i 0.876878 0.506266i 0.00724998 0.999974i \(-0.497692\pi\)
0.869628 + 0.493708i \(0.164359\pi\)
\(284\) −5.62680 + 3.24864i −0.333889 + 0.192771i
\(285\) 0 0
\(286\) 10.2596 5.92336i 0.606660 0.350255i
\(287\) 9.65849 7.25136i 0.570123 0.428035i
\(288\) 0 0
\(289\) 3.45333 + 5.98134i 0.203137 + 0.351843i
\(290\) 33.7684 1.98295
\(291\) 0 0
\(292\) 7.63728i 0.446938i
\(293\) 10.7079 18.5467i 0.625564 1.08351i −0.362868 0.931841i \(-0.618202\pi\)
0.988432 0.151668i \(-0.0484643\pi\)
\(294\) 0 0
\(295\) −13.3008 23.0376i −0.774401 1.34130i
\(296\) −4.27214 + 2.46652i −0.248313 + 0.143364i
\(297\) 0 0
\(298\) 7.73163 13.3916i 0.447881 0.775753i
\(299\) 4.88053 8.45333i 0.282248 0.488869i
\(300\) 0 0
\(301\) 2.29804 + 18.9946i 0.132457 + 1.09483i
\(302\) 4.82821 + 2.78757i 0.277833 + 0.160407i
\(303\) 0 0
\(304\) 3.07237i 0.176212i
\(305\) 26.6681 + 15.3968i 1.52701 + 0.881621i
\(306\) 0 0
\(307\) 19.4537i 1.11028i −0.831756 0.555142i \(-0.812664\pi\)
0.831756 0.555142i \(-0.187336\pi\)
\(308\) 4.17791 0.505459i 0.238058 0.0288012i
\(309\) 0 0
\(310\) −29.8816 −1.69716
\(311\) 3.40706 + 5.90120i 0.193197 + 0.334626i 0.946308 0.323267i \(-0.104781\pi\)
−0.753111 + 0.657893i \(0.771448\pi\)
\(312\) 0 0
\(313\) 14.4121 + 8.32084i 0.814621 + 0.470322i 0.848558 0.529102i \(-0.177471\pi\)
−0.0339371 + 0.999424i \(0.510805\pi\)
\(314\) 6.98525 0.394200
\(315\) 0 0
\(316\) −23.3304 −1.31244
\(317\) −4.39757 2.53894i −0.246992 0.142601i 0.371394 0.928475i \(-0.378880\pi\)
−0.618386 + 0.785874i \(0.712213\pi\)
\(318\) 0 0
\(319\) −2.81778 4.88053i −0.157765 0.273257i
\(320\) −9.00440 −0.503361
\(321\) 0 0
\(322\) 6.83752 5.13344i 0.381040 0.286075i
\(323\) 2.00546i 0.111587i
\(324\) 0 0
\(325\) −45.5944 26.3240i −2.52912 1.46019i
\(326\) 20.3479i 1.12697i
\(327\) 0 0
\(328\) 4.60862 + 2.66079i 0.254468 + 0.146917i
\(329\) −5.38635 + 4.04394i −0.296959 + 0.222950i
\(330\) 0 0
\(331\) −8.16521 + 14.1426i −0.448801 + 0.777346i −0.998308 0.0581430i \(-0.981482\pi\)
0.549507 + 0.835489i \(0.314815\pi\)
\(332\) 6.93293 12.0082i 0.380494 0.659035i
\(333\) 0 0
\(334\) −5.88319 + 3.39666i −0.321914 + 0.185857i
\(335\) 9.70875 + 16.8160i 0.530445 + 0.918758i
\(336\) 0 0
\(337\) 1.97753 3.42518i 0.107723 0.186582i −0.807124 0.590381i \(-0.798977\pi\)
0.914847 + 0.403800i \(0.132311\pi\)
\(338\) 32.4567i 1.76541i
\(339\) 0 0
\(340\) 16.5082 0.895282
\(341\) 2.49344 + 4.31877i 0.135028 + 0.233875i
\(342\) 0 0
\(343\) −6.54494 17.3252i −0.353393 0.935475i
\(344\) −7.30087 + 4.21516i −0.393636 + 0.227266i
\(345\) 0 0
\(346\) 15.3062 8.83705i 0.822868 0.475083i
\(347\) −6.35400 + 3.66849i −0.341101 + 0.196935i −0.660759 0.750598i \(-0.729765\pi\)
0.319658 + 0.947533i \(0.396432\pi\)
\(348\) 0 0
\(349\) 22.0917 12.7547i 1.18254 0.682741i 0.225941 0.974141i \(-0.427454\pi\)
0.956601 + 0.291400i \(0.0941210\pi\)
\(350\) −27.6881 36.8793i −1.47999 1.97128i
\(351\) 0 0
\(352\) 3.84471 + 6.65923i 0.204924 + 0.354938i
\(353\) 0.0207896 0.00110652 0.000553260 1.00000i \(-0.499824\pi\)
0.000553260 1.00000i \(0.499824\pi\)
\(354\) 0 0
\(355\) 18.1342i 0.962464i
\(356\) 7.87979 13.6482i 0.417628 0.723353i
\(357\) 0 0
\(358\) −16.9220 29.3098i −0.894358 1.54907i
\(359\) −31.3709 + 18.1120i −1.65569 + 0.955915i −0.681024 + 0.732261i \(0.738465\pi\)
−0.974669 + 0.223654i \(0.928201\pi\)
\(360\) 0 0
\(361\) −9.30077 + 16.1094i −0.489514 + 0.847863i
\(362\) −15.2434 + 26.4023i −0.801174 + 1.38767i
\(363\) 0 0
\(364\) −7.84744 + 18.3966i −0.411318 + 0.964243i
\(365\) −18.4602 10.6580i −0.966253 0.557866i
\(366\) 0 0
\(367\) 8.87897i 0.463479i 0.972778 + 0.231739i \(0.0744416\pi\)
−0.972778 + 0.231739i \(0.925558\pi\)
\(368\) 7.42629 + 4.28757i 0.387122 + 0.223505i
\(369\) 0 0
\(370\) 29.5590i 1.53670i
\(371\) 0.115028 + 0.153212i 0.00597193 + 0.00795435i
\(372\) 0 0
\(373\) −12.8188 −0.663731 −0.331865 0.943327i \(-0.607678\pi\)
−0.331865 + 0.943327i \(0.607678\pi\)
\(374\) −3.39666 5.88319i −0.175637 0.304213i
\(375\) 0 0
\(376\) −2.57014 1.48387i −0.132545 0.0765247i
\(377\) 26.7831 1.37940
\(378\) 0 0
\(379\) 3.13828 0.161203 0.0806013 0.996746i \(-0.474316\pi\)
0.0806013 + 0.996746i \(0.474316\pi\)
\(380\) 2.84059 + 1.64002i 0.145719 + 0.0841311i
\(381\) 0 0
\(382\) −6.57187 11.3828i −0.336246 0.582395i
\(383\) −27.5190 −1.40616 −0.703078 0.711113i \(-0.748192\pi\)
−0.703078 + 0.711113i \(0.748192\pi\)
\(384\) 0 0
\(385\) −4.60862 + 10.8039i −0.234877 + 0.550617i
\(386\) 5.82878i 0.296677i
\(387\) 0 0
\(388\) 0.813312 + 0.469566i 0.0412896 + 0.0238386i
\(389\) 18.2436i 0.924989i −0.886622 0.462494i \(-0.846955\pi\)
0.886622 0.462494i \(-0.153045\pi\)
\(390\) 0 0
\(391\) −4.84744 2.79867i −0.245146 0.141535i
\(392\) 5.89011 5.64775i 0.297495 0.285255i
\(393\) 0 0
\(394\) 1.77284 3.07065i 0.0893143 0.154697i
\(395\) 32.5582 56.3925i 1.63818 2.83741i
\(396\) 0 0
\(397\) 1.01255 0.584593i 0.0508182 0.0293399i −0.474376 0.880323i \(-0.657326\pi\)
0.525194 + 0.850983i \(0.323993\pi\)
\(398\) −7.94251 13.7568i −0.398122 0.689567i
\(399\) 0 0
\(400\) 23.1257 40.0550i 1.15629 2.00275i
\(401\) 13.9594i 0.697101i 0.937290 + 0.348551i \(0.113326\pi\)
−0.937290 + 0.348551i \(0.886674\pi\)
\(402\) 0 0
\(403\) −23.7003 −1.18060
\(404\) −4.49180 7.78003i −0.223476 0.387071i
\(405\) 0 0
\(406\) 21.5791 + 9.20499i 1.07095 + 0.456836i
\(407\) 4.27214 2.46652i 0.211762 0.122261i
\(408\) 0 0
\(409\) −17.6427 + 10.1860i −0.872378 + 0.503667i −0.868138 0.496324i \(-0.834683\pi\)
−0.00424001 + 0.999991i \(0.501350\pi\)
\(410\) 27.6150 15.9435i 1.36381 0.787394i
\(411\) 0 0
\(412\) 11.0467 6.37780i 0.544230 0.314212i
\(413\) −2.21974 18.3474i −0.109226 0.902818i
\(414\) 0 0
\(415\) 19.3502 + 33.5155i 0.949862 + 1.64521i
\(416\) −36.5442 −1.79173
\(417\) 0 0
\(418\) 1.34977i 0.0660196i
\(419\) −12.7603 + 22.1015i −0.623383 + 1.07973i 0.365469 + 0.930824i \(0.380909\pi\)
−0.988851 + 0.148907i \(0.952425\pi\)
\(420\) 0 0
\(421\) −0.0466721 0.0808384i −0.00227466 0.00393982i 0.864886 0.501969i \(-0.167391\pi\)
−0.867160 + 0.498029i \(0.834057\pi\)
\(422\) −19.7265 + 11.3891i −0.960271 + 0.554413i
\(423\) 0 0
\(424\) −0.0422078 + 0.0731060i −0.00204979 + 0.00355034i
\(425\) −15.0951 + 26.1455i −0.732220 + 1.26824i
\(426\) 0 0
\(427\) 12.8447 + 17.1086i 0.621599 + 0.827942i
\(428\) 18.6314 + 10.7568i 0.900581 + 0.519951i
\(429\) 0 0
\(430\) 50.5147i 2.43603i
\(431\) −28.7271 16.5856i −1.38374 0.798901i −0.391137 0.920333i \(-0.627918\pi\)
−0.992600 + 0.121432i \(0.961251\pi\)
\(432\) 0 0
\(433\) 17.9518i 0.862706i −0.902183 0.431353i \(-0.858036\pi\)
0.902183 0.431353i \(-0.141964\pi\)
\(434\) −19.0953 8.14548i −0.916602 0.390995i
\(435\) 0 0
\(436\) 19.7344 0.945104
\(437\) −0.556071 0.963144i −0.0266005 0.0460734i
\(438\) 0 0
\(439\) 8.69215 + 5.01841i 0.414854 + 0.239516i 0.692873 0.721060i \(-0.256345\pi\)
−0.278019 + 0.960575i \(0.589678\pi\)
\(440\) −5.17536 −0.246726
\(441\) 0 0
\(442\) 32.2855 1.53566
\(443\) −22.8266 13.1790i −1.08453 0.626151i −0.152412 0.988317i \(-0.548704\pi\)
−0.932114 + 0.362166i \(0.882037\pi\)
\(444\) 0 0
\(445\) 21.9929 + 38.0928i 1.04256 + 1.80577i
\(446\) −34.7343 −1.64472
\(447\) 0 0
\(448\) −5.75409 2.45453i −0.271855 0.115965i
\(449\) 24.0264i 1.13388i −0.823761 0.566938i \(-0.808128\pi\)
0.823761 0.566938i \(-0.191872\pi\)
\(450\) 0 0
\(451\) −4.60862 2.66079i −0.217011 0.125292i
\(452\) 27.0988i 1.27462i
\(453\) 0 0
\(454\) −9.09061 5.24847i −0.426644 0.246323i
\(455\) −33.5155 44.6411i −1.57123 2.09281i
\(456\) 0 0
\(457\) −10.4111 + 18.0326i −0.487012 + 0.843529i −0.999888 0.0149333i \(-0.995246\pi\)
0.512877 + 0.858462i \(0.328580\pi\)
\(458\) −10.2146 + 17.6921i −0.477295 + 0.826700i
\(459\) 0 0
\(460\) 7.92824 4.57737i 0.369656 0.213421i
\(461\) 4.17618 + 7.23336i 0.194504 + 0.336891i 0.946738 0.322005i \(-0.104357\pi\)
−0.752234 + 0.658896i \(0.771024\pi\)
\(462\) 0 0
\(463\) −5.90666 + 10.2306i −0.274506 + 0.475458i −0.970010 0.243064i \(-0.921848\pi\)
0.695505 + 0.718522i \(0.255181\pi\)
\(464\) 23.5291i 1.09231i
\(465\) 0 0
\(466\) −18.9605 −0.878329
\(467\) 14.5789 + 25.2514i 0.674630 + 1.16849i 0.976577 + 0.215169i \(0.0690302\pi\)
−0.301947 + 0.953325i \(0.597636\pi\)
\(468\) 0 0
\(469\) 1.62028 + 13.3925i 0.0748174 + 0.618409i
\(470\) −15.4003 + 8.89138i −0.710364 + 0.410129i
\(471\) 0 0
\(472\) 7.05213 4.07155i 0.324601 0.187408i
\(473\) 7.30087 4.21516i 0.335694 0.193813i
\(474\) 0 0
\(475\) −5.19488 + 2.99926i −0.238357 + 0.137616i
\(476\) 10.5493 + 4.50000i 0.483524 + 0.206257i
\(477\) 0 0
\(478\) −15.2064 26.3383i −0.695526 1.20469i
\(479\) 40.5236 1.85157 0.925785 0.378051i \(-0.123406\pi\)
0.925785 + 0.378051i \(0.123406\pi\)
\(480\) 0 0
\(481\) 23.4445i 1.06898i
\(482\) 21.9130 37.9544i 0.998110 1.72878i
\(483\) 0 0
\(484\) 6.57733 + 11.3923i 0.298970 + 0.517830i
\(485\) −2.26999 + 1.31058i −0.103075 + 0.0595105i
\(486\) 0 0
\(487\) −6.20916 + 10.7546i −0.281364 + 0.487336i −0.971721 0.236132i \(-0.924120\pi\)
0.690357 + 0.723469i \(0.257453\pi\)
\(488\) −4.71319 + 8.16348i −0.213356 + 0.369543i
\(489\) 0 0
\(490\) −11.6608 47.4860i −0.526779 2.14520i
\(491\) −5.34443 3.08561i −0.241191 0.139252i 0.374533 0.927214i \(-0.377803\pi\)
−0.615724 + 0.787962i \(0.711136\pi\)
\(492\) 0 0
\(493\) 15.3584i 0.691708i
\(494\) 5.55542 + 3.20742i 0.249950 + 0.144309i
\(495\) 0 0
\(496\) 20.8209i 0.934884i
\(497\) 4.94324 11.5883i 0.221735 0.519808i
\(498\) 0 0
\(499\) −2.96052 −0.132531 −0.0662656 0.997802i \(-0.521108\pi\)
−0.0662656 + 0.997802i \(0.521108\pi\)
\(500\) −11.6984 20.2623i −0.523170 0.906157i
\(501\) 0 0
\(502\) −31.6482 18.2721i −1.41253 0.815524i
\(503\) −4.33485 −0.193282 −0.0966408 0.995319i \(-0.530810\pi\)
−0.0966408 + 0.995319i \(0.530810\pi\)
\(504\) 0 0
\(505\) 25.0737 1.11577
\(506\) −3.26257 1.88364i −0.145039 0.0837382i
\(507\) 0 0
\(508\) −6.07633 10.5245i −0.269594 0.466950i
\(509\) 28.9485 1.28312 0.641560 0.767073i \(-0.278288\pi\)
0.641560 + 0.767073i \(0.278288\pi\)
\(510\) 0 0
\(511\) −8.89138 11.8429i −0.393332 0.523900i
\(512\) 20.7564i 0.917311i
\(513\) 0 0
\(514\) 36.8611 + 21.2818i 1.62587 + 0.938698i
\(515\) 35.6015i 1.56879i
\(516\) 0 0
\(517\) 2.57014 + 1.48387i 0.113034 + 0.0652605i
\(518\) −8.05753 + 18.8891i −0.354028 + 0.829940i
\(519\) 0 0
\(520\) 12.2980 21.3008i 0.539305 0.934103i
\(521\) −6.08031 + 10.5314i −0.266383 + 0.461389i −0.967925 0.251239i \(-0.919162\pi\)
0.701542 + 0.712628i \(0.252495\pi\)
\(522\) 0 0
\(523\) −33.1564 + 19.1429i −1.44983 + 0.837059i −0.998471 0.0552848i \(-0.982393\pi\)
−0.451357 + 0.892343i \(0.649060\pi\)
\(524\) 4.60855 + 7.98225i 0.201326 + 0.348706i
\(525\) 0 0
\(526\) 8.82497 15.2853i 0.384787 0.666471i
\(527\) 13.5906i 0.592016i
\(528\) 0 0
\(529\) 19.8960 0.865041
\(530\) 0.252910 + 0.438053i 0.0109857 + 0.0190278i
\(531\) 0 0
\(532\) 1.36817 + 1.82234i 0.0593178 + 0.0790087i
\(533\) 21.9026 12.6455i 0.948707 0.547736i
\(534\) 0 0
\(535\) −52.0011 + 30.0229i −2.24820 + 1.29800i
\(536\) −5.14762 + 2.97198i −0.222344 + 0.128370i
\(537\) 0 0
\(538\) −33.0890 + 19.1039i −1.42657 + 0.823629i
\(539\) −5.89011 + 5.64775i −0.253705 + 0.243266i
\(540\) 0 0
\(541\) −0.254094 0.440104i −0.0109244 0.0189216i 0.860512 0.509431i \(-0.170144\pi\)
−0.871436 + 0.490509i \(0.836811\pi\)
\(542\) 36.1049 1.55084
\(543\) 0 0
\(544\) 20.9557i 0.898470i
\(545\) −27.5398 + 47.7003i −1.17968 + 2.04326i
\(546\) 0 0
\(547\) 20.1482 + 34.8977i 0.861475 + 1.49212i 0.870505 + 0.492159i \(0.163792\pi\)
−0.00903012 + 0.999959i \(0.502874\pi\)
\(548\) −19.9233 + 11.5027i −0.851082 + 0.491372i
\(549\) 0 0
\(550\) −10.1598 + 17.5972i −0.433213 + 0.750348i
\(551\) 1.52579 2.64275i 0.0650008 0.112585i
\(552\) 0 0
\(553\) 36.1779 27.1615i 1.53844 1.15502i
\(554\) 13.2100 + 7.62682i 0.561241 + 0.324033i
\(555\) 0 0
\(556\) 1.11026i 0.0470857i
\(557\) 37.6165 + 21.7179i 1.59386 + 0.920216i 0.992636 + 0.121137i \(0.0386541\pi\)
0.601226 + 0.799079i \(0.294679\pi\)
\(558\) 0 0
\(559\) 40.0653i 1.69458i
\(560\) 39.2174 29.4435i 1.65724 1.24422i
\(561\) 0 0
\(562\) 41.7507 1.76115
\(563\) −3.16661 5.48473i −0.133457 0.231154i 0.791550 0.611104i \(-0.209274\pi\)
−0.925007 + 0.379951i \(0.875941\pi\)
\(564\) 0 0
\(565\) 65.5011 + 37.8171i 2.75565 + 1.59098i
\(566\) 31.2434 1.31326
\(567\) 0 0
\(568\) 5.55114 0.232921
\(569\) 7.12974 + 4.11636i 0.298894 + 0.172567i 0.641946 0.766750i \(-0.278127\pi\)
−0.343052 + 0.939316i \(0.611461\pi\)
\(570\) 0 0
\(571\) −4.24864 7.35885i −0.177800 0.307958i 0.763327 0.646013i \(-0.223565\pi\)
−0.941127 + 0.338054i \(0.890231\pi\)
\(572\) 8.81248 0.368468
\(573\) 0 0
\(574\) 21.9929 2.66079i 0.917966 0.111059i
\(575\) 16.7422i 0.698198i
\(576\) 0 0
\(577\) 34.1905 + 19.7399i 1.42337 + 0.821783i 0.996585 0.0825702i \(-0.0263129\pi\)
0.426785 + 0.904353i \(0.359646\pi\)
\(578\) 12.6685i 0.526940i
\(579\) 0 0
\(580\) 21.7541 + 12.5597i 0.903290 + 0.521514i
\(581\) 3.22932 + 26.6921i 0.133975 + 1.10738i
\(582\) 0 0
\(583\) 0.0422078 0.0731060i 0.00174807 0.00302774i
\(584\) 3.26257 5.65093i 0.135006 0.233837i
\(585\) 0 0
\(586\) 34.0191 19.6409i 1.40532 0.811360i
\(587\) 12.0560 + 20.8816i 0.497603 + 0.861874i 0.999996 0.00276510i \(-0.000880160\pi\)
−0.502393 + 0.864640i \(0.667547\pi\)
\(588\) 0 0
\(589\) −1.35017 + 2.33856i −0.0556327 + 0.0963587i
\(590\) 48.7937i 2.00880i
\(591\) 0 0
\(592\) −20.5961 −0.846493
\(593\) 9.46830 + 16.3996i 0.388816 + 0.673450i 0.992291 0.123933i \(-0.0395507\pi\)
−0.603474 + 0.797382i \(0.706217\pi\)
\(594\) 0 0
\(595\) −25.5988 + 19.2190i −1.04945 + 0.787901i
\(596\) 9.96166 5.75136i 0.408045 0.235585i
\(597\) 0 0
\(598\) 15.5055 8.95208i 0.634065 0.366078i
\(599\) 30.0332 17.3397i 1.22713 0.708481i 0.260698 0.965420i \(-0.416047\pi\)
0.966427 + 0.256939i \(0.0827141\pi\)
\(600\) 0 0
\(601\) −11.4929 + 6.63544i −0.468806 + 0.270665i −0.715740 0.698367i \(-0.753910\pi\)
0.246934 + 0.969032i \(0.420577\pi\)
\(602\) −13.7699 + 32.2805i −0.561219 + 1.31565i
\(603\) 0 0
\(604\) 2.07361 + 3.59159i 0.0843738 + 0.146140i
\(605\) −36.7153 −1.49269
\(606\) 0 0
\(607\) 25.0148i 1.01532i −0.861557 0.507660i \(-0.830510\pi\)
0.861557 0.507660i \(-0.169490\pi\)
\(608\) −2.08186 + 3.60589i −0.0844306 + 0.146238i
\(609\) 0 0
\(610\) 28.2415 + 48.9158i 1.14347 + 1.98054i
\(611\) −12.2146 + 7.05213i −0.494152 + 0.285299i
\(612\) 0 0
\(613\) 22.0549 38.2001i 0.890787 1.54289i 0.0518543 0.998655i \(-0.483487\pi\)
0.838933 0.544234i \(-0.183180\pi\)
\(614\) 17.8415 30.9023i 0.720022 1.24712i
\(615\) 0 0
\(616\) −3.30722 1.41076i −0.133252 0.0568412i
\(617\) 16.7463 + 9.66849i 0.674181 + 0.389239i 0.797659 0.603109i \(-0.206071\pi\)
−0.123478 + 0.992347i \(0.539405\pi\)
\(618\) 0 0
\(619\) 11.0598i 0.444531i −0.974986 0.222265i \(-0.928655\pi\)
0.974986 0.222265i \(-0.0713452\pi\)
\(620\) −19.2501 11.1141i −0.773105 0.446352i
\(621\) 0 0
\(622\) 12.4987i 0.501154i
\(623\) 3.67036 + 30.3376i 0.147050 + 1.21545i
\(624\) 0 0
\(625\) 17.7882 0.711529
\(626\) 15.2624 + 26.4353i 0.610010 + 1.05657i
\(627\) 0 0
\(628\) 4.50000 + 2.59808i 0.179570 + 0.103675i
\(629\) 13.4439 0.536043
\(630\) 0 0
\(631\) −27.6015 −1.09880 −0.549400 0.835560i \(-0.685144\pi\)
−0.549400 + 0.835560i \(0.685144\pi\)
\(632\) 17.2625 + 9.96652i 0.686666 + 0.396447i
\(633\) 0 0
\(634\) −4.65703 8.06621i −0.184954 0.320350i
\(635\) 33.9187 1.34602
\(636\) 0 0
\(637\) −9.24864 37.6631i −0.366444 1.49227i
\(638\) 10.3370i 0.409245i
\(639\) 0 0
\(640\) 29.2047 + 16.8613i 1.15442 + 0.666503i
\(641\) 6.07241i 0.239846i 0.992783 + 0.119923i \(0.0382648\pi\)
−0.992783 + 0.119923i \(0.961735\pi\)
\(642\) 0 0
\(643\) −11.4929 6.63544i −0.453236 0.261676i 0.255960 0.966687i \(-0.417609\pi\)
−0.709196 + 0.705011i \(0.750942\pi\)
\(644\) 6.31415 0.763910i 0.248812 0.0301023i
\(645\) 0 0
\(646\) 1.83925 3.18567i 0.0723643 0.125339i
\(647\) −15.3688 + 26.6195i −0.604210 + 1.04652i 0.387966 + 0.921674i \(0.373178\pi\)
−0.992176 + 0.124848i \(0.960156\pi\)
\(648\) 0 0
\(649\) −7.05213 + 4.07155i −0.276820 + 0.159822i
\(650\) −48.2846 83.6313i −1.89388 3.28029i
\(651\) 0 0
\(652\) −7.56815 + 13.1084i −0.296391 + 0.513365i
\(653\) 37.2185i 1.45647i −0.685325 0.728237i \(-0.740340\pi\)
0.685325 0.728237i \(-0.259660\pi\)
\(654\) 0 0
\(655\) −25.7254 −1.00518
\(656\) 11.1091 + 19.2415i 0.433738 + 0.751256i
\(657\) 0 0
\(658\) −12.2650 + 1.48387i −0.478140 + 0.0578472i
\(659\) −40.0576 + 23.1273i −1.56042 + 0.900911i −0.563209 + 0.826314i \(0.690433\pi\)
−0.997214 + 0.0745963i \(0.976233\pi\)
\(660\) 0 0
\(661\) −11.4219 + 6.59445i −0.444262 + 0.256495i −0.705404 0.708806i \(-0.749234\pi\)
0.261142 + 0.965300i \(0.415901\pi\)
\(662\) −25.9409 + 14.9770i −1.00822 + 0.582097i
\(663\) 0 0
\(664\) −10.2596 + 5.92336i −0.398148 + 0.229871i
\(665\) −6.31415 + 0.763910i −0.244852 + 0.0296232i
\(666\) 0 0
\(667\) −4.25856 7.37604i −0.164892 0.285601i
\(668\) −5.05339 −0.195521
\(669\) 0 0
\(670\) 35.6164i 1.37598i
\(671\) 4.71319 8.16348i 0.181951 0.315148i
\(672\) 0 0
\(673\) −20.4633 35.4434i −0.788800 1.36624i −0.926702 0.375796i \(-0.877369\pi\)
0.137902 0.990446i \(-0.455964\pi\)
\(674\) 6.28262 3.62727i 0.241998 0.139717i
\(675\) 0 0
\(676\) −12.0719 + 20.9091i −0.464303 + 0.804196i
\(677\) −0.808981 + 1.40120i −0.0310917 + 0.0538524i −0.881153 0.472832i \(-0.843232\pi\)
0.850061 + 0.526684i \(0.176565\pi\)
\(678\) 0 0
\(679\) −1.80785 + 0.218721i −0.0693790 + 0.00839374i
\(680\) −12.2146 7.05213i −0.468410 0.270437i
\(681\) 0 0
\(682\) 9.14716i 0.350263i
\(683\) −22.9977 13.2778i −0.879984 0.508059i −0.00933109 0.999956i \(-0.502970\pi\)
−0.870653 + 0.491897i \(0.836304\pi\)
\(684\) 0 0
\(685\) 64.2094i 2.45332i
\(686\) 5.49271 33.5237i 0.209713 1.27994i
\(687\) 0 0
\(688\) −35.1976 −1.34190
\(689\) 0.200594 + 0.347439i 0.00764201 + 0.0132364i
\(690\) 0 0
\(691\) −32.5917 18.8168i −1.23985 0.715826i −0.270784 0.962640i \(-0.587283\pi\)
−0.969063 + 0.246814i \(0.920616\pi\)
\(692\) 13.1473 0.499787
\(693\) 0 0
\(694\) −13.4578 −0.510851
\(695\) 2.68364 + 1.54940i 0.101796 + 0.0587722i
\(696\) 0 0
\(697\) −7.25136 12.5597i −0.274665 0.475734i
\(698\) 46.7903 1.77104
\(699\) 0 0
\(700\) −4.12028 34.0564i −0.155732 1.28721i
\(701\) 24.3228i 0.918659i −0.888266 0.459330i \(-0.848090\pi\)
0.888266 0.459330i \(-0.151910\pi\)
\(702\) 0 0
\(703\) 2.31331 + 1.33559i 0.0872482 + 0.0503728i
\(704\) 2.75637i 0.103885i
\(705\) 0 0
\(706\) 0.0330243 + 0.0190666i 0.00124289 + 0.000717581i
\(707\) 16.0229 + 6.83489i 0.602603 + 0.257053i
\(708\) 0 0
\(709\) −0.517010 + 0.895487i −0.0194167 + 0.0336307i −0.875570 0.483090i \(-0.839514\pi\)
0.856154 + 0.516721i \(0.172848\pi\)
\(710\) 16.6313 28.8062i 0.624161 1.08108i
\(711\) 0 0
\(712\) −11.6608 + 6.73234i −0.437005 + 0.252305i
\(713\) 3.76839 + 6.52704i 0.141127 + 0.244440i
\(714\) 0 0
\(715\) −12.2980 + 21.3008i −0.459921 + 0.796606i
\(716\) 25.1758i 0.940863i
\(717\) 0 0
\(718\) −66.4436 −2.47965
\(719\) −8.37315 14.5027i −0.312266 0.540861i 0.666587 0.745428i \(-0.267755\pi\)
−0.978853 + 0.204567i \(0.934421\pi\)
\(720\) 0 0
\(721\) −9.70469 + 22.7505i −0.361422 + 0.847273i
\(722\) −29.5486 + 17.0599i −1.09968 + 0.634903i
\(723\) 0 0
\(724\) −19.6400 + 11.3392i −0.729915 + 0.421417i
\(725\) −39.7839 + 22.9693i −1.47754 + 0.853057i
\(726\) 0 0
\(727\) 28.4902 16.4488i 1.05664 0.610053i 0.132141 0.991231i \(-0.457815\pi\)
0.924502 + 0.381178i \(0.124482\pi\)
\(728\) 13.6653 10.2596i 0.506469 0.380244i
\(729\) 0 0
\(730\) −19.5494 33.8606i −0.723556 1.25324i
\(731\) 22.9749 0.849757
\(732\) 0 0
\(733\) 19.9120i 0.735466i −0.929931 0.367733i \(-0.880134\pi\)
0.929931 0.367733i \(-0.119866\pi\)
\(734\) −8.14310 + 14.1043i −0.300567 + 0.520598i
\(735\) 0 0
\(736\) 5.81058 + 10.0642i 0.214181 + 0.370972i
\(737\) 5.14762 2.97198i 0.189615 0.109474i
\(738\) 0 0
\(739\) 25.3349 43.8813i 0.931959 1.61420i 0.151990 0.988382i \(-0.451432\pi\)
0.779969 0.625819i \(-0.215235\pi\)
\(740\) −10.9941 + 19.0423i −0.404151 + 0.700009i
\(741\) 0 0
\(742\) 0.0422078 + 0.348871i 0.00154950 + 0.0128075i
\(743\) 38.3208 + 22.1245i 1.40586 + 0.811671i 0.994985 0.100023i \(-0.0318917\pi\)
0.410870 + 0.911694i \(0.365225\pi\)
\(744\) 0 0
\(745\) 32.1047i 1.17623i
\(746\) −20.3626 11.7564i −0.745529 0.430431i
\(747\) 0 0
\(748\) 5.05339i 0.184770i
\(749\) −41.4143 + 5.01047i −1.51325 + 0.183078i
\(750\) 0 0
\(751\) 2.34460 0.0855557 0.0427779 0.999085i \(-0.486379\pi\)
0.0427779 + 0.999085i \(0.486379\pi\)
\(752\) −6.19533 10.7306i −0.225921 0.391306i
\(753\) 0 0
\(754\) 42.5450 + 24.5634i 1.54940 + 0.894546i
\(755\) −11.5751 −0.421260
\(756\) 0 0
\(757\) −24.8530 −0.903298 −0.451649 0.892196i \(-0.649164\pi\)
−0.451649 + 0.892196i \(0.649164\pi\)
\(758\) 4.98516 + 2.87819i 0.181069 + 0.104540i
\(759\) 0 0
\(760\) −1.40120 2.42694i −0.0508267 0.0880345i
\(761\) −0.882087 −0.0319756 −0.0159878 0.999872i \(-0.505089\pi\)
−0.0159878 + 0.999872i \(0.505089\pi\)
\(762\) 0 0
\(763\) −30.6015 + 22.9749i −1.10785 + 0.831747i
\(764\) 9.77730i 0.353730i
\(765\) 0 0
\(766\) −43.7140 25.2383i −1.57945 0.911896i
\(767\) 38.7003i 1.39739i
\(768\) 0 0
\(769\) 17.9310 + 10.3524i 0.646607 + 0.373319i 0.787155 0.616755i \(-0.211553\pi\)
−0.140548 + 0.990074i \(0.544886\pi\)
\(770\) −17.2293 + 12.9353i −0.620900 + 0.466157i
\(771\) 0 0
\(772\) −2.16794 + 3.75499i −0.0780260 + 0.135145i
\(773\) −4.70279 + 8.14548i −0.169148 + 0.292972i −0.938120 0.346309i \(-0.887435\pi\)
0.768973 + 0.639282i \(0.220768\pi\)
\(774\) 0 0
\(775\) 35.2047 20.3254i 1.26459 0.730111i
\(776\) −0.401187 0.694877i −0.0144018 0.0249446i
\(777\) 0 0
\(778\) 16.7316 28.9800i 0.599858 1.03898i
\(779\) 2.88157i 0.103243i
\(780\) 0 0
\(781\) −5.55114 −0.198635
\(782\) −5.13344 8.89138i −0.183571 0.317955i
\(783\) 0 0
\(784\) 33.0873 8.12497i 1.18169 0.290178i
\(785\) −12.5597 + 7.25136i −0.448276 + 0.258812i
\(786\) 0 0
\(787\) 21.7855 12.5779i 0.776569 0.448352i −0.0586440 0.998279i \(-0.518678\pi\)
0.835213 + 0.549927i \(0.185344\pi\)
\(788\) 2.28418 1.31877i 0.0813705 0.0469793i
\(789\) 0 0
\(790\) 103.438 59.7197i 3.68014 2.12473i
\(791\) 31.5486 + 42.0214i 1.12174 + 1.49411i
\(792\) 0 0
\(793\) 22.3996 + 38.7972i 0.795432 + 1.37773i
\(794\) 2.14457 0.0761080
\(795\) 0 0
\(796\) 11.8165i 0.418824i
\(797\) −15.3584 + 26.6015i −0.544023 + 0.942275i 0.454645 + 0.890673i \(0.349766\pi\)
−0.998668 + 0.0516020i \(0.983567\pi\)
\(798\) 0 0
\(799\) 4.04394 + 7.00431i 0.143064 + 0.247795i
\(800\) 54.2831 31.3404i 1.91920 1.10805i
\(801\) 0 0
\(802\) −12.8025 + 22.1746i −0.452072 + 0.783012i
\(803\) −3.26257 + 5.65093i −0.115134 + 0.199417i
\(804\) 0 0
\(805\) −6.96509 + 16.3281i −0.245487 + 0.575491i
\(806\) −37.6480 21.7361i −1.32609 0.765621i
\(807\) 0 0
\(808\) 7.67541i 0.270020i
\(809\) −12.3629 7.13774i −0.434657 0.250950i 0.266671 0.963788i \(-0.414076\pi\)
−0.701329 + 0.712838i \(0.747409\pi\)
\(810\) 0 0
\(811\) 10.0160i 0.351711i 0.984416 + 0.175855i \(0.0562691\pi\)
−0.984416 + 0.175855i \(0.943731\pi\)
\(812\) 10.4779 + 13.9561i 0.367701 + 0.489762i
\(813\) 0 0
\(814\) 9.04841 0.317146
\(815\) −21.1231 36.5863i −0.739909 1.28156i
\(816\) 0 0
\(817\) 3.95333 + 2.28245i 0.138309 + 0.0798530i
\(818\) −37.3674 −1.30652
\(819\) 0 0
\(820\) 23.7200 0.828337
\(821\) 10.7914 + 6.23043i 0.376623 + 0.217444i 0.676348 0.736582i \(-0.263562\pi\)
−0.299725 + 0.954026i \(0.596895\pi\)
\(822\) 0 0
\(823\) 2.29804 + 3.98032i 0.0801045 + 0.138745i 0.903295 0.429021i \(-0.141141\pi\)
−0.823190 + 0.567766i \(0.807808\pi\)
\(824\) −10.8981 −0.379654
\(825\) 0 0
\(826\) 13.3008 31.1807i 0.462793 1.08492i
\(827\) 37.9330i 1.31906i −0.751678 0.659531i \(-0.770755\pi\)
0.751678 0.659531i \(-0.229245\pi\)
\(828\) 0 0
\(829\) −31.8690 18.3996i −1.10686 0.639044i −0.168843 0.985643i \(-0.554003\pi\)
−0.938013 + 0.346599i \(0.887337\pi\)
\(830\) 70.9858i 2.46395i
\(831\) 0 0
\(832\) −11.3447 6.54987i −0.393307 0.227076i
\(833\) −21.5974 + 5.30350i −0.748305 + 0.183755i
\(834\) 0 0
\(835\) 7.05213 12.2146i 0.244049 0.422705i
\(836\) 0.502032 0.869545i 0.0173631 0.0300738i
\(837\) 0 0
\(838\) −40.5396 + 23.4055i −1.40042 + 0.808531i
\(839\) 10.6785 + 18.4956i 0.368662 + 0.638541i 0.989357 0.145512i \(-0.0464828\pi\)
−0.620695 + 0.784052i \(0.713149\pi\)
\(840\) 0 0
\(841\) −2.81505 + 4.87580i −0.0970706 + 0.168131i
\(842\) 0.171216i 0.00590049i
\(843\) 0 0
\(844\) −16.9441 −0.583242
\(845\) −33.6932 58.3584i −1.15908 2.00759i
\(846\) 0 0
\(847\) −23.4623 10.0083i −0.806173 0.343889i
\(848\) −0.305226 + 0.176223i −0.0104815 + 0.00605151i
\(849\) 0 0
\(850\) −47.9572 + 27.6881i −1.64492 + 0.949693i
\(851\) 6.45657 3.72770i 0.221328 0.127784i
\(852\) 0 0
\(853\) 42.8709 24.7515i 1.46787 0.847476i 0.468519 0.883453i \(-0.344788\pi\)
0.999353 + 0.0359772i \(0.0114544\pi\)
\(854\) 4.71319 + 38.9572i 0.161282 + 1.33309i
\(855\) 0 0
\(856\) −9.19041 15.9183i −0.314122 0.544075i
\(857\) −14.0162 −0.478784 −0.239392 0.970923i \(-0.576948\pi\)
−0.239392 + 0.970923i \(0.576948\pi\)
\(858\) 0 0
\(859\) 1.21490i 0.0414517i 0.999785 + 0.0207259i \(0.00659772\pi\)
−0.999785 + 0.0207259i \(0.993402\pi\)
\(860\) −18.7883 + 32.5423i −0.640676 + 1.10968i
\(861\) 0 0
\(862\) −30.4220 52.6925i −1.03618 1.79471i
\(863\) 31.2396 18.0362i 1.06341 0.613960i 0.137036 0.990566i \(-0.456242\pi\)
0.926373 + 0.376606i \(0.122909\pi\)
\(864\) 0 0
\(865\) −18.3474 + 31.7787i −0.623832 + 1.08051i
\(866\) 16.4639 28.5164i 0.559467 0.969026i
\(867\) 0 0
\(868\) −9.27184 12.3497i −0.314707 0.419176i
\(869\) −17.2625 9.96652i −0.585591 0.338091i
\(870\) 0 0
\(871\) 28.2489i 0.957177i
\(872\) −14.6017 8.43032i −0.494477 0.285487i
\(873\) 0 0
\(874\) 2.03994i 0.0690020i
\(875\) 41.7300 + 17.8008i 1.41073 + 0.601776i
\(876\) 0 0
\(877\) −11.1921 −0.377932 −0.188966 0.981984i \(-0.560514\pi\)
−0.188966 + 0.981984i \(0.560514\pi\)
\(878\) 9.20499 + 15.9435i 0.310653 + 0.538067i
\(879\) 0 0
\(880\) −18.7129 10.8039i −0.630811 0.364199i
\(881\) −4.16372 −0.140279 −0.0701397 0.997537i \(-0.522345\pi\)
−0.0701397 + 0.997537i \(0.522345\pi\)
\(882\) 0 0
\(883\) −38.7433 −1.30382 −0.651908 0.758298i \(-0.726031\pi\)
−0.651908 + 0.758298i \(0.726031\pi\)
\(884\) 20.7988 + 12.0082i 0.699539 + 0.403879i
\(885\) 0 0
\(886\) −24.1734 41.8696i −0.812121 1.40664i
\(887\) −38.0824 −1.27868 −0.639342 0.768923i \(-0.720793\pi\)
−0.639342 + 0.768923i \(0.720793\pi\)
\(888\) 0 0
\(889\) 21.6751 + 9.24597i 0.726961 + 0.310100i
\(890\) 80.6807i 2.70442i
\(891\) 0 0
\(892\) −22.3764 12.9190i −0.749216 0.432560i
\(893\) 1.60699i 0.0537759i
\(894\) 0 0
\(895\) 60.8529 + 35.1334i 2.03409 + 1.17438i
\(896\) 14.0665 + 18.7359i 0.469927 + 0.625922i
\(897\) 0 0
\(898\) 22.0351 38.1660i 0.735322 1.27361i
\(899\) −10.3400 + 17.9094i −0.344858 + 0.597311i
\(900\) 0 0
\(901\) 0.199234 0.115028i 0.00663743 0.00383212i
\(902\) −4.88053 8.45333i −0.162504 0.281465i
\(903\) 0 0
\(904\) −11.5763 + 20.0508i −0.385023 + 0.666880i
\(905\) 63.2964i 2.10404i
\(906\) 0 0
\(907\) 1.54767 0.0513894 0.0256947 0.999670i \(-0.491820\pi\)
0.0256947 + 0.999670i \(0.491820\pi\)
\(908\) −3.90421 6.76228i −0.129566 0.224414i
\(909\) 0 0
\(910\) −12.2980 101.650i −0.407676 3.36967i
\(911\) 33.7493 19.4852i 1.11816 0.645573i 0.177233 0.984169i \(-0.443285\pi\)
0.940932 + 0.338596i \(0.109952\pi\)
\(912\) 0 0
\(913\) 10.2596 5.92336i 0.339542 0.196034i
\(914\) −33.0762 + 19.0965i −1.09406 + 0.631657i
\(915\) 0 0
\(916\) −13.1608 + 7.59836i −0.434843 + 0.251057i
\(917\) −16.4394 7.01255i −0.542875 0.231575i
\(918\) 0 0
\(919\) −5.86991 10.1670i −0.193630 0.335378i 0.752820 0.658226i \(-0.228693\pi\)
−0.946451 + 0.322848i \(0.895360\pi\)
\(920\) −7.82162 −0.257871
\(921\) 0 0
\(922\) 15.3203i 0.504546i
\(923\) 13.1910 22.8474i 0.434186 0.752033i
\(924\) 0 0
\(925\) −20.1060 34.8246i −0.661081 1.14503i
\(926\) −18.7655 + 10.8342i −0.616671 + 0.356035i
\(927\) 0 0
\(928\) −15.9435 + 27.6150i −0.523371 + 0.906506i
\(929\) 22.3142 38.6493i 0.732105 1.26804i −0.223877 0.974617i \(-0.571871\pi\)
0.955982 0.293425i \(-0.0947952\pi\)
\(930\) 0 0
\(931\) −4.24318 1.23302i −0.139064 0.0404107i
\(932\) −12.2146 7.05213i −0.400104 0.231000i
\(933\) 0 0
\(934\) 53.4824i 1.75000i
\(935\) 12.2146 + 7.05213i 0.399462 + 0.230629i
\(936\) 0 0
\(937\) 33.3351i 1.08901i −0.838758 0.544505i \(-0.816718\pi\)
0.838758 0.544505i \(-0.183282\pi\)
\(938\) −9.70875 + 22.7600i −0.317002 + 0.743141i
\(939\) 0 0
\(940\) −13.2282 −0.431455
\(941\) 16.9992 + 29.4435i 0.554159 + 0.959831i 0.997968 + 0.0637100i \(0.0202933\pi\)
−0.443810 + 0.896121i \(0.646373\pi\)
\(942\) 0 0
\(943\) −6.96509 4.02130i −0.226815 0.130952i
\(944\) 33.9984 1.10655
\(945\) 0 0
\(946\) 15.4633 0.502754
\(947\) −39.9637 23.0731i −1.29865 0.749774i −0.318476 0.947931i \(-0.603171\pi\)
−0.980170 + 0.198157i \(0.936504\pi\)
\(948\) 0 0
\(949\) −15.5055 26.8562i −0.503329 0.871791i
\(950\) −11.0028 −0.356977
\(951\) 0 0
\(952\) −5.88319 7.83615i −0.190675 0.253971i
\(953\) 35.1143i 1.13746i −0.822523 0.568731i \(-0.807434\pi\)
0.822523 0.568731i \(-0.192566\pi\)
\(954\) 0 0
\(955\) 23.6329 + 13.6445i 0.764744 + 0.441525i
\(956\) 22.6234i 0.731692i
\(957\) 0 0
\(958\) 64.3717 + 37.1650i 2.07976 + 1.20075i
\(959\) 17.5030 41.0318i 0.565201 1.32499i
\(960\) 0 0
\(961\) −6.35017 + 10.9988i −0.204844 + 0.354800i
\(962\) −21.5014 + 37.2415i −0.693234 + 1.20072i
\(963\) 0 0
\(964\) 28.2334 16.3005i 0.909335 0.525005i
\(965\) −6.05084 10.4804i −0.194784 0.337375i
\(966\) 0 0
\(967\) 6.70742 11.6176i 0.215696 0.373597i −0.737792 0.675029i \(-0.764131\pi\)
0.953488 + 0.301432i \(0.0974646\pi\)
\(968\) 11.2391i 0.361238i
\(969\) 0 0
\(970\) −4.80785 −0.154371
\(971\) 9.19460 + 15.9255i 0.295069 + 0.511074i 0.975001 0.222201i \(-0.0713241\pi\)
−0.679932 + 0.733275i \(0.737991\pi\)
\(972\) 0 0
\(973\) 1.29258 + 1.72166i 0.0414381 + 0.0551938i
\(974\) −19.7265 + 11.3891i −0.632078 + 0.364930i
\(975\) 0 0
\(976\) −34.0835 + 19.6781i −1.09099 + 0.629882i
\(977\) −19.6181 + 11.3265i −0.627638 + 0.362367i −0.779837 0.625983i \(-0.784698\pi\)
0.152199 + 0.988350i \(0.451365\pi\)
\(978\) 0 0
\(979\) 11.6608 6.73234i 0.372679 0.215166i
\(980\) 10.1498 34.9282i 0.324223 1.11574i
\(981\) 0 0
\(982\) −5.65976 9.80298i −0.180610 0.312826i
\(983\) −39.3408 −1.25478 −0.627388 0.778707i \(-0.715876\pi\)
−0.627388 + 0.778707i \(0.715876\pi\)
\(984\) 0 0
\(985\) 7.36151i 0.234557i
\(986\) 14.0855 24.3968i 0.448574 0.776954i
\(987\) 0 0
\(988\) 2.38592 + 4.13254i 0.0759063 + 0.131474i
\(989\) 11.0339 6.37045i 0.350859 0.202569i
\(990\) 0 0
\(991\) −0.475797 + 0.824104i −0.0151142 + 0.0261785i −0.873484 0.486854i \(-0.838145\pi\)
0.858369 + 0.513032i \(0.171478\pi\)
\(992\) 14.1084 24.4364i 0.447941 0.775857i
\(993\) 0 0
\(994\) 18.4803 13.8745i 0.586158 0.440073i
\(995\) 28.5618 + 16.4902i 0.905471 + 0.522774i
\(996\) 0 0
\(997\) 31.4640i 0.996475i 0.867041 + 0.498238i \(0.166019\pi\)
−0.867041 + 0.498238i \(0.833981\pi\)
\(998\) −4.70279 2.71516i −0.148864 0.0859468i
\(999\) 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 567.2.s.f.458.5 12
3.2 odd 2 inner 567.2.s.f.458.2 12
7.5 odd 6 567.2.i.f.215.2 12
9.2 odd 6 567.2.i.f.269.5 12
9.4 even 3 189.2.p.d.80.2 yes 12
9.5 odd 6 189.2.p.d.80.5 yes 12
9.7 even 3 567.2.i.f.269.2 12
21.5 even 6 567.2.i.f.215.5 12
63.4 even 3 1323.2.c.d.1322.3 12
63.5 even 6 189.2.p.d.26.2 12
63.31 odd 6 1323.2.c.d.1322.4 12
63.32 odd 6 1323.2.c.d.1322.10 12
63.40 odd 6 189.2.p.d.26.5 yes 12
63.47 even 6 inner 567.2.s.f.26.5 12
63.59 even 6 1323.2.c.d.1322.9 12
63.61 odd 6 inner 567.2.s.f.26.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.p.d.26.2 12 63.5 even 6
189.2.p.d.26.5 yes 12 63.40 odd 6
189.2.p.d.80.2 yes 12 9.4 even 3
189.2.p.d.80.5 yes 12 9.5 odd 6
567.2.i.f.215.2 12 7.5 odd 6
567.2.i.f.215.5 12 21.5 even 6
567.2.i.f.269.2 12 9.7 even 3
567.2.i.f.269.5 12 9.2 odd 6
567.2.s.f.26.2 12 63.61 odd 6 inner
567.2.s.f.26.5 12 63.47 even 6 inner
567.2.s.f.458.2 12 3.2 odd 2 inner
567.2.s.f.458.5 12 1.1 even 1 trivial
1323.2.c.d.1322.3 12 63.4 even 3
1323.2.c.d.1322.4 12 63.31 odd 6
1323.2.c.d.1322.9 12 63.59 even 6
1323.2.c.d.1322.10 12 63.32 odd 6