Properties

Label 567.2.i.f.269.5
Level $567$
Weight $2$
Character 567.269
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(215,567)]
 
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([5, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.215");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.i (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: \(\Z[a_1, \ldots, a_{7}]\)
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 269.5
Root \(1.90412 - 1.09935i\) of defining polynomial
Character \(\chi\) \(=\) 567.269
Dual form 567.2.i.f.215.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.83424i q^{2} -1.36445 q^{4} +(-1.90412 + 3.29804i) q^{5} +(0.317776 + 2.62660i) q^{7} +1.16576i q^{8} +O(q^{10})\) \(q+1.83424i q^{2} -1.36445 q^{4} +(-1.90412 + 3.29804i) q^{5} +(0.317776 + 2.62660i) q^{7} +1.16576i q^{8} +(-6.04940 - 3.49262i) q^{10} +(-1.00958 + 0.582878i) q^{11} +(4.79804 - 2.77015i) q^{13} +(-4.81782 + 0.582878i) q^{14} -4.86718 q^{16} +(1.58850 - 2.75136i) q^{17} +(-0.546672 + 0.315621i) q^{19} +(2.59808 - 4.50000i) q^{20} +(-1.06914 - 1.85181i) q^{22} +(1.52579 + 0.880915i) q^{23} +(-4.75136 - 8.22961i) q^{25} +(5.08112 + 8.80077i) q^{26} +(-0.433589 - 3.58386i) q^{28} +(-4.18658 - 2.41712i) q^{29} +4.27781i q^{31} -6.59607i q^{32} +(5.04667 + 2.91370i) q^{34} +(-9.26770 - 3.95333i) q^{35} +(-2.11581 - 3.66470i) q^{37} +(-0.578926 - 1.00273i) q^{38} +(-3.84471 - 2.21974i) q^{40} +(2.28245 + 3.95333i) q^{41} +(-3.61581 + 6.26277i) q^{43} +(1.37751 - 0.795307i) q^{44} +(-1.61581 + 2.79867i) q^{46} +2.54576 q^{47} +(-6.79804 + 1.66934i) q^{49} +(15.0951 - 8.71516i) q^{50} +(-6.54667 + 3.77972i) q^{52} +(0.0627112 + 0.0362063i) q^{53} -4.43949i q^{55} +(-3.06197 + 0.370450i) q^{56} +(4.43359 - 7.67920i) q^{58} +6.98525 q^{59} +8.08606i q^{61} -7.84655 q^{62} +2.36445 q^{64} +21.0988i q^{65} +5.09880 q^{67} +(-2.16743 + 3.75409i) q^{68} +(7.25136 - 16.9992i) q^{70} -4.76183i q^{71} +(4.84744 + 2.79867i) q^{73} +(6.72194 - 3.88092i) q^{74} +(0.745906 - 0.430649i) q^{76} +(-1.85181 - 2.46652i) q^{77} +17.0988 q^{79} +(9.26770 - 16.0521i) q^{80} +(-7.25136 + 4.18658i) q^{82} +(5.08112 - 8.80077i) q^{83} +(6.04940 + 10.4779i) q^{85} +(-11.4874 - 6.63228i) q^{86} +(-0.679494 - 1.17692i) q^{88} +(5.77508 + 10.0027i) q^{89} +(8.80077 + 11.7222i) q^{91} +(-2.08186 - 1.20196i) q^{92} +4.66954i q^{94} -2.40393i q^{95} +(-0.596074 - 0.344143i) q^{97} +(-3.06197 - 12.4693i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 16 q^{4} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 16 q^{4} + 4 q^{7} - 6 q^{10} + 24 q^{13} + 8 q^{16} - 6 q^{19} + 20 q^{22} - 24 q^{25} + 28 q^{28} + 60 q^{34} + 8 q^{37} - 12 q^{40} - 10 q^{43} + 14 q^{46} - 48 q^{49} - 78 q^{52} + 20 q^{58} + 28 q^{64} - 72 q^{67} + 54 q^{70} - 42 q^{73} + 108 q^{76} + 72 q^{79} - 54 q^{82} + 6 q^{85} - 74 q^{88} + 6 q^{91} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.83424i 1.29701i 0.761212 + 0.648503i \(0.224605\pi\)
−0.761212 + 0.648503i \(0.775395\pi\)
\(3\) 0 0
\(4\) −1.36445 −0.682224
\(5\) −1.90412 + 3.29804i −0.851549 + 1.47493i 0.0282601 + 0.999601i \(0.491003\pi\)
−0.879810 + 0.475326i \(0.842330\pi\)
\(6\) 0 0
\(7\) 0.317776 + 2.62660i 0.120108 + 0.992761i
\(8\) 1.16576i 0.412157i
\(9\) 0 0
\(10\) −6.04940 3.49262i −1.91299 1.10446i
\(11\) −1.00958 + 0.582878i −0.304398 + 0.175744i −0.644417 0.764674i \(-0.722900\pi\)
0.340019 + 0.940419i \(0.389567\pi\)
\(12\) 0 0
\(13\) 4.79804 2.77015i 1.33074 0.768301i 0.345324 0.938484i \(-0.387769\pi\)
0.985412 + 0.170183i \(0.0544359\pi\)
\(14\) −4.81782 + 0.582878i −1.28762 + 0.155781i
\(15\) 0 0
\(16\) −4.86718 −1.21679
\(17\) 1.58850 2.75136i 0.385268 0.667304i −0.606538 0.795054i \(-0.707442\pi\)
0.991806 + 0.127750i \(0.0407756\pi\)
\(18\) 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
\(23\) 1.52579 + 0.880915i 0.318149 + 0.183684i 0.650567 0.759449i \(-0.274531\pi\)
−0.332418 + 0.943132i \(0.607865\pi\)
\(24\) 0 0
\(25\) −4.75136 8.22961i −0.950273 1.64592i
\(26\) 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 0.0580901 0.998311i \(-0.481499\pi\)
−0.835518 + 0.549463i \(0.814832\pi\)
\(30\) 0 0
\(31\) 4.27781i 0.768317i 0.923267 + 0.384159i \(0.125508\pi\)
−0.923267 + 0.384159i \(0.874492\pi\)
\(32\) 6.59607i 1.16603i
\(33\) 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 \(0.946417\pi\)
\(38\) −0.578926 1.00273i −0.0939142 0.162664i
\(39\) 0 0
\(40\) −3.84471 2.21974i −0.607902 0.350972i
\(41\) 2.28245 + 3.95333i 0.356460 + 0.617406i 0.987367 0.158452i \(-0.0506504\pi\)
−0.630907 + 0.775858i \(0.717317\pi\)
\(42\) 0 0
\(43\) −3.61581 + 6.26277i −0.551406 + 0.955064i 0.446767 + 0.894650i \(0.352575\pi\)
−0.998173 + 0.0604134i \(0.980758\pi\)
\(44\) 1.37751 0.795307i 0.207668 0.119897i
\(45\) 0 0
\(46\) −1.61581 + 2.79867i −0.238239 + 0.412641i
\(47\) 2.54576 0.371337 0.185669 0.982612i \(-0.440555\pi\)
0.185669 + 0.982612i \(0.440555\pi\)
\(48\) 0 0
\(49\) −6.79804 + 1.66934i −0.971148 + 0.238477i
\(50\) 15.0951 8.71516i 2.13477 1.23251i
\(51\) 0 0
\(52\) −6.54667 + 3.77972i −0.907860 + 0.524153i
\(53\) 0.0627112 + 0.0362063i 0.00861404 + 0.00497332i 0.504301 0.863528i \(-0.331750\pi\)
−0.495687 + 0.868501i \(0.665084\pi\)
\(54\) 0 0
\(55\) 4.43949i 0.598620i
\(56\) −3.06197 + 0.370450i −0.409174 + 0.0495034i
\(57\) 0 0
\(58\) 4.43359 7.67920i 0.582159 1.00833i
\(59\) 6.98525 0.909402 0.454701 0.890644i \(-0.349746\pi\)
0.454701 + 0.890644i \(0.349746\pi\)
\(60\) 0 0
\(61\) 8.08606i 1.03531i 0.855588 + 0.517657i \(0.173196\pi\)
−0.855588 + 0.517657i \(0.826804\pi\)
\(62\) −7.84655 −0.996512
\(63\) 0 0
\(64\) 2.36445 0.295556
\(65\) 21.0988i 2.61698i
\(66\) 0 0
\(67\) 5.09880 0.622918 0.311459 0.950260i \(-0.399182\pi\)
0.311459 + 0.950260i \(0.399182\pi\)
\(68\) −2.16743 + 3.75409i −0.262839 + 0.455251i
\(69\) 0 0
\(70\) 7.25136 16.9992i 0.866704 2.03180i
\(71\) 4.76183i 0.565125i −0.959249 0.282563i \(-0.908815\pi\)
0.959249 0.282563i \(-0.0911845\pi\)
\(72\) 0 0
\(73\) 4.84744 + 2.79867i 0.567350 + 0.327560i 0.756090 0.654467i \(-0.227107\pi\)
−0.188740 + 0.982027i \(0.560440\pi\)
\(74\) 6.72194 3.88092i 0.781410 0.451147i
\(75\) 0 0
\(76\) 0.745906 0.430649i 0.0855612 0.0493988i
\(77\) −1.85181 2.46652i −0.211033 0.281086i
\(78\) 0 0
\(79\) 17.0988 1.92377 0.961883 0.273462i \(-0.0881687\pi\)
0.961883 + 0.273462i \(0.0881687\pi\)
\(80\) 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 −0.439960 0.898017i \(-0.645007\pi\)
0.997686 0.0679922i \(-0.0216593\pi\)
\(84\) 0 0
\(85\) 6.04940 + 10.4779i 0.656150 + 1.13648i
\(86\) −11.4874 6.63228i −1.23872 0.715177i
\(87\) 0 0
\(88\) −0.679494 1.17692i −0.0724344 0.125460i
\(89\) 5.77508 + 10.0027i 0.612157 + 1.06029i 0.990876 + 0.134776i \(0.0430313\pi\)
−0.378719 + 0.925512i \(0.623635\pi\)
\(90\) 0 0
\(91\) 8.80077 + 11.7222i 0.922571 + 1.22882i
\(92\) −2.08186 1.20196i −0.217049 0.125313i
\(93\) 0 0
\(94\) 4.66954i 0.481627i
\(95\) 2.40393i 0.246638i
\(96\) 0 0
\(97\) −0.596074 0.344143i −0.0605221 0.0349425i 0.469434 0.882968i \(-0.344458\pi\)
−0.529956 + 0.848025i \(0.677791\pi\)
\(98\) −3.06197 12.4693i −0.309306 1.25958i
\(99\) 0 0
\(100\) 6.48299 + 11.2289i 0.648299 + 1.12289i
\(101\) −3.29203 5.70196i −0.327569 0.567367i 0.654460 0.756097i \(-0.272896\pi\)
−0.982029 + 0.188730i \(0.939563\pi\)
\(102\) 0 0
\(103\) 8.09607 + 4.67427i 0.797730 + 0.460570i 0.842677 0.538420i \(-0.180979\pi\)
−0.0449469 + 0.998989i \(0.514312\pi\)
\(104\) 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 −0.983739 0.179604i \(-0.942518\pi\)
−0.336328 + 0.941745i \(0.609185\pi\)
\(108\) 0 0
\(109\) 7.23163 12.5255i 0.692664 1.19973i −0.278298 0.960495i \(-0.589770\pi\)
0.970962 0.239235i \(-0.0768965\pi\)
\(110\) 8.14310 0.776414
\(111\) 0 0
\(112\) −1.54667 12.7841i −0.146147 1.20799i
\(113\) −17.1998 + 9.93032i −1.61802 + 0.934166i −0.630591 + 0.776115i \(0.717188\pi\)
−0.987431 + 0.158051i \(0.949479\pi\)
\(114\) 0 0
\(115\) −5.81058 + 3.35474i −0.541840 + 0.312831i
\(116\) 5.71237 + 3.29804i 0.530380 + 0.306215i
\(117\) 0 0
\(118\) 12.8126i 1.17950i
\(119\) 7.73152 + 3.29804i 0.708747 + 0.302331i
\(120\) 0 0
\(121\) −4.82051 + 8.34936i −0.438228 + 0.759033i
\(122\) −14.8318 −1.34281
\(123\) 0 0
\(124\) 5.83685i 0.524165i
\(125\) 17.1475 1.53372
\(126\) 0 0
\(127\) −8.90666 −0.790338 −0.395169 0.918608i \(-0.629314\pi\)
−0.395169 + 0.918608i \(0.629314\pi\)
\(128\) 8.85517i 0.782694i
\(129\) 0 0
\(130\) −38.7003 −3.39424
\(131\) 3.37760 5.85017i 0.295102 0.511132i −0.679907 0.733299i \(-0.737980\pi\)
0.975009 + 0.222167i \(0.0713131\pi\)
\(132\) 0 0
\(133\) −1.00273 1.33559i −0.0869477 0.115810i
\(134\) 9.35245i 0.807928i
\(135\) 0 0
\(136\) 3.20742 + 1.85181i 0.275034 + 0.158791i
\(137\) −14.6017 + 8.43032i −1.24751 + 0.720251i −0.970612 0.240649i \(-0.922640\pi\)
−0.276898 + 0.960899i \(0.589307\pi\)
\(138\) 0 0
\(139\) 0.704693 0.406855i 0.0597713 0.0345089i −0.469817 0.882764i \(-0.655680\pi\)
0.529588 + 0.848255i \(0.322347\pi\)
\(140\) 12.6453 + 5.39411i 1.06872 + 0.455886i
\(141\) 0 0
\(142\) 8.73436 0.732971
\(143\) −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
\(149\) −7.30087 4.21516i −0.598110 0.345319i 0.170187 0.985412i \(-0.445563\pi\)
−0.768298 + 0.640092i \(0.778896\pi\)
\(150\) 0 0
\(151\) −1.51974 2.63227i −0.123675 0.214211i 0.797539 0.603267i \(-0.206135\pi\)
−0.921214 + 0.389056i \(0.872801\pi\)
\(152\) −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
\(157\) 3.80824i 0.303931i 0.988386 + 0.151966i \(0.0485603\pi\)
−0.988386 + 0.151966i \(0.951440\pi\)
\(158\) 31.3634i 2.49514i
\(159\) 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 \(0.690276\pi\)
\(164\) −3.11429 5.39411i −0.243185 0.421209i
\(165\) 0 0
\(166\) 16.1427 + 9.32002i 1.25292 + 0.723374i
\(167\) 1.85181 + 3.20742i 0.143297 + 0.248198i 0.928736 0.370741i \(-0.120896\pi\)
−0.785439 + 0.618939i \(0.787563\pi\)
\(168\) 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
\(173\) 9.63564 0.732584 0.366292 0.930500i \(-0.380627\pi\)
0.366292 + 0.930500i \(0.380627\pi\)
\(174\) 0 0
\(175\) 20.1060 15.0951i 1.51987 1.14108i
\(176\) 4.91378 2.83697i 0.370390 0.213845i
\(177\) 0 0
\(178\) −18.3474 + 10.5929i −1.37520 + 0.793971i
\(179\) 15.9792 + 9.22562i 1.19435 + 0.689556i 0.959289 0.282426i \(-0.0911392\pi\)
0.235056 + 0.971982i \(0.424473\pi\)
\(180\) 0 0
\(181\) 16.6209i 1.23542i 0.786406 + 0.617710i \(0.211940\pi\)
−0.786406 + 0.617710i \(0.788060\pi\)
\(182\) −21.5014 + 16.1427i −1.59379 + 1.19658i
\(183\) 0 0
\(184\) −1.02693 + 1.77870i −0.0757065 + 0.131128i
\(185\) 16.1151 1.18480
\(186\) 0 0
\(187\) 3.70361i 0.270835i
\(188\) −3.47356 −0.253335
\(189\) 0 0
\(190\) 4.40939 0.319890
\(191\) 7.16576i 0.518496i −0.965811 0.259248i \(-0.916525\pi\)
0.965811 0.259248i \(-0.0834747\pi\)
\(192\) 0 0
\(193\) −3.17776 −0.228740 −0.114370 0.993438i \(-0.536485\pi\)
−0.114370 + 0.993438i \(0.536485\pi\)
\(194\) 0.631243 1.09334i 0.0453206 0.0784975i
\(195\) 0 0
\(196\) 9.27557 2.27773i 0.662541 0.162695i
\(197\) 1.93305i 0.137724i 0.997626 + 0.0688619i \(0.0219368\pi\)
−0.997626 + 0.0688619i \(0.978063\pi\)
\(198\) 0 0
\(199\) −7.50000 4.33013i −0.531661 0.306955i 0.210032 0.977695i \(-0.432643\pi\)
−0.741693 + 0.670740i \(0.765977\pi\)
\(200\) 9.59372 5.53894i 0.678378 0.391662i
\(201\) 0 0
\(202\) 10.4588 6.03838i 0.735878 0.424859i
\(203\) 5.01841 11.7646i 0.352224 0.825710i
\(204\) 0 0
\(205\) −17.3843 −1.21417
\(206\) −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 0.569190 0.822206i \(-0.307257\pi\)
−0.996646 + 0.0818303i \(0.973923\pi\)
\(212\) −0.0855662 0.0494016i −0.00587671 0.00339292i
\(213\) 0 0
\(214\) −14.4605 25.0464i −0.988501 1.71213i
\(215\) −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
\(220\) 6.05745i 0.408393i
\(221\) 17.6015i 1.18401i
\(222\) 0 0
\(223\) 16.3996 + 9.46830i 1.09820 + 0.634044i 0.935747 0.352673i \(-0.114727\pi\)
0.162450 + 0.986717i \(0.448060\pi\)
\(224\) 17.3252 2.09607i 1.15759 0.140050i
\(225\) 0 0
\(226\) −18.2146 31.5486i −1.21162 2.09858i
\(227\) −2.86138 4.95606i −0.189917 0.328945i 0.755306 0.655373i \(-0.227488\pi\)
−0.945222 + 0.326428i \(0.894155\pi\)
\(228\) 0 0
\(229\) −9.64548 5.56882i −0.637391 0.367998i 0.146218 0.989252i \(-0.453290\pi\)
−0.783609 + 0.621255i \(0.786623\pi\)
\(230\) −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 −0.177230 0.984169i \(-0.556714\pi\)
0.763701 + 0.645571i \(0.223380\pi\)
\(234\) 0 0
\(235\) −4.84744 + 8.39601i −0.316212 + 0.547695i
\(236\) −9.53101 −0.620416
\(237\) 0 0
\(238\) −6.04940 + 14.1815i −0.392124 + 0.919249i
\(239\) −14.3592 + 8.29030i −0.928821 + 0.536255i −0.886438 0.462846i \(-0.846828\pi\)
−0.0423824 + 0.999101i \(0.513495\pi\)
\(240\) 0 0
\(241\) −20.6921 + 11.9466i −1.33290 + 0.769549i −0.985743 0.168258i \(-0.946186\pi\)
−0.347155 + 0.937808i \(0.612852\pi\)
\(242\) −15.3148 8.84198i −0.984470 0.568384i
\(243\) 0 0
\(244\) 11.0330i 0.706316i
\(245\) 7.43875 25.5988i 0.475244 1.63545i
\(246\) 0 0
\(247\) −1.74864 + 3.02873i −0.111263 + 0.192713i
\(248\) −4.98689 −0.316668
\(249\) 0 0
\(250\) 31.4527i 1.98924i
\(251\) 19.9233 1.25755 0.628774 0.777588i \(-0.283557\pi\)
0.628774 + 0.777588i \(0.283557\pi\)
\(252\) 0 0
\(253\) −2.05387 −0.129125
\(254\) 16.3370i 1.02507i
\(255\) 0 0
\(256\) 20.9714 1.31072
\(257\) 11.6025 20.0961i 0.723742 1.25356i −0.235747 0.971814i \(-0.575754\pi\)
0.959490 0.281744i \(-0.0909130\pi\)
\(258\) 0 0
\(259\) 8.95333 6.72194i 0.556333 0.417681i
\(260\) 28.7882i 1.78537i
\(261\) 0 0
\(262\) 10.7306 + 6.19533i 0.662941 + 0.382749i
\(263\) 8.33330 4.81123i 0.513853 0.296673i −0.220563 0.975373i \(-0.570789\pi\)
0.734416 + 0.678699i \(0.237456\pi\)
\(264\) 0 0
\(265\) −0.238820 + 0.137883i −0.0146706 + 0.00847006i
\(266\) 2.44980 1.83925i 0.150207 0.112772i
\(267\) 0 0
\(268\) −6.95705 −0.424970
\(269\) 10.4152 18.0396i 0.635024 1.09989i −0.351487 0.936193i \(-0.614324\pi\)
0.986510 0.163700i \(-0.0523429\pi\)
\(270\) 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
\(275\) 9.59372 + 5.53894i 0.578523 + 0.334010i
\(276\) 0 0
\(277\) −4.15802 7.20190i −0.249831 0.432720i 0.713648 0.700505i \(-0.247042\pi\)
−0.963479 + 0.267784i \(0.913708\pi\)
\(278\) 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 0.955072 0.296375i \(-0.0957780\pi\)
0.220867 + 0.975304i \(0.429111\pi\)
\(282\) 0 0
\(283\) 17.0334i 1.01253i 0.862378 + 0.506266i \(0.168974\pi\)
−0.862378 + 0.506266i \(0.831026\pi\)
\(284\) 6.49727i 0.385542i
\(285\) 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
\(290\) 16.8842 + 29.2443i 0.991474 + 1.71728i
\(291\) 0 0
\(292\) −6.61408 3.81864i −0.387060 0.223469i
\(293\) −10.7079 18.5467i −0.625564 1.08351i −0.988432 0.151668i \(-0.951536\pi\)
0.362868 0.931841i \(-0.381798\pi\)
\(294\) 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
\(299\) 9.76106 0.564497
\(300\) 0 0
\(301\) −17.5988 7.50713i −1.01438 0.432704i
\(302\) 4.82821 2.78757i 0.277833 0.160407i
\(303\) 0 0
\(304\) 2.66075 1.53618i 0.152604 0.0881062i
\(305\) −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 \(-0.187336\pi\)
\(308\) 2.52669 + 3.36544i 0.143972 + 0.191764i
\(309\) 0 0
\(310\) 14.9408 25.8782i 0.848579 1.46978i
\(311\) 6.81412 0.386393 0.193197 0.981160i \(-0.438115\pi\)
0.193197 + 0.981160i \(0.438115\pi\)
\(312\) 0 0
\(313\) 16.6417i 0.940643i −0.882495 0.470322i \(-0.844138\pi\)
0.882495 0.470322i \(-0.155862\pi\)
\(314\) −6.98525 −0.394200
\(315\) 0 0
\(316\) −23.3304 −1.31244
\(317\) 5.07787i 0.285202i −0.989780 0.142601i \(-0.954453\pi\)
0.989780 0.142601i \(-0.0455465\pi\)
\(318\) 0 0
\(319\) 5.63555 0.315530
\(320\) −4.50220 + 7.79804i −0.251681 + 0.435924i
\(321\) 0 0
\(322\) −7.86445 3.35474i −0.438269 0.186952i
\(323\) 2.00546i 0.111587i
\(324\) 0 0
\(325\) −45.5944 26.3240i −2.52912 1.46019i
\(326\) −17.6218 + 10.1739i −0.975981 + 0.563483i
\(327\) 0 0
\(328\) −4.60862 + 2.66079i −0.254468 + 0.146917i
\(329\) 0.808981 + 6.68669i 0.0446006 + 0.368649i
\(330\) 0 0
\(331\) 16.3304 0.897602 0.448801 0.893632i \(-0.351851\pi\)
0.448801 + 0.893632i \(0.351851\pi\)
\(332\) −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 0.914847 0.403800i \(-0.132311\pi\)
−0.807124 + 0.590381i \(0.798977\pi\)
\(338\) 28.1083 + 16.2284i 1.52889 + 0.882706i
\(339\) 0 0
\(340\) −8.25409 14.2965i −0.447641 0.775337i
\(341\) −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
\(346\) 17.6741i 0.950166i
\(347\) 7.33697i 0.393869i 0.980417 + 0.196935i \(0.0630987\pi\)
−0.980417 + 0.196935i \(0.936901\pi\)
\(348\) 0 0
\(349\) −22.0917 12.7547i −1.18254 0.682741i −0.225941 0.974141i \(-0.572546\pi\)
−0.956601 + 0.291400i \(0.905879\pi\)
\(350\) 27.6881 + 36.8793i 1.47999 + 1.97128i
\(351\) 0 0
\(352\) 3.84471 + 6.65923i 0.204924 + 0.354938i
\(353\) 0.0103948 + 0.0180043i 0.000553260 + 0.000958274i 0.866302 0.499521i \(-0.166491\pi\)
−0.865749 + 0.500479i \(0.833157\pi\)
\(354\) 0 0
\(355\) 15.7047 + 9.06711i 0.833519 + 0.481232i
\(356\) −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 \(-0.261535\pi\)
0.974669 0.223654i \(-0.0717985\pi\)
\(360\) 0 0
\(361\) −9.30077 + 16.1094i −0.489514 + 0.847863i
\(362\) −30.4867 −1.60235
\(363\) 0 0
\(364\) −12.0082 15.9944i −0.629400 0.838333i
\(365\) −18.4602 + 10.6580i −0.966253 + 0.557866i
\(366\) 0 0
\(367\) 7.68942 4.43949i 0.401384 0.231739i −0.285697 0.958320i \(-0.592225\pi\)
0.687081 + 0.726581i \(0.258892\pi\)
\(368\) −7.42629 4.28757i −0.387122 0.223505i
\(369\) 0 0
\(370\) 29.5590i 1.53670i
\(371\) −0.0751713 + 0.176223i −0.00390270 + 0.00914902i
\(372\) 0 0
\(373\) 6.40939 11.1014i 0.331865 0.574808i −0.651012 0.759067i \(-0.725655\pi\)
0.982878 + 0.184260i \(0.0589887\pi\)
\(374\) −6.79333 −0.351274
\(375\) 0 0
\(376\) 2.96774i 0.153049i
\(377\) −26.7831 −1.37940
\(378\) 0 0
\(379\) 3.13828 0.161203 0.0806013 0.996746i \(-0.474316\pi\)
0.0806013 + 0.996746i \(0.474316\pi\)
\(380\) 3.28003i 0.168262i
\(381\) 0 0
\(382\) 13.1437 0.672492
\(383\) −13.7595 + 23.8322i −0.703078 + 1.21777i 0.264303 + 0.964440i \(0.414858\pi\)
−0.967381 + 0.253327i \(0.918475\pi\)
\(384\) 0 0
\(385\) 11.6608 1.41076i 0.594287 0.0718991i
\(386\) 5.82878i 0.296677i
\(387\) 0 0
\(388\) 0.813312 + 0.469566i 0.0412896 + 0.0238386i
\(389\) 15.7994 9.12181i 0.801064 0.462494i −0.0427793 0.999085i \(-0.513621\pi\)
0.843843 + 0.536590i \(0.180288\pi\)
\(390\) 0 0
\(391\) 4.84744 2.79867i 0.245146 0.141535i
\(392\) −1.94604 7.92486i −0.0982901 0.400266i
\(393\) 0 0
\(394\) −3.54568 −0.178629
\(395\) −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
\(401\) 12.0892 + 6.97972i 0.603707 + 0.348551i 0.770499 0.637442i \(-0.220007\pi\)
−0.166791 + 0.985992i \(0.553341\pi\)
\(402\) 0 0
\(403\) 11.8502 + 20.5251i 0.590299 + 1.02243i
\(404\) 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
\(409\) 20.3721i 1.00733i −0.863898 0.503667i \(-0.831984\pi\)
0.863898 0.503667i \(-0.168016\pi\)
\(410\) 31.8870i 1.57479i
\(411\) 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
\(416\) −18.2721 31.6482i −0.895863 1.55168i
\(417\) 0 0
\(418\) 1.16894 + 0.674887i 0.0571747 + 0.0330098i
\(419\) 12.7603 + 22.1015i 0.623383 + 1.07973i 0.988851 + 0.148907i \(0.0475755\pi\)
−0.365469 + 0.930824i \(0.619091\pi\)
\(420\) 0 0
\(421\) −0.0466721 + 0.0808384i −0.00227466 + 0.00393982i −0.867160 0.498029i \(-0.834057\pi\)
0.864886 + 0.501969i \(0.167391\pi\)
\(422\) 19.7265 11.3891i 0.960271 0.554413i
\(423\) 0 0
\(424\) −0.0422078 + 0.0731060i −0.00204979 + 0.00355034i
\(425\) −30.1902 −1.46444
\(426\) 0 0
\(427\) −21.2388 + 2.56955i −1.02782 + 0.124349i
\(428\) 18.6314 10.7568i 0.900581 0.519951i
\(429\) 0 0
\(430\) 43.7470 25.2573i 2.10967 1.21802i
\(431\) 28.7271 + 16.5856i 1.38374 + 0.798901i 0.992600 0.121432i \(-0.0387486\pi\)
0.391137 + 0.920333i \(0.372082\pi\)
\(432\) 0 0
\(433\) 17.9518i 0.862706i −0.902183 0.431353i \(-0.858036\pi\)
0.902183 0.431353i \(-0.141964\pi\)
\(434\) −2.49344 20.6097i −0.119689 0.989298i
\(435\) 0 0
\(436\) −9.86718 + 17.0905i −0.472552 + 0.818484i
\(437\) −1.11214 −0.0532010
\(438\) 0 0
\(439\) 10.0368i 0.479032i −0.970892 0.239516i \(-0.923011\pi\)
0.970892 0.239516i \(-0.0769887\pi\)
\(440\) 5.17536 0.246726
\(441\) 0 0
\(442\) 32.2855 1.53566
\(443\) 26.3579i 1.25230i −0.779702 0.626151i \(-0.784629\pi\)
0.779702 0.626151i \(-0.215371\pi\)
\(444\) 0 0
\(445\) −43.9858 −2.08513
\(446\) −17.3672 + 30.0808i −0.822359 + 1.42437i
\(447\) 0 0
\(448\) 0.751365 + 6.21046i 0.0354986 + 0.293416i
\(449\) 24.0264i 1.13388i 0.823761 + 0.566938i \(0.191872\pi\)
−0.823761 + 0.566938i \(0.808128\pi\)
\(450\) 0 0
\(451\) −4.60862 2.66079i −0.217011 0.125292i
\(452\) 23.4683 13.5494i 1.10385 0.637310i
\(453\) 0 0
\(454\) 9.09061 5.24847i 0.426644 0.246323i
\(455\) −55.4181 + 6.70469i −2.59804 + 0.314321i
\(456\) 0 0
\(457\) 20.8222 0.974023 0.487012 0.873395i \(-0.338087\pi\)
0.487012 + 0.873395i \(0.338087\pi\)
\(458\) 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 \(-0.895643\pi\)
0.752234 + 0.658896i \(0.228976\pi\)
\(462\) 0 0
\(463\) −5.90666 10.2306i −0.274506 0.475458i 0.695505 0.718522i \(-0.255181\pi\)
−0.970010 + 0.243064i \(0.921848\pi\)
\(464\) 20.3768 + 11.7646i 0.945970 + 0.546156i
\(465\) 0 0
\(466\) 9.48026 + 16.4203i 0.439165 + 0.760655i
\(467\) −14.5789 25.2514i −0.674630 1.16849i −0.976577 0.215169i \(-0.930970\pi\)
0.301947 0.953325i \(-0.402364\pi\)
\(468\) 0 0
\(469\) 1.62028 + 13.3925i 0.0748174 + 0.618409i
\(470\) −15.4003 8.89138i −0.710364 0.410129i
\(471\) 0 0
\(472\) 8.14310i 0.374817i
\(473\) 8.43032i 0.387626i
\(474\) 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
\(479\) 20.2618 + 35.0944i 0.925785 + 1.60351i 0.790294 + 0.612728i \(0.209928\pi\)
0.135491 + 0.990779i \(0.456739\pi\)
\(480\) 0 0
\(481\) −20.3035 11.7222i −0.925760 0.534488i
\(482\) −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 \(0.257453\pi\)
\(488\) −9.42637 −0.426712
\(489\) 0 0
\(490\) 46.9544 + 13.6445i 2.12118 + 0.616395i
\(491\) −5.34443 + 3.08561i −0.241191 + 0.139252i −0.615724 0.787962i \(-0.711136\pi\)
0.374533 + 0.927214i \(0.377803\pi\)
\(492\) 0 0
\(493\) −13.3008 + 7.67920i −0.599036 + 0.345854i
\(494\) −5.55542 3.20742i −0.249950 0.144309i
\(495\) 0 0
\(496\) 20.8209i 0.934884i
\(497\) 12.5074 1.51320i 0.561034 0.0678761i
\(498\) 0 0
\(499\) 1.48026 2.56389i 0.0662656 0.114775i −0.830989 0.556289i \(-0.812225\pi\)
0.897255 + 0.441513i \(0.145558\pi\)
\(500\) −23.3969 −1.04634
\(501\) 0 0
\(502\) 36.5442i 1.63105i
\(503\) 4.33485 0.193282 0.0966408 0.995319i \(-0.469190\pi\)
0.0966408 + 0.995319i \(0.469190\pi\)
\(504\) 0 0
\(505\) 25.0737 1.11577
\(506\) 3.76729i 0.167476i
\(507\) 0 0
\(508\) 12.1527 0.539188
\(509\) 14.4742 25.0701i 0.641560 1.11121i −0.343525 0.939144i \(-0.611621\pi\)
0.985085 0.172071i \(-0.0550457\pi\)
\(510\) 0 0
\(511\) −5.81058 + 13.6216i −0.257045 + 0.602585i
\(512\) 20.7564i 0.917311i
\(513\) 0 0
\(514\) 36.8611 + 21.2818i 1.62587 + 0.938698i
\(515\) −30.8318 + 17.8008i −1.35861 + 0.784395i
\(516\) 0 0
\(517\) −2.57014 + 1.48387i −0.113034 + 0.0652605i
\(518\) 12.3297 + 16.4226i 0.541735 + 0.721567i
\(519\) 0 0
\(520\) −24.5961 −1.07861
\(521\) 6.08031 10.5314i 0.266383 0.461389i −0.701542 0.712628i \(-0.747505\pi\)
0.967925 + 0.251239i \(0.0808381\pi\)
\(522\) 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
\(527\) 11.7698 + 6.79531i 0.512701 + 0.296008i
\(528\) 0 0
\(529\) −9.94798 17.2304i −0.432521 0.749148i
\(530\) −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
\(535\) 60.0457i 2.59600i
\(536\) 5.94396i 0.256740i
\(537\) 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 \(0.836811\pi\)
\(542\) 18.0524 + 31.2677i 0.775419 + 1.34306i
\(543\) 0 0
\(544\) −18.1482 10.4779i −0.778098 0.449235i
\(545\) 27.5398 + 47.7003i 1.17968 + 2.04326i
\(546\) 0 0
\(547\) 20.1482 34.8977i 0.861475 1.49212i −0.00903012 0.999959i \(-0.502874\pi\)
0.870505 0.492159i \(-0.163792\pi\)
\(548\) 19.9233 11.5027i 0.851082 0.491372i
\(549\) 0 0
\(550\) −10.1598 + 17.5972i −0.433213 + 0.750348i
\(551\) 3.05158 0.130002
\(552\) 0 0
\(553\) 5.43359 + 44.9117i 0.231060 + 1.90984i
\(554\) 13.2100 7.62682i 0.561241 0.324033i
\(555\) 0 0
\(556\) −0.961517 + 0.555132i −0.0407774 + 0.0235428i
\(557\) −37.6165 21.7179i −1.59386 0.920216i −0.992636 0.121137i \(-0.961346\pi\)
−0.601226 0.799079i \(-0.705321\pi\)
\(558\) 0 0
\(559\) 40.0653i 1.69458i
\(560\) 45.1076 + 19.2415i 1.90614 + 0.813104i
\(561\) 0 0
\(562\) −20.8754 + 36.1572i −0.880574 + 1.52520i
\(563\) −6.33322 −0.266913 −0.133457 0.991055i \(-0.542608\pi\)
−0.133457 + 0.991055i \(0.542608\pi\)
\(564\) 0 0
\(565\) 75.6342i 3.18195i
\(566\) −31.2434 −1.31326
\(567\) 0 0
\(568\) 5.55114 0.232921
\(569\) 8.23271i 0.345133i 0.984998 + 0.172567i \(0.0552060\pi\)
−0.984998 + 0.172567i \(0.944794\pi\)
\(570\) 0 0
\(571\) 8.49727 0.355600 0.177800 0.984067i \(-0.443102\pi\)
0.177800 + 0.984067i \(0.443102\pi\)
\(572\) 4.40624 7.63183i 0.184234 0.319103i
\(573\) 0 0
\(574\) −13.3008 17.7160i −0.555163 0.739453i
\(575\) 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 \(0.359646\pi\)
\(578\) −10.9712 + 6.33424i −0.456343 + 0.263470i
\(579\) 0 0
\(580\) −21.7541 + 12.5597i −0.903290 + 0.521514i
\(581\) 24.7307 + 10.5494i 1.02600 + 0.437663i
\(582\) 0 0
\(583\) −0.0844155 −0.00349613
\(584\) −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 \(-0.999120\pi\)
0.502393 + 0.864640i \(0.332453\pi\)
\(588\) 0 0
\(589\) −1.35017 2.33856i −0.0556327 0.0963587i
\(590\) −42.2566 24.3968i −1.73968 1.00440i
\(591\) 0 0
\(592\) 10.2980 + 17.8367i 0.423247 + 0.733085i
\(593\) −9.46830 16.3996i −0.388816 0.673450i 0.603474 0.797382i \(-0.293783\pi\)
−0.992291 + 0.123933i \(0.960449\pi\)
\(594\) 0 0
\(595\) −25.5988 + 19.2190i −1.04945 + 0.787901i
\(596\) 9.96166 + 5.75136i 0.408045 + 0.235585i
\(597\) 0 0
\(598\) 17.9042i 0.732156i
\(599\) 34.6794i 1.41696i −0.705730 0.708481i \(-0.749381\pi\)
0.705730 0.708481i \(-0.250619\pi\)
\(600\) 0 0
\(601\) 11.4929 + 6.63544i 0.468806 + 0.270665i 0.715740 0.698367i \(-0.246090\pi\)
−0.246934 + 0.969032i \(0.579423\pi\)
\(602\) 13.7699 32.2805i 0.561219 1.31565i
\(603\) 0 0
\(604\) 2.07361 + 3.59159i 0.0843738 + 0.146140i
\(605\) −18.3577 31.7964i −0.746345 1.29271i
\(606\) 0 0
\(607\) 21.6635 + 12.5074i 0.879294 + 0.507660i 0.870425 0.492300i \(-0.163844\pi\)
0.00886811 + 0.999961i \(0.497177\pi\)
\(608\) 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 \(-0.183180\pi\)
\(614\) 35.6829 1.44004
\(615\) 0 0
\(616\) 2.87537 2.15876i 0.115852 0.0869787i
\(617\) 16.7463 9.66849i 0.674181 0.389239i −0.123478 0.992347i \(-0.539405\pi\)
0.797659 + 0.603109i \(0.206071\pi\)
\(618\) 0 0
\(619\) −9.57807 + 5.52990i −0.384975 + 0.222265i −0.679981 0.733230i \(-0.738012\pi\)
0.295006 + 0.955496i \(0.404679\pi\)
\(620\) 19.2501 + 11.1141i 0.773105 + 0.446352i
\(621\) 0 0
\(622\) 12.4987i 0.501154i
\(623\) −24.4380 + 18.3474i −0.979087 + 0.735075i
\(624\) 0 0
\(625\) −8.89411 + 15.4051i −0.355764 + 0.616202i
\(626\) 30.5249 1.22002
\(627\) 0 0
\(628\) 5.19615i 0.207349i
\(629\) −13.4439 −0.536043
\(630\) 0 0
\(631\) −27.6015 −1.09880 −0.549400 0.835560i \(-0.685144\pi\)
−0.549400 + 0.835560i \(0.685144\pi\)
\(632\) 19.9330i 0.792894i
\(633\) 0 0
\(634\) 9.31405 0.369908
\(635\) 16.9594 29.3745i 0.673012 1.16569i
\(636\) 0 0
\(637\) −27.9929 + 26.8411i −1.10912 + 1.06348i
\(638\) 10.3370i 0.409245i
\(639\) 0 0
\(640\) 29.2047 + 16.8613i 1.15442 + 0.666503i
\(641\) −5.25886 + 3.03621i −0.207713 + 0.119923i −0.600248 0.799814i \(-0.704931\pi\)
0.392535 + 0.919737i \(0.371598\pi\)
\(642\) 0 0
\(643\) 11.4929 6.63544i 0.453236 0.261676i −0.255960 0.966687i \(-0.582391\pi\)
0.709196 + 0.705011i \(0.249058\pi\)
\(644\) 2.49551 5.85017i 0.0983368 0.230529i
\(645\) 0 0
\(646\) −3.67850 −0.144729
\(647\) 15.3688 26.6195i 0.604210 1.04652i −0.387966 0.921674i \(-0.626822\pi\)
0.992176 0.124848i \(-0.0398444\pi\)
\(648\) 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
\(653\) −32.2322 18.6093i −1.26134 0.728237i −0.288009 0.957628i \(-0.592993\pi\)
−0.973334 + 0.229391i \(0.926327\pi\)
\(654\) 0 0
\(655\) 12.8627 + 22.2789i 0.502588 + 0.870508i
\(656\) −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 −0.997214 0.0745963i \(-0.976233\pi\)
−0.563209 0.826314i \(-0.690433\pi\)
\(660\) 0 0
\(661\) 13.1889i 0.512989i −0.966546 0.256495i \(-0.917432\pi\)
0.966546 0.256495i \(-0.0825676\pi\)
\(662\) 29.9540i 1.16419i
\(663\) 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
\(668\) −2.52669 4.37636i −0.0977607 0.169326i
\(669\) 0 0
\(670\) −30.8447 17.8082i −1.19164 0.687991i
\(671\) −4.71319 8.16348i −0.181951 0.315148i
\(672\) 0 0
\(673\) −20.4633 + 35.4434i −0.788800 + 1.36624i 0.137902 + 0.990446i \(0.455964\pi\)
−0.926702 + 0.375796i \(0.877369\pi\)
\(674\) −6.28262 + 3.62727i −0.241998 + 0.139717i
\(675\) 0 0
\(676\) −12.0719 + 20.9091i −0.464303 + 0.804196i
\(677\) −1.61796 −0.0621834 −0.0310917 0.999517i \(-0.509898\pi\)
−0.0310917 + 0.999517i \(0.509898\pi\)
\(678\) 0 0
\(679\) 0.714508 1.67501i 0.0274203 0.0642809i
\(680\) −12.2146 + 7.05213i −0.468410 + 0.270437i
\(681\) 0 0
\(682\) 7.92168 4.57358i 0.303337 0.175131i
\(683\) 22.9977 + 13.2778i 0.879984 + 0.508059i 0.870653 0.491897i \(-0.163696\pi\)
0.00933109 + 0.999956i \(0.497030\pi\)
\(684\) 0 0
\(685\) 64.2094i 2.45332i
\(686\) 31.7787 12.0050i 1.21332 0.458353i
\(687\) 0 0
\(688\) 17.5988 30.4820i 0.670948 1.16212i
\(689\) 0.401187 0.0152840
\(690\) 0 0
\(691\) 37.6337i 1.43165i 0.698278 + 0.715826i \(0.253950\pi\)
−0.698278 + 0.715826i \(0.746050\pi\)
\(692\) −13.1473 −0.499787
\(693\) 0 0
\(694\) −13.4578 −0.510851
\(695\) 3.09880i 0.117544i
\(696\) 0 0
\(697\) 14.5027 0.549330
\(698\) 23.3951 40.5216i 0.885519 1.53376i
\(699\) 0 0
\(700\) −27.4336 + 20.5965i −1.03689 + 0.778474i
\(701\) 24.3228i 0.918659i 0.888266 + 0.459330i \(0.151910\pi\)
−0.888266 + 0.459330i \(0.848090\pi\)
\(702\) 0 0
\(703\) 2.31331 + 1.33559i 0.0872482 + 0.0503728i
\(704\) −2.38709 + 1.37819i −0.0899668 + 0.0519423i
\(705\) 0 0
\(706\) −0.0330243 + 0.0190666i −0.00124289 + 0.000717581i
\(707\) 13.9306 10.4588i 0.523916 0.393343i
\(708\) 0 0
\(709\) 1.03402 0.0388334 0.0194167 0.999811i \(-0.493819\pi\)
0.0194167 + 0.999811i \(0.493819\pi\)
\(710\) −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
\(716\) −21.8029 12.5879i −0.814811 0.470431i
\(717\) 0 0
\(718\) 33.2218 + 57.5419i 1.23983 + 2.14744i
\(719\) 8.37315 + 14.5027i 0.312266 + 0.540861i 0.978853 0.204567i \(-0.0655787\pi\)
−0.666587 + 0.745428i \(0.732245\pi\)
\(720\) 0 0
\(721\) −9.70469 + 22.7505i −0.361422 + 0.847273i
\(722\) −29.5486 17.0599i −1.09968 0.634903i
\(723\) 0 0
\(724\) 22.6783i 0.842834i
\(725\) 45.9385i 1.70611i
\(726\) 0 0
\(727\) −28.4902 16.4488i −1.05664 0.610053i −0.132141 0.991231i \(-0.542185\pi\)
−0.924502 + 0.381178i \(0.875518\pi\)
\(728\) −13.6653 + 10.2596i −0.506469 + 0.380244i
\(729\) 0 0
\(730\) −19.5494 33.8606i −0.723556 1.25324i
\(731\) 11.4874 + 19.8968i 0.424879 + 0.735911i
\(732\) 0 0
\(733\) 17.2443 + 9.95599i 0.636932 + 0.367733i 0.783432 0.621478i \(-0.213467\pi\)
−0.146500 + 0.989211i \(0.546801\pi\)
\(734\) 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 \(-0.215235\pi\)
\(740\) −21.9882 −0.808301
\(741\) 0 0
\(742\) −0.323235 0.137883i −0.0118663 0.00506183i
\(743\) 38.3208 22.1245i 1.40586 0.811671i 0.410870 0.911694i \(-0.365225\pi\)
0.994985 + 0.100023i \(0.0318917\pi\)
\(744\) 0 0
\(745\) 27.8035 16.0524i 1.01864 0.588113i
\(746\) 20.3626 + 11.7564i 0.745529 + 0.430431i
\(747\) 0 0
\(748\) 5.05339i 0.184770i
\(749\) −25.0464 33.3606i −0.915174 1.21897i
\(750\) 0 0
\(751\) −1.17230 + 2.03048i −0.0427779 + 0.0740934i −0.886622 0.462496i \(-0.846954\pi\)
0.843844 + 0.536589i \(0.180287\pi\)
\(752\) −12.3907 −0.451841
\(753\) 0 0
\(754\) 49.1268i 1.78909i
\(755\) 11.5751 0.421260
\(756\) 0 0
\(757\) −24.8530 −0.903298 −0.451649 0.892196i \(-0.649164\pi\)
−0.451649 + 0.892196i \(0.649164\pi\)
\(758\) 5.75637i 0.209081i
\(759\) 0 0
\(760\) 2.80239 0.101653
\(761\) −0.441044 + 0.763910i −0.0159878 + 0.0276917i −0.873909 0.486090i \(-0.838423\pi\)
0.857921 + 0.513782i \(0.171756\pi\)
\(762\) 0 0
\(763\) 35.1976 + 15.0143i 1.27424 + 0.543553i
\(764\) 9.77730i 0.353730i
\(765\) 0 0
\(766\) −43.7140 25.2383i −1.57945 0.911896i
\(767\) 33.5155 19.3502i 1.21017 0.698694i
\(768\) 0 0
\(769\) −17.9310 + 10.3524i −0.646607 + 0.373319i −0.787155 0.616755i \(-0.788447\pi\)
0.140548 + 0.990074i \(0.455114\pi\)
\(770\) 2.58768 + 21.3887i 0.0932536 + 0.770793i
\(771\) 0 0
\(772\) 4.33589 0.156052
\(773\) 4.70279 8.14548i 0.169148 0.292972i −0.768973 0.639282i \(-0.779232\pi\)
0.938120 + 0.346309i \(0.112565\pi\)
\(774\) 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
\(779\) −2.49551 1.44078i −0.0894109 0.0516214i
\(780\) 0 0
\(781\) 2.77557 + 4.80743i 0.0993176 + 0.172023i
\(782\) 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
\(787\) 25.1557i 0.896705i 0.893857 + 0.448352i \(0.147989\pi\)
−0.893857 + 0.448352i \(0.852011\pi\)
\(788\) 2.63754i 0.0939585i
\(789\) 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
\(794\) 1.07229 + 1.85725i 0.0380540 + 0.0659115i
\(795\) 0 0
\(796\) 10.2334 + 5.90823i 0.362712 + 0.209412i
\(797\) 15.3584 + 26.6015i 0.544023 + 0.942275i 0.998668 + 0.0516020i \(0.0164327\pi\)
−0.454645 + 0.890673i \(0.650234\pi\)
\(798\) 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
\(803\) −6.52514 −0.230267
\(804\) 0 0
\(805\) −10.6580 14.1960i −0.375646 0.500344i
\(806\) −37.6480 + 21.7361i −1.32609 + 0.765621i
\(807\) 0 0
\(808\) 6.64710 3.83771i 0.233844 0.135010i
\(809\) 12.3629 + 7.13774i 0.434657 + 0.250950i 0.701329 0.712838i \(-0.252591\pi\)
−0.266671 + 0.963788i \(0.585924\pi\)
\(810\) 0 0
\(811\) 10.0160i 0.351711i 0.984416 + 0.175855i \(0.0562691\pi\)
−0.984416 + 0.175855i \(0.943731\pi\)
\(812\) −6.84736 + 16.0521i −0.240295 + 0.563319i
\(813\) 0 0
\(814\) −4.52420 + 7.83615i −0.158573 + 0.274657i
\(815\) −42.2462 −1.47982
\(816\) 0 0
\(817\) 4.56491i 0.159706i
\(818\) 37.3674 1.30652
\(819\) 0 0
\(820\) 23.7200 0.828337
\(821\) 12.4609i 0.434887i 0.976073 + 0.217444i \(0.0697718\pi\)
−0.976073 + 0.217444i \(0.930228\pi\)
\(822\) 0 0
\(823\) −4.59607 −0.160209 −0.0801045 0.996786i \(-0.525525\pi\)
−0.0801045 + 0.996786i \(0.525525\pi\)
\(824\) −5.44906 + 9.43805i −0.189827 + 0.328790i
\(825\) 0 0
\(826\) −33.6537 + 4.07155i −1.17096 + 0.141667i
\(827\) 37.9330i 1.31906i 0.751678 + 0.659531i \(0.229245\pi\)
−0.751678 + 0.659531i \(0.770755\pi\)
\(828\) 0 0
\(829\) −31.8690 18.3996i −1.10686 0.639044i −0.168843 0.985643i \(-0.554003\pi\)
−0.938013 + 0.346599i \(0.887337\pi\)
\(830\) −61.4755 + 35.4929i −2.13385 + 1.23198i
\(831\) 0 0
\(832\) 11.3447 6.54987i 0.393307 0.227076i
\(833\) −6.20573 + 21.3556i −0.215016 + 0.739929i
\(834\) 0 0
\(835\) −14.1043 −0.488098
\(836\) −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 \(-0.953517\pi\)
0.620695 + 0.784052i \(0.286851\pi\)
\(840\) 0 0
\(841\) −2.81505 4.87580i −0.0970706 0.168131i
\(842\) −0.148277 0.0856080i −0.00510997 0.00295025i
\(843\) 0 0
\(844\) 8.47207 + 14.6741i 0.291621 + 0.505102i
\(845\) 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
\(850\) 55.3762i 1.89939i
\(851\) 7.45541i 0.255568i
\(852\) 0 0
\(853\) −42.8709 24.7515i −1.46787 0.847476i −0.468519 0.883453i \(-0.655212\pi\)
−0.999353 + 0.0359772i \(0.988546\pi\)
\(854\) −4.71319 38.9572i −0.161282 1.33309i
\(855\) 0 0
\(856\) −9.19041 15.9183i −0.314122 0.544075i
\(857\) −7.00810 12.1384i −0.239392 0.414639i 0.721148 0.692781i \(-0.243615\pi\)
−0.960540 + 0.278142i \(0.910282\pi\)
\(858\) 0 0
\(859\) −1.05213 0.607448i −0.0358983 0.0207259i 0.481943 0.876202i \(-0.339931\pi\)
−0.517842 + 0.855476i \(0.673264\pi\)
\(860\) 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 −0.926373 0.376606i \(-0.877091\pi\)
−0.137036 + 0.990566i \(0.543758\pi\)
\(864\) 0 0
\(865\) −18.3474 + 31.7787i −0.623832 + 1.08051i
\(866\) 32.9279 1.11893
\(867\) 0 0
\(868\) 15.3311 1.85481i 0.520370 0.0629564i
\(869\) −17.2625 + 9.96652i −0.585591 + 0.338091i
\(870\) 0 0
\(871\) 24.4642 14.1244i 0.828939 0.478588i
\(872\) 14.6017 + 8.43032i 0.494477 + 0.285487i
\(873\) 0 0
\(874\) 2.03994i 0.0690020i
\(875\) 5.44906 + 45.0396i 0.184212 + 1.52262i
\(876\) 0 0
\(877\) 5.59607 9.69268i 0.188966 0.327299i −0.755940 0.654641i \(-0.772820\pi\)
0.944906 + 0.327342i \(0.106153\pi\)
\(878\) 18.4100 0.621307
\(879\) 0 0
\(880\) 21.6078i 0.728398i
\(881\) 4.16372 0.140279 0.0701397 0.997537i \(-0.477655\pi\)
0.0701397 + 0.997537i \(0.477655\pi\)
\(882\) 0 0
\(883\) −38.7433 −1.30382 −0.651908 0.758298i \(-0.726031\pi\)
−0.651908 + 0.758298i \(0.726031\pi\)
\(884\) 24.0164i 0.807758i
\(885\) 0 0
\(886\) 48.3468 1.62424
\(887\) −19.0412 + 32.9804i −0.639342 + 1.10737i 0.346236 + 0.938148i \(0.387460\pi\)
−0.985577 + 0.169225i \(0.945874\pi\)
\(888\) 0 0
\(889\) −2.83032 23.3942i −0.0949259 0.784617i
\(890\) 80.6807i 2.70442i
\(891\) 0 0
\(892\) −22.3764 12.9190i −0.749216 0.432560i
\(893\) −1.39170 + 0.803496i −0.0465713 + 0.0268880i
\(894\) 0 0
\(895\) −60.8529 + 35.1334i −2.03409 + 1.17438i
\(896\) 23.2590 2.81396i 0.777028 0.0940079i
\(897\) 0 0
\(898\) −44.0702 −1.47064
\(899\) 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
\(905\) −54.8163 31.6482i −1.82216 1.05202i
\(906\) 0 0
\(907\) −0.773833 1.34032i −0.0256947 0.0445046i 0.852892 0.522087i \(-0.174846\pi\)
−0.878587 + 0.477583i \(0.841513\pi\)
\(908\) 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 0.940932 0.338596i \(-0.109952\pi\)
0.177233 + 0.984169i \(0.443285\pi\)
\(912\) 0 0
\(913\) 11.8467i 0.392069i
\(914\) 38.1931i 1.26331i
\(915\) 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 \(0.895360\pi\)
\(920\) −3.91081 6.77373i −0.128936 0.223323i
\(921\) 0 0
\(922\) −13.2677 7.66013i −0.436950 0.252273i
\(923\) −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
\(929\) 44.6284 1.46421 0.732105 0.681192i \(-0.238538\pi\)
0.732105 + 0.681192i \(0.238538\pi\)
\(930\) 0 0
\(931\) 3.18942 3.05819i 0.104529 0.100228i
\(932\) −12.2146 + 7.05213i −0.400104 + 0.231000i
\(933\) 0 0
\(934\) 46.3171 26.7412i 1.51554 0.874999i
\(935\) −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 \(-0.183282\pi\)
\(938\) −24.5651 + 2.97198i −0.802079 + 0.0970387i
\(939\) 0 0
\(940\) 6.61408 11.4559i 0.215727 0.373651i
\(941\) 33.9984 1.10832 0.554159 0.832411i \(-0.313040\pi\)
0.554159 + 0.832411i \(0.313040\pi\)
\(942\) 0 0
\(943\) 8.04260i 0.261903i
\(944\) −33.9984 −1.10655
\(945\) 0 0
\(946\) 15.4633 0.502754
\(947\) 46.1461i 1.49955i −0.661694 0.749774i \(-0.730162\pi\)
0.661694 0.749774i \(-0.269838\pi\)
\(948\) 0 0
\(949\) 31.0109 1.00666
\(950\) −5.50138 + 9.52867i −0.178488 + 0.309151i
\(951\) 0 0
\(952\) −3.84471 + 9.01307i −0.124608 + 0.292115i
\(953\) 35.1143i 1.13746i 0.822523 + 0.568731i \(0.192566\pi\)
−0.822523 + 0.568731i \(0.807434\pi\)
\(954\) 0 0
\(955\) 23.6329 + 13.6445i 0.764744 + 0.441525i
\(956\) 19.5924 11.3117i 0.633664 0.365846i
\(957\) 0 0
\(958\) −64.3717 + 37.1650i −2.07976 + 1.20075i
\(959\) −26.7831 35.6739i −0.864873 1.15197i
\(960\) 0 0
\(961\) 12.7003 0.409688
\(962\) 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 0.953488 0.301432i \(-0.0974646\pi\)
−0.737792 + 0.675029i \(0.764131\pi\)
\(968\) −9.73332 5.61954i −0.312841 0.180619i
\(969\) 0 0
\(970\) 2.40393 + 4.16372i 0.0771854 + 0.133689i
\(971\) −9.19460 15.9255i −0.295069 0.511074i 0.679932 0.733275i \(-0.262009\pi\)
−0.975001 + 0.222201i \(0.928676\pi\)
\(972\) 0 0
\(973\) 1.29258 + 1.72166i 0.0414381 + 0.0551938i
\(974\) −19.7265 11.3891i −0.632078 0.364930i
\(975\) 0 0
\(976\) 39.3563i 1.25976i
\(977\) 22.6530i 0.724734i 0.932035 + 0.362367i \(0.118031\pi\)
−0.932035 + 0.362367i \(0.881969\pi\)
\(978\) 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
\(983\) −19.6704 34.0701i −0.627388 1.08667i −0.988074 0.153981i \(-0.950791\pi\)
0.360685 0.932688i \(-0.382543\pi\)
\(984\) 0 0
\(985\) −6.37526 3.68076i −0.203133 0.117279i
\(986\) −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 \(0.171478\pi\)
\(992\) 28.2168 0.895883
\(993\) 0 0
\(994\) 2.77557 + 22.9416i 0.0880357 + 0.727665i
\(995\) 28.5618 16.4902i 0.905471 0.522774i
\(996\) 0 0
\(997\) 27.2486 15.7320i 0.862973 0.498238i −0.00203378 0.999998i \(-0.500647\pi\)
0.865007 + 0.501760i \(0.167314\pi\)
\(998\) 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.i.f.269.5 12
3.2 odd 2 inner 567.2.i.f.269.2 12
7.5 odd 6 567.2.s.f.26.5 12
9.2 odd 6 189.2.p.d.80.2 yes 12
9.4 even 3 567.2.s.f.458.2 12
9.5 odd 6 567.2.s.f.458.5 12
9.7 even 3 189.2.p.d.80.5 yes 12
21.5 even 6 567.2.s.f.26.2 12
63.5 even 6 inner 567.2.i.f.215.2 12
63.11 odd 6 1323.2.c.d.1322.3 12
63.25 even 3 1323.2.c.d.1322.10 12
63.38 even 6 1323.2.c.d.1322.4 12
63.40 odd 6 inner 567.2.i.f.215.5 12
63.47 even 6 189.2.p.d.26.5 yes 12
63.52 odd 6 1323.2.c.d.1322.9 12
63.61 odd 6 189.2.p.d.26.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
189.2.p.d.26.2 12 63.61 odd 6
189.2.p.d.26.5 yes 12 63.47 even 6
189.2.p.d.80.2 yes 12 9.2 odd 6
189.2.p.d.80.5 yes 12 9.7 even 3
567.2.i.f.215.2 12 63.5 even 6 inner
567.2.i.f.215.5 12 63.40 odd 6 inner
567.2.i.f.269.2 12 3.2 odd 2 inner
567.2.i.f.269.5 12 1.1 even 1 trivial
567.2.s.f.26.2 12 21.5 even 6
567.2.s.f.26.5 12 7.5 odd 6
567.2.s.f.458.2 12 9.4 even 3
567.2.s.f.458.5 12 9.5 odd 6
1323.2.c.d.1322.3 12 63.11 odd 6
1323.2.c.d.1322.4 12 63.38 even 6
1323.2.c.d.1322.9 12 63.52 odd 6
1323.2.c.d.1322.10 12 63.25 even 3