Properties

Label 201.2.p.a.44.1
Level $201$
Weight $2$
Character 201.44
Analytic conductor $1.605$
Analytic rank $0$
Dimension $20$
CM discriminant -3
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [201,2,Mod(2,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(66))
 
chi = DirichletCharacter(H, H._module([33, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.2");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 201.p (of order \(66\), degree \(20\), 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: \(1.60499308063\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\Q(\zeta_{33})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{66}]$

Embedding invariants

Embedding label 44.1
Root \(-0.786053 - 0.618159i\) of defining polynomial
Character \(\chi\) \(=\) 201.44
Dual form 201.2.p.a.32.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.71442 - 0.246497i) q^{3} +(1.77767 - 0.916453i) q^{4} +(-3.50336 - 3.67422i) q^{7} +(2.87848 + 0.845198i) q^{9} +O(q^{10})\) \(q+(-1.71442 - 0.246497i) q^{3} +(1.77767 - 0.916453i) q^{4} +(-3.50336 - 3.67422i) q^{7} +(2.87848 + 0.845198i) q^{9} +(-3.27358 + 1.13300i) q^{12} +(0.687743 - 3.56835i) q^{13} +(2.32023 - 3.25830i) q^{16} +(-1.65758 - 1.58050i) q^{19} +(5.10055 + 7.16272i) q^{21} +(3.27430 - 3.77875i) q^{25} +(-4.72659 - 2.15856i) q^{27} +(-9.59507 - 3.32089i) q^{28} +(1.88589 + 9.78494i) q^{31} +(5.89157 - 1.13551i) q^{36} +(5.89230 + 10.2058i) q^{37} +(-2.05867 + 5.94812i) q^{39} +(2.24962 + 3.50047i) q^{43} +(-4.78101 + 5.01418i) q^{48} +(-0.893274 + 18.7521i) q^{49} +(-2.04764 - 6.97363i) q^{52} +(2.45221 + 3.11824i) q^{57} +(-1.34031 - 14.0363i) q^{61} +(-6.97891 - 13.5372i) q^{63} +(1.13852 - 7.91857i) q^{64} +(-4.25333 - 6.99351i) q^{67} +(5.46168 - 0.521527i) q^{73} +(-6.54498 + 5.67126i) q^{75} +(-4.39510 - 1.29052i) q^{76} +(15.3567 - 5.31502i) q^{79} +(7.57128 + 4.86577i) q^{81} +(15.6314 + 8.05855i) q^{84} +(-15.5203 + 9.97429i) q^{91} +(-0.821260 - 17.2404i) q^{93} +(-15.6466 + 9.03356i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 2 q^{4} - 6 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q - 2 q^{4} - 6 q^{7} + 6 q^{9} - 6 q^{12} - 3 q^{13} + 4 q^{16} - 8 q^{19} + 6 q^{21} + 10 q^{25} - 12 q^{28} + 15 q^{31} + 6 q^{36} + 10 q^{37} - 3 q^{39} - 12 q^{48} - 5 q^{49} - 154 q^{52} - 75 q^{57} + 15 q^{61} - 15 q^{63} + 16 q^{64} + 5 q^{67} + 60 q^{73} - 32 q^{76} + 134 q^{79} - 18 q^{81} + 186 q^{84} - 12 q^{91} - 15 q^{93} + 9 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{61}{66}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 0.971812 0.235759i \(-0.0757576\pi\)
−0.971812 + 0.235759i \(0.924242\pi\)
\(3\) −1.71442 0.246497i −0.989821 0.142315i
\(4\) 1.77767 0.916453i 0.888835 0.458227i
\(5\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(6\) 0 0
\(7\) −3.50336 3.67422i −1.32415 1.38872i −0.866162 0.499763i \(-0.833421\pi\)
−0.457983 0.888961i \(-0.651428\pi\)
\(8\) 0 0
\(9\) 2.87848 + 0.845198i 0.959493 + 0.281733i
\(10\) 0 0
\(11\) 0 0 0.0950560 0.995472i \(-0.469697\pi\)
−0.0950560 + 0.995472i \(0.530303\pi\)
\(12\) −3.27358 + 1.13300i −0.945001 + 0.327068i
\(13\) 0.687743 3.56835i 0.190745 0.989681i −0.752753 0.658303i \(-0.771274\pi\)
0.943498 0.331378i \(-0.107514\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.32023 3.25830i 0.580057 0.814576i
\(17\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(18\) 0 0
\(19\) −1.65758 1.58050i −0.380276 0.362593i 0.475700 0.879607i \(-0.342195\pi\)
−0.855976 + 0.517015i \(0.827043\pi\)
\(20\) 0 0
\(21\) 5.10055 + 7.16272i 1.11303 + 1.56303i
\(22\) 0 0
\(23\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(24\) 0 0
\(25\) 3.27430 3.77875i 0.654861 0.755750i
\(26\) 0 0
\(27\) −4.72659 2.15856i −0.909632 0.415415i
\(28\) −9.59507 3.32089i −1.81330 0.627588i
\(29\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0 0
\(31\) 1.88589 + 9.78494i 0.338716 + 1.75743i 0.607589 + 0.794252i \(0.292137\pi\)
−0.268872 + 0.963176i \(0.586651\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 5.89157 1.13551i 0.981929 0.189251i
\(37\) 5.89230 + 10.2058i 0.968688 + 1.67782i 0.699363 + 0.714767i \(0.253467\pi\)
0.269325 + 0.963049i \(0.413199\pi\)
\(38\) 0 0
\(39\) −2.05867 + 5.94812i −0.329650 + 0.952462i
\(40\) 0 0
\(41\) 0 0 0.998867 0.0475819i \(-0.0151515\pi\)
−0.998867 + 0.0475819i \(0.984848\pi\)
\(42\) 0 0
\(43\) 2.24962 + 3.50047i 0.343063 + 0.533817i 0.969321 0.245800i \(-0.0790505\pi\)
−0.626258 + 0.779616i \(0.715414\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(48\) −4.78101 + 5.01418i −0.690079 + 0.723734i
\(49\) −0.893274 + 18.7521i −0.127611 + 2.67888i
\(50\) 0 0
\(51\) 0 0
\(52\) −2.04764 6.97363i −0.283957 0.967069i
\(53\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.45221 + 3.11824i 0.324803 + 0.413021i
\(58\) 0 0
\(59\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(60\) 0 0
\(61\) −1.34031 14.0363i −0.171609 1.79717i −0.514188 0.857677i \(-0.671907\pi\)
0.342580 0.939489i \(-0.388699\pi\)
\(62\) 0 0
\(63\) −6.97891 13.5372i −0.879259 1.70553i
\(64\) 1.13852 7.91857i 0.142315 0.989821i
\(65\) 0 0
\(66\) 0 0
\(67\) −4.25333 6.99351i −0.519627 0.854393i
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(72\) 0 0
\(73\) 5.46168 0.521527i 0.639242 0.0610402i 0.229598 0.973286i \(-0.426259\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) 0 0
\(75\) −6.54498 + 5.67126i −0.755750 + 0.654861i
\(76\) −4.39510 1.29052i −0.504152 0.148032i
\(77\) 0 0
\(78\) 0 0
\(79\) 15.3567 5.31502i 1.72777 0.597986i 0.731307 0.682048i \(-0.238911\pi\)
0.996461 + 0.0840621i \(0.0267894\pi\)
\(80\) 0 0
\(81\) 7.57128 + 4.86577i 0.841254 + 0.540641i
\(82\) 0 0
\(83\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(84\) 15.6314 + 8.05855i 1.70553 + 0.879259i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(90\) 0 0
\(91\) −15.5203 + 9.97429i −1.62697 + 1.04559i
\(92\) 0 0
\(93\) −0.821260 17.2404i −0.0851607 1.78774i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −15.6466 + 9.03356i −1.58867 + 0.917219i −0.595143 + 0.803620i \(0.702905\pi\)
−0.993527 + 0.113599i \(0.963762\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.35759 9.71812i 0.235759 0.971812i
\(101\) 0 0 −0.971812 0.235759i \(-0.924242\pi\)
0.971812 + 0.235759i \(0.0757576\pi\)
\(102\) 0 0
\(103\) 19.8014 3.81640i 1.95109 0.376042i 0.953998 0.299812i \(-0.0969239\pi\)
0.997090 0.0762298i \(-0.0242882\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(108\) −10.3805 + 0.494486i −0.998867 + 0.0475819i
\(109\) 7.88028 + 6.82830i 0.754794 + 0.654033i 0.944762 0.327758i \(-0.106293\pi\)
−0.189968 + 0.981790i \(0.560838\pi\)
\(110\) 0 0
\(111\) −7.58619 18.9494i −0.720050 1.79860i
\(112\) −20.1003 + 2.88999i −1.89930 + 0.273078i
\(113\) 0 0 0.814576 0.580057i \(-0.196970\pi\)
−0.814576 + 0.580057i \(0.803030\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 4.99561 9.69013i 0.461844 0.895853i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −10.8012 2.08176i −0.981929 0.189251i
\(122\) 0 0
\(123\) 0 0
\(124\) 12.3199 + 15.6661i 1.10636 + 1.40686i
\(125\) 0 0
\(126\) 0 0
\(127\) 11.8418 11.2911i 1.05079 1.00193i 0.0507955 0.998709i \(-0.483824\pi\)
0.999995 0.00321749i \(-0.00102416\pi\)
\(128\) 0 0
\(129\) −2.99393 6.55580i −0.263601 0.577206i
\(130\) 0 0
\(131\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(132\) 0 0
\(133\) 11.6274i 1.00822i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(138\) 0 0
\(139\) −9.21749 + 4.20949i −0.781817 + 0.357044i −0.766008 0.642831i \(-0.777760\pi\)
−0.0158092 + 0.999875i \(0.505032\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 9.43264 7.41791i 0.786053 0.618159i
\(145\) 0 0
\(146\) 0 0
\(147\) 6.15379 31.9289i 0.507556 2.63345i
\(148\) 19.8277 + 12.7425i 1.62982 + 1.04742i
\(149\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(150\) 0 0
\(151\) −5.58800 2.88081i −0.454745 0.234437i 0.215608 0.976480i \(-0.430827\pi\)
−0.670352 + 0.742043i \(0.733857\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 1.79155 + 12.4605i 0.143438 + 0.997636i
\(157\) −7.03443 + 2.81616i −0.561409 + 0.224754i −0.634970 0.772537i \(-0.718988\pi\)
0.0735617 + 0.997291i \(0.476563\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −2.00036 + 3.46472i −0.156680 + 0.271378i −0.933670 0.358136i \(-0.883413\pi\)
0.776989 + 0.629514i \(0.216746\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(168\) 0 0
\(169\) −0.191328 0.0765960i −0.0147175 0.00589200i
\(170\) 0 0
\(171\) −3.43549 5.95043i −0.262718 0.455041i
\(172\) 7.20709 + 4.16102i 0.549536 + 0.317275i
\(173\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(174\) 0 0
\(175\) −25.3550 + 1.20781i −1.91666 + 0.0913017i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(180\) 0 0
\(181\) −20.9975 16.5126i −1.56073 1.22737i −0.854599 0.519288i \(-0.826197\pi\)
−0.706129 0.708083i \(-0.749560\pi\)
\(182\) 0 0
\(183\) −1.16205 + 24.3945i −0.0859016 + 1.80330i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 8.62791 + 24.9287i 0.627588 + 1.81330i
\(190\) 0 0
\(191\) 0 0 −0.618159 0.786053i \(-0.712121\pi\)
0.618159 + 0.786053i \(0.287879\pi\)
\(192\) −3.90380 + 13.2951i −0.281733 + 0.959493i
\(193\) 17.3277 + 19.9972i 1.24727 + 1.43943i 0.854216 + 0.519918i \(0.174037\pi\)
0.393058 + 0.919514i \(0.371417\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 15.5975 + 34.1538i 1.11411 + 2.43956i
\(197\) 0 0 −0.458227 0.888835i \(-0.651515\pi\)
0.458227 + 0.888835i \(0.348485\pi\)
\(198\) 0 0
\(199\) 1.12987 + 4.65738i 0.0800942 + 0.330153i 0.997736 0.0672563i \(-0.0214245\pi\)
−0.917642 + 0.397409i \(0.869909\pi\)
\(200\) 0 0
\(201\) 5.56813 + 13.0382i 0.392745 + 0.919647i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −10.0310 10.5203i −0.695527 0.729448i
\(209\) 0 0
\(210\) 0 0
\(211\) −22.8217 + 17.9472i −1.57111 + 1.23554i −0.763589 + 0.645703i \(0.776565\pi\)
−0.807524 + 0.589834i \(0.799193\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 29.3450 41.2094i 1.99207 2.79747i
\(218\) 0 0
\(219\) −9.49218 0.452168i −0.641422 0.0305547i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 3.14969 + 21.9066i 0.210919 + 1.46697i 0.770097 + 0.637927i \(0.220208\pi\)
−0.559178 + 0.829048i \(0.688883\pi\)
\(224\) 0 0
\(225\) 12.6188 8.10961i 0.841254 0.540641i
\(226\) 0 0
\(227\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(228\) 7.21694 + 3.29587i 0.477954 + 0.218274i
\(229\) 23.2211 + 8.03689i 1.53449 + 0.531093i 0.958187 0.286143i \(-0.0923732\pi\)
0.576304 + 0.817235i \(0.304494\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.371662 0.928368i \(-0.378788\pi\)
−0.371662 + 0.928368i \(0.621212\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −27.6380 + 5.32680i −1.79528 + 0.346013i
\(238\) 0 0
\(239\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 0 0
\(241\) 7.88943 17.2754i 0.508203 1.11281i −0.465512 0.885041i \(-0.654130\pi\)
0.973715 0.227768i \(-0.0731428\pi\)
\(242\) 0 0
\(243\) −11.7810 10.2083i −0.755750 0.654861i
\(244\) −15.2462 23.7236i −0.976041 1.51875i
\(245\) 0 0
\(246\) 0 0
\(247\) −6.77978 + 4.82786i −0.431387 + 0.307189i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.458227 0.888835i \(-0.348485\pi\)
−0.458227 + 0.888835i \(0.651515\pi\)
\(252\) −24.8124 17.6688i −1.56303 1.11303i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −5.23309 15.1200i −0.327068 0.945001i
\(257\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(258\) 0 0
\(259\) 16.8553 57.4040i 1.04734 3.56691i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −13.9702 8.53418i −0.853369 0.521308i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 30.9757 + 4.45363i 1.88164 + 0.270539i 0.985042 0.172313i \(-0.0551240\pi\)
0.896595 + 0.442851i \(0.146033\pi\)
\(272\) 0 0
\(273\) 29.0669 13.2744i 1.75921 0.803405i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −13.0353 3.82752i −0.783218 0.229974i −0.134410 0.990926i \(-0.542914\pi\)
−0.648808 + 0.760952i \(0.724732\pi\)
\(278\) 0 0
\(279\) −2.84171 + 29.7597i −0.170129 + 1.78167i
\(280\) 0 0
\(281\) 0 0 0.189251 0.981929i \(-0.439394\pi\)
−0.189251 + 0.981929i \(0.560606\pi\)
\(282\) 0 0
\(283\) −21.8251 + 6.40842i −1.29737 + 0.380941i −0.856274 0.516522i \(-0.827227\pi\)
−0.441091 + 0.897462i \(0.645408\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 9.86097 + 13.8478i 0.580057 + 0.814576i
\(290\) 0 0
\(291\) 29.0516 11.6305i 1.70303 0.681792i
\(292\) 9.23112 5.93248i 0.540210 0.347172i
\(293\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −6.43738 + 16.0798i −0.371662 + 0.928368i
\(301\) 4.98028 20.5290i 0.287058 1.18327i
\(302\) 0 0
\(303\) 0 0
\(304\) −8.99574 + 1.73379i −0.515941 + 0.0994395i
\(305\) 0 0
\(306\) 0 0
\(307\) −9.93642 + 28.7094i −0.567101 + 1.63853i 0.187437 + 0.982277i \(0.439982\pi\)
−0.754539 + 0.656255i \(0.772139\pi\)
\(308\) 0 0
\(309\) −34.8886 + 1.66195i −1.98475 + 0.0945451i
\(310\) 0 0
\(311\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(312\) 0 0
\(313\) −20.1846 + 2.90210i −1.14090 + 0.164037i −0.686753 0.726891i \(-0.740965\pi\)
−0.454146 + 0.890927i \(0.650056\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 22.4283 23.5221i 1.26169 1.32322i
\(317\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 17.9185 + 1.71101i 0.995472 + 0.0950560i
\(325\) −11.2320 14.2827i −0.623040 0.792259i
\(326\) 0 0
\(327\) −11.8270 13.6490i −0.654033 0.754794i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 2.82554 + 5.48078i 0.155306 + 0.301251i 0.953633 0.300973i \(-0.0973116\pi\)
−0.798327 + 0.602224i \(0.794281\pi\)
\(332\) 0 0
\(333\) 8.33497 + 34.3572i 0.456754 + 1.88276i
\(334\) 0 0
\(335\) 0 0
\(336\) 35.1728 1.91883
\(337\) −35.6286 + 8.64340i −1.94081 + 0.470836i −0.957730 + 0.287668i \(0.907120\pi\)
−0.983082 + 0.183168i \(0.941365\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 45.1716 39.1414i 2.43904 2.11344i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.945001 0.327068i \(-0.106061\pi\)
−0.945001 + 0.327068i \(0.893939\pi\)
\(348\) 0 0
\(349\) −28.6340 18.4020i −1.53274 0.985034i −0.989350 0.145556i \(-0.953503\pi\)
−0.543394 0.839478i \(-0.682861\pi\)
\(350\) 0 0
\(351\) −10.9532 + 15.3816i −0.584637 + 0.821007i
\(352\) 0 0
\(353\) 0 0 −0.998867 0.0475819i \(-0.984848\pi\)
0.998867 + 0.0475819i \(0.0151515\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(360\) 0 0
\(361\) −0.654462 13.7388i −0.0344453 0.723097i
\(362\) 0 0
\(363\) 18.0047 + 6.23148i 0.945001 + 0.327068i
\(364\) −18.4490 + 31.9546i −0.966991 + 1.67488i
\(365\) 0 0
\(366\) 0 0
\(367\) 7.23551 18.0734i 0.377691 0.943426i −0.610751 0.791823i \(-0.709132\pi\)
0.988441 0.151603i \(-0.0484435\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −17.2599 29.8951i −0.894886 1.54999i
\(373\) 33.3959 + 19.2811i 1.72917 + 0.998338i 0.893400 + 0.449262i \(0.148313\pi\)
0.835773 + 0.549076i \(0.185020\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −6.22836 15.5577i −0.319929 0.799145i −0.997944 0.0640964i \(-0.979583\pi\)
0.678014 0.735049i \(-0.262841\pi\)
\(380\) 0 0
\(381\) −23.0851 + 16.4388i −1.18268 + 0.842185i
\(382\) 0 0
\(383\) 0 0 0.690079 0.723734i \(-0.257576\pi\)
−0.690079 + 0.723734i \(0.742424\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.51688 + 11.9774i 0.178773 + 0.608845i
\(388\) −19.5356 + 30.3981i −0.991772 + 1.54323i
\(389\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 9.29651 + 20.3565i 0.466579 + 1.02166i 0.985938 + 0.167109i \(0.0534431\pi\)
−0.519360 + 0.854556i \(0.673830\pi\)
\(398\) 0 0
\(399\) 2.86611 19.9343i 0.143485 0.997961i
\(400\) −4.71518 19.4362i −0.235759 0.971812i
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 36.2131 1.80390
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 27.8255 + 29.1825i 1.37588 + 1.44298i 0.744869 + 0.667211i \(0.232512\pi\)
0.631013 + 0.775772i \(0.282639\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 31.7028 24.9314i 1.56188 1.22828i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 16.8403 4.94475i 0.824672 0.242146i
\(418\) 0 0
\(419\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(420\) 0 0
\(421\) −28.8996 27.5557i −1.40848 1.34298i −0.863323 0.504652i \(-0.831621\pi\)
−0.545159 0.838333i \(-0.683531\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −46.8769 + 54.0988i −2.26853 + 2.61803i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) −18.0000 + 10.3923i −0.866025 + 0.500000i
\(433\) −5.43786 28.2143i −0.261327 1.35589i −0.840996 0.541041i \(-0.818030\pi\)
0.579669 0.814852i \(-0.303182\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 20.2664 + 4.91657i 0.970583 + 0.235461i
\(437\) 0 0
\(438\) 0 0
\(439\) 19.5867 + 33.9252i 0.934824 + 1.61916i 0.774947 + 0.632026i \(0.217776\pi\)
0.159877 + 0.987137i \(0.448890\pi\)
\(440\) 0 0
\(441\) −18.4205 + 53.2226i −0.877168 + 2.53441i
\(442\) 0 0
\(443\) 0 0 0.998867 0.0475819i \(-0.0151515\pi\)
−0.998867 + 0.0475819i \(0.984848\pi\)
\(444\) −30.8520 26.7334i −1.46417 1.26871i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −33.0832 + 23.5584i −1.56303 + 1.11303i
\(449\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 8.87007 + 6.31635i 0.416752 + 0.296768i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −7.01518 20.2690i −0.328156 0.948146i −0.981563 0.191139i \(-0.938782\pi\)
0.653407 0.757007i \(-0.273339\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(462\) 0 0
\(463\) 4.01101 + 42.0052i 0.186407 + 1.95215i 0.288769 + 0.957399i \(0.406754\pi\)
−0.102362 + 0.994747i \(0.532640\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(468\) 21.8041i 1.00790i
\(469\) −10.7947 + 40.1284i −0.498454 + 1.85296i
\(470\) 0 0
\(471\) 12.7541 3.09412i 0.587680 0.142570i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −11.3998 + 1.08855i −0.523057 + 0.0499459i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(480\) 0 0
\(481\) 40.4701 14.0068i 1.84528 0.638656i
\(482\) 0 0
\(483\) 0 0
\(484\) −21.1088 + 6.19812i −0.959493 + 0.281733i
\(485\) 0 0
\(486\) 0 0
\(487\) 17.0636 + 0.812840i 0.773226 + 0.0368333i 0.430486 0.902597i \(-0.358342\pi\)
0.342739 + 0.939430i \(0.388645\pi\)
\(488\) 0 0
\(489\) 4.28350 5.44691i 0.193707 0.246318i
\(490\) 0 0
\(491\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 36.2580 + 16.5585i 1.62803 + 0.743498i
\(497\) 0 0
\(498\) 0 0
\(499\) −3.26271 + 1.88372i −0.146059 + 0.0843271i −0.571248 0.820777i \(-0.693541\pi\)
0.425190 + 0.905104i \(0.360207\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.971812 0.235759i \(-0.924242\pi\)
0.971812 + 0.235759i \(0.0757576\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.309135 + 0.178479i 0.0137292 + 0.00792655i
\(508\) 10.7030 30.9244i 0.474870 1.37205i
\(509\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(510\) 0 0
\(511\) −21.0504 18.2403i −0.931217 0.806904i
\(512\) 0 0
\(513\) 4.42311 + 11.0484i 0.195285 + 0.487798i
\(514\) 0 0
\(515\) 0 0
\(516\) −11.3303 8.91026i −0.498789 0.392252i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(522\) 0 0
\(523\) −4.92085 0.948415i −0.215174 0.0414713i 0.0805251 0.996753i \(-0.474340\pi\)
−0.295699 + 0.955281i \(0.595552\pi\)
\(524\) 0 0
\(525\) 43.7669 + 4.17923i 1.91014 + 0.182397i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 16.6459 15.8718i 0.723734 0.690079i
\(530\) 0 0
\(531\) 0 0
\(532\) 10.6560 + 20.6697i 0.461995 + 0.896145i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −24.7751 + 11.3144i −1.06517 + 0.486445i −0.869351 0.494195i \(-0.835463\pi\)
−0.195816 + 0.980641i \(0.562736\pi\)
\(542\) 0 0
\(543\) 31.9282 + 33.4853i 1.37017 + 1.43699i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0.306466 3.20945i 0.0131035 0.137226i −0.986553 0.163443i \(-0.947740\pi\)
0.999656 + 0.0262168i \(0.00834602\pi\)
\(548\) 0 0
\(549\) 8.00542 41.5361i 0.341663 1.77272i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −73.3287 37.8036i −3.11825 1.60757i
\(554\) 0 0
\(555\) 0 0
\(556\) −12.5279 + 15.9305i −0.531300 + 0.675603i
\(557\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(558\) 0 0
\(559\) 14.0380 5.61999i 0.593746 0.237700i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −8.64703 44.8651i −0.363141 1.88416i
\(568\) 0 0
\(569\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(570\) 0 0
\(571\) −14.1677 5.67190i −0.592901 0.237362i 0.0557537 0.998445i \(-0.482244\pi\)
−0.648655 + 0.761083i \(0.724668\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 9.96996 21.8312i 0.415415 0.909632i
\(577\) −29.3997 + 1.40048i −1.22392 + 0.0583027i −0.649568 0.760303i \(-0.725050\pi\)
−0.574355 + 0.818606i \(0.694747\pi\)
\(578\) 0 0
\(579\) −24.7777 38.5549i −1.02973 1.60229i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.814576 0.580057i \(-0.803030\pi\)
0.814576 + 0.580057i \(0.196970\pi\)
\(588\) −18.3219 62.3987i −0.755583 2.57328i
\(589\) 12.3391 19.2000i 0.508424 0.791124i
\(590\) 0 0
\(591\) 0 0
\(592\) 46.9249 + 4.48079i 1.92860 + 0.184159i
\(593\) 0 0 −0.618159 0.786053i \(-0.712121\pi\)
0.618159 + 0.786053i \(0.287879\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.789042 8.26322i −0.0322933 0.338191i
\(598\) 0 0
\(599\) 0 0 −0.458227 0.888835i \(-0.651515\pi\)
0.458227 + 0.888835i \(0.348485\pi\)
\(600\) 0 0
\(601\) 7.03356 + 28.9927i 0.286905 + 1.18264i 0.914659 + 0.404226i \(0.132459\pi\)
−0.627754 + 0.778411i \(0.716026\pi\)
\(602\) 0 0
\(603\) −6.33223 23.7256i −0.257868 0.966180i
\(604\) −12.5737 −0.511619
\(605\) 0 0
\(606\) 0 0
\(607\) 34.7079 17.8932i 1.40875 0.726261i 0.424897 0.905242i \(-0.360310\pi\)
0.983853 + 0.178981i \(0.0572799\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −37.7044 + 29.6510i −1.52286 + 1.19759i −0.607930 + 0.793990i \(0.708000\pi\)
−0.914934 + 0.403603i \(0.867758\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(618\) 0 0
\(619\) −16.3767 + 22.9979i −0.658237 + 0.924364i −0.999880 0.0154656i \(-0.995077\pi\)
0.341644 + 0.939829i \(0.389016\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 14.6042 + 20.5088i 0.584637 + 0.821007i
\(625\) −3.55787 24.7455i −0.142315 0.989821i
\(626\) 0 0
\(627\) 0 0
\(628\) −9.92402 + 11.4529i −0.396012 + 0.457022i
\(629\) 0 0
\(630\) 0 0
\(631\) −37.8957 13.1158i −1.50860 0.522132i −0.557279 0.830326i \(-0.688154\pi\)
−0.951324 + 0.308193i \(0.900276\pi\)
\(632\) 0 0
\(633\) 43.5500 25.1436i 1.73096 0.999368i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 66.2998 + 16.0842i 2.62689 + 0.637277i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(642\) 0 0
\(643\) 6.97674 15.2769i 0.275136 0.602463i −0.720738 0.693207i \(-0.756197\pi\)
0.995874 + 0.0907437i \(0.0289244\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.371662 0.928368i \(-0.621212\pi\)
0.371662 + 0.928368i \(0.378788\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −60.4677 + 63.4167i −2.36992 + 2.48550i
\(652\) −0.380724 + 7.99238i −0.0149103 + 0.313006i
\(653\) 0 0 0.458227 0.888835i \(-0.348485\pi\)
−0.458227 + 0.888835i \(0.651515\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 16.1621 + 3.11500i 0.630545 + 0.121528i
\(658\) 0 0
\(659\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(660\) 0 0
\(661\) −3.76889 + 12.8357i −0.146593 + 0.499250i −0.999749 0.0224061i \(-0.992867\pi\)
0.853156 + 0.521656i \(0.174685\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 38.3335i 1.48206i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 8.94884 + 1.28665i 0.344952 + 0.0495967i 0.312614 0.949880i \(-0.398795\pi\)
0.0323386 + 0.999477i \(0.489705\pi\)
\(674\) 0 0
\(675\) −23.6329 + 10.7928i −0.909632 + 0.415415i
\(676\) −0.410314 + 0.0391803i −0.0157813 + 0.00150693i
\(677\) 0 0 −0.690079 0.723734i \(-0.742424\pi\)
0.690079 + 0.723734i \(0.257576\pi\)
\(678\) 0 0
\(679\) 88.0069 + 25.8411i 3.37739 + 0.991692i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.189251 0.981929i \(-0.439394\pi\)
−0.189251 + 0.981929i \(0.560606\pi\)
\(684\) −11.5605 7.42945i −0.442025 0.284072i
\(685\) 0 0
\(686\) 0 0
\(687\) −37.8296 19.5025i −1.44329 0.744068i
\(688\) 16.6252 + 0.791957i 0.633830 + 0.0301931i
\(689\) 0 0
\(690\) 0 0
\(691\) 25.8176 + 36.2558i 0.982149 + 1.37924i 0.924620 + 0.380891i \(0.124383\pi\)
0.0575291 + 0.998344i \(0.481678\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −43.9660 + 25.3838i −1.66176 + 0.959416i
\(701\) 0 0 −0.189251 0.981929i \(-0.560606\pi\)
0.189251 + 0.981929i \(0.439394\pi\)
\(702\) 0 0
\(703\) 6.36326 26.2297i 0.239995 0.989272i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 16.7245 48.3223i 0.628103 1.81478i 0.0501074 0.998744i \(-0.484044\pi\)
0.577995 0.816040i \(-0.303835\pi\)
\(710\) 0 0
\(711\) 48.6963 2.31969i 1.82625 0.0869952i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(720\) 0 0
\(721\) −83.3937 59.3844i −3.10574 2.21159i
\(722\) 0 0
\(723\) −17.7841 + 27.6727i −0.661399 + 1.02916i
\(724\) −52.4596 10.1108i −1.94964 0.375763i
\(725\) 0 0
\(726\) 0 0
\(727\) 26.2512 + 33.3811i 0.973602 + 1.23804i 0.971256 + 0.238039i \(0.0765045\pi\)
0.00234654 + 0.999997i \(0.499253\pi\)
\(728\) 0 0
\(729\) 17.6812 + 20.4052i 0.654861 + 0.755750i
\(730\) 0 0
\(731\) 0 0
\(732\) 20.2907 + 44.4304i 0.749966 + 1.64220i
\(733\) −2.68340 5.20507i −0.0991137 0.192254i 0.834065 0.551666i \(-0.186008\pi\)
−0.933179 + 0.359412i \(0.882977\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −17.9341 + 4.35077i −0.659717 + 0.160046i −0.551621 0.834095i \(-0.685990\pi\)
−0.108096 + 0.994140i \(0.534475\pi\)
\(740\) 0 0
\(741\) 12.8134 6.60579i 0.470714 0.242670i
\(742\) 0 0
\(743\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −28.9231 18.5878i −1.05542 0.678278i −0.106667 0.994295i \(-0.534018\pi\)
−0.948753 + 0.316017i \(0.897654\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 38.1836 + 36.4080i 1.38872 + 1.32415i
\(757\) −31.3711 + 39.8916i −1.14020 + 1.44989i −0.266231 + 0.963909i \(0.585778\pi\)
−0.873972 + 0.485977i \(0.838464\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(762\) 0 0
\(763\) −2.51879 52.8759i −0.0911862 1.91423i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 5.24468 + 27.2120i 0.189251 + 0.981929i
\(769\) −7.43992 + 18.5840i −0.268290 + 0.670157i −0.999934 0.0115309i \(-0.996330\pi\)
0.731643 + 0.681688i \(0.238754\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 49.1294 + 19.6685i 1.76821 + 0.707883i
\(773\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(774\) 0 0
\(775\) 43.1498 + 24.9126i 1.54999 + 0.894886i
\(776\) 0 0
\(777\) −43.0470 + 94.2599i −1.54430 + 3.38155i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 59.0276 + 46.4198i 2.10813 + 1.65785i
\(785\) 0 0
\(786\) 0 0
\(787\) 20.4325 39.6336i 0.728341 1.41279i −0.175309 0.984514i \(-0.556092\pi\)
0.903650 0.428272i \(-0.140877\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −51.0082 4.87070i −1.81136 0.172963i
\(794\) 0 0
\(795\) 0 0
\(796\) 6.27680 + 7.24382i 0.222475 + 0.256750i
\(797\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 21.8472 + 18.0748i 0.770493 + 0.637449i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(810\) 0 0
\(811\) −0.271593 0.284838i −0.00953690 0.0100020i 0.718948 0.695064i \(-0.244624\pi\)
−0.728485 + 0.685062i \(0.759775\pi\)
\(812\) 0 0
\(813\) −52.0075 15.2708i −1.82398 0.535570i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 1.80358 9.35785i 0.0630992 0.327390i
\(818\) 0 0
\(819\) −53.1051 + 15.5931i −1.85564 + 0.544866i
\(820\) 0 0
\(821\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(822\) 0 0
\(823\) −8.18233 7.80184i −0.285218 0.271955i 0.533940 0.845522i \(-0.320711\pi\)
−0.819159 + 0.573567i \(0.805559\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(828\) 0 0
\(829\) 37.1698 42.8962i 1.29096 1.48985i 0.518022 0.855367i \(-0.326668\pi\)
0.772939 0.634481i \(-0.218786\pi\)
\(830\) 0 0
\(831\) 21.4046 + 9.77515i 0.742517 + 0.339096i
\(832\) −27.4732 9.50857i −0.952462 0.329650i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 12.2075 50.3202i 0.421955 1.73932i
\(838\) 0 0
\(839\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(840\) 0 0
\(841\) −14.5000 25.1147i −0.500000 0.866025i
\(842\) 0 0
\(843\) 0 0
\(844\) −24.1218 + 52.8193i −0.830305 + 1.81811i
\(845\) 0 0
\(846\) 0 0
\(847\) 30.1917 + 46.9792i 1.03740 + 1.61422i
\(848\) 0 0
\(849\) 38.9970 5.60692i 1.33837 0.192429i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 1.21415 25.4882i 0.0415718 0.872699i −0.877732 0.479151i \(-0.840945\pi\)
0.919304 0.393548i \(-0.128752\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(858\) 0 0
\(859\) 0.637099 + 1.84078i 0.0217376 + 0.0628065i 0.955348 0.295484i \(-0.0954809\pi\)
−0.933610 + 0.358291i \(0.883360\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −13.4924 26.1716i −0.458227 0.888835i
\(868\) 14.3994 100.150i 0.488747 3.39931i
\(869\) 0 0
\(870\) 0 0
\(871\) −27.8805 + 10.3676i −0.944693 + 0.351294i
\(872\) 0 0
\(873\) −52.6735 + 12.7785i −1.78273 + 0.432485i
\(874\) 0 0
\(875\) 0 0
\(876\) −17.2884 + 7.89533i −0.584120 + 0.266758i
\(877\) 8.81998 0.842206i 0.297829 0.0284393i 0.0549283 0.998490i \(-0.482507\pi\)
0.242901 + 0.970051i \(0.421901\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(882\) 0 0
\(883\) 15.4030 5.33103i 0.518352 0.179403i −0.0553507 0.998467i \(-0.517628\pi\)
0.573703 + 0.819064i \(0.305506\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(888\) 0 0
\(889\) −82.9722 3.95245i −2.78280 0.132561i
\(890\) 0 0
\(891\) 0 0
\(892\) 25.6755 + 36.0562i 0.859679 + 1.20725i
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 15.0000 25.9808i 0.500000 0.866025i
\(901\) 0 0
\(902\) 0 0
\(903\) −13.5986 + 33.9677i −0.452534 + 1.13037i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 23.9072 4.60773i 0.793824 0.152997i 0.223811 0.974633i \(-0.428150\pi\)
0.570013 + 0.821635i \(0.306938\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(912\) 15.8499 0.755022i 0.524841 0.0250013i
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 48.6448 6.99407i 1.60727 0.231091i
\(917\) 0 0
\(918\) 0 0
\(919\) −41.5788 + 43.6066i −1.37156 + 1.43845i −0.605110 + 0.796142i \(0.706871\pi\)
−0.766448 + 0.642307i \(0.777978\pi\)
\(920\) 0 0
\(921\) 24.1120 46.7707i 0.794517 1.54115i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 57.8582 + 11.1512i 1.90236 + 0.366651i
\(926\) 0 0
\(927\) 60.2235 + 5.75065i 1.97800 + 0.188876i
\(928\) 0 0
\(929\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(930\) 0 0
\(931\) 31.1185 29.6714i 1.01987 0.972442i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 28.6078i 0.934576i 0.884105 + 0.467288i \(0.154769\pi\)
−0.884105 + 0.467288i \(0.845231\pi\)
\(938\) 0 0
\(939\) 35.3202 1.15263
\(940\) 0 0
\(941\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(948\) −44.2496 + 34.7983i −1.43716 + 1.13019i
\(949\) 1.89524 19.8479i 0.0615221 0.644289i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −63.4091 + 25.3852i −2.04545 + 0.818877i
\(962\) 0 0
\(963\) 0 0
\(964\) −1.80732 37.9403i −0.0582099 1.22198i
\(965\) 0 0
\(966\) 0 0
\(967\) 20.2272 35.0346i 0.650464 1.12664i −0.332547 0.943087i \(-0.607908\pi\)
0.983010 0.183550i \(-0.0587588\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(972\) −30.2981 7.35024i −0.971812 0.235759i
\(973\) 47.7587 + 19.1197i 1.53107 + 0.612950i
\(974\) 0 0
\(975\) 15.7358 + 27.2551i 0.503948 + 0.872863i
\(976\) −48.8444 28.2003i −1.56347 0.902670i
\(977\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 16.9120 + 26.3155i 0.539957 + 0.840190i
\(982\) 0 0
\(983\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) −7.62771 + 14.7957i −0.242670 + 0.470714i
\(989\) 0 0
\(990\) 0 0
\(991\) −11.5245 + 17.9324i −0.366086 + 0.569642i −0.974614 0.223891i \(-0.928124\pi\)
0.608528 + 0.793533i \(0.291760\pi\)
\(992\) 0 0
\(993\) −3.49317 10.0929i −0.110852 0.320287i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −39.4855 45.5687i −1.25052 1.44317i −0.849912 0.526924i \(-0.823345\pi\)
−0.400606 0.916251i \(-0.631200\pi\)
\(998\) 0 0
\(999\) −5.82071 60.9573i −0.184159 1.92860i
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 201.2.p.a.44.1 yes 20
3.2 odd 2 CM 201.2.p.a.44.1 yes 20
67.32 odd 66 inner 201.2.p.a.32.1 20
201.32 even 66 inner 201.2.p.a.32.1 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.2.p.a.32.1 20 67.32 odd 66 inner
201.2.p.a.32.1 20 201.32 even 66 inner
201.2.p.a.44.1 yes 20 1.1 even 1 trivial
201.2.p.a.44.1 yes 20 3.2 odd 2 CM