Properties

Label 201.3.o.a.83.1
Level $201$
Weight $3$
Character 201.83
Analytic conductor $5.477$
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] = [201,3,Mod(17,201)]
 
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, 64]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.17");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.o (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: \(5.47685331364\)
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 83.1
Root \(0.0475819 - 0.998867i\) of defining polynomial
Character \(\chi\) \(=\) 201.83
Dual form 201.3.o.a.155.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.24625 - 2.72890i) q^{3} +(3.71347 + 1.48665i) q^{4} +(4.57895 + 13.2300i) q^{7} +(-5.89375 + 6.80175i) q^{9} +O(q^{10})\) \(q+(-1.24625 - 2.72890i) q^{3} +(3.71347 + 1.48665i) q^{4} +(4.57895 + 13.2300i) q^{7} +(-5.89375 + 6.80175i) q^{9} +(-0.570983 - 11.9864i) q^{12} +(5.24308 + 2.70300i) q^{13} +(11.5797 + 11.0413i) q^{16} +(4.71229 - 13.6153i) q^{19} +(30.3968 - 28.9833i) q^{21} +(21.0313 - 13.5160i) q^{25} +(25.9063 + 7.60678i) q^{27} +(-2.66459 + 55.9366i) q^{28} +(-26.2673 + 13.5418i) q^{31} +(-31.9981 + 16.4962i) q^{36} +(7.79205 + 13.4962i) q^{37} +(0.842032 - 17.6764i) q^{39} +(11.9674 - 83.2351i) q^{43} +(15.6993 - 45.3600i) q^{48} +(-115.550 + 90.8693i) q^{49} +(15.4516 + 17.8321i) q^{52} +(-43.0273 + 4.10861i) q^{57} +(-19.5408 - 80.5485i) q^{61} +(-116.974 - 46.8295i) q^{63} +(26.5866 + 58.2164i) q^{64} +(-24.7789 + 62.2495i) q^{67} +(-30.3921 - 125.278i) q^{73} +(-63.0940 - 40.5481i) q^{75} +(37.7401 - 43.5544i) q^{76} +(7.51611 + 157.783i) q^{79} +(-11.5275 - 80.1755i) q^{81} +(155.966 - 62.4393i) q^{84} +(-11.7529 + 81.7429i) q^{91} +(69.6896 + 54.8045i) q^{93} +(-79.5897 - 137.853i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 6 q^{3} + 4 q^{4} + 2 q^{7} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 6 q^{3} + 4 q^{4} + 2 q^{7} - 18 q^{9} - 12 q^{12} + 23 q^{13} + 16 q^{16} + 26 q^{19} - 6 q^{21} - 50 q^{25} + 54 q^{27} + 8 q^{28} - 13 q^{31} + 36 q^{36} + 26 q^{37} - 69 q^{39} + 122 q^{43} - 48 q^{48} - 45 q^{49} + 828 q^{52} - 441 q^{57} + 47 q^{61} - 1269 q^{63} - 128 q^{64} + 109 q^{67} - 924 q^{73} + 150 q^{75} - 208 q^{76} + 252 q^{79} - 162 q^{81} + 1692 q^{84} - 92 q^{91} + 39 q^{93} + 167 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{33}\right)\)

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 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(3\) −1.24625 2.72890i −0.415415 0.909632i
\(4\) 3.71347 + 1.48665i 0.928368 + 0.371662i
\(5\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(6\) 0 0
\(7\) 4.57895 + 13.2300i 0.654136 + 1.89000i 0.327586 + 0.944821i \(0.393765\pi\)
0.326550 + 0.945180i \(0.394114\pi\)
\(8\) 0 0
\(9\) −5.89375 + 6.80175i −0.654861 + 0.755750i
\(10\) 0 0
\(11\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(12\) −0.570983 11.9864i −0.0475819 0.998867i
\(13\) 5.24308 + 2.70300i 0.403314 + 0.207923i 0.647934 0.761696i \(-0.275633\pi\)
−0.244621 + 0.969619i \(0.578663\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 11.5797 + 11.0413i 0.723734 + 0.690079i
\(17\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(18\) 0 0
\(19\) 4.71229 13.6153i 0.248015 0.716593i −0.750435 0.660944i \(-0.770156\pi\)
0.998450 0.0556487i \(-0.0177227\pi\)
\(20\) 0 0
\(21\) 30.3968 28.9833i 1.44747 1.38016i
\(22\) 0 0
\(23\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(24\) 0 0
\(25\) 21.0313 13.5160i 0.841254 0.540641i
\(26\) 0 0
\(27\) 25.9063 + 7.60678i 0.959493 + 0.281733i
\(28\) −2.66459 + 55.9366i −0.0951638 + 1.99773i
\(29\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0 0
\(31\) −26.2673 + 13.5418i −0.847334 + 0.436831i −0.826490 0.562952i \(-0.809666\pi\)
−0.0208440 + 0.999783i \(0.506635\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −31.9981 + 16.4962i −0.888835 + 0.458227i
\(37\) 7.79205 + 13.4962i 0.210596 + 0.364763i 0.951901 0.306405i \(-0.0991262\pi\)
−0.741305 + 0.671168i \(0.765793\pi\)
\(38\) 0 0
\(39\) 0.842032 17.6764i 0.0215906 0.453241i
\(40\) 0 0
\(41\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(42\) 0 0
\(43\) 11.9674 83.2351i 0.278312 1.93570i −0.0682370 0.997669i \(-0.521737\pi\)
0.346549 0.938032i \(-0.387354\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(48\) 15.6993 45.3600i 0.327068 0.945001i
\(49\) −115.550 + 90.8693i −2.35816 + 1.85448i
\(50\) 0 0
\(51\) 0 0
\(52\) 15.4516 + 17.8321i 0.297147 + 0.342925i
\(53\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −43.0273 + 4.10861i −0.754865 + 0.0720809i
\(58\) 0 0
\(59\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(60\) 0 0
\(61\) −19.5408 80.5485i −0.320342 1.32047i −0.873269 0.487238i \(-0.838005\pi\)
0.552928 0.833229i \(-0.313511\pi\)
\(62\) 0 0
\(63\) −116.974 46.8295i −1.85674 0.743325i
\(64\) 26.5866 + 58.2164i 0.415415 + 0.909632i
\(65\) 0 0
\(66\) 0 0
\(67\) −24.7789 + 62.2495i −0.369835 + 0.929098i
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(72\) 0 0
\(73\) −30.3921 125.278i −0.416331 1.71614i −0.664384 0.747392i \(-0.731306\pi\)
0.248053 0.968746i \(-0.420209\pi\)
\(74\) 0 0
\(75\) −63.0940 40.5481i −0.841254 0.540641i
\(76\) 37.7401 43.5544i 0.496580 0.573084i
\(77\) 0 0
\(78\) 0 0
\(79\) 7.51611 + 157.783i 0.0951406 + 1.99725i 0.0696203 + 0.997574i \(0.477821\pi\)
0.0255204 + 0.999674i \(0.491876\pi\)
\(80\) 0 0
\(81\) −11.5275 80.1755i −0.142315 0.989821i
\(82\) 0 0
\(83\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(84\) 155.966 62.4393i 1.85674 0.743325i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(90\) 0 0
\(91\) −11.7529 + 81.7429i −0.129152 + 0.898274i
\(92\) 0 0
\(93\) 69.6896 + 54.8045i 0.749350 + 0.589296i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −79.5897 137.853i −0.820513 1.42117i −0.905301 0.424771i \(-0.860355\pi\)
0.0847884 0.996399i \(-0.472979\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 98.1929 18.9251i 0.981929 0.189251i
\(101\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(102\) 0 0
\(103\) 159.460 82.2071i 1.54815 0.798128i 0.548866 0.835911i \(-0.315060\pi\)
0.999286 + 0.0377830i \(0.0120296\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(108\) 84.8937 + 66.7612i 0.786053 + 0.618159i
\(109\) −106.160 + 68.2251i −0.973948 + 0.625918i −0.927824 0.373017i \(-0.878323\pi\)
−0.0461237 + 0.998936i \(0.514687\pi\)
\(110\) 0 0
\(111\) 27.1190 38.0833i 0.244315 0.343093i
\(112\) −93.0529 + 203.758i −0.830830 + 1.81926i
\(113\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −49.2865 + 19.7313i −0.421252 + 0.168644i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −107.549 55.4454i −0.888835 0.458227i
\(122\) 0 0
\(123\) 0 0
\(124\) −117.675 + 11.2366i −0.948991 + 0.0906177i
\(125\) 0 0
\(126\) 0 0
\(127\) 65.6307 + 189.627i 0.516777 + 1.49313i 0.837757 + 0.546043i \(0.183867\pi\)
−0.320980 + 0.947086i \(0.604012\pi\)
\(128\) 0 0
\(129\) −242.054 + 71.0736i −1.87639 + 0.550958i
\(130\) 0 0
\(131\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(132\) 0 0
\(133\) 201.707 1.51660
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(138\) 0 0
\(139\) 228.842 67.1941i 1.64635 0.483411i 0.678426 0.734669i \(-0.262662\pi\)
0.967920 + 0.251258i \(0.0808442\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −143.348 + 13.6881i −0.995472 + 0.0950560i
\(145\) 0 0
\(146\) 0 0
\(147\) 391.976 + 202.078i 2.66651 + 1.37468i
\(148\) 8.87140 + 61.7019i 0.0599419 + 0.416905i
\(149\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(150\) 0 0
\(151\) 24.9115 9.97306i 0.164977 0.0660468i −0.287704 0.957719i \(-0.592892\pi\)
0.452681 + 0.891673i \(0.350468\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 29.4055 64.3891i 0.188497 0.412750i
\(157\) 172.384 242.080i 1.09799 1.54191i 0.286006 0.958228i \(-0.407672\pi\)
0.811983 0.583681i \(-0.198388\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 157.666 273.085i 0.967273 1.67537i 0.263894 0.964552i \(-0.414993\pi\)
0.703379 0.710815i \(-0.251674\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(168\) 0 0
\(169\) −77.8459 109.319i −0.460627 0.646860i
\(170\) 0 0
\(171\) 64.8345 + 112.297i 0.379149 + 0.656706i
\(172\) 168.182 291.300i 0.977803 1.69360i
\(173\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(174\) 0 0
\(175\) 275.119 + 216.356i 1.57211 + 1.23632i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(180\) 0 0
\(181\) −35.2453 3.36552i −0.194725 0.0185940i −0.00276243 0.999996i \(-0.500879\pi\)
−0.191963 + 0.981402i \(0.561485\pi\)
\(182\) 0 0
\(183\) −195.456 + 153.708i −1.06806 + 0.839935i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 17.9860 + 377.572i 0.0951638 + 1.99773i
\(190\) 0 0
\(191\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(192\) 125.733 145.104i 0.654861 0.755750i
\(193\) −306.727 197.122i −1.58926 1.02136i −0.972114 0.234507i \(-0.924652\pi\)
−0.617146 0.786849i \(-0.711711\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −564.182 + 165.659i −2.87848 + 0.845197i
\(197\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(198\) 0 0
\(199\) −239.059 46.0748i −1.20130 0.231532i −0.450936 0.892556i \(-0.648910\pi\)
−0.750364 + 0.661025i \(0.770122\pi\)
\(200\) 0 0
\(201\) 200.753 9.95906i 0.998772 0.0495476i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 30.8690 + 89.1902i 0.148409 + 0.428799i
\(209\) 0 0
\(210\) 0 0
\(211\) −146.928 + 14.0299i −0.696342 + 0.0664926i −0.437224 0.899353i \(-0.644038\pi\)
−0.259119 + 0.965845i \(0.583432\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −299.434 285.510i −1.37988 1.31572i
\(218\) 0 0
\(219\) −303.995 + 239.064i −1.38810 + 1.09162i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 179.911 393.951i 0.806777 1.76660i 0.186099 0.982531i \(-0.440416\pi\)
0.620679 0.784065i \(-0.286857\pi\)
\(224\) 0 0
\(225\) −32.0208 + 222.710i −0.142315 + 0.989821i
\(226\) 0 0
\(227\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(228\) −165.889 48.7093i −0.727582 0.213637i
\(229\) −11.0694 + 232.376i −0.0483380 + 1.01474i 0.836245 + 0.548357i \(0.184746\pi\)
−0.884583 + 0.466384i \(0.845557\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 421.205 217.146i 1.77724 0.916230i
\(238\) 0 0
\(239\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(240\) 0 0
\(241\) −414.491 121.705i −1.71988 0.505002i −0.734973 0.678096i \(-0.762805\pi\)
−0.984905 + 0.173094i \(0.944624\pi\)
\(242\) 0 0
\(243\) −204.425 + 131.376i −0.841254 + 0.540641i
\(244\) 47.1830 328.165i 0.193373 1.34494i
\(245\) 0 0
\(246\) 0 0
\(247\) 61.5089 58.6486i 0.249024 0.237444i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(252\) −364.762 347.800i −1.44747 1.38016i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 12.1810 + 255.710i 0.0475819 + 0.998867i
\(257\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(258\) 0 0
\(259\) −142.876 + 164.887i −0.551644 + 0.636631i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −184.559 + 194.324i −0.688653 + 0.725091i
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 136.841 + 299.641i 0.504950 + 1.10569i 0.974829 + 0.222955i \(0.0715702\pi\)
−0.469879 + 0.882731i \(0.655703\pi\)
\(272\) 0 0
\(273\) 237.715 69.7994i 0.870750 0.255675i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 57.3563 66.1927i 0.207062 0.238963i −0.642714 0.766106i \(-0.722192\pi\)
0.849776 + 0.527144i \(0.176737\pi\)
\(278\) 0 0
\(279\) 62.7055 258.475i 0.224751 0.926435i
\(280\) 0 0
\(281\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(282\) 0 0
\(283\) 349.132 + 402.920i 1.23368 + 1.42374i 0.870604 + 0.491985i \(0.163729\pi\)
0.363078 + 0.931759i \(0.381726\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 209.159 199.433i 0.723734 0.690079i
\(290\) 0 0
\(291\) −276.999 + 388.991i −0.951888 + 1.33674i
\(292\) 73.3843 510.399i 0.251316 1.74794i
\(293\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −174.017 244.373i −0.580057 0.814576i
\(301\) 1156.00 222.801i 3.84053 0.740202i
\(302\) 0 0
\(303\) 0 0
\(304\) 204.897 105.632i 0.674003 0.347472i
\(305\) 0 0
\(306\) 0 0
\(307\) −1.28232 + 26.9191i −0.00417692 + 0.0876844i −0.999993 0.00369387i \(-0.998824\pi\)
0.995816 + 0.0913783i \(0.0291272\pi\)
\(308\) 0 0
\(309\) −423.060 332.698i −1.36913 1.07669i
\(310\) 0 0
\(311\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(312\) 0 0
\(313\) −152.780 + 334.541i −0.488115 + 1.06882i 0.492037 + 0.870574i \(0.336252\pi\)
−0.980152 + 0.198248i \(0.936475\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −206.657 + 597.095i −0.653977 + 1.88954i
\(317\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 76.3859 314.867i 0.235759 0.971812i
\(325\) 146.803 14.0180i 0.451701 0.0431322i
\(326\) 0 0
\(327\) 318.481 + 204.675i 0.973948 + 0.625918i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −285.636 114.351i −0.862949 0.345473i −0.102392 0.994744i \(-0.532650\pi\)
−0.760557 + 0.649272i \(0.775074\pi\)
\(332\) 0 0
\(333\) −137.722 26.5438i −0.413580 0.0797111i
\(334\) 0 0
\(335\) 0 0
\(336\) 672.000 2.00000
\(337\) 484.600 + 93.3990i 1.43798 + 0.277148i 0.847884 0.530182i \(-0.177877\pi\)
0.590099 + 0.807331i \(0.299089\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1154.20 741.759i −3.36501 2.16256i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.0475819 0.998867i \(-0.515152\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(348\) 0 0
\(349\) 41.8566 + 291.119i 0.119933 + 0.834153i 0.957627 + 0.288012i \(0.0929944\pi\)
−0.837694 + 0.546140i \(0.816097\pi\)
\(350\) 0 0
\(351\) 115.268 + 109.908i 0.328398 + 0.313127i
\(352\) 0 0
\(353\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(360\) 0 0
\(361\) 120.595 + 94.8373i 0.334060 + 0.262707i
\(362\) 0 0
\(363\) −17.2722 + 362.589i −0.0475819 + 0.998867i
\(364\) −165.167 + 286.078i −0.453755 + 0.785927i
\(365\) 0 0
\(366\) 0 0
\(367\) 424.519 + 596.154i 1.15673 + 1.62440i 0.640553 + 0.767914i \(0.278705\pi\)
0.516175 + 0.856483i \(0.327356\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 177.315 + 307.119i 0.476654 + 0.825589i
\(373\) −367.605 + 636.711i −0.985537 + 1.70700i −0.346012 + 0.938230i \(0.612465\pi\)
−0.639525 + 0.768771i \(0.720869\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −361.820 + 508.106i −0.954671 + 1.34065i −0.0145184 + 0.999895i \(0.504622\pi\)
−0.940153 + 0.340753i \(0.889318\pi\)
\(380\) 0 0
\(381\) 435.681 415.421i 1.14352 1.09035i
\(382\) 0 0
\(383\) 0 0 0.327068 0.945001i \(-0.393939\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 495.611 + 571.966i 1.28065 + 1.47795i
\(388\) −90.6144 630.237i −0.233542 1.62432i
\(389\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −146.119 + 42.9043i −0.368057 + 0.108071i −0.460531 0.887644i \(-0.652341\pi\)
0.0924735 + 0.995715i \(0.470523\pi\)
\(398\) 0 0
\(399\) −251.377 550.438i −0.630017 1.37954i
\(400\) 392.771 + 75.7005i 0.981929 + 0.189251i
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) −174.325 −0.432568
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 147.932 + 427.422i 0.361693 + 1.04504i 0.968246 + 0.249999i \(0.0804304\pi\)
−0.606554 + 0.795043i \(0.707448\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 714.362 68.2133i 1.73389 0.165566i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −468.559 540.746i −1.12364 1.29675i
\(418\) 0 0
\(419\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(420\) 0 0
\(421\) 254.548 735.469i 0.604628 1.74696i −0.0583265 0.998298i \(-0.518576\pi\)
0.662954 0.748660i \(-0.269302\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 976.180 627.353i 2.28614 1.46921i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(432\) 216.000 + 374.123i 0.500000 + 0.866025i
\(433\) 604.597 311.691i 1.39630 0.719842i 0.414550 0.910027i \(-0.363939\pi\)
0.981748 + 0.190185i \(0.0609088\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −495.650 + 95.5288i −1.13681 + 0.219103i
\(437\) 0 0
\(438\) 0 0
\(439\) −118.589 205.402i −0.270134 0.467886i 0.698762 0.715354i \(-0.253735\pi\)
−0.968896 + 0.247469i \(0.920401\pi\)
\(440\) 0 0
\(441\) 62.9508 1321.50i 0.142746 2.99660i
\(442\) 0 0
\(443\) 0 0 −0.786053 0.618159i \(-0.787879\pi\)
0.786053 + 0.618159i \(0.212121\pi\)
\(444\) 157.322 101.105i 0.354329 0.227714i
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −648.466 + 618.311i −1.44747 + 1.38016i
\(449\) 0 0 −0.995472 0.0950560i \(-0.969697\pi\)
0.995472 + 0.0950560i \(0.0303030\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −58.2613 55.5520i −0.128612 0.122631i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 31.3595 + 658.316i 0.0686203 + 1.44052i 0.726382 + 0.687291i \(0.241200\pi\)
−0.657762 + 0.753226i \(0.728497\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(462\) 0 0
\(463\) 216.996 + 894.470i 0.468674 + 1.93190i 0.340907 + 0.940097i \(0.389266\pi\)
0.127767 + 0.991804i \(0.459219\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.981929 0.189251i \(-0.939394\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(468\) −212.358 −0.453755
\(469\) −937.023 42.7879i −1.99792 0.0912321i
\(470\) 0 0
\(471\) −875.443 168.728i −1.85869 0.358233i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −84.9184 350.039i −0.178776 0.736923i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(480\) 0 0
\(481\) 4.37410 + 91.8237i 0.00909377 + 0.190902i
\(482\) 0 0
\(483\) 0 0
\(484\) −316.953 365.783i −0.654861 0.755750i
\(485\) 0 0
\(486\) 0 0
\(487\) −746.545 + 587.090i −1.53295 + 1.20552i −0.629363 + 0.777111i \(0.716684\pi\)
−0.903584 + 0.428412i \(0.859073\pi\)
\(488\) 0 0
\(489\) −941.710 89.9224i −1.92579 0.183890i
\(490\) 0 0
\(491\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −453.687 133.215i −0.914692 0.268578i
\(497\) 0 0
\(498\) 0 0
\(499\) 258.752 + 448.171i 0.518541 + 0.898139i 0.999768 + 0.0215432i \(0.00685793\pi\)
−0.481227 + 0.876596i \(0.659809\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −201.306 + 348.672i −0.397053 + 0.687716i
\(508\) −38.1919 + 801.746i −0.0751808 + 1.57824i
\(509\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(510\) 0 0
\(511\) 1518.27 975.730i 2.97117 1.90945i
\(512\) 0 0
\(513\) 225.646 316.876i 0.439856 0.617692i
\(514\) 0 0
\(515\) 0 0
\(516\) −1004.52 95.9204i −1.94675 0.185892i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(522\) 0 0
\(523\) −813.591 419.435i −1.55562 0.801979i −0.556048 0.831150i \(-0.687683\pi\)
−0.999574 + 0.0291707i \(0.990713\pi\)
\(524\) 0 0
\(525\) 247.547 1020.40i 0.471518 1.94362i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −173.019 499.905i −0.327068 0.945001i
\(530\) 0 0
\(531\) 0 0
\(532\) 749.035 + 299.868i 1.40796 + 0.563662i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −807.399 + 237.074i −1.49242 + 0.438214i −0.923312 0.384050i \(-0.874529\pi\)
−0.569107 + 0.822264i \(0.692711\pi\)
\(542\) 0 0
\(543\) 34.7401 + 100.375i 0.0639782 + 0.184853i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 195.738 806.844i 0.357840 1.47504i −0.453919 0.891043i \(-0.649975\pi\)
0.811759 0.583992i \(-0.198510\pi\)
\(548\) 0 0
\(549\) 663.039 + 341.820i 1.20772 + 0.622624i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −2053.05 + 821.917i −3.71257 + 1.48629i
\(554\) 0 0
\(555\) 0 0
\(556\) 949.693 + 90.6847i 1.70808 + 0.163102i
\(557\) 0 0 0.723734 0.690079i \(-0.242424\pi\)
−0.723734 + 0.690079i \(0.757576\pi\)
\(558\) 0 0
\(559\) 287.730 404.061i 0.514723 0.722828i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1007.94 519.629i 1.77767 0.916453i
\(568\) 0 0
\(569\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(570\) 0 0
\(571\) 471.875 + 662.655i 0.826400 + 1.16052i 0.984894 + 0.173157i \(0.0553968\pi\)
−0.158494 + 0.987360i \(0.550664\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −552.668 162.278i −0.959493 0.281733i
\(577\) −893.023 702.281i −1.54770 1.21712i −0.882350 0.470593i \(-0.844040\pi\)
−0.665350 0.746532i \(-0.731718\pi\)
\(578\) 0 0
\(579\) −155.667 + 1082.69i −0.268855 + 1.86993i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(588\) 1155.17 + 1333.14i 1.96458 + 2.26725i
\(589\) 60.5953 + 421.449i 0.102878 + 0.715534i
\(590\) 0 0
\(591\) 0 0
\(592\) −58.7855 + 242.317i −0.0992998 + 0.409319i
\(593\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 172.192 + 709.787i 0.288429 + 1.18892i
\(598\) 0 0
\(599\) 0 0 −0.928368 0.371662i \(-0.878788\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(600\) 0 0
\(601\) 909.585 + 175.308i 1.51345 + 0.291694i 0.877327 0.479892i \(-0.159324\pi\)
0.636125 + 0.771586i \(0.280536\pi\)
\(602\) 0 0
\(603\) −277.365 535.423i −0.459975 0.887932i
\(604\) 107.335 0.177706
\(605\) 0 0
\(606\) 0 0
\(607\) −583.793 233.715i −0.961767 0.385034i −0.162968 0.986631i \(-0.552107\pi\)
−0.798799 + 0.601598i \(0.794531\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −582.654 + 55.6367i −0.950496 + 0.0907614i −0.558772 0.829321i \(-0.688727\pi\)
−0.391724 + 0.920083i \(0.628121\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(618\) 0 0
\(619\) −894.133 852.554i −1.44448 1.37731i −0.766559 0.642174i \(-0.778033\pi\)
−0.677921 0.735135i \(-0.737119\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 204.920 195.391i 0.328398 0.313127i
\(625\) 259.634 568.520i 0.415415 0.909632i
\(626\) 0 0
\(627\) 0 0
\(628\) 1000.03 642.681i 1.59241 1.02338i
\(629\) 0 0
\(630\) 0 0
\(631\) 59.5019 1249.10i 0.0942978 1.97955i −0.0873006 0.996182i \(-0.527824\pi\)
0.181598 0.983373i \(-0.441873\pi\)
\(632\) 0 0
\(633\) 221.395 + 383.467i 0.349755 + 0.605793i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −851.456 + 164.105i −1.33667 + 0.257621i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 0 0
\(643\) 1227.26 + 360.356i 1.90864 + 0.560429i 0.983531 + 0.180739i \(0.0578488\pi\)
0.925114 + 0.379690i \(0.123969\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −405.959 + 1172.94i −0.623593 + 1.80175i
\(652\) 991.468 779.699i 1.52066 1.19586i
\(653\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 1031.23 + 531.638i 1.56961 + 0.809190i
\(658\) 0 0
\(659\) 0 0 0.235759 0.971812i \(-0.424242\pi\)
−0.235759 + 0.971812i \(0.575758\pi\)
\(660\) 0 0
\(661\) −394.555 + 455.341i −0.596906 + 0.688866i −0.971151 0.238463i \(-0.923356\pi\)
0.374245 + 0.927330i \(0.377902\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −1299.26 −1.94210
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 392.715 + 859.927i 0.583529 + 1.27775i 0.939274 + 0.343168i \(0.111500\pi\)
−0.355745 + 0.934583i \(0.615773\pi\)
\(674\) 0 0
\(675\) 647.658 190.169i 0.959493 0.281733i
\(676\) −126.559 521.684i −0.187218 0.771721i
\(677\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(678\) 0 0
\(679\) 1459.36 1684.20i 2.14929 2.48041i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.888835 0.458227i \(-0.848485\pi\)
0.888835 + 0.458227i \(0.151515\pi\)
\(684\) 73.8153 + 513.397i 0.107917 + 0.750580i
\(685\) 0 0
\(686\) 0 0
\(687\) 647.924 259.390i 0.943121 0.377569i
\(688\) 1057.60 831.706i 1.53721 1.20888i
\(689\) 0 0
\(690\) 0 0
\(691\) −965.108 + 920.229i −1.39668 + 1.33173i −0.517153 + 0.855893i \(0.673008\pi\)
−0.879531 + 0.475842i \(0.842144\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 700.000 + 1212.44i 1.00000 + 1.73205i
\(701\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(702\) 0 0
\(703\) 220.473 42.4927i 0.313617 0.0604448i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 27.7178 581.868i 0.0390942 0.820689i −0.891141 0.453726i \(-0.850095\pi\)
0.930236 0.366963i \(-0.119602\pi\)
\(710\) 0 0
\(711\) −1117.50 878.808i −1.57172 1.23602i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.786053 0.618159i \(-0.212121\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(720\) 0 0
\(721\) 1817.76 + 1733.23i 2.52116 + 2.40392i
\(722\) 0 0
\(723\) 184.435 + 1282.78i 0.255098 + 1.77424i
\(724\) −125.879 64.8952i −0.173866 0.0896342i
\(725\) 0 0
\(726\) 0 0
\(727\) −466.979 + 44.5911i −0.642337 + 0.0613358i −0.411141 0.911572i \(-0.634870\pi\)
−0.231196 + 0.972907i \(0.574264\pi\)
\(728\) 0 0
\(729\) 613.274 + 394.127i 0.841254 + 0.540641i
\(730\) 0 0
\(731\) 0 0
\(732\) −954.329 + 280.216i −1.30373 + 0.382809i
\(733\) −1357.76 543.565i −1.85233 0.741562i −0.951745 0.306889i \(-0.900712\pi\)
−0.900588 0.434674i \(-0.856864\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 438.558 + 84.5251i 0.593448 + 0.114378i 0.477128 0.878834i \(-0.341678\pi\)
0.116320 + 0.993212i \(0.462890\pi\)
\(740\) 0 0
\(741\) −236.701 94.7608i −0.319435 0.127882i
\(742\) 0 0
\(743\) 0 0 −0.235759 0.971812i \(-0.575758\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 151.218 + 1051.75i 0.201356 + 1.40046i 0.800266 + 0.599645i \(0.204691\pi\)
−0.598910 + 0.800816i \(0.704399\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −494.527 + 1428.84i −0.654136 + 1.89000i
\(757\) 1416.51 + 135.260i 1.87122 + 0.178680i 0.968075 0.250660i \(-0.0806478\pi\)
0.903143 + 0.429340i \(0.141254\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(762\) 0 0
\(763\) −1388.72 1092.10i −1.82008 1.43133i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 682.626 351.918i 0.888835 0.458227i
\(769\) 21.8885 + 30.7381i 0.0284635 + 0.0399715i 0.828563 0.559897i \(-0.189159\pi\)
−0.800099 + 0.599868i \(0.795220\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −845.972 1188.00i −1.09582 1.53886i
\(773\) 0 0 0.888835 0.458227i \(-0.151515\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(774\) 0 0
\(775\) −369.407 + 639.831i −0.476654 + 0.825589i
\(776\) 0 0
\(777\) 628.019 + 184.403i 0.808261 + 0.237327i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −2341.35 223.572i −2.98641 0.285168i
\(785\) 0 0
\(786\) 0 0
\(787\) 1317.28 527.358i 1.67380 0.670087i 0.676028 0.736876i \(-0.263700\pi\)
0.997767 + 0.0667893i \(0.0212755\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 115.268 475.141i 0.145357 0.599169i
\(794\) 0 0
\(795\) 0 0
\(796\) −819.240 526.494i −1.02920 0.661424i
\(797\) 0 0 −0.327068 0.945001i \(-0.606061\pi\)
0.327068 + 0.945001i \(0.393939\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 760.297 + 261.467i 0.945643 + 0.325208i
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(810\) 0 0
\(811\) 352.914 + 1019.68i 0.435159 + 1.25731i 0.923143 + 0.384457i \(0.125611\pi\)
−0.487984 + 0.872853i \(0.662268\pi\)
\(812\) 0 0
\(813\) 647.151 746.852i 0.796003 0.918637i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −1076.87 555.167i −1.31808 0.679519i
\(818\) 0 0
\(819\) −486.726 561.712i −0.594293 0.685851i
\(820\) 0 0
\(821\) 0 0 0.928368 0.371662i \(-0.121212\pi\)
−0.928368 + 0.371662i \(0.878788\pi\)
\(822\) 0 0
\(823\) −417.834 + 1207.25i −0.507696 + 1.46689i 0.342041 + 0.939685i \(0.388882\pi\)
−0.849737 + 0.527206i \(0.823239\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.580057 0.814576i \(-0.303030\pi\)
−0.580057 + 0.814576i \(0.696970\pi\)
\(828\) 0 0
\(829\) 855.918 550.065i 1.03247 0.663528i 0.0893571 0.996000i \(-0.471519\pi\)
0.943113 + 0.332471i \(0.107882\pi\)
\(830\) 0 0
\(831\) −252.113 74.0270i −0.303385 0.0890818i
\(832\) −17.9633 + 377.097i −0.0215906 + 0.453241i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −783.499 + 151.007i −0.936080 + 0.180415i
\(838\) 0 0
\(839\) 0 0 −0.580057 0.814576i \(-0.696970\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(840\) 0 0
\(841\) −420.500 728.327i −0.500000 0.866025i
\(842\) 0 0
\(843\) 0 0
\(844\) −566.472 166.331i −0.671175 0.197075i
\(845\) 0 0
\(846\) 0 0
\(847\) 241.081 1676.76i 0.284630 1.97964i
\(848\) 0 0
\(849\) 664.422 1454.88i 0.782593 1.71364i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 253.494 199.350i 0.297180 0.233705i −0.458424 0.888733i \(-0.651586\pi\)
0.755604 + 0.655029i \(0.227344\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(858\) 0 0
\(859\) 49.3101 + 1035.15i 0.0574041 + 1.20506i 0.825378 + 0.564580i \(0.190962\pi\)
−0.767974 + 0.640481i \(0.778735\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −804.895 322.231i −0.928368 0.371662i
\(868\) −687.488 1505.39i −0.792037 1.73432i
\(869\) 0 0
\(870\) 0 0
\(871\) −298.178 + 259.402i −0.342340 + 0.297821i
\(872\) 0 0
\(873\) 1406.73 + 271.124i 1.61137 + 0.310566i
\(874\) 0 0
\(875\) 0 0
\(876\) −1484.28 + 435.824i −1.69438 + 0.497516i
\(877\) 413.476 + 1704.37i 0.471467 + 1.94341i 0.250030 + 0.968238i \(0.419559\pi\)
0.221437 + 0.975175i \(0.428925\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 0.995472 0.0950560i \(-0.0303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(882\) 0 0
\(883\) −54.0331 1134.29i −0.0611926 1.28459i −0.795575 0.605855i \(-0.792831\pi\)
0.734382 0.678736i \(-0.237472\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 −0.723734 0.690079i \(-0.757576\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(888\) 0 0
\(889\) −2208.25 + 1736.59i −2.48397 + 1.95342i
\(890\) 0 0
\(891\) 0 0
\(892\) 1253.76 1195.46i 1.40556 1.34020i
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −450.000 + 779.423i −0.500000 + 0.866025i
\(901\) 0 0
\(902\) 0 0
\(903\) −2048.66 2876.94i −2.26873 3.18598i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −633.585 + 326.636i −0.698550 + 0.360127i −0.770640 0.637271i \(-0.780063\pi\)
0.0720903 + 0.997398i \(0.477033\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(912\) −543.609 427.499i −0.596063 0.468749i
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −386.567 + 846.464i −0.422016 + 0.924087i
\(917\) 0 0
\(918\) 0 0
\(919\) 122.381 353.597i 0.133168 0.384763i −0.858628 0.512600i \(-0.828682\pi\)
0.991795 + 0.127837i \(0.0408036\pi\)
\(920\) 0 0
\(921\) 75.0575 30.0485i 0.0814957 0.0326259i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 346.293 + 178.526i 0.374370 + 0.193001i
\(926\) 0 0
\(927\) −380.662 + 1569.11i −0.410639 + 1.69268i
\(928\) 0 0
\(929\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(930\) 0 0
\(931\) 692.706 + 2001.44i 0.744045 + 2.14978i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 50.8835 0.0543047 0.0271524 0.999631i \(-0.491356\pi\)
0.0271524 + 0.999631i \(0.491356\pi\)
\(938\) 0 0
\(939\) 1103.33 1.17501
\(940\) 0 0
\(941\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(948\) 1886.95 180.182i 1.99046 0.190066i
\(949\) 179.278 738.993i 0.188912 0.778707i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −50.8406 + 71.3956i −0.0529038 + 0.0742930i
\(962\) 0 0
\(963\) 0 0
\(964\) −1358.27 1068.15i −1.40899 1.10804i
\(965\) 0 0
\(966\) 0 0
\(967\) 924.605 1601.46i 0.956158 1.65611i 0.224464 0.974482i \(-0.427937\pi\)
0.731695 0.681633i \(-0.238730\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.981929 0.189251i \(-0.0606061\pi\)
−0.981929 + 0.189251i \(0.939394\pi\)
\(972\) −954.435 + 183.952i −0.981929 + 0.189251i
\(973\) 1936.84 + 2719.90i 1.99058 + 2.79538i
\(974\) 0 0
\(975\) −221.206 383.140i −0.226878 0.392964i
\(976\) 663.079 1148.49i 0.679384 1.17673i
\(977\) 0 0 0.0475819 0.998867i \(-0.484848\pi\)
−0.0475819 + 0.998867i \(0.515152\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 161.632 1124.18i 0.164763 1.14595i
\(982\) 0 0
\(983\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 315.602 126.348i 0.319435 0.127882i
\(989\) 0 0
\(990\) 0 0
\(991\) 73.1650 + 508.874i 0.0738295 + 0.513495i 0.992858 + 0.119304i \(0.0380663\pi\)
−0.919028 + 0.394192i \(0.871025\pi\)
\(992\) 0 0
\(993\) 43.9194 + 921.981i 0.0442290 + 0.928480i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1139.05 732.020i −1.14247 0.734223i −0.174347 0.984684i \(-0.555781\pi\)
−0.968127 + 0.250461i \(0.919418\pi\)
\(998\) 0 0
\(999\) 99.2005 + 408.910i 0.0992998 + 0.409319i
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 201.3.o.a.83.1 20
3.2 odd 2 CM 201.3.o.a.83.1 20
67.21 even 33 inner 201.3.o.a.155.1 yes 20
201.155 odd 66 inner 201.3.o.a.155.1 yes 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.3.o.a.83.1 20 1.1 even 1 trivial
201.3.o.a.83.1 20 3.2 odd 2 CM
201.3.o.a.155.1 yes 20 67.21 even 33 inner
201.3.o.a.155.1 yes 20 201.155 odd 66 inner