Properties

Label 1900.3.e.f.1101.11
Level $1900$
Weight $3$
Character 1900.1101
Analytic conductor $51.771$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1900,3,Mod(1101,1900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1900.1101");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1900.e (of order \(2\), degree \(1\), 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: \(51.7712502285\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 62x^{10} + 1445x^{8} + 15924x^{6} + 83244x^{4} + 170640x^{2} + 55600 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{12}\cdot 5 \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1101.11
Root \(3.53755i\) of defining polynomial
Character \(\chi\) \(=\) 1900.1101
Dual form 1900.3.e.f.1101.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.53755i q^{3} -0.468611 q^{7} -3.51429 q^{9} +O(q^{10})\) \(q+3.53755i q^{3} -0.468611 q^{7} -3.51429 q^{9} -14.1082 q^{11} +11.0914i q^{13} +22.0318 q^{17} +(16.8411 + 8.79644i) q^{19} -1.65774i q^{21} +41.1864 q^{23} +19.4060i q^{27} +46.7187i q^{29} -33.9265i q^{31} -49.9085i q^{33} -62.6340i q^{37} -39.2365 q^{39} +23.5359i q^{41} +32.8769 q^{43} -43.2839 q^{47} -48.7804 q^{49} +77.9388i q^{51} +99.9844i q^{53} +(-31.1179 + 59.5763i) q^{57} +66.7119i q^{59} -36.0483 q^{61} +1.64684 q^{63} +93.5215i q^{67} +145.699i q^{69} -124.406i q^{71} -41.3341 q^{73} +6.61125 q^{77} -27.2511i q^{79} -100.278 q^{81} +32.9101 q^{83} -165.270 q^{87} -86.3670i q^{89} -5.19755i q^{91} +120.017 q^{93} +20.8071i q^{97} +49.5803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 12 q^{7} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 12 q^{7} - 16 q^{9} - 32 q^{11} + 12 q^{17} + 24 q^{19} - 4 q^{23} + 124 q^{39} + 176 q^{43} + 72 q^{47} - 24 q^{49} - 140 q^{57} + 152 q^{61} - 48 q^{63} + 148 q^{73} - 376 q^{77} - 468 q^{81} + 208 q^{83} + 84 q^{87} + 184 q^{93} + 392 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) 3.53755i 1.17918i 0.807701 + 0.589592i \(0.200712\pi\)
−0.807701 + 0.589592i \(0.799288\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.468611 −0.0669444 −0.0334722 0.999440i \(-0.510657\pi\)
−0.0334722 + 0.999440i \(0.510657\pi\)
\(8\) 0 0
\(9\) −3.51429 −0.390477
\(10\) 0 0
\(11\) −14.1082 −1.28256 −0.641281 0.767306i \(-0.721597\pi\)
−0.641281 + 0.767306i \(0.721597\pi\)
\(12\) 0 0
\(13\) 11.0914i 0.853185i 0.904444 + 0.426593i \(0.140286\pi\)
−0.904444 + 0.426593i \(0.859714\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 22.0318 1.29599 0.647995 0.761644i \(-0.275608\pi\)
0.647995 + 0.761644i \(0.275608\pi\)
\(18\) 0 0
\(19\) 16.8411 + 8.79644i 0.886374 + 0.462971i
\(20\) 0 0
\(21\) 1.65774i 0.0789398i
\(22\) 0 0
\(23\) 41.1864 1.79071 0.895357 0.445348i \(-0.146920\pi\)
0.895357 + 0.445348i \(0.146920\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 19.4060i 0.718740i
\(28\) 0 0
\(29\) 46.7187i 1.61099i 0.592604 + 0.805494i \(0.298100\pi\)
−0.592604 + 0.805494i \(0.701900\pi\)
\(30\) 0 0
\(31\) 33.9265i 1.09440i −0.837001 0.547201i \(-0.815693\pi\)
0.837001 0.547201i \(-0.184307\pi\)
\(32\) 0 0
\(33\) 49.9085i 1.51238i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 62.6340i 1.69281i −0.532540 0.846405i \(-0.678762\pi\)
0.532540 0.846405i \(-0.321238\pi\)
\(38\) 0 0
\(39\) −39.2365 −1.00606
\(40\) 0 0
\(41\) 23.5359i 0.574046i 0.957924 + 0.287023i \(0.0926656\pi\)
−0.957924 + 0.287023i \(0.907334\pi\)
\(42\) 0 0
\(43\) 32.8769 0.764579 0.382289 0.924043i \(-0.375136\pi\)
0.382289 + 0.924043i \(0.375136\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −43.2839 −0.920935 −0.460468 0.887677i \(-0.652318\pi\)
−0.460468 + 0.887677i \(0.652318\pi\)
\(48\) 0 0
\(49\) −48.7804 −0.995518
\(50\) 0 0
\(51\) 77.9388i 1.52821i
\(52\) 0 0
\(53\) 99.9844i 1.88650i 0.332086 + 0.943249i \(0.392248\pi\)
−0.332086 + 0.943249i \(0.607752\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −31.1179 + 59.5763i −0.545928 + 1.04520i
\(58\) 0 0
\(59\) 66.7119i 1.13071i 0.824848 + 0.565355i \(0.191261\pi\)
−0.824848 + 0.565355i \(0.808739\pi\)
\(60\) 0 0
\(61\) −36.0483 −0.590956 −0.295478 0.955350i \(-0.595479\pi\)
−0.295478 + 0.955350i \(0.595479\pi\)
\(62\) 0 0
\(63\) 1.64684 0.0261402
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 93.5215i 1.39584i 0.716174 + 0.697921i \(0.245892\pi\)
−0.716174 + 0.697921i \(0.754108\pi\)
\(68\) 0 0
\(69\) 145.699i 2.11158i
\(70\) 0 0
\(71\) 124.406i 1.75220i −0.482128 0.876101i \(-0.660136\pi\)
0.482128 0.876101i \(-0.339864\pi\)
\(72\) 0 0
\(73\) −41.3341 −0.566220 −0.283110 0.959087i \(-0.591366\pi\)
−0.283110 + 0.959087i \(0.591366\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.61125 0.0858604
\(78\) 0 0
\(79\) 27.2511i 0.344950i −0.985014 0.172475i \(-0.944824\pi\)
0.985014 0.172475i \(-0.0551764\pi\)
\(80\) 0 0
\(81\) −100.278 −1.23800
\(82\) 0 0
\(83\) 32.9101 0.396507 0.198253 0.980151i \(-0.436473\pi\)
0.198253 + 0.980151i \(0.436473\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −165.270 −1.89965
\(88\) 0 0
\(89\) 86.3670i 0.970416i −0.874399 0.485208i \(-0.838744\pi\)
0.874399 0.485208i \(-0.161256\pi\)
\(90\) 0 0
\(91\) 5.19755i 0.0571160i
\(92\) 0 0
\(93\) 120.017 1.29050
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 20.8071i 0.214506i 0.994232 + 0.107253i \(0.0342054\pi\)
−0.994232 + 0.107253i \(0.965795\pi\)
\(98\) 0 0
\(99\) 49.5803 0.500811
\(100\) 0 0
\(101\) −118.267 −1.17096 −0.585482 0.810685i \(-0.699095\pi\)
−0.585482 + 0.810685i \(0.699095\pi\)
\(102\) 0 0
\(103\) 107.875i 1.04733i 0.851924 + 0.523666i \(0.175436\pi\)
−0.851924 + 0.523666i \(0.824564\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.6498i 0.155606i −0.996969 0.0778029i \(-0.975210\pi\)
0.996969 0.0778029i \(-0.0247905\pi\)
\(108\) 0 0
\(109\) 34.4048i 0.315640i −0.987468 0.157820i \(-0.949553\pi\)
0.987468 0.157820i \(-0.0504466\pi\)
\(110\) 0 0
\(111\) 221.571 1.99614
\(112\) 0 0
\(113\) 34.2888i 0.303441i −0.988423 0.151720i \(-0.951519\pi\)
0.988423 0.151720i \(-0.0484813\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 38.9784i 0.333149i
\(118\) 0 0
\(119\) −10.3244 −0.0867593
\(120\) 0 0
\(121\) 78.0409 0.644966
\(122\) 0 0
\(123\) −83.2594 −0.676906
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 245.621i 1.93402i 0.254733 + 0.967012i \(0.418013\pi\)
−0.254733 + 0.967012i \(0.581987\pi\)
\(128\) 0 0
\(129\) 116.304i 0.901580i
\(130\) 0 0
\(131\) 196.826 1.50249 0.751245 0.660024i \(-0.229454\pi\)
0.751245 + 0.660024i \(0.229454\pi\)
\(132\) 0 0
\(133\) −7.89192 4.12211i −0.0593377 0.0309933i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −249.410 −1.82051 −0.910255 0.414049i \(-0.864114\pi\)
−0.910255 + 0.414049i \(0.864114\pi\)
\(138\) 0 0
\(139\) 116.069 0.835030 0.417515 0.908670i \(-0.362901\pi\)
0.417515 + 0.908670i \(0.362901\pi\)
\(140\) 0 0
\(141\) 153.119i 1.08595i
\(142\) 0 0
\(143\) 156.480i 1.09426i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 172.563i 1.17390i
\(148\) 0 0
\(149\) −220.978 −1.48308 −0.741538 0.670911i \(-0.765903\pi\)
−0.741538 + 0.670911i \(0.765903\pi\)
\(150\) 0 0
\(151\) 237.670i 1.57397i 0.616972 + 0.786985i \(0.288359\pi\)
−0.616972 + 0.786985i \(0.711641\pi\)
\(152\) 0 0
\(153\) −77.4263 −0.506054
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −35.3231 −0.224988 −0.112494 0.993652i \(-0.535884\pi\)
−0.112494 + 0.993652i \(0.535884\pi\)
\(158\) 0 0
\(159\) −353.700 −2.22453
\(160\) 0 0
\(161\) −19.3004 −0.119878
\(162\) 0 0
\(163\) −71.4216 −0.438169 −0.219085 0.975706i \(-0.570307\pi\)
−0.219085 + 0.975706i \(0.570307\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 185.054i 1.10811i 0.832481 + 0.554054i \(0.186920\pi\)
−0.832481 + 0.554054i \(0.813080\pi\)
\(168\) 0 0
\(169\) 45.9807 0.272075
\(170\) 0 0
\(171\) −59.1845 30.9133i −0.346108 0.180779i
\(172\) 0 0
\(173\) 231.572i 1.33857i −0.743006 0.669284i \(-0.766601\pi\)
0.743006 0.669284i \(-0.233399\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −235.997 −1.33332
\(178\) 0 0
\(179\) 165.841i 0.926487i −0.886231 0.463244i \(-0.846685\pi\)
0.886231 0.463244i \(-0.153315\pi\)
\(180\) 0 0
\(181\) 25.0838i 0.138585i −0.997596 0.0692923i \(-0.977926\pi\)
0.997596 0.0692923i \(-0.0220741\pi\)
\(182\) 0 0
\(183\) 127.523i 0.696846i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −310.829 −1.66219
\(188\) 0 0
\(189\) 9.09386i 0.0481156i
\(190\) 0 0
\(191\) −52.0646 −0.272590 −0.136295 0.990668i \(-0.543519\pi\)
−0.136295 + 0.990668i \(0.543519\pi\)
\(192\) 0 0
\(193\) 70.3184i 0.364344i −0.983267 0.182172i \(-0.941687\pi\)
0.983267 0.182172i \(-0.0583128\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 131.361 0.666809 0.333404 0.942784i \(-0.391803\pi\)
0.333404 + 0.942784i \(0.391803\pi\)
\(198\) 0 0
\(199\) −120.966 −0.607870 −0.303935 0.952693i \(-0.598301\pi\)
−0.303935 + 0.952693i \(0.598301\pi\)
\(200\) 0 0
\(201\) −330.837 −1.64596
\(202\) 0 0
\(203\) 21.8929i 0.107847i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −144.741 −0.699233
\(208\) 0 0
\(209\) −237.597 124.102i −1.13683 0.593789i
\(210\) 0 0
\(211\) 381.578i 1.80843i 0.427082 + 0.904213i \(0.359541\pi\)
−0.427082 + 0.904213i \(0.640459\pi\)
\(212\) 0 0
\(213\) 440.094 2.06617
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 15.8983i 0.0732641i
\(218\) 0 0
\(219\) 146.222i 0.667678i
\(220\) 0 0
\(221\) 244.364i 1.10572i
\(222\) 0 0
\(223\) 155.025i 0.695181i 0.937646 + 0.347591i \(0.113000\pi\)
−0.937646 + 0.347591i \(0.887000\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 237.583i 1.04662i 0.852142 + 0.523310i \(0.175303\pi\)
−0.852142 + 0.523310i \(0.824697\pi\)
\(228\) 0 0
\(229\) −275.640 −1.20367 −0.601834 0.798621i \(-0.705563\pi\)
−0.601834 + 0.798621i \(0.705563\pi\)
\(230\) 0 0
\(231\) 23.3877i 0.101245i
\(232\) 0 0
\(233\) 271.591 1.16562 0.582812 0.812607i \(-0.301952\pi\)
0.582812 + 0.812607i \(0.301952\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 96.4021 0.406760
\(238\) 0 0
\(239\) −236.246 −0.988476 −0.494238 0.869327i \(-0.664553\pi\)
−0.494238 + 0.869327i \(0.664553\pi\)
\(240\) 0 0
\(241\) 346.159i 1.43634i −0.695866 0.718171i \(-0.744979\pi\)
0.695866 0.718171i \(-0.255021\pi\)
\(242\) 0 0
\(243\) 180.086i 0.741096i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −97.5649 + 186.791i −0.395000 + 0.756241i
\(248\) 0 0
\(249\) 116.421i 0.467555i
\(250\) 0 0
\(251\) 222.337 0.885805 0.442903 0.896570i \(-0.353949\pi\)
0.442903 + 0.896570i \(0.353949\pi\)
\(252\) 0 0
\(253\) −581.066 −2.29670
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 143.232i 0.557324i −0.960389 0.278662i \(-0.910109\pi\)
0.960389 0.278662i \(-0.0898909\pi\)
\(258\) 0 0
\(259\) 29.3510i 0.113324i
\(260\) 0 0
\(261\) 164.183i 0.629054i
\(262\) 0 0
\(263\) 240.308 0.913718 0.456859 0.889539i \(-0.348974\pi\)
0.456859 + 0.889539i \(0.348974\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 305.528 1.14430
\(268\) 0 0
\(269\) 261.289i 0.971335i 0.874144 + 0.485668i \(0.161423\pi\)
−0.874144 + 0.485668i \(0.838577\pi\)
\(270\) 0 0
\(271\) −234.829 −0.866527 −0.433263 0.901267i \(-0.642638\pi\)
−0.433263 + 0.901267i \(0.642638\pi\)
\(272\) 0 0
\(273\) 18.3866 0.0673503
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 28.6370 0.103383 0.0516913 0.998663i \(-0.483539\pi\)
0.0516913 + 0.998663i \(0.483539\pi\)
\(278\) 0 0
\(279\) 119.227i 0.427339i
\(280\) 0 0
\(281\) 35.2442i 0.125424i −0.998032 0.0627121i \(-0.980025\pi\)
0.998032 0.0627121i \(-0.0199750\pi\)
\(282\) 0 0
\(283\) 159.486 0.563554 0.281777 0.959480i \(-0.409076\pi\)
0.281777 + 0.959480i \(0.409076\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 11.0292i 0.0384291i
\(288\) 0 0
\(289\) 196.402 0.679591
\(290\) 0 0
\(291\) −73.6061 −0.252942
\(292\) 0 0
\(293\) 79.8129i 0.272399i −0.990681 0.136199i \(-0.956511\pi\)
0.990681 0.136199i \(-0.0434888\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 273.783i 0.921829i
\(298\) 0 0
\(299\) 456.816i 1.52781i
\(300\) 0 0
\(301\) −15.4065 −0.0511843
\(302\) 0 0
\(303\) 418.377i 1.38078i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 135.726i 0.442105i −0.975262 0.221052i \(-0.929051\pi\)
0.975262 0.221052i \(-0.0709492\pi\)
\(308\) 0 0
\(309\) −381.614 −1.23500
\(310\) 0 0
\(311\) 131.701 0.423475 0.211737 0.977327i \(-0.432088\pi\)
0.211737 + 0.977327i \(0.432088\pi\)
\(312\) 0 0
\(313\) −570.037 −1.82120 −0.910602 0.413285i \(-0.864381\pi\)
−0.910602 + 0.413285i \(0.864381\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 334.101i 1.05395i −0.849882 0.526974i \(-0.823327\pi\)
0.849882 0.526974i \(-0.176673\pi\)
\(318\) 0 0
\(319\) 659.116i 2.06619i
\(320\) 0 0
\(321\) 58.8997 0.183488
\(322\) 0 0
\(323\) 371.040 + 193.802i 1.14873 + 0.600006i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 121.709 0.372198
\(328\) 0 0
\(329\) 20.2833 0.0616514
\(330\) 0 0
\(331\) 63.3605i 0.191421i 0.995409 + 0.0957107i \(0.0305124\pi\)
−0.995409 + 0.0957107i \(0.969488\pi\)
\(332\) 0 0
\(333\) 220.114i 0.661003i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 153.496i 0.455479i 0.973722 + 0.227739i \(0.0731335\pi\)
−0.973722 + 0.227739i \(0.926867\pi\)
\(338\) 0 0
\(339\) 121.298 0.357812
\(340\) 0 0
\(341\) 478.641i 1.40364i
\(342\) 0 0
\(343\) 45.8210 0.133589
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 272.066 0.784052 0.392026 0.919954i \(-0.371774\pi\)
0.392026 + 0.919954i \(0.371774\pi\)
\(348\) 0 0
\(349\) 187.833 0.538205 0.269102 0.963112i \(-0.413273\pi\)
0.269102 + 0.963112i \(0.413273\pi\)
\(350\) 0 0
\(351\) −215.240 −0.613219
\(352\) 0 0
\(353\) 30.8460 0.0873825 0.0436913 0.999045i \(-0.486088\pi\)
0.0436913 + 0.999045i \(0.486088\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 36.5230i 0.102305i
\(358\) 0 0
\(359\) 513.758 1.43108 0.715541 0.698571i \(-0.246180\pi\)
0.715541 + 0.698571i \(0.246180\pi\)
\(360\) 0 0
\(361\) 206.245 + 296.284i 0.571316 + 0.820730i
\(362\) 0 0
\(363\) 276.074i 0.760535i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 22.6982 0.0618481 0.0309240 0.999522i \(-0.490155\pi\)
0.0309240 + 0.999522i \(0.490155\pi\)
\(368\) 0 0
\(369\) 82.7119i 0.224152i
\(370\) 0 0
\(371\) 46.8538i 0.126290i
\(372\) 0 0
\(373\) 108.632i 0.291238i −0.989341 0.145619i \(-0.953483\pi\)
0.989341 0.145619i \(-0.0465174\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −518.176 −1.37447
\(378\) 0 0
\(379\) 203.467i 0.536852i 0.963300 + 0.268426i \(0.0865035\pi\)
−0.963300 + 0.268426i \(0.913497\pi\)
\(380\) 0 0
\(381\) −868.897 −2.28057
\(382\) 0 0
\(383\) 38.4623i 0.100424i −0.998739 0.0502119i \(-0.984010\pi\)
0.998739 0.0502119i \(-0.0159897\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −115.539 −0.298550
\(388\) 0 0
\(389\) 521.954 1.34179 0.670893 0.741555i \(-0.265911\pi\)
0.670893 + 0.741555i \(0.265911\pi\)
\(390\) 0 0
\(391\) 907.413 2.32075
\(392\) 0 0
\(393\) 696.283i 1.77171i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −369.352 −0.930357 −0.465179 0.885217i \(-0.654010\pi\)
−0.465179 + 0.885217i \(0.654010\pi\)
\(398\) 0 0
\(399\) 14.5822 27.9181i 0.0365468 0.0699702i
\(400\) 0 0
\(401\) 128.575i 0.320636i −0.987065 0.160318i \(-0.948748\pi\)
0.987065 0.160318i \(-0.0512520\pi\)
\(402\) 0 0
\(403\) 376.292 0.933727
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 883.652i 2.17113i
\(408\) 0 0
\(409\) 611.222i 1.49443i 0.664583 + 0.747215i \(0.268609\pi\)
−0.664583 + 0.747215i \(0.731391\pi\)
\(410\) 0 0
\(411\) 882.301i 2.14672i
\(412\) 0 0
\(413\) 31.2619i 0.0756947i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 410.601i 0.984655i
\(418\) 0 0
\(419\) −218.656 −0.521853 −0.260927 0.965359i \(-0.584028\pi\)
−0.260927 + 0.965359i \(0.584028\pi\)
\(420\) 0 0
\(421\) 534.615i 1.26987i −0.772566 0.634935i \(-0.781027\pi\)
0.772566 0.634935i \(-0.218973\pi\)
\(422\) 0 0
\(423\) 152.112 0.359604
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 16.8926 0.0395612
\(428\) 0 0
\(429\) 553.555 1.29034
\(430\) 0 0
\(431\) 81.6513i 0.189446i −0.995504 0.0947231i \(-0.969803\pi\)
0.995504 0.0947231i \(-0.0301966\pi\)
\(432\) 0 0
\(433\) 90.7988i 0.209697i 0.994488 + 0.104848i \(0.0334357\pi\)
−0.994488 + 0.104848i \(0.966564\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 693.625 + 362.294i 1.58724 + 0.829048i
\(438\) 0 0
\(439\) 89.4005i 0.203646i −0.994803 0.101823i \(-0.967533\pi\)
0.994803 0.101823i \(-0.0324675\pi\)
\(440\) 0 0
\(441\) 171.429 0.388727
\(442\) 0 0
\(443\) −127.590 −0.288013 −0.144007 0.989577i \(-0.545999\pi\)
−0.144007 + 0.989577i \(0.545999\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 781.723i 1.74882i
\(448\) 0 0
\(449\) 441.576i 0.983465i −0.870746 0.491733i \(-0.836364\pi\)
0.870746 0.491733i \(-0.163636\pi\)
\(450\) 0 0
\(451\) 332.049i 0.736250i
\(452\) 0 0
\(453\) −840.769 −1.85600
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −166.817 −0.365027 −0.182513 0.983203i \(-0.558423\pi\)
−0.182513 + 0.983203i \(0.558423\pi\)
\(458\) 0 0
\(459\) 427.550i 0.931481i
\(460\) 0 0
\(461\) −377.705 −0.819317 −0.409659 0.912239i \(-0.634352\pi\)
−0.409659 + 0.912239i \(0.634352\pi\)
\(462\) 0 0
\(463\) 161.036 0.347810 0.173905 0.984762i \(-0.444361\pi\)
0.173905 + 0.984762i \(0.444361\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 63.1149 0.135150 0.0675749 0.997714i \(-0.478474\pi\)
0.0675749 + 0.997714i \(0.478474\pi\)
\(468\) 0 0
\(469\) 43.8252i 0.0934438i
\(470\) 0 0
\(471\) 124.958i 0.265303i
\(472\) 0 0
\(473\) −463.833 −0.980620
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 351.374i 0.736634i
\(478\) 0 0
\(479\) −536.087 −1.11918 −0.559589 0.828770i \(-0.689041\pi\)
−0.559589 + 0.828770i \(0.689041\pi\)
\(480\) 0 0
\(481\) 694.699 1.44428
\(482\) 0 0
\(483\) 68.2763i 0.141359i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 247.634i 0.508490i −0.967140 0.254245i \(-0.918173\pi\)
0.967140 0.254245i \(-0.0818269\pi\)
\(488\) 0 0
\(489\) 252.658i 0.516683i
\(490\) 0 0
\(491\) 895.324 1.82347 0.911735 0.410779i \(-0.134743\pi\)
0.911735 + 0.410779i \(0.134743\pi\)
\(492\) 0 0
\(493\) 1029.30i 2.08783i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 58.2982i 0.117300i
\(498\) 0 0
\(499\) 78.2101 0.156734 0.0783669 0.996925i \(-0.475029\pi\)
0.0783669 + 0.996925i \(0.475029\pi\)
\(500\) 0 0
\(501\) −654.638 −1.30666
\(502\) 0 0
\(503\) 568.406 1.13003 0.565015 0.825080i \(-0.308870\pi\)
0.565015 + 0.825080i \(0.308870\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 162.659i 0.320827i
\(508\) 0 0
\(509\) 528.251i 1.03782i 0.854829 + 0.518911i \(0.173662\pi\)
−0.854829 + 0.518911i \(0.826338\pi\)
\(510\) 0 0
\(511\) 19.3696 0.0379053
\(512\) 0 0
\(513\) −170.704 + 326.818i −0.332756 + 0.637073i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 610.658 1.18116
\(518\) 0 0
\(519\) 819.200 1.57842
\(520\) 0 0
\(521\) 1004.23i 1.92750i 0.266807 + 0.963750i \(0.414031\pi\)
−0.266807 + 0.963750i \(0.585969\pi\)
\(522\) 0 0
\(523\) 588.915i 1.12603i 0.826446 + 0.563016i \(0.190359\pi\)
−0.826446 + 0.563016i \(0.809641\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 747.462i 1.41833i
\(528\) 0 0
\(529\) 1167.32 2.20666
\(530\) 0 0
\(531\) 234.445i 0.441516i
\(532\) 0 0
\(533\) −261.046 −0.489767
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 586.672 1.09250
\(538\) 0 0
\(539\) 688.203 1.27681
\(540\) 0 0
\(541\) 431.404 0.797420 0.398710 0.917077i \(-0.369458\pi\)
0.398710 + 0.917077i \(0.369458\pi\)
\(542\) 0 0
\(543\) 88.7353 0.163417
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 257.771i 0.471244i −0.971845 0.235622i \(-0.924287\pi\)
0.971845 0.235622i \(-0.0757127\pi\)
\(548\) 0 0
\(549\) 126.684 0.230755
\(550\) 0 0
\(551\) −410.958 + 786.794i −0.745840 + 1.42794i
\(552\) 0 0
\(553\) 12.7701i 0.0230925i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 616.514 1.10685 0.553424 0.832900i \(-0.313321\pi\)
0.553424 + 0.832900i \(0.313321\pi\)
\(558\) 0 0
\(559\) 364.651i 0.652327i
\(560\) 0 0
\(561\) 1099.58i 1.96003i
\(562\) 0 0
\(563\) 79.5657i 0.141324i 0.997500 + 0.0706622i \(0.0225113\pi\)
−0.997500 + 0.0706622i \(0.977489\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 46.9915 0.0828775
\(568\) 0 0
\(569\) 118.993i 0.209127i 0.994518 + 0.104563i \(0.0333445\pi\)
−0.994518 + 0.104563i \(0.966655\pi\)
\(570\) 0 0
\(571\) −1004.19 −1.75865 −0.879323 0.476227i \(-0.842004\pi\)
−0.879323 + 0.476227i \(0.842004\pi\)
\(572\) 0 0
\(573\) 184.181i 0.321434i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 795.249 1.37825 0.689123 0.724644i \(-0.257996\pi\)
0.689123 + 0.724644i \(0.257996\pi\)
\(578\) 0 0
\(579\) 248.755 0.429629
\(580\) 0 0
\(581\) −15.4220 −0.0265439
\(582\) 0 0
\(583\) 1410.60i 2.41955i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −192.221 −0.327463 −0.163732 0.986505i \(-0.552353\pi\)
−0.163732 + 0.986505i \(0.552353\pi\)
\(588\) 0 0
\(589\) 298.432 571.359i 0.506676 0.970049i
\(590\) 0 0
\(591\) 464.698i 0.786290i
\(592\) 0 0
\(593\) 83.5456 0.140886 0.0704432 0.997516i \(-0.477559\pi\)
0.0704432 + 0.997516i \(0.477559\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 427.924i 0.716791i
\(598\) 0 0
\(599\) 665.445i 1.11093i −0.831541 0.555463i \(-0.812541\pi\)
0.831541 0.555463i \(-0.187459\pi\)
\(600\) 0 0
\(601\) 648.842i 1.07960i 0.841792 + 0.539802i \(0.181501\pi\)
−0.841792 + 0.539802i \(0.818499\pi\)
\(602\) 0 0
\(603\) 328.662i 0.545044i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 212.490i 0.350066i −0.984563 0.175033i \(-0.943997\pi\)
0.984563 0.175033i \(-0.0560032\pi\)
\(608\) 0 0
\(609\) 77.4472 0.127171
\(610\) 0 0
\(611\) 480.080i 0.785728i
\(612\) 0 0
\(613\) −878.692 −1.43343 −0.716715 0.697366i \(-0.754355\pi\)
−0.716715 + 0.697366i \(0.754355\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 77.9272 0.126300 0.0631501 0.998004i \(-0.479885\pi\)
0.0631501 + 0.998004i \(0.479885\pi\)
\(618\) 0 0
\(619\) −744.679 −1.20304 −0.601518 0.798860i \(-0.705437\pi\)
−0.601518 + 0.798860i \(0.705437\pi\)
\(620\) 0 0
\(621\) 799.264i 1.28706i
\(622\) 0 0
\(623\) 40.4725i 0.0649639i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 439.017 840.514i 0.700187 1.34053i
\(628\) 0 0
\(629\) 1379.94i 2.19387i
\(630\) 0 0
\(631\) 583.634 0.924934 0.462467 0.886636i \(-0.346964\pi\)
0.462467 + 0.886636i \(0.346964\pi\)
\(632\) 0 0
\(633\) −1349.85 −2.13247
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 541.043i 0.849361i
\(638\) 0 0
\(639\) 437.200i 0.684194i
\(640\) 0 0
\(641\) 835.068i 1.30276i −0.758753 0.651379i \(-0.774191\pi\)
0.758753 0.651379i \(-0.225809\pi\)
\(642\) 0 0
\(643\) 348.076 0.541331 0.270666 0.962673i \(-0.412756\pi\)
0.270666 + 0.962673i \(0.412756\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 667.701 1.03199 0.515997 0.856590i \(-0.327421\pi\)
0.515997 + 0.856590i \(0.327421\pi\)
\(648\) 0 0
\(649\) 941.184i 1.45021i
\(650\) 0 0
\(651\) −56.2411 −0.0863919
\(652\) 0 0
\(653\) 913.560 1.39902 0.699510 0.714623i \(-0.253402\pi\)
0.699510 + 0.714623i \(0.253402\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 145.260 0.221096
\(658\) 0 0
\(659\) 654.040i 0.992474i −0.868187 0.496237i \(-0.834715\pi\)
0.868187 0.496237i \(-0.165285\pi\)
\(660\) 0 0
\(661\) 284.200i 0.429955i 0.976619 + 0.214977i \(0.0689678\pi\)
−0.976619 + 0.214977i \(0.931032\pi\)
\(662\) 0 0
\(663\) −864.451 −1.30385
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 1924.18i 2.88482i
\(668\) 0 0
\(669\) −548.411 −0.819747
\(670\) 0 0
\(671\) 508.576 0.757938
\(672\) 0 0
\(673\) 652.742i 0.969899i 0.874542 + 0.484950i \(0.161162\pi\)
−0.874542 + 0.484950i \(0.838838\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 548.221i 0.809781i 0.914365 + 0.404890i \(0.132690\pi\)
−0.914365 + 0.404890i \(0.867310\pi\)
\(678\) 0 0
\(679\) 9.75041i 0.0143600i
\(680\) 0 0
\(681\) −840.462 −1.23416
\(682\) 0 0
\(683\) 183.490i 0.268653i −0.990937 0.134327i \(-0.957113\pi\)
0.990937 0.134327i \(-0.0428872\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 975.092i 1.41935i
\(688\) 0 0
\(689\) −1108.97 −1.60953
\(690\) 0 0
\(691\) −700.503 −1.01375 −0.506876 0.862019i \(-0.669200\pi\)
−0.506876 + 0.862019i \(0.669200\pi\)
\(692\) 0 0
\(693\) −23.2339 −0.0335265
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 518.539i 0.743958i
\(698\) 0 0
\(699\) 960.766i 1.37449i
\(700\) 0 0
\(701\) 353.859 0.504791 0.252396 0.967624i \(-0.418782\pi\)
0.252396 + 0.967624i \(0.418782\pi\)
\(702\) 0 0
\(703\) 550.956 1054.83i 0.783721 1.50046i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 55.4214 0.0783895
\(708\) 0 0
\(709\) −592.019 −0.835006 −0.417503 0.908676i \(-0.637095\pi\)
−0.417503 + 0.908676i \(0.637095\pi\)
\(710\) 0 0
\(711\) 95.7682i 0.134695i
\(712\) 0 0
\(713\) 1397.31i 1.95976i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 835.732i 1.16560i
\(718\) 0 0
\(719\) 385.615 0.536321 0.268160 0.963374i \(-0.413584\pi\)
0.268160 + 0.963374i \(0.413584\pi\)
\(720\) 0 0
\(721\) 50.5515i 0.0701130i
\(722\) 0 0
\(723\) 1224.55 1.69371
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1136.34 1.56306 0.781530 0.623867i \(-0.214439\pi\)
0.781530 + 0.623867i \(0.214439\pi\)
\(728\) 0 0
\(729\) −265.440 −0.364116
\(730\) 0 0
\(731\) 724.338 0.990887
\(732\) 0 0
\(733\) 871.591 1.18907 0.594537 0.804068i \(-0.297335\pi\)
0.594537 + 0.804068i \(0.297335\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1319.42i 1.79026i
\(738\) 0 0
\(739\) 605.269 0.819038 0.409519 0.912301i \(-0.365696\pi\)
0.409519 + 0.912301i \(0.365696\pi\)
\(740\) 0 0
\(741\) −660.785 345.141i −0.891748 0.465778i
\(742\) 0 0
\(743\) 490.677i 0.660400i 0.943911 + 0.330200i \(0.107116\pi\)
−0.943911 + 0.330200i \(0.892884\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −115.656 −0.154827
\(748\) 0 0
\(749\) 7.80229i 0.0104169i
\(750\) 0 0
\(751\) 1075.66i 1.43230i −0.697948 0.716149i \(-0.745903\pi\)
0.697948 0.716149i \(-0.254097\pi\)
\(752\) 0 0
\(753\) 786.530i 1.04453i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 775.132 1.02395 0.511976 0.859000i \(-0.328914\pi\)
0.511976 + 0.859000i \(0.328914\pi\)
\(758\) 0 0
\(759\) 2055.55i 2.70824i
\(760\) 0 0
\(761\) 801.361 1.05304 0.526519 0.850164i \(-0.323497\pi\)
0.526519 + 0.850164i \(0.323497\pi\)
\(762\) 0 0
\(763\) 16.1225i 0.0211303i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −739.929 −0.964705
\(768\) 0 0
\(769\) 419.799 0.545902 0.272951 0.962028i \(-0.412000\pi\)
0.272951 + 0.962028i \(0.412000\pi\)
\(770\) 0 0
\(771\) 506.692 0.657188
\(772\) 0 0
\(773\) 518.154i 0.670316i 0.942162 + 0.335158i \(0.108790\pi\)
−0.942162 + 0.335158i \(0.891210\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −103.831 −0.133630
\(778\) 0 0
\(779\) −207.032 + 396.370i −0.265766 + 0.508819i
\(780\) 0 0
\(781\) 1755.15i 2.24731i
\(782\) 0 0
\(783\) −906.622 −1.15788
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 393.934i 0.500551i −0.968175 0.250276i \(-0.919479\pi\)
0.968175 0.250276i \(-0.0805212\pi\)
\(788\) 0 0
\(789\) 850.102i 1.07744i
\(790\) 0 0
\(791\) 16.0681i 0.0203136i
\(792\) 0 0
\(793\) 399.827i 0.504195i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 305.628i 0.383474i 0.981446 + 0.191737i \(0.0614120\pi\)
−0.981446 + 0.191737i \(0.938588\pi\)
\(798\) 0 0
\(799\) −953.625 −1.19352
\(800\) 0 0
\(801\) 303.519i 0.378925i
\(802\) 0 0
\(803\) 583.149 0.726213
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −924.325 −1.14538
\(808\) 0 0
\(809\) 1186.46 1.46657 0.733285 0.679921i \(-0.237986\pi\)
0.733285 + 0.679921i \(0.237986\pi\)
\(810\) 0 0
\(811\) 1581.99i 1.95067i 0.220740 + 0.975333i \(0.429153\pi\)
−0.220740 + 0.975333i \(0.570847\pi\)
\(812\) 0 0
\(813\) 830.719i 1.02180i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 553.683 + 289.200i 0.677703 + 0.353978i
\(818\) 0 0
\(819\) 18.2657i 0.0223025i
\(820\) 0 0
\(821\) −95.9928 −0.116922 −0.0584609 0.998290i \(-0.518619\pi\)
−0.0584609 + 0.998290i \(0.518619\pi\)
\(822\) 0 0
\(823\) −1292.87 −1.57093 −0.785464 0.618908i \(-0.787576\pi\)
−0.785464 + 0.618908i \(0.787576\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 44.7405i 0.0540998i 0.999634 + 0.0270499i \(0.00861130\pi\)
−0.999634 + 0.0270499i \(0.991389\pi\)
\(828\) 0 0
\(829\) 802.912i 0.968530i −0.874921 0.484265i \(-0.839087\pi\)
0.874921 0.484265i \(-0.160913\pi\)
\(830\) 0 0
\(831\) 101.305i 0.121907i
\(832\) 0 0
\(833\) −1074.72 −1.29018
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 658.377 0.786591
\(838\) 0 0
\(839\) 346.934i 0.413509i −0.978393 0.206754i \(-0.933710\pi\)
0.978393 0.206754i \(-0.0662901\pi\)
\(840\) 0 0
\(841\) −1341.63 −1.59528
\(842\) 0 0
\(843\) 124.678 0.147898
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −36.5708 −0.0431769
\(848\) 0 0
\(849\) 564.190i 0.664534i
\(850\) 0 0
\(851\) 2579.67i 3.03134i
\(852\) 0 0
\(853\) −766.503 −0.898597 −0.449298 0.893382i \(-0.648326\pi\)
−0.449298 + 0.893382i \(0.648326\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1701.81i 1.98577i 0.119063 + 0.992887i \(0.462011\pi\)
−0.119063 + 0.992887i \(0.537989\pi\)
\(858\) 0 0
\(859\) 436.740 0.508429 0.254214 0.967148i \(-0.418183\pi\)
0.254214 + 0.967148i \(0.418183\pi\)
\(860\) 0 0
\(861\) 39.0163 0.0453151
\(862\) 0 0
\(863\) 555.776i 0.644004i −0.946739 0.322002i \(-0.895644\pi\)
0.946739 0.322002i \(-0.104356\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 694.782i 0.801364i
\(868\) 0 0
\(869\) 384.463i 0.442420i
\(870\) 0 0
\(871\) −1037.28 −1.19091
\(872\) 0 0
\(873\) 73.1221i 0.0837595i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 506.241i 0.577242i −0.957443 0.288621i \(-0.906803\pi\)
0.957443 0.288621i \(-0.0931967\pi\)
\(878\) 0 0
\(879\) 282.342 0.321209
\(880\) 0 0
\(881\) 1208.80 1.37208 0.686038 0.727566i \(-0.259348\pi\)
0.686038 + 0.727566i \(0.259348\pi\)
\(882\) 0 0
\(883\) −221.477 −0.250823 −0.125412 0.992105i \(-0.540025\pi\)
−0.125412 + 0.992105i \(0.540025\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1533.50i 1.72886i −0.502753 0.864430i \(-0.667680\pi\)
0.502753 0.864430i \(-0.332320\pi\)
\(888\) 0 0
\(889\) 115.101i 0.129472i
\(890\) 0 0
\(891\) 1414.75 1.58782
\(892\) 0 0
\(893\) −728.949 380.745i −0.816292 0.426366i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −1616.01 −1.80157
\(898\) 0 0
\(899\) 1585.00 1.76307
\(900\) 0 0
\(901\) 2202.84i 2.44488i
\(902\) 0 0
\(903\) 54.5012i 0.0603557i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 670.343i 0.739077i −0.929215 0.369539i \(-0.879516\pi\)
0.929215 0.369539i \(-0.120484\pi\)
\(908\) 0 0
\(909\) 415.626 0.457234
\(910\) 0 0
\(911\) 351.217i 0.385529i −0.981245 0.192765i \(-0.938255\pi\)
0.981245 0.192765i \(-0.0617454\pi\)
\(912\) 0 0
\(913\) −464.301 −0.508545
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −92.2348 −0.100583
\(918\) 0 0
\(919\) −701.167 −0.762967 −0.381484 0.924376i \(-0.624587\pi\)
−0.381484 + 0.924376i \(0.624587\pi\)
\(920\) 0 0
\(921\) 480.139 0.521323
\(922\) 0 0
\(923\) 1379.84 1.49495
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 379.105i 0.408959i
\(928\) 0 0
\(929\) −1521.71 −1.63801 −0.819004 0.573787i \(-0.805474\pi\)
−0.819004 + 0.573787i \(0.805474\pi\)
\(930\) 0 0
\(931\) −821.516 429.094i −0.882401 0.460896i
\(932\) 0 0
\(933\) 465.898i 0.499355i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −1462.89 −1.56125 −0.780624 0.625001i \(-0.785098\pi\)
−0.780624 + 0.625001i \(0.785098\pi\)
\(938\) 0 0
\(939\) 2016.54i 2.14754i
\(940\) 0 0
\(941\) 460.939i 0.489840i −0.969543 0.244920i \(-0.921238\pi\)
0.969543 0.244920i \(-0.0787617\pi\)
\(942\) 0 0
\(943\) 969.359i 1.02795i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −707.825 −0.747439 −0.373719 0.927542i \(-0.621918\pi\)
−0.373719 + 0.927542i \(0.621918\pi\)
\(948\) 0 0
\(949\) 458.453i 0.483091i
\(950\) 0 0
\(951\) 1181.90 1.24280
\(952\) 0 0
\(953\) 1553.32i 1.62993i 0.579511 + 0.814964i \(0.303243\pi\)
−0.579511 + 0.814964i \(0.696757\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 2331.66 2.43642
\(958\) 0 0
\(959\) 116.876 0.121873
\(960\) 0 0
\(961\) −190.004 −0.197715
\(962\) 0 0
\(963\) 58.5124i 0.0607605i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −155.746 −0.161061 −0.0805307 0.996752i \(-0.525661\pi\)
−0.0805307 + 0.996752i \(0.525661\pi\)
\(968\) 0 0
\(969\) −685.584 + 1312.58i −0.707517 + 1.35457i
\(970\) 0 0
\(971\) 297.557i 0.306444i −0.988192 0.153222i \(-0.951035\pi\)
0.988192 0.153222i \(-0.0489649\pi\)
\(972\) 0 0
\(973\) −54.3913 −0.0559006
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 618.917i 0.633487i 0.948511 + 0.316744i \(0.102589\pi\)
−0.948511 + 0.316744i \(0.897411\pi\)
\(978\) 0 0
\(979\) 1218.48i 1.24462i
\(980\) 0 0
\(981\) 120.908i 0.123250i
\(982\) 0 0
\(983\) 632.754i 0.643697i −0.946791 0.321848i \(-0.895696\pi\)
0.946791 0.321848i \(-0.104304\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 71.7534i 0.0726984i
\(988\) 0 0
\(989\) 1354.08 1.36914
\(990\) 0 0
\(991\) 1876.53i 1.89358i −0.321858 0.946788i \(-0.604308\pi\)
0.321858 0.946788i \(-0.395692\pi\)
\(992\) 0 0
\(993\) −224.141 −0.225721
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 270.045 0.270857 0.135429 0.990787i \(-0.456759\pi\)
0.135429 + 0.990787i \(0.456759\pi\)
\(998\) 0 0
\(999\) 1215.47 1.21669
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 1900.3.e.f.1101.11 12
5.2 odd 4 1900.3.g.c.949.21 24
5.3 odd 4 1900.3.g.c.949.4 24
5.4 even 2 380.3.e.a.341.2 12
15.14 odd 2 3420.3.o.a.721.9 12
19.18 odd 2 inner 1900.3.e.f.1101.2 12
20.19 odd 2 1520.3.h.b.721.11 12
95.18 even 4 1900.3.g.c.949.22 24
95.37 even 4 1900.3.g.c.949.3 24
95.94 odd 2 380.3.e.a.341.11 yes 12
285.284 even 2 3420.3.o.a.721.10 12
380.379 even 2 1520.3.h.b.721.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
380.3.e.a.341.2 12 5.4 even 2
380.3.e.a.341.11 yes 12 95.94 odd 2
1520.3.h.b.721.2 12 380.379 even 2
1520.3.h.b.721.11 12 20.19 odd 2
1900.3.e.f.1101.2 12 19.18 odd 2 inner
1900.3.e.f.1101.11 12 1.1 even 1 trivial
1900.3.g.c.949.3 24 95.37 even 4
1900.3.g.c.949.4 24 5.3 odd 4
1900.3.g.c.949.21 24 5.2 odd 4
1900.3.g.c.949.22 24 95.18 even 4
3420.3.o.a.721.9 12 15.14 odd 2
3420.3.o.a.721.10 12 285.284 even 2