Properties

Label 1900.3.e.g.1101.10
Level $1900$
Weight $3$
Character 1900.1101
Analytic conductor $51.771$
Analytic rank $0$
Dimension $14$
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: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} + 89x^{12} + 3026x^{10} + 49092x^{8} + 390297x^{6} + 1440495x^{4} + 1994425x^{2} + 151875 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1101.10
Root \(2.16913i\) of defining polynomial
Character \(\chi\) \(=\) 1900.1101
Dual form 1900.3.e.g.1101.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.16913i q^{3} +8.18099 q^{7} +4.29489 q^{9} +O(q^{10})\) \(q+2.16913i q^{3} +8.18099 q^{7} +4.29489 q^{9} +3.30255 q^{11} -8.86162i q^{13} +10.2495 q^{17} +(18.5676 - 4.03031i) q^{19} +17.7456i q^{21} +0.896508 q^{23} +28.8383i q^{27} +17.9058i q^{29} -40.8943i q^{31} +7.16364i q^{33} -7.68123i q^{37} +19.2220 q^{39} -69.9101i q^{41} +25.9969 q^{43} -12.4912 q^{47} +17.9286 q^{49} +22.2324i q^{51} -55.9407i q^{53} +(8.74226 + 40.2755i) q^{57} -105.529i q^{59} -48.2803 q^{61} +35.1365 q^{63} -14.6303i q^{67} +1.94464i q^{69} -2.89388i q^{71} +75.9531 q^{73} +27.0181 q^{77} +86.1594i q^{79} -23.8998 q^{81} +52.0562 q^{83} -38.8400 q^{87} +39.5469i q^{89} -72.4968i q^{91} +88.7050 q^{93} +172.660i q^{97} +14.1841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 4 q^{7} - 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 4 q^{7} - 52 q^{9} + 4 q^{11} + 6 q^{17} - 29 q^{19} + 28 q^{23} - 56 q^{39} - 22 q^{43} - 84 q^{47} + 138 q^{49} + 5 q^{57} - 50 q^{61} - 234 q^{63} + 204 q^{73} - 68 q^{77} + 66 q^{81} - 256 q^{83} - 18 q^{87} - 118 q^{93} + 92 q^{99}+O(q^{100}) \) 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
\(3\) 2.16913i 0.723042i 0.932364 + 0.361521i \(0.117742\pi\)
−0.932364 + 0.361521i \(0.882258\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 8.18099 1.16871 0.584356 0.811497i \(-0.301347\pi\)
0.584356 + 0.811497i \(0.301347\pi\)
\(8\) 0 0
\(9\) 4.29489 0.477211
\(10\) 0 0
\(11\) 3.30255 0.300232 0.150116 0.988668i \(-0.452035\pi\)
0.150116 + 0.988668i \(0.452035\pi\)
\(12\) 0 0
\(13\) 8.86162i 0.681663i −0.940124 0.340832i \(-0.889291\pi\)
0.940124 0.340832i \(-0.110709\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 10.2495 0.602910 0.301455 0.953480i \(-0.402528\pi\)
0.301455 + 0.953480i \(0.402528\pi\)
\(18\) 0 0
\(19\) 18.5676 4.03031i 0.977243 0.212122i
\(20\) 0 0
\(21\) 17.7456i 0.845028i
\(22\) 0 0
\(23\) 0.896508 0.0389786 0.0194893 0.999810i \(-0.493796\pi\)
0.0194893 + 0.999810i \(0.493796\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 28.8383i 1.06808i
\(28\) 0 0
\(29\) 17.9058i 0.617442i 0.951153 + 0.308721i \(0.0999010\pi\)
−0.951153 + 0.308721i \(0.900099\pi\)
\(30\) 0 0
\(31\) 40.8943i 1.31917i −0.751629 0.659586i \(-0.770732\pi\)
0.751629 0.659586i \(-0.229268\pi\)
\(32\) 0 0
\(33\) 7.16364i 0.217080i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 7.68123i 0.207601i −0.994598 0.103800i \(-0.966900\pi\)
0.994598 0.103800i \(-0.0331003\pi\)
\(38\) 0 0
\(39\) 19.2220 0.492871
\(40\) 0 0
\(41\) 69.9101i 1.70512i −0.522626 0.852562i \(-0.675048\pi\)
0.522626 0.852562i \(-0.324952\pi\)
\(42\) 0 0
\(43\) 25.9969 0.604579 0.302290 0.953216i \(-0.402249\pi\)
0.302290 + 0.953216i \(0.402249\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −12.4912 −0.265770 −0.132885 0.991131i \(-0.542424\pi\)
−0.132885 + 0.991131i \(0.542424\pi\)
\(48\) 0 0
\(49\) 17.9286 0.365889
\(50\) 0 0
\(51\) 22.2324i 0.435929i
\(52\) 0 0
\(53\) 55.9407i 1.05549i −0.849404 0.527743i \(-0.823038\pi\)
0.849404 0.527743i \(-0.176962\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 8.74226 + 40.2755i 0.153373 + 0.706588i
\(58\) 0 0
\(59\) 105.529i 1.78862i −0.447444 0.894312i \(-0.647666\pi\)
0.447444 0.894312i \(-0.352334\pi\)
\(60\) 0 0
\(61\) −48.2803 −0.791480 −0.395740 0.918363i \(-0.629512\pi\)
−0.395740 + 0.918363i \(0.629512\pi\)
\(62\) 0 0
\(63\) 35.1365 0.557722
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 14.6303i 0.218363i −0.994022 0.109181i \(-0.965177\pi\)
0.994022 0.109181i \(-0.0348229\pi\)
\(68\) 0 0
\(69\) 1.94464i 0.0281832i
\(70\) 0 0
\(71\) 2.89388i 0.0407588i −0.999792 0.0203794i \(-0.993513\pi\)
0.999792 0.0203794i \(-0.00648742\pi\)
\(72\) 0 0
\(73\) 75.9531 1.04045 0.520227 0.854028i \(-0.325847\pi\)
0.520227 + 0.854028i \(0.325847\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 27.0181 0.350885
\(78\) 0 0
\(79\) 86.1594i 1.09063i 0.838233 + 0.545313i \(0.183589\pi\)
−0.838233 + 0.545313i \(0.816411\pi\)
\(80\) 0 0
\(81\) −23.8998 −0.295060
\(82\) 0 0
\(83\) 52.0562 0.627183 0.313591 0.949558i \(-0.398468\pi\)
0.313591 + 0.949558i \(0.398468\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −38.8400 −0.446437
\(88\) 0 0
\(89\) 39.5469i 0.444347i 0.975007 + 0.222174i \(0.0713151\pi\)
−0.975007 + 0.222174i \(0.928685\pi\)
\(90\) 0 0
\(91\) 72.4968i 0.796668i
\(92\) 0 0
\(93\) 88.7050 0.953817
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 172.660i 1.78000i 0.455962 + 0.889999i \(0.349295\pi\)
−0.455962 + 0.889999i \(0.650705\pi\)
\(98\) 0 0
\(99\) 14.1841 0.143274
\(100\) 0 0
\(101\) −143.421 −1.42001 −0.710007 0.704194i \(-0.751308\pi\)
−0.710007 + 0.704194i \(0.751308\pi\)
\(102\) 0 0
\(103\) 101.659i 0.986979i 0.869752 + 0.493490i \(0.164279\pi\)
−0.869752 + 0.493490i \(0.835721\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 155.201i 1.45048i −0.688497 0.725239i \(-0.741729\pi\)
0.688497 0.725239i \(-0.258271\pi\)
\(108\) 0 0
\(109\) 52.7937i 0.484345i −0.970233 0.242173i \(-0.922140\pi\)
0.970233 0.242173i \(-0.0778601\pi\)
\(110\) 0 0
\(111\) 16.6616 0.150104
\(112\) 0 0
\(113\) 90.0032i 0.796488i 0.917279 + 0.398244i \(0.130380\pi\)
−0.917279 + 0.398244i \(0.869620\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 38.0597i 0.325297i
\(118\) 0 0
\(119\) 83.8508 0.704629
\(120\) 0 0
\(121\) −110.093 −0.909861
\(122\) 0 0
\(123\) 151.644 1.23288
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 74.1001i 0.583466i −0.956500 0.291733i \(-0.905768\pi\)
0.956500 0.291733i \(-0.0942318\pi\)
\(128\) 0 0
\(129\) 56.3906i 0.437136i
\(130\) 0 0
\(131\) −59.3187 −0.452814 −0.226407 0.974033i \(-0.572698\pi\)
−0.226407 + 0.974033i \(0.572698\pi\)
\(132\) 0 0
\(133\) 151.902 32.9720i 1.14212 0.247909i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 153.881 1.12322 0.561610 0.827402i \(-0.310182\pi\)
0.561610 + 0.827402i \(0.310182\pi\)
\(138\) 0 0
\(139\) 42.6118 0.306560 0.153280 0.988183i \(-0.451016\pi\)
0.153280 + 0.988183i \(0.451016\pi\)
\(140\) 0 0
\(141\) 27.0950i 0.192163i
\(142\) 0 0
\(143\) 29.2659i 0.204657i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 38.8893i 0.264553i
\(148\) 0 0
\(149\) 43.1276 0.289447 0.144723 0.989472i \(-0.453771\pi\)
0.144723 + 0.989472i \(0.453771\pi\)
\(150\) 0 0
\(151\) 88.7161i 0.587524i 0.955879 + 0.293762i \(0.0949073\pi\)
−0.955879 + 0.293762i \(0.905093\pi\)
\(152\) 0 0
\(153\) 44.0204 0.287715
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 86.8111 0.552937 0.276469 0.961023i \(-0.410836\pi\)
0.276469 + 0.961023i \(0.410836\pi\)
\(158\) 0 0
\(159\) 121.342 0.763160
\(160\) 0 0
\(161\) 7.33432 0.0455548
\(162\) 0 0
\(163\) 116.020 0.711781 0.355890 0.934528i \(-0.384178\pi\)
0.355890 + 0.934528i \(0.384178\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 184.203i 1.10301i 0.834172 + 0.551505i \(0.185946\pi\)
−0.834172 + 0.551505i \(0.814054\pi\)
\(168\) 0 0
\(169\) 90.4717 0.535335
\(170\) 0 0
\(171\) 79.7460 17.3098i 0.466351 0.101227i
\(172\) 0 0
\(173\) 180.352i 1.04250i 0.853404 + 0.521249i \(0.174534\pi\)
−0.853404 + 0.521249i \(0.825466\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 228.905 1.29325
\(178\) 0 0
\(179\) 62.4477i 0.348870i −0.984669 0.174435i \(-0.944190\pi\)
0.984669 0.174435i \(-0.0558099\pi\)
\(180\) 0 0
\(181\) 229.533i 1.26814i 0.773277 + 0.634069i \(0.218616\pi\)
−0.773277 + 0.634069i \(0.781384\pi\)
\(182\) 0 0
\(183\) 104.726i 0.572273i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 33.8494 0.181013
\(188\) 0 0
\(189\) 235.926i 1.24828i
\(190\) 0 0
\(191\) −250.559 −1.31182 −0.655912 0.754837i \(-0.727716\pi\)
−0.655912 + 0.754837i \(0.727716\pi\)
\(192\) 0 0
\(193\) 144.603i 0.749239i −0.927179 0.374619i \(-0.877773\pi\)
0.927179 0.374619i \(-0.122227\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 172.063 0.873414 0.436707 0.899604i \(-0.356145\pi\)
0.436707 + 0.899604i \(0.356145\pi\)
\(198\) 0 0
\(199\) 334.796 1.68239 0.841196 0.540731i \(-0.181852\pi\)
0.841196 + 0.540731i \(0.181852\pi\)
\(200\) 0 0
\(201\) 31.7350 0.157885
\(202\) 0 0
\(203\) 146.487i 0.721613i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 3.85041 0.0186010
\(208\) 0 0
\(209\) 61.3205 13.3103i 0.293399 0.0636857i
\(210\) 0 0
\(211\) 47.6699i 0.225924i −0.993599 0.112962i \(-0.963966\pi\)
0.993599 0.112962i \(-0.0360338\pi\)
\(212\) 0 0
\(213\) 6.27718 0.0294703
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 334.556i 1.54173i
\(218\) 0 0
\(219\) 164.752i 0.752292i
\(220\) 0 0
\(221\) 90.8270i 0.410982i
\(222\) 0 0
\(223\) 289.875i 1.29989i 0.759981 + 0.649945i \(0.225208\pi\)
−0.759981 + 0.649945i \(0.774792\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 39.5372i 0.174172i 0.996201 + 0.0870862i \(0.0277556\pi\)
−0.996201 + 0.0870862i \(0.972244\pi\)
\(228\) 0 0
\(229\) 2.51216 0.0109701 0.00548507 0.999985i \(-0.498254\pi\)
0.00548507 + 0.999985i \(0.498254\pi\)
\(230\) 0 0
\(231\) 58.6057i 0.253704i
\(232\) 0 0
\(233\) 161.184 0.691775 0.345887 0.938276i \(-0.387578\pi\)
0.345887 + 0.938276i \(0.387578\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −186.891 −0.788568
\(238\) 0 0
\(239\) 140.111 0.586240 0.293120 0.956076i \(-0.405306\pi\)
0.293120 + 0.956076i \(0.405306\pi\)
\(240\) 0 0
\(241\) 12.3672i 0.0513163i −0.999671 0.0256582i \(-0.991832\pi\)
0.999671 0.0256582i \(-0.00816814\pi\)
\(242\) 0 0
\(243\) 207.703i 0.854745i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −35.7151 164.539i −0.144596 0.666151i
\(248\) 0 0
\(249\) 112.916i 0.453479i
\(250\) 0 0
\(251\) −463.827 −1.84792 −0.923958 0.382494i \(-0.875065\pi\)
−0.923958 + 0.382494i \(0.875065\pi\)
\(252\) 0 0
\(253\) 2.96076 0.0117026
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 244.454i 0.951185i 0.879666 + 0.475592i \(0.157766\pi\)
−0.879666 + 0.475592i \(0.842234\pi\)
\(258\) 0 0
\(259\) 62.8401i 0.242626i
\(260\) 0 0
\(261\) 76.9037i 0.294650i
\(262\) 0 0
\(263\) −67.3381 −0.256038 −0.128019 0.991772i \(-0.540862\pi\)
−0.128019 + 0.991772i \(0.540862\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −85.7822 −0.321281
\(268\) 0 0
\(269\) 11.2184i 0.0417040i 0.999783 + 0.0208520i \(0.00663788\pi\)
−0.999783 + 0.0208520i \(0.993362\pi\)
\(270\) 0 0
\(271\) 96.9961 0.357919 0.178960 0.983856i \(-0.442727\pi\)
0.178960 + 0.983856i \(0.442727\pi\)
\(272\) 0 0
\(273\) 157.255 0.576025
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −34.6288 −0.125014 −0.0625069 0.998045i \(-0.519910\pi\)
−0.0625069 + 0.998045i \(0.519910\pi\)
\(278\) 0 0
\(279\) 175.637i 0.629523i
\(280\) 0 0
\(281\) 334.616i 1.19080i 0.803428 + 0.595402i \(0.203007\pi\)
−0.803428 + 0.595402i \(0.796993\pi\)
\(282\) 0 0
\(283\) 219.370 0.775158 0.387579 0.921836i \(-0.373311\pi\)
0.387579 + 0.921836i \(0.373311\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 571.934i 1.99280i
\(288\) 0 0
\(289\) −183.948 −0.636499
\(290\) 0 0
\(291\) −374.521 −1.28701
\(292\) 0 0
\(293\) 7.91053i 0.0269984i −0.999909 0.0134992i \(-0.995703\pi\)
0.999909 0.0134992i \(-0.00429706\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 95.2399i 0.320673i
\(298\) 0 0
\(299\) 7.94451i 0.0265703i
\(300\) 0 0
\(301\) 212.680 0.706580
\(302\) 0 0
\(303\) 311.099i 1.02673i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 245.743i 0.800466i 0.916413 + 0.400233i \(0.131071\pi\)
−0.916413 + 0.400233i \(0.868929\pi\)
\(308\) 0 0
\(309\) −220.511 −0.713627
\(310\) 0 0
\(311\) −512.022 −1.64637 −0.823187 0.567771i \(-0.807806\pi\)
−0.823187 + 0.567771i \(0.807806\pi\)
\(312\) 0 0
\(313\) 502.653 1.60592 0.802960 0.596033i \(-0.203257\pi\)
0.802960 + 0.596033i \(0.203257\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 173.029i 0.545834i 0.962038 + 0.272917i \(0.0879885\pi\)
−0.962038 + 0.272917i \(0.912012\pi\)
\(318\) 0 0
\(319\) 59.1349i 0.185376i
\(320\) 0 0
\(321\) 336.651 1.04876
\(322\) 0 0
\(323\) 190.308 41.3086i 0.589190 0.127890i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 114.516 0.350202
\(328\) 0 0
\(329\) −102.190 −0.310609
\(330\) 0 0
\(331\) 287.986i 0.870049i −0.900419 0.435025i \(-0.856740\pi\)
0.900419 0.435025i \(-0.143260\pi\)
\(332\) 0 0
\(333\) 32.9901i 0.0990694i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 135.116i 0.400939i 0.979700 + 0.200469i \(0.0642467\pi\)
−0.979700 + 0.200469i \(0.935753\pi\)
\(338\) 0 0
\(339\) −195.228 −0.575894
\(340\) 0 0
\(341\) 135.056i 0.396057i
\(342\) 0 0
\(343\) −254.195 −0.741093
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −302.548 −0.871896 −0.435948 0.899972i \(-0.643587\pi\)
−0.435948 + 0.899972i \(0.643587\pi\)
\(348\) 0 0
\(349\) −241.844 −0.692964 −0.346482 0.938057i \(-0.612624\pi\)
−0.346482 + 0.938057i \(0.612624\pi\)
\(350\) 0 0
\(351\) 255.554 0.728074
\(352\) 0 0
\(353\) −182.840 −0.517960 −0.258980 0.965883i \(-0.583386\pi\)
−0.258980 + 0.965883i \(0.583386\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 181.883i 0.509476i
\(358\) 0 0
\(359\) 187.980 0.523622 0.261811 0.965119i \(-0.415680\pi\)
0.261811 + 0.965119i \(0.415680\pi\)
\(360\) 0 0
\(361\) 328.513 149.667i 0.910009 0.414589i
\(362\) 0 0
\(363\) 238.806i 0.657867i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 168.184 0.458268 0.229134 0.973395i \(-0.426411\pi\)
0.229134 + 0.973395i \(0.426411\pi\)
\(368\) 0 0
\(369\) 300.256i 0.813703i
\(370\) 0 0
\(371\) 457.651i 1.23356i
\(372\) 0 0
\(373\) 677.168i 1.81546i 0.419550 + 0.907732i \(0.362188\pi\)
−0.419550 + 0.907732i \(0.637812\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 158.675 0.420888
\(378\) 0 0
\(379\) 410.871i 1.08409i −0.840349 0.542046i \(-0.817650\pi\)
0.840349 0.542046i \(-0.182350\pi\)
\(380\) 0 0
\(381\) 160.732 0.421870
\(382\) 0 0
\(383\) 253.500i 0.661880i 0.943652 + 0.330940i \(0.107366\pi\)
−0.943652 + 0.330940i \(0.892634\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 111.654 0.288512
\(388\) 0 0
\(389\) 105.069 0.270101 0.135051 0.990839i \(-0.456880\pi\)
0.135051 + 0.990839i \(0.456880\pi\)
\(390\) 0 0
\(391\) 9.18873 0.0235006
\(392\) 0 0
\(393\) 128.670i 0.327404i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −38.8390 −0.0978313 −0.0489156 0.998803i \(-0.515577\pi\)
−0.0489156 + 0.998803i \(0.515577\pi\)
\(398\) 0 0
\(399\) 71.5203 + 329.493i 0.179249 + 0.825798i
\(400\) 0 0
\(401\) 386.689i 0.964311i −0.876086 0.482155i \(-0.839854\pi\)
0.876086 0.482155i \(-0.160146\pi\)
\(402\) 0 0
\(403\) −362.390 −0.899231
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 25.3677i 0.0623284i
\(408\) 0 0
\(409\) 299.046i 0.731165i 0.930779 + 0.365582i \(0.119130\pi\)
−0.930779 + 0.365582i \(0.880870\pi\)
\(410\) 0 0
\(411\) 333.787i 0.812134i
\(412\) 0 0
\(413\) 863.330i 2.09039i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 92.4304i 0.221656i
\(418\) 0 0
\(419\) −228.600 −0.545585 −0.272793 0.962073i \(-0.587947\pi\)
−0.272793 + 0.962073i \(0.587947\pi\)
\(420\) 0 0
\(421\) 373.332i 0.886775i 0.896330 + 0.443387i \(0.146223\pi\)
−0.896330 + 0.443387i \(0.853777\pi\)
\(422\) 0 0
\(423\) −53.6484 −0.126828
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −394.980 −0.925012
\(428\) 0 0
\(429\) 63.4815 0.147976
\(430\) 0 0
\(431\) 216.245i 0.501729i −0.968022 0.250865i \(-0.919285\pi\)
0.968022 0.250865i \(-0.0807149\pi\)
\(432\) 0 0
\(433\) 652.519i 1.50697i −0.657464 0.753486i \(-0.728371\pi\)
0.657464 0.753486i \(-0.271629\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 16.6460 3.61321i 0.0380916 0.00826821i
\(438\) 0 0
\(439\) 607.514i 1.38386i −0.721965 0.691929i \(-0.756761\pi\)
0.721965 0.691929i \(-0.243239\pi\)
\(440\) 0 0
\(441\) 77.0014 0.174606
\(442\) 0 0
\(443\) −513.684 −1.15956 −0.579779 0.814774i \(-0.696861\pi\)
−0.579779 + 0.814774i \(0.696861\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 93.5491i 0.209282i
\(448\) 0 0
\(449\) 223.870i 0.498596i −0.968427 0.249298i \(-0.919800\pi\)
0.968427 0.249298i \(-0.0801998\pi\)
\(450\) 0 0
\(451\) 230.881i 0.511932i
\(452\) 0 0
\(453\) −192.436 −0.424804
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 438.522 0.959567 0.479784 0.877387i \(-0.340715\pi\)
0.479784 + 0.877387i \(0.340715\pi\)
\(458\) 0 0
\(459\) 295.577i 0.643959i
\(460\) 0 0
\(461\) 703.015 1.52498 0.762489 0.647001i \(-0.223977\pi\)
0.762489 + 0.647001i \(0.223977\pi\)
\(462\) 0 0
\(463\) −642.827 −1.38839 −0.694197 0.719785i \(-0.744240\pi\)
−0.694197 + 0.719785i \(0.744240\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −927.468 −1.98601 −0.993006 0.118061i \(-0.962332\pi\)
−0.993006 + 0.118061i \(0.962332\pi\)
\(468\) 0 0
\(469\) 119.690i 0.255203i
\(470\) 0 0
\(471\) 188.304i 0.399797i
\(472\) 0 0
\(473\) 85.8561 0.181514
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 240.260i 0.503689i
\(478\) 0 0
\(479\) 257.644 0.537880 0.268940 0.963157i \(-0.413327\pi\)
0.268940 + 0.963157i \(0.413327\pi\)
\(480\) 0 0
\(481\) −68.0682 −0.141514
\(482\) 0 0
\(483\) 15.9091i 0.0329380i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 609.090i 1.25070i 0.780345 + 0.625349i \(0.215043\pi\)
−0.780345 + 0.625349i \(0.784957\pi\)
\(488\) 0 0
\(489\) 251.663i 0.514647i
\(490\) 0 0
\(491\) 138.936 0.282966 0.141483 0.989941i \(-0.454813\pi\)
0.141483 + 0.989941i \(0.454813\pi\)
\(492\) 0 0
\(493\) 183.525i 0.372262i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 23.6748i 0.0476354i
\(498\) 0 0
\(499\) 228.666 0.458248 0.229124 0.973397i \(-0.426414\pi\)
0.229124 + 0.973397i \(0.426414\pi\)
\(500\) 0 0
\(501\) −399.558 −0.797522
\(502\) 0 0
\(503\) −465.208 −0.924868 −0.462434 0.886654i \(-0.653024\pi\)
−0.462434 + 0.886654i \(0.653024\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 196.244i 0.387070i
\(508\) 0 0
\(509\) 395.633i 0.777276i 0.921391 + 0.388638i \(0.127054\pi\)
−0.921391 + 0.388638i \(0.872946\pi\)
\(510\) 0 0
\(511\) 621.372 1.21599
\(512\) 0 0
\(513\) 116.227 + 535.459i 0.226564 + 1.04378i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −41.2528 −0.0797926
\(518\) 0 0
\(519\) −391.207 −0.753770
\(520\) 0 0
\(521\) 204.842i 0.393172i 0.980487 + 0.196586i \(0.0629854\pi\)
−0.980487 + 0.196586i \(0.937015\pi\)
\(522\) 0 0
\(523\) 755.700i 1.44493i −0.691406 0.722466i \(-0.743008\pi\)
0.691406 0.722466i \(-0.256992\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 419.146i 0.795343i
\(528\) 0 0
\(529\) −528.196 −0.998481
\(530\) 0 0
\(531\) 453.235i 0.853550i
\(532\) 0 0
\(533\) −619.517 −1.16232
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 135.457 0.252248
\(538\) 0 0
\(539\) 59.2100 0.109852
\(540\) 0 0
\(541\) 458.741 0.847951 0.423975 0.905674i \(-0.360634\pi\)
0.423975 + 0.905674i \(0.360634\pi\)
\(542\) 0 0
\(543\) −497.886 −0.916916
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 731.948i 1.33811i −0.743211 0.669057i \(-0.766698\pi\)
0.743211 0.669057i \(-0.233302\pi\)
\(548\) 0 0
\(549\) −207.359 −0.377702
\(550\) 0 0
\(551\) 72.1661 + 332.469i 0.130973 + 0.603391i
\(552\) 0 0
\(553\) 704.869i 1.27463i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 534.752 0.960057 0.480028 0.877253i \(-0.340626\pi\)
0.480028 + 0.877253i \(0.340626\pi\)
\(558\) 0 0
\(559\) 230.375i 0.412120i
\(560\) 0 0
\(561\) 73.4236i 0.130880i
\(562\) 0 0
\(563\) 408.400i 0.725401i −0.931906 0.362700i \(-0.881855\pi\)
0.931906 0.362700i \(-0.118145\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −195.524 −0.344840
\(568\) 0 0
\(569\) 465.410i 0.817944i −0.912547 0.408972i \(-0.865887\pi\)
0.912547 0.408972i \(-0.134113\pi\)
\(570\) 0 0
\(571\) −60.8428 −0.106555 −0.0532774 0.998580i \(-0.516967\pi\)
−0.0532774 + 0.998580i \(0.516967\pi\)
\(572\) 0 0
\(573\) 543.493i 0.948504i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 657.921 1.14024 0.570122 0.821560i \(-0.306896\pi\)
0.570122 + 0.821560i \(0.306896\pi\)
\(578\) 0 0
\(579\) 313.662 0.541731
\(580\) 0 0
\(581\) 425.871 0.732996
\(582\) 0 0
\(583\) 184.747i 0.316890i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1050.70 −1.78996 −0.894978 0.446110i \(-0.852809\pi\)
−0.894978 + 0.446110i \(0.852809\pi\)
\(588\) 0 0
\(589\) −164.817 759.311i −0.279825 1.28915i
\(590\) 0 0
\(591\) 373.225i 0.631515i
\(592\) 0 0
\(593\) −520.953 −0.878505 −0.439252 0.898364i \(-0.644757\pi\)
−0.439252 + 0.898364i \(0.644757\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 726.214i 1.21644i
\(598\) 0 0
\(599\) 518.236i 0.865169i 0.901593 + 0.432584i \(0.142398\pi\)
−0.901593 + 0.432584i \(0.857602\pi\)
\(600\) 0 0
\(601\) 312.656i 0.520226i −0.965578 0.260113i \(-0.916240\pi\)
0.965578 0.260113i \(-0.0837598\pi\)
\(602\) 0 0
\(603\) 62.8356i 0.104205i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 40.6637i 0.0669913i −0.999439 0.0334956i \(-0.989336\pi\)
0.999439 0.0334956i \(-0.0106640\pi\)
\(608\) 0 0
\(609\) −317.750 −0.521756
\(610\) 0 0
\(611\) 110.692i 0.181166i
\(612\) 0 0
\(613\) −23.2110 −0.0378646 −0.0189323 0.999821i \(-0.506027\pi\)
−0.0189323 + 0.999821i \(0.506027\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −782.983 −1.26902 −0.634508 0.772916i \(-0.718797\pi\)
−0.634508 + 0.772916i \(0.718797\pi\)
\(618\) 0 0
\(619\) −669.801 −1.08207 −0.541034 0.841000i \(-0.681967\pi\)
−0.541034 + 0.841000i \(0.681967\pi\)
\(620\) 0 0
\(621\) 25.8538i 0.0416325i
\(622\) 0 0
\(623\) 323.533i 0.519314i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 28.8717 + 133.012i 0.0460474 + 0.212140i
\(628\) 0 0
\(629\) 78.7286i 0.125165i
\(630\) 0 0
\(631\) −190.219 −0.301457 −0.150728 0.988575i \(-0.548162\pi\)
−0.150728 + 0.988575i \(0.548162\pi\)
\(632\) 0 0
\(633\) 103.402 0.163352
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 158.876i 0.249413i
\(638\) 0 0
\(639\) 12.4289i 0.0194505i
\(640\) 0 0
\(641\) 519.869i 0.811029i 0.914089 + 0.405514i \(0.132908\pi\)
−0.914089 + 0.405514i \(0.867092\pi\)
\(642\) 0 0
\(643\) −594.211 −0.924123 −0.462062 0.886848i \(-0.652890\pi\)
−0.462062 + 0.886848i \(0.652890\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −830.788 −1.28406 −0.642031 0.766679i \(-0.721908\pi\)
−0.642031 + 0.766679i \(0.721908\pi\)
\(648\) 0 0
\(649\) 348.514i 0.537002i
\(650\) 0 0
\(651\) 725.694 1.11474
\(652\) 0 0
\(653\) −726.157 −1.11203 −0.556016 0.831172i \(-0.687671\pi\)
−0.556016 + 0.831172i \(0.687671\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 326.211 0.496516
\(658\) 0 0
\(659\) 30.7289i 0.0466295i 0.999728 + 0.0233148i \(0.00742199\pi\)
−0.999728 + 0.0233148i \(0.992578\pi\)
\(660\) 0 0
\(661\) 721.605i 1.09169i −0.837887 0.545844i \(-0.816209\pi\)
0.837887 0.545844i \(-0.183791\pi\)
\(662\) 0 0
\(663\) 197.015 0.297157
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 16.0527i 0.0240670i
\(668\) 0 0
\(669\) −628.776 −0.939875
\(670\) 0 0
\(671\) −159.448 −0.237627
\(672\) 0 0
\(673\) 435.074i 0.646469i 0.946319 + 0.323235i \(0.104770\pi\)
−0.946319 + 0.323235i \(0.895230\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 607.496i 0.897335i −0.893699 0.448667i \(-0.851899\pi\)
0.893699 0.448667i \(-0.148101\pi\)
\(678\) 0 0
\(679\) 1412.53i 2.08031i
\(680\) 0 0
\(681\) −85.7611 −0.125934
\(682\) 0 0
\(683\) 291.254i 0.426434i 0.977005 + 0.213217i \(0.0683941\pi\)
−0.977005 + 0.213217i \(0.931606\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 5.44920i 0.00793188i
\(688\) 0 0
\(689\) −495.726 −0.719486
\(690\) 0 0
\(691\) −444.232 −0.642883 −0.321441 0.946929i \(-0.604167\pi\)
−0.321441 + 0.946929i \(0.604167\pi\)
\(692\) 0 0
\(693\) 116.040 0.167446
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 716.542i 1.02804i
\(698\) 0 0
\(699\) 349.627i 0.500182i
\(700\) 0 0
\(701\) 481.762 0.687250 0.343625 0.939107i \(-0.388345\pi\)
0.343625 + 0.939107i \(0.388345\pi\)
\(702\) 0 0
\(703\) −30.9578 142.622i −0.0440367 0.202877i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1173.33 −1.65959
\(708\) 0 0
\(709\) −1135.31 −1.60128 −0.800642 0.599143i \(-0.795508\pi\)
−0.800642 + 0.599143i \(0.795508\pi\)
\(710\) 0 0
\(711\) 370.046i 0.520458i
\(712\) 0 0
\(713\) 36.6621i 0.0514195i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 303.919i 0.423876i
\(718\) 0 0
\(719\) 12.5461 0.0174493 0.00872467 0.999962i \(-0.497223\pi\)
0.00872467 + 0.999962i \(0.497223\pi\)
\(720\) 0 0
\(721\) 831.670i 1.15350i
\(722\) 0 0
\(723\) 26.8261 0.0371038
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 387.455 0.532951 0.266475 0.963842i \(-0.414141\pi\)
0.266475 + 0.963842i \(0.414141\pi\)
\(728\) 0 0
\(729\) −665.632 −0.913076
\(730\) 0 0
\(731\) 266.455 0.364507
\(732\) 0 0
\(733\) −550.259 −0.750694 −0.375347 0.926884i \(-0.622477\pi\)
−0.375347 + 0.926884i \(0.622477\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 48.3173i 0.0655595i
\(738\) 0 0
\(739\) −72.2829 −0.0978118 −0.0489059 0.998803i \(-0.515573\pi\)
−0.0489059 + 0.998803i \(0.515573\pi\)
\(740\) 0 0
\(741\) 356.906 77.4706i 0.481655 0.104549i
\(742\) 0 0
\(743\) 330.742i 0.445144i 0.974916 + 0.222572i \(0.0714453\pi\)
−0.974916 + 0.222572i \(0.928555\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 223.576 0.299298
\(748\) 0 0
\(749\) 1269.70i 1.69519i
\(750\) 0 0
\(751\) 964.716i 1.28458i 0.766464 + 0.642288i \(0.222015\pi\)
−0.766464 + 0.642288i \(0.777985\pi\)
\(752\) 0 0
\(753\) 1006.10i 1.33612i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 865.952 1.14393 0.571963 0.820279i \(-0.306182\pi\)
0.571963 + 0.820279i \(0.306182\pi\)
\(758\) 0 0
\(759\) 6.42226i 0.00846148i
\(760\) 0 0
\(761\) 280.071 0.368030 0.184015 0.982923i \(-0.441091\pi\)
0.184015 + 0.982923i \(0.441091\pi\)
\(762\) 0 0
\(763\) 431.904i 0.566061i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −935.156 −1.21924
\(768\) 0 0
\(769\) −627.438 −0.815915 −0.407957 0.913001i \(-0.633759\pi\)
−0.407957 + 0.913001i \(0.633759\pi\)
\(770\) 0 0
\(771\) −530.252 −0.687746
\(772\) 0 0
\(773\) 684.186i 0.885105i 0.896743 + 0.442552i \(0.145927\pi\)
−0.896743 + 0.442552i \(0.854073\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 136.308 0.175429
\(778\) 0 0
\(779\) −281.760 1298.06i −0.361694 1.66632i
\(780\) 0 0
\(781\) 9.55717i 0.0122371i
\(782\) 0 0
\(783\) −516.374 −0.659481
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 918.570i 1.16718i −0.812049 0.583589i \(-0.801648\pi\)
0.812049 0.583589i \(-0.198352\pi\)
\(788\) 0 0
\(789\) 146.065i 0.185126i
\(790\) 0 0
\(791\) 736.315i 0.930866i
\(792\) 0 0
\(793\) 427.841i 0.539522i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1245.67i 1.56295i −0.623938 0.781474i \(-0.714468\pi\)
0.623938 0.781474i \(-0.285532\pi\)
\(798\) 0 0
\(799\) −128.028 −0.160236
\(800\) 0 0
\(801\) 169.850i 0.212047i
\(802\) 0 0
\(803\) 250.839 0.312377
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −24.3341 −0.0301537
\(808\) 0 0
\(809\) 1198.51 1.48148 0.740738 0.671794i \(-0.234476\pi\)
0.740738 + 0.671794i \(0.234476\pi\)
\(810\) 0 0
\(811\) 295.291i 0.364107i 0.983289 + 0.182054i \(0.0582744\pi\)
−0.983289 + 0.182054i \(0.941726\pi\)
\(812\) 0 0
\(813\) 210.397i 0.258791i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 482.701 104.776i 0.590821 0.128244i
\(818\) 0 0
\(819\) 311.366i 0.380179i
\(820\) 0 0
\(821\) −271.018 −0.330107 −0.165054 0.986285i \(-0.552780\pi\)
−0.165054 + 0.986285i \(0.552780\pi\)
\(822\) 0 0
\(823\) 146.642 0.178180 0.0890900 0.996024i \(-0.471604\pi\)
0.0890900 + 0.996024i \(0.471604\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1037.94i 1.25506i 0.778591 + 0.627532i \(0.215935\pi\)
−0.778591 + 0.627532i \(0.784065\pi\)
\(828\) 0 0
\(829\) 1008.15i 1.21610i 0.793898 + 0.608050i \(0.208048\pi\)
−0.793898 + 0.608050i \(0.791952\pi\)
\(830\) 0 0
\(831\) 75.1143i 0.0903903i
\(832\) 0 0
\(833\) 183.759 0.220599
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 1179.32 1.40899
\(838\) 0 0
\(839\) 1596.51i 1.90287i 0.307850 + 0.951435i \(0.400390\pi\)
−0.307850 + 0.951435i \(0.599610\pi\)
\(840\) 0 0
\(841\) 520.381 0.618765
\(842\) 0 0
\(843\) −725.824 −0.861002
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −900.671 −1.06337
\(848\) 0 0
\(849\) 475.841i 0.560472i
\(850\) 0 0
\(851\) 6.88629i 0.00809199i
\(852\) 0 0
\(853\) −733.131 −0.859474 −0.429737 0.902954i \(-0.641394\pi\)
−0.429737 + 0.902954i \(0.641394\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 473.032i 0.551963i 0.961163 + 0.275981i \(0.0890028\pi\)
−0.961163 + 0.275981i \(0.910997\pi\)
\(858\) 0 0
\(859\) 694.138 0.808077 0.404038 0.914742i \(-0.367606\pi\)
0.404038 + 0.914742i \(0.367606\pi\)
\(860\) 0 0
\(861\) 1240.60 1.44088
\(862\) 0 0
\(863\) 301.961i 0.349897i 0.984578 + 0.174948i \(0.0559759\pi\)
−0.984578 + 0.174948i \(0.944024\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 399.007i 0.460216i
\(868\) 0 0
\(869\) 284.546i 0.327440i
\(870\) 0 0
\(871\) −129.648 −0.148850
\(872\) 0 0
\(873\) 741.556i 0.849434i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 954.932i 1.08886i 0.838806 + 0.544431i \(0.183254\pi\)
−0.838806 + 0.544431i \(0.816746\pi\)
\(878\) 0 0
\(879\) 17.1589 0.0195210
\(880\) 0 0
\(881\) −355.458 −0.403471 −0.201736 0.979440i \(-0.564658\pi\)
−0.201736 + 0.979440i \(0.564658\pi\)
\(882\) 0 0
\(883\) −378.377 −0.428514 −0.214257 0.976777i \(-0.568733\pi\)
−0.214257 + 0.976777i \(0.568733\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1001.77i 1.12939i −0.825301 0.564693i \(-0.808994\pi\)
0.825301 0.564693i \(-0.191006\pi\)
\(888\) 0 0
\(889\) 606.212i 0.681904i
\(890\) 0 0
\(891\) −78.9303 −0.0885863
\(892\) 0 0
\(893\) −231.932 + 50.3434i −0.259722 + 0.0563756i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 17.2326 0.0192114
\(898\) 0 0
\(899\) 732.247 0.814513
\(900\) 0 0
\(901\) 573.363i 0.636363i
\(902\) 0 0
\(903\) 461.331i 0.510887i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 1687.59i 1.86063i 0.366765 + 0.930314i \(0.380465\pi\)
−0.366765 + 0.930314i \(0.619535\pi\)
\(908\) 0 0
\(909\) −615.980 −0.677646
\(910\) 0 0
\(911\) 932.015i 1.02307i −0.859263 0.511534i \(-0.829077\pi\)
0.859263 0.511534i \(-0.170923\pi\)
\(912\) 0 0
\(913\) 171.918 0.188300
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −485.286 −0.529210
\(918\) 0 0
\(919\) 702.329 0.764232 0.382116 0.924114i \(-0.375195\pi\)
0.382116 + 0.924114i \(0.375195\pi\)
\(920\) 0 0
\(921\) −533.047 −0.578770
\(922\) 0 0
\(923\) −25.6444 −0.0277838
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 436.614i 0.470997i
\(928\) 0 0
\(929\) 1337.11 1.43930 0.719650 0.694337i \(-0.244302\pi\)
0.719650 + 0.694337i \(0.244302\pi\)
\(930\) 0 0
\(931\) 332.891 72.2578i 0.357563 0.0776131i
\(932\) 0 0
\(933\) 1110.64i 1.19040i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 1370.84 1.46301 0.731507 0.681834i \(-0.238817\pi\)
0.731507 + 0.681834i \(0.238817\pi\)
\(938\) 0 0
\(939\) 1090.32i 1.16115i
\(940\) 0 0
\(941\) 879.481i 0.934624i 0.884093 + 0.467312i \(0.154777\pi\)
−0.884093 + 0.467312i \(0.845223\pi\)
\(942\) 0 0
\(943\) 62.6749i 0.0664633i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −235.757 −0.248951 −0.124476 0.992223i \(-0.539725\pi\)
−0.124476 + 0.992223i \(0.539725\pi\)
\(948\) 0 0
\(949\) 673.068i 0.709239i
\(950\) 0 0
\(951\) −375.322 −0.394661
\(952\) 0 0
\(953\) 518.106i 0.543657i 0.962346 + 0.271829i \(0.0876284\pi\)
−0.962346 + 0.271829i \(0.912372\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −128.271 −0.134034
\(958\) 0 0
\(959\) 1258.90 1.31272
\(960\) 0 0
\(961\) −711.348 −0.740216
\(962\) 0 0
\(963\) 666.573i 0.692184i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 54.2136 0.0560637 0.0280319 0.999607i \(-0.491076\pi\)
0.0280319 + 0.999607i \(0.491076\pi\)
\(968\) 0 0
\(969\) 89.6035 + 412.803i 0.0924701 + 0.426009i
\(970\) 0 0
\(971\) 1229.47i 1.26619i −0.774075 0.633093i \(-0.781785\pi\)
0.774075 0.633093i \(-0.218215\pi\)
\(972\) 0 0
\(973\) 348.607 0.358280
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 957.658i 0.980202i −0.871666 0.490101i \(-0.836960\pi\)
0.871666 0.490101i \(-0.163040\pi\)
\(978\) 0 0
\(979\) 130.606i 0.133407i
\(980\) 0 0
\(981\) 226.743i 0.231135i
\(982\) 0 0
\(983\) 1624.35i 1.65244i −0.563348 0.826220i \(-0.690487\pi\)
0.563348 0.826220i \(-0.309513\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 221.664i 0.224583i
\(988\) 0 0
\(989\) 23.3064 0.0235657
\(990\) 0 0
\(991\) 496.019i 0.500524i −0.968178 0.250262i \(-0.919483\pi\)
0.968178 0.250262i \(-0.0805167\pi\)
\(992\) 0 0
\(993\) 624.678 0.629082
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −231.271 −0.231967 −0.115983 0.993251i \(-0.537002\pi\)
−0.115983 + 0.993251i \(0.537002\pi\)
\(998\) 0 0
\(999\) 221.514 0.221735
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.g.1101.10 yes 14
5.2 odd 4 1900.3.g.d.949.19 28
5.3 odd 4 1900.3.g.d.949.10 28
5.4 even 2 1900.3.e.h.1101.5 yes 14
19.18 odd 2 inner 1900.3.e.g.1101.5 14
95.18 even 4 1900.3.g.d.949.20 28
95.37 even 4 1900.3.g.d.949.9 28
95.94 odd 2 1900.3.e.h.1101.10 yes 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1900.3.e.g.1101.5 14 19.18 odd 2 inner
1900.3.e.g.1101.10 yes 14 1.1 even 1 trivial
1900.3.e.h.1101.5 yes 14 5.4 even 2
1900.3.e.h.1101.10 yes 14 95.94 odd 2
1900.3.g.d.949.9 28 95.37 even 4
1900.3.g.d.949.10 28 5.3 odd 4
1900.3.g.d.949.19 28 5.2 odd 4
1900.3.g.d.949.20 28 95.18 even 4