Properties

Label 1900.3.e.g.1101.11
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 1101.11
Root \(2.93221i\) of defining polynomial
Character \(\chi\) \(=\) 1900.1101
Dual form 1900.3.e.g.1101.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.93221i q^{3} -5.62705 q^{7} +0.402160 q^{9} +O(q^{10})\) \(q+2.93221i q^{3} -5.62705 q^{7} +0.402160 q^{9} -17.4504 q^{11} +7.35569i q^{13} +25.3144 q^{17} +(-2.59985 + 18.8213i) q^{19} -16.4997i q^{21} -19.3107 q^{23} +27.5691i q^{27} +4.89731i q^{29} +45.2147i q^{31} -51.1681i q^{33} -25.2986i q^{37} -21.5684 q^{39} -16.2721i q^{41} -28.0559 q^{43} +38.9299 q^{47} -17.3363 q^{49} +74.2270i q^{51} -81.9687i q^{53} +(-55.1879 - 7.62329i) q^{57} -61.0035i q^{59} -94.1024 q^{61} -2.26297 q^{63} -109.942i q^{67} -56.6231i q^{69} +57.6965i q^{71} -36.4469 q^{73} +98.1940 q^{77} -112.540i q^{79} -77.2188 q^{81} +42.1499 q^{83} -14.3599 q^{87} -101.024i q^{89} -41.3909i q^{91} -132.579 q^{93} -148.954i q^{97} -7.01784 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 4 q^{7} - 52 q^{9}+O(q^{10}) \) 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
\(3\) 2.93221i 0.977402i 0.872451 + 0.488701i \(0.162529\pi\)
−0.872451 + 0.488701i \(0.837471\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −5.62705 −0.803864 −0.401932 0.915669i \(-0.631661\pi\)
−0.401932 + 0.915669i \(0.631661\pi\)
\(8\) 0 0
\(9\) 0.402160 0.0446844
\(10\) 0 0
\(11\) −17.4504 −1.58640 −0.793198 0.608963i \(-0.791586\pi\)
−0.793198 + 0.608963i \(0.791586\pi\)
\(12\) 0 0
\(13\) 7.35569i 0.565823i 0.959146 + 0.282911i \(0.0913002\pi\)
−0.959146 + 0.282911i \(0.908700\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 25.3144 1.48908 0.744541 0.667577i \(-0.232668\pi\)
0.744541 + 0.667577i \(0.232668\pi\)
\(18\) 0 0
\(19\) −2.59985 + 18.8213i −0.136834 + 0.990594i
\(20\) 0 0
\(21\) 16.4997i 0.785699i
\(22\) 0 0
\(23\) −19.3107 −0.839598 −0.419799 0.907617i \(-0.637899\pi\)
−0.419799 + 0.907617i \(0.637899\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 27.5691i 1.02108i
\(28\) 0 0
\(29\) 4.89731i 0.168873i 0.996429 + 0.0844363i \(0.0269089\pi\)
−0.996429 + 0.0844363i \(0.973091\pi\)
\(30\) 0 0
\(31\) 45.2147i 1.45854i 0.684226 + 0.729270i \(0.260140\pi\)
−0.684226 + 0.729270i \(0.739860\pi\)
\(32\) 0 0
\(33\) 51.1681i 1.55055i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 25.2986i 0.683746i −0.939746 0.341873i \(-0.888939\pi\)
0.939746 0.341873i \(-0.111061\pi\)
\(38\) 0 0
\(39\) −21.5684 −0.553036
\(40\) 0 0
\(41\) 16.2721i 0.396881i −0.980113 0.198440i \(-0.936412\pi\)
0.980113 0.198440i \(-0.0635876\pi\)
\(42\) 0 0
\(43\) −28.0559 −0.652462 −0.326231 0.945290i \(-0.605779\pi\)
−0.326231 + 0.945290i \(0.605779\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 38.9299 0.828296 0.414148 0.910209i \(-0.364080\pi\)
0.414148 + 0.910209i \(0.364080\pi\)
\(48\) 0 0
\(49\) −17.3363 −0.353802
\(50\) 0 0
\(51\) 74.2270i 1.45543i
\(52\) 0 0
\(53\) 81.9687i 1.54658i −0.634053 0.773289i \(-0.718610\pi\)
0.634053 0.773289i \(-0.281390\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −55.1879 7.62329i −0.968209 0.133742i
\(58\) 0 0
\(59\) 61.0035i 1.03396i −0.855998 0.516979i \(-0.827056\pi\)
0.855998 0.516979i \(-0.172944\pi\)
\(60\) 0 0
\(61\) −94.1024 −1.54266 −0.771331 0.636434i \(-0.780409\pi\)
−0.771331 + 0.636434i \(0.780409\pi\)
\(62\) 0 0
\(63\) −2.26297 −0.0359202
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 109.942i 1.64092i −0.571705 0.820459i \(-0.693718\pi\)
0.571705 0.820459i \(-0.306282\pi\)
\(68\) 0 0
\(69\) 56.6231i 0.820625i
\(70\) 0 0
\(71\) 57.6965i 0.812627i 0.913734 + 0.406313i \(0.133186\pi\)
−0.913734 + 0.406313i \(0.866814\pi\)
\(72\) 0 0
\(73\) −36.4469 −0.499272 −0.249636 0.968340i \(-0.580311\pi\)
−0.249636 + 0.968340i \(0.580311\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 98.1940 1.27525
\(78\) 0 0
\(79\) 112.540i 1.42455i −0.701900 0.712276i \(-0.747665\pi\)
0.701900 0.712276i \(-0.252335\pi\)
\(80\) 0 0
\(81\) −77.2188 −0.953319
\(82\) 0 0
\(83\) 42.1499 0.507830 0.253915 0.967227i \(-0.418282\pi\)
0.253915 + 0.967227i \(0.418282\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −14.3599 −0.165057
\(88\) 0 0
\(89\) 101.024i 1.13510i −0.823339 0.567549i \(-0.807892\pi\)
0.823339 0.567549i \(-0.192108\pi\)
\(90\) 0 0
\(91\) 41.3909i 0.454845i
\(92\) 0 0
\(93\) −132.579 −1.42558
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 148.954i 1.53560i −0.640687 0.767802i \(-0.721350\pi\)
0.640687 0.767802i \(-0.278650\pi\)
\(98\) 0 0
\(99\) −7.01784 −0.0708872
\(100\) 0 0
\(101\) 35.3143 0.349647 0.174823 0.984600i \(-0.444065\pi\)
0.174823 + 0.984600i \(0.444065\pi\)
\(102\) 0 0
\(103\) 63.2704i 0.614276i −0.951665 0.307138i \(-0.900629\pi\)
0.951665 0.307138i \(-0.0993712\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 197.887i 1.84942i 0.380677 + 0.924708i \(0.375691\pi\)
−0.380677 + 0.924708i \(0.624309\pi\)
\(108\) 0 0
\(109\) 179.503i 1.64682i 0.567450 + 0.823408i \(0.307930\pi\)
−0.567450 + 0.823408i \(0.692070\pi\)
\(110\) 0 0
\(111\) 74.1807 0.668295
\(112\) 0 0
\(113\) 20.3688i 0.180255i −0.995930 0.0901276i \(-0.971273\pi\)
0.995930 0.0901276i \(-0.0287275\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 2.95817i 0.0252835i
\(118\) 0 0
\(119\) −142.445 −1.19702
\(120\) 0 0
\(121\) 183.515 1.51665
\(122\) 0 0
\(123\) 47.7132 0.387912
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 93.0448i 0.732636i −0.930490 0.366318i \(-0.880618\pi\)
0.930490 0.366318i \(-0.119382\pi\)
\(128\) 0 0
\(129\) 82.2656i 0.637718i
\(130\) 0 0
\(131\) −207.262 −1.58215 −0.791077 0.611717i \(-0.790479\pi\)
−0.791077 + 0.611717i \(0.790479\pi\)
\(132\) 0 0
\(133\) 14.6295 105.908i 0.109996 0.796303i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −143.376 −1.04654 −0.523268 0.852168i \(-0.675287\pi\)
−0.523268 + 0.852168i \(0.675287\pi\)
\(138\) 0 0
\(139\) −158.125 −1.13759 −0.568794 0.822480i \(-0.692590\pi\)
−0.568794 + 0.822480i \(0.692590\pi\)
\(140\) 0 0
\(141\) 114.151i 0.809579i
\(142\) 0 0
\(143\) 128.360i 0.897619i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 50.8337i 0.345807i
\(148\) 0 0
\(149\) 211.739 1.42107 0.710534 0.703663i \(-0.248453\pi\)
0.710534 + 0.703663i \(0.248453\pi\)
\(150\) 0 0
\(151\) 242.067i 1.60310i 0.597930 + 0.801548i \(0.295990\pi\)
−0.597930 + 0.801548i \(0.704010\pi\)
\(152\) 0 0
\(153\) 10.1804 0.0665388
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 137.436 0.875386 0.437693 0.899125i \(-0.355796\pi\)
0.437693 + 0.899125i \(0.355796\pi\)
\(158\) 0 0
\(159\) 240.349 1.51163
\(160\) 0 0
\(161\) 108.663 0.674923
\(162\) 0 0
\(163\) 173.770 1.06607 0.533037 0.846092i \(-0.321051\pi\)
0.533037 + 0.846092i \(0.321051\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.88276i 0.0352261i −0.999845 0.0176131i \(-0.994393\pi\)
0.999845 0.0176131i \(-0.00560670\pi\)
\(168\) 0 0
\(169\) 114.894 0.679845
\(170\) 0 0
\(171\) −1.04555 + 7.56917i −0.00611435 + 0.0442641i
\(172\) 0 0
\(173\) 254.130i 1.46896i −0.678630 0.734480i \(-0.737426\pi\)
0.678630 0.734480i \(-0.262574\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 178.875 1.01059
\(178\) 0 0
\(179\) 144.808i 0.808984i −0.914541 0.404492i \(-0.867448\pi\)
0.914541 0.404492i \(-0.132552\pi\)
\(180\) 0 0
\(181\) 98.4770i 0.544072i 0.962287 + 0.272036i \(0.0876969\pi\)
−0.962287 + 0.272036i \(0.912303\pi\)
\(182\) 0 0
\(183\) 275.928i 1.50780i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −441.745 −2.36227
\(188\) 0 0
\(189\) 155.133i 0.820807i
\(190\) 0 0
\(191\) 326.880 1.71141 0.855706 0.517462i \(-0.173123\pi\)
0.855706 + 0.517462i \(0.173123\pi\)
\(192\) 0 0
\(193\) 140.497i 0.727965i −0.931406 0.363982i \(-0.881417\pi\)
0.931406 0.363982i \(-0.118583\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −344.527 −1.74887 −0.874433 0.485146i \(-0.838767\pi\)
−0.874433 + 0.485146i \(0.838767\pi\)
\(198\) 0 0
\(199\) −202.257 −1.01637 −0.508184 0.861249i \(-0.669683\pi\)
−0.508184 + 0.861249i \(0.669683\pi\)
\(200\) 0 0
\(201\) 322.371 1.60384
\(202\) 0 0
\(203\) 27.5574i 0.135751i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −7.76601 −0.0375170
\(208\) 0 0
\(209\) 45.3683 328.438i 0.217073 1.57147i
\(210\) 0 0
\(211\) 126.032i 0.597308i −0.954361 0.298654i \(-0.903462\pi\)
0.954361 0.298654i \(-0.0965377\pi\)
\(212\) 0 0
\(213\) −169.178 −0.794263
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 254.426i 1.17247i
\(218\) 0 0
\(219\) 106.870i 0.487990i
\(220\) 0 0
\(221\) 186.205i 0.842556i
\(222\) 0 0
\(223\) 359.998i 1.61434i −0.590320 0.807169i \(-0.700998\pi\)
0.590320 0.807169i \(-0.299002\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 82.6104i 0.363922i −0.983306 0.181961i \(-0.941755\pi\)
0.983306 0.181961i \(-0.0582445\pi\)
\(228\) 0 0
\(229\) −42.1892 −0.184232 −0.0921161 0.995748i \(-0.529363\pi\)
−0.0921161 + 0.995748i \(0.529363\pi\)
\(230\) 0 0
\(231\) 287.925i 1.24643i
\(232\) 0 0
\(233\) −125.229 −0.537463 −0.268731 0.963215i \(-0.586604\pi\)
−0.268731 + 0.963215i \(0.586604\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 329.989 1.39236
\(238\) 0 0
\(239\) −177.271 −0.741720 −0.370860 0.928689i \(-0.620937\pi\)
−0.370860 + 0.928689i \(0.620937\pi\)
\(240\) 0 0
\(241\) 86.2189i 0.357755i −0.983871 0.178877i \(-0.942753\pi\)
0.983871 0.178877i \(-0.0572465\pi\)
\(242\) 0 0
\(243\) 21.7001i 0.0893009i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −138.444 19.1237i −0.560500 0.0774238i
\(248\) 0 0
\(249\) 123.592i 0.496354i
\(250\) 0 0
\(251\) −300.306 −1.19644 −0.598219 0.801332i \(-0.704125\pi\)
−0.598219 + 0.801332i \(0.704125\pi\)
\(252\) 0 0
\(253\) 336.980 1.33194
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 232.749i 0.905639i 0.891602 + 0.452820i \(0.149582\pi\)
−0.891602 + 0.452820i \(0.850418\pi\)
\(258\) 0 0
\(259\) 142.356i 0.549639i
\(260\) 0 0
\(261\) 1.96950i 0.00754598i
\(262\) 0 0
\(263\) 280.549 1.06673 0.533363 0.845886i \(-0.320928\pi\)
0.533363 + 0.845886i \(0.320928\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 296.223 1.10945
\(268\) 0 0
\(269\) 112.923i 0.419787i 0.977724 + 0.209893i \(0.0673117\pi\)
−0.977724 + 0.209893i \(0.932688\pi\)
\(270\) 0 0
\(271\) −95.7071 −0.353163 −0.176581 0.984286i \(-0.556504\pi\)
−0.176581 + 0.984286i \(0.556504\pi\)
\(272\) 0 0
\(273\) 121.367 0.444566
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −53.9033 −0.194597 −0.0972983 0.995255i \(-0.531020\pi\)
−0.0972983 + 0.995255i \(0.531020\pi\)
\(278\) 0 0
\(279\) 18.1836i 0.0651740i
\(280\) 0 0
\(281\) 68.4137i 0.243465i 0.992563 + 0.121732i \(0.0388450\pi\)
−0.992563 + 0.121732i \(0.961155\pi\)
\(282\) 0 0
\(283\) −378.615 −1.33786 −0.668932 0.743324i \(-0.733248\pi\)
−0.668932 + 0.743324i \(0.733248\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 91.5640i 0.319038i
\(288\) 0 0
\(289\) 351.818 1.21736
\(290\) 0 0
\(291\) 436.763 1.50090
\(292\) 0 0
\(293\) 20.3415i 0.0694249i 0.999397 + 0.0347125i \(0.0110515\pi\)
−0.999397 + 0.0347125i \(0.988948\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 481.090i 1.61983i
\(298\) 0 0
\(299\) 142.044i 0.475063i
\(300\) 0 0
\(301\) 157.872 0.524491
\(302\) 0 0
\(303\) 103.549i 0.341746i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 315.163i 1.02659i 0.858212 + 0.513296i \(0.171576\pi\)
−0.858212 + 0.513296i \(0.828424\pi\)
\(308\) 0 0
\(309\) 185.522 0.600394
\(310\) 0 0
\(311\) 188.579 0.606363 0.303182 0.952933i \(-0.401951\pi\)
0.303182 + 0.952933i \(0.401951\pi\)
\(312\) 0 0
\(313\) −154.013 −0.492055 −0.246028 0.969263i \(-0.579125\pi\)
−0.246028 + 0.969263i \(0.579125\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4.01072i 0.0126521i −0.999980 0.00632606i \(-0.997986\pi\)
0.999980 0.00632606i \(-0.00201366\pi\)
\(318\) 0 0
\(319\) 85.4598i 0.267899i
\(320\) 0 0
\(321\) −580.247 −1.80762
\(322\) 0 0
\(323\) −65.8135 + 476.449i −0.203757 + 1.47508i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −526.340 −1.60960
\(328\) 0 0
\(329\) −219.061 −0.665838
\(330\) 0 0
\(331\) 97.1158i 0.293401i −0.989181 0.146701i \(-0.953135\pi\)
0.989181 0.146701i \(-0.0468654\pi\)
\(332\) 0 0
\(333\) 10.1741i 0.0305528i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 193.889i 0.575337i 0.957730 + 0.287669i \(0.0928801\pi\)
−0.957730 + 0.287669i \(0.907120\pi\)
\(338\) 0 0
\(339\) 59.7257 0.176182
\(340\) 0 0
\(341\) 789.014i 2.31382i
\(342\) 0 0
\(343\) 373.278 1.08827
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 238.983 0.688712 0.344356 0.938839i \(-0.388097\pi\)
0.344356 + 0.938839i \(0.388097\pi\)
\(348\) 0 0
\(349\) −46.7033 −0.133820 −0.0669102 0.997759i \(-0.521314\pi\)
−0.0669102 + 0.997759i \(0.521314\pi\)
\(350\) 0 0
\(351\) −202.790 −0.577749
\(352\) 0 0
\(353\) −323.922 −0.917627 −0.458813 0.888533i \(-0.651725\pi\)
−0.458813 + 0.888533i \(0.651725\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 417.679i 1.16997i
\(358\) 0 0
\(359\) −290.600 −0.809472 −0.404736 0.914434i \(-0.632637\pi\)
−0.404736 + 0.914434i \(0.632637\pi\)
\(360\) 0 0
\(361\) −347.482 97.8649i −0.962553 0.271094i
\(362\) 0 0
\(363\) 538.104i 1.48238i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 218.143 0.594396 0.297198 0.954816i \(-0.403948\pi\)
0.297198 + 0.954816i \(0.403948\pi\)
\(368\) 0 0
\(369\) 6.54399i 0.0177344i
\(370\) 0 0
\(371\) 461.242i 1.24324i
\(372\) 0 0
\(373\) 244.913i 0.656603i 0.944573 + 0.328302i \(0.106476\pi\)
−0.944573 + 0.328302i \(0.893524\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −36.0231 −0.0955519
\(378\) 0 0
\(379\) 550.720i 1.45309i −0.687120 0.726543i \(-0.741126\pi\)
0.687120 0.726543i \(-0.258874\pi\)
\(380\) 0 0
\(381\) 272.827 0.716080
\(382\) 0 0
\(383\) 349.640i 0.912897i −0.889750 0.456449i \(-0.849121\pi\)
0.889750 0.456449i \(-0.150879\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −11.2829 −0.0291549
\(388\) 0 0
\(389\) −348.489 −0.895858 −0.447929 0.894069i \(-0.647838\pi\)
−0.447929 + 0.894069i \(0.647838\pi\)
\(390\) 0 0
\(391\) −488.840 −1.25023
\(392\) 0 0
\(393\) 607.736i 1.54640i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −25.4266 −0.0640468 −0.0320234 0.999487i \(-0.510195\pi\)
−0.0320234 + 0.999487i \(0.510195\pi\)
\(398\) 0 0
\(399\) 310.545 + 42.8966i 0.778309 + 0.107510i
\(400\) 0 0
\(401\) 638.917i 1.59331i 0.604435 + 0.796654i \(0.293399\pi\)
−0.604435 + 0.796654i \(0.706601\pi\)
\(402\) 0 0
\(403\) −332.586 −0.825275
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 441.469i 1.08469i
\(408\) 0 0
\(409\) 522.383i 1.27722i 0.769531 + 0.638610i \(0.220490\pi\)
−0.769531 + 0.638610i \(0.779510\pi\)
\(410\) 0 0
\(411\) 420.407i 1.02289i
\(412\) 0 0
\(413\) 343.270i 0.831162i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 463.655i 1.11188i
\(418\) 0 0
\(419\) −621.068 −1.48226 −0.741132 0.671360i \(-0.765711\pi\)
−0.741132 + 0.671360i \(0.765711\pi\)
\(420\) 0 0
\(421\) 303.897i 0.721845i −0.932596 0.360922i \(-0.882462\pi\)
0.932596 0.360922i \(-0.117538\pi\)
\(422\) 0 0
\(423\) 15.6561 0.0370120
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 529.519 1.24009
\(428\) 0 0
\(429\) 376.377 0.877335
\(430\) 0 0
\(431\) 86.3824i 0.200423i −0.994966 0.100212i \(-0.968048\pi\)
0.994966 0.100212i \(-0.0319520\pi\)
\(432\) 0 0
\(433\) 51.3805i 0.118662i −0.998238 0.0593308i \(-0.981103\pi\)
0.998238 0.0593308i \(-0.0188967\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 50.2050 363.453i 0.114886 0.831701i
\(438\) 0 0
\(439\) 736.743i 1.67823i −0.543954 0.839115i \(-0.683074\pi\)
0.543954 0.839115i \(-0.316926\pi\)
\(440\) 0 0
\(441\) −6.97197 −0.0158095
\(442\) 0 0
\(443\) 50.2064 0.113333 0.0566664 0.998393i \(-0.481953\pi\)
0.0566664 + 0.998393i \(0.481953\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 620.863i 1.38896i
\(448\) 0 0
\(449\) 211.982i 0.472121i 0.971738 + 0.236060i \(0.0758563\pi\)
−0.971738 + 0.236060i \(0.924144\pi\)
\(450\) 0 0
\(451\) 283.954i 0.629610i
\(452\) 0 0
\(453\) −709.792 −1.56687
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 438.611 0.959761 0.479880 0.877334i \(-0.340680\pi\)
0.479880 + 0.877334i \(0.340680\pi\)
\(458\) 0 0
\(459\) 697.895i 1.52047i
\(460\) 0 0
\(461\) −206.072 −0.447011 −0.223506 0.974703i \(-0.571750\pi\)
−0.223506 + 0.974703i \(0.571750\pi\)
\(462\) 0 0
\(463\) 164.050 0.354319 0.177159 0.984182i \(-0.443309\pi\)
0.177159 + 0.984182i \(0.443309\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 296.903 0.635766 0.317883 0.948130i \(-0.397028\pi\)
0.317883 + 0.948130i \(0.397028\pi\)
\(468\) 0 0
\(469\) 618.646i 1.31908i
\(470\) 0 0
\(471\) 402.990i 0.855604i
\(472\) 0 0
\(473\) 489.585 1.03506
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 32.9645i 0.0691080i
\(478\) 0 0
\(479\) 319.593 0.667208 0.333604 0.942713i \(-0.391735\pi\)
0.333604 + 0.942713i \(0.391735\pi\)
\(480\) 0 0
\(481\) 186.089 0.386879
\(482\) 0 0
\(483\) 318.621i 0.659671i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 257.490i 0.528727i 0.964423 + 0.264364i \(0.0851619\pi\)
−0.964423 + 0.264364i \(0.914838\pi\)
\(488\) 0 0
\(489\) 509.530i 1.04198i
\(490\) 0 0
\(491\) −897.982 −1.82888 −0.914442 0.404716i \(-0.867370\pi\)
−0.914442 + 0.404716i \(0.867370\pi\)
\(492\) 0 0
\(493\) 123.972i 0.251465i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 324.661i 0.653241i
\(498\) 0 0
\(499\) −786.631 −1.57641 −0.788207 0.615410i \(-0.788990\pi\)
−0.788207 + 0.615410i \(0.788990\pi\)
\(500\) 0 0
\(501\) 17.2495 0.0344301
\(502\) 0 0
\(503\) −48.2524 −0.0959292 −0.0479646 0.998849i \(-0.515273\pi\)
−0.0479646 + 0.998849i \(0.515273\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 336.892i 0.664482i
\(508\) 0 0
\(509\) 974.111i 1.91377i 0.290460 + 0.956887i \(0.406192\pi\)
−0.290460 + 0.956887i \(0.593808\pi\)
\(510\) 0 0
\(511\) 205.088 0.401347
\(512\) 0 0
\(513\) −518.886 71.6754i −1.01147 0.139718i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −679.341 −1.31401
\(518\) 0 0
\(519\) 745.162 1.43576
\(520\) 0 0
\(521\) 442.872i 0.850043i −0.905183 0.425021i \(-0.860267\pi\)
0.905183 0.425021i \(-0.139733\pi\)
\(522\) 0 0
\(523\) 104.045i 0.198940i −0.995041 0.0994699i \(-0.968285\pi\)
0.995041 0.0994699i \(-0.0317147\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1144.58i 2.17189i
\(528\) 0 0
\(529\) −156.095 −0.295076
\(530\) 0 0
\(531\) 24.5332i 0.0462018i
\(532\) 0 0
\(533\) 119.693 0.224564
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 424.608 0.790703
\(538\) 0 0
\(539\) 302.525 0.561271
\(540\) 0 0
\(541\) −463.659 −0.857042 −0.428521 0.903532i \(-0.640965\pi\)
−0.428521 + 0.903532i \(0.640965\pi\)
\(542\) 0 0
\(543\) −288.755 −0.531777
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 456.359i 0.834294i 0.908839 + 0.417147i \(0.136970\pi\)
−0.908839 + 0.417147i \(0.863030\pi\)
\(548\) 0 0
\(549\) −37.8442 −0.0689330
\(550\) 0 0
\(551\) −92.1736 12.7322i −0.167284 0.0231075i
\(552\) 0 0
\(553\) 633.266i 1.14515i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 188.836 0.339024 0.169512 0.985528i \(-0.445781\pi\)
0.169512 + 0.985528i \(0.445781\pi\)
\(558\) 0 0
\(559\) 206.370i 0.369178i
\(560\) 0 0
\(561\) 1295.29i 2.30889i
\(562\) 0 0
\(563\) 561.830i 0.997923i 0.866624 + 0.498961i \(0.166285\pi\)
−0.866624 + 0.498961i \(0.833715\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 434.514 0.766339
\(568\) 0 0
\(569\) 34.7296i 0.0610362i 0.999534 + 0.0305181i \(0.00971573\pi\)
−0.999534 + 0.0305181i \(0.990284\pi\)
\(570\) 0 0
\(571\) −215.723 −0.377798 −0.188899 0.981997i \(-0.560492\pi\)
−0.188899 + 0.981997i \(0.560492\pi\)
\(572\) 0 0
\(573\) 958.479i 1.67274i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −698.445 −1.21048 −0.605239 0.796044i \(-0.706922\pi\)
−0.605239 + 0.796044i \(0.706922\pi\)
\(578\) 0 0
\(579\) 411.967 0.711515
\(580\) 0 0
\(581\) −237.180 −0.408226
\(582\) 0 0
\(583\) 1430.38i 2.45349i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −312.489 −0.532349 −0.266175 0.963925i \(-0.585760\pi\)
−0.266175 + 0.963925i \(0.585760\pi\)
\(588\) 0 0
\(589\) −851.000 117.551i −1.44482 0.199578i
\(590\) 0 0
\(591\) 1010.22i 1.70935i
\(592\) 0 0
\(593\) 1086.81 1.83273 0.916367 0.400339i \(-0.131108\pi\)
0.916367 + 0.400339i \(0.131108\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 593.060i 0.993400i
\(598\) 0 0
\(599\) 791.665i 1.32164i 0.750543 + 0.660822i \(0.229792\pi\)
−0.750543 + 0.660822i \(0.770208\pi\)
\(600\) 0 0
\(601\) 113.205i 0.188362i −0.995555 0.0941808i \(-0.969977\pi\)
0.995555 0.0941808i \(-0.0300232\pi\)
\(602\) 0 0
\(603\) 44.2141i 0.0733235i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 193.212i 0.318306i 0.987254 + 0.159153i \(0.0508764\pi\)
−0.987254 + 0.159153i \(0.949124\pi\)
\(608\) 0 0
\(609\) 80.8040 0.132683
\(610\) 0 0
\(611\) 286.357i 0.468669i
\(612\) 0 0
\(613\) 133.846 0.218346 0.109173 0.994023i \(-0.465180\pi\)
0.109173 + 0.994023i \(0.465180\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −602.743 −0.976893 −0.488447 0.872594i \(-0.662436\pi\)
−0.488447 + 0.872594i \(0.662436\pi\)
\(618\) 0 0
\(619\) 136.718 0.220869 0.110434 0.993883i \(-0.464776\pi\)
0.110434 + 0.993883i \(0.464776\pi\)
\(620\) 0 0
\(621\) 532.380i 0.857294i
\(622\) 0 0
\(623\) 568.466i 0.912465i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 963.049 + 133.029i 1.53596 + 0.212168i
\(628\) 0 0
\(629\) 640.418i 1.01815i
\(630\) 0 0
\(631\) 1197.46 1.89772 0.948862 0.315691i \(-0.102236\pi\)
0.948862 + 0.315691i \(0.102236\pi\)
\(632\) 0 0
\(633\) 369.552 0.583811
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 127.521i 0.200189i
\(638\) 0 0
\(639\) 23.2032i 0.0363118i
\(640\) 0 0
\(641\) 144.826i 0.225938i 0.993599 + 0.112969i \(0.0360360\pi\)
−0.993599 + 0.112969i \(0.963964\pi\)
\(642\) 0 0
\(643\) 423.852 0.659179 0.329589 0.944124i \(-0.393090\pi\)
0.329589 + 0.944124i \(0.393090\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −767.957 −1.18695 −0.593475 0.804852i \(-0.702245\pi\)
−0.593475 + 0.804852i \(0.702245\pi\)
\(648\) 0 0
\(649\) 1064.53i 1.64027i
\(650\) 0 0
\(651\) 746.029 1.14597
\(652\) 0 0
\(653\) 148.725 0.227756 0.113878 0.993495i \(-0.463673\pi\)
0.113878 + 0.993495i \(0.463673\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −14.6575 −0.0223097
\(658\) 0 0
\(659\) 1058.23i 1.60581i −0.596109 0.802904i \(-0.703287\pi\)
0.596109 0.802904i \(-0.296713\pi\)
\(660\) 0 0
\(661\) 714.976i 1.08166i −0.841132 0.540829i \(-0.818111\pi\)
0.841132 0.540829i \(-0.181889\pi\)
\(662\) 0 0
\(663\) −545.991 −0.823516
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 94.5706i 0.141785i
\(668\) 0 0
\(669\) 1055.59 1.57786
\(670\) 0 0
\(671\) 1642.12 2.44727
\(672\) 0 0
\(673\) 624.276i 0.927602i 0.885939 + 0.463801i \(0.153515\pi\)
−0.885939 + 0.463801i \(0.846485\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 79.4837i 0.117406i 0.998275 + 0.0587029i \(0.0186965\pi\)
−0.998275 + 0.0587029i \(0.981304\pi\)
\(678\) 0 0
\(679\) 838.170i 1.23442i
\(680\) 0 0
\(681\) 242.231 0.355699
\(682\) 0 0
\(683\) 918.987i 1.34552i 0.739863 + 0.672758i \(0.234890\pi\)
−0.739863 + 0.672758i \(0.765110\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 123.707i 0.180069i
\(688\) 0 0
\(689\) 602.936 0.875089
\(690\) 0 0
\(691\) −555.126 −0.803366 −0.401683 0.915779i \(-0.631575\pi\)
−0.401683 + 0.915779i \(0.631575\pi\)
\(692\) 0 0
\(693\) 39.4897 0.0569837
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 411.919i 0.590988i
\(698\) 0 0
\(699\) 367.197i 0.525318i
\(700\) 0 0
\(701\) 73.5776 0.104961 0.0524805 0.998622i \(-0.483287\pi\)
0.0524805 + 0.998622i \(0.483287\pi\)
\(702\) 0 0
\(703\) 476.152 + 65.7724i 0.677314 + 0.0935596i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −198.715 −0.281069
\(708\) 0 0
\(709\) −578.030 −0.815275 −0.407638 0.913144i \(-0.633647\pi\)
−0.407638 + 0.913144i \(0.633647\pi\)
\(710\) 0 0
\(711\) 45.2589i 0.0636553i
\(712\) 0 0
\(713\) 873.131i 1.22459i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 519.795i 0.724959i
\(718\) 0 0
\(719\) −870.924 −1.21130 −0.605649 0.795732i \(-0.707087\pi\)
−0.605649 + 0.795732i \(0.707087\pi\)
\(720\) 0 0
\(721\) 356.026i 0.493794i
\(722\) 0 0
\(723\) 252.812 0.349670
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −651.673 −0.896386 −0.448193 0.893937i \(-0.647932\pi\)
−0.448193 + 0.893937i \(0.647932\pi\)
\(728\) 0 0
\(729\) −758.599 −1.04060
\(730\) 0 0
\(731\) −710.217 −0.971569
\(732\) 0 0
\(733\) 16.2720 0.0221992 0.0110996 0.999938i \(-0.496467\pi\)
0.0110996 + 0.999938i \(0.496467\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1918.52i 2.60315i
\(738\) 0 0
\(739\) 970.120 1.31275 0.656373 0.754436i \(-0.272090\pi\)
0.656373 + 0.754436i \(0.272090\pi\)
\(740\) 0 0
\(741\) 56.0746 405.945i 0.0756742 0.547835i
\(742\) 0 0
\(743\) 669.599i 0.901211i 0.892723 + 0.450605i \(0.148792\pi\)
−0.892723 + 0.450605i \(0.851208\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 16.9510 0.0226921
\(748\) 0 0
\(749\) 1113.52i 1.48668i
\(750\) 0 0
\(751\) 798.869i 1.06374i 0.846826 + 0.531870i \(0.178511\pi\)
−0.846826 + 0.531870i \(0.821489\pi\)
\(752\) 0 0
\(753\) 880.560i 1.16940i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 843.963 1.11488 0.557439 0.830218i \(-0.311784\pi\)
0.557439 + 0.830218i \(0.311784\pi\)
\(758\) 0 0
\(759\) 988.094i 1.30184i
\(760\) 0 0
\(761\) 174.165 0.228863 0.114431 0.993431i \(-0.463495\pi\)
0.114431 + 0.993431i \(0.463495\pi\)
\(762\) 0 0
\(763\) 1010.07i 1.32382i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 448.723 0.585037
\(768\) 0 0
\(769\) 215.531 0.280274 0.140137 0.990132i \(-0.455246\pi\)
0.140137 + 0.990132i \(0.455246\pi\)
\(770\) 0 0
\(771\) −682.469 −0.885174
\(772\) 0 0
\(773\) 589.413i 0.762501i 0.924472 + 0.381251i \(0.124507\pi\)
−0.924472 + 0.381251i \(0.875493\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −417.418 −0.537218
\(778\) 0 0
\(779\) 306.262 + 42.3050i 0.393148 + 0.0543068i
\(780\) 0 0
\(781\) 1006.82i 1.28915i
\(782\) 0 0
\(783\) −135.014 −0.172432
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 1145.89i 1.45602i −0.685568 0.728009i \(-0.740446\pi\)
0.685568 0.728009i \(-0.259554\pi\)
\(788\) 0 0
\(789\) 822.628i 1.04262i
\(790\) 0 0
\(791\) 114.616i 0.144901i
\(792\) 0 0
\(793\) 692.188i 0.872873i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1240.74i 1.55677i 0.627789 + 0.778384i \(0.283960\pi\)
−0.627789 + 0.778384i \(0.716040\pi\)
\(798\) 0 0
\(799\) 985.488 1.23340
\(800\) 0 0
\(801\) 40.6277i 0.0507212i
\(802\) 0 0
\(803\) 636.011 0.792044
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −331.113 −0.410301
\(808\) 0 0
\(809\) 214.567 0.265225 0.132612 0.991168i \(-0.457663\pi\)
0.132612 + 0.991168i \(0.457663\pi\)
\(810\) 0 0
\(811\) 443.871i 0.547313i 0.961827 + 0.273657i \(0.0882332\pi\)
−0.961827 + 0.273657i \(0.911767\pi\)
\(812\) 0 0
\(813\) 280.633i 0.345182i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 72.9409 528.047i 0.0892790 0.646325i
\(818\) 0 0
\(819\) 16.6457i 0.0203245i
\(820\) 0 0
\(821\) 239.094 0.291223 0.145611 0.989342i \(-0.453485\pi\)
0.145611 + 0.989342i \(0.453485\pi\)
\(822\) 0 0
\(823\) 367.550 0.446598 0.223299 0.974750i \(-0.428317\pi\)
0.223299 + 0.974750i \(0.428317\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 432.940i 0.523507i 0.965135 + 0.261753i \(0.0843007\pi\)
−0.965135 + 0.261753i \(0.915699\pi\)
\(828\) 0 0
\(829\) 424.324i 0.511851i 0.966697 + 0.255925i \(0.0823801\pi\)
−0.966697 + 0.255925i \(0.917620\pi\)
\(830\) 0 0
\(831\) 158.056i 0.190199i
\(832\) 0 0
\(833\) −438.858 −0.526841
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1246.53 −1.48928
\(838\) 0 0
\(839\) 1198.38i 1.42834i −0.699974 0.714169i \(-0.746805\pi\)
0.699974 0.714169i \(-0.253195\pi\)
\(840\) 0 0
\(841\) 817.016 0.971482
\(842\) 0 0
\(843\) −200.603 −0.237963
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −1032.65 −1.21918
\(848\) 0 0
\(849\) 1110.18i 1.30763i
\(850\) 0 0
\(851\) 488.535i 0.574071i
\(852\) 0 0
\(853\) 1631.88 1.91311 0.956555 0.291553i \(-0.0941721\pi\)
0.956555 + 0.291553i \(0.0941721\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1704.86i 1.98933i −0.103147 0.994666i \(-0.532891\pi\)
0.103147 0.994666i \(-0.467109\pi\)
\(858\) 0 0
\(859\) −1190.68 −1.38612 −0.693061 0.720879i \(-0.743738\pi\)
−0.693061 + 0.720879i \(0.743738\pi\)
\(860\) 0 0
\(861\) −268.485 −0.311829
\(862\) 0 0
\(863\) 1219.71i 1.41334i 0.707543 + 0.706670i \(0.249803\pi\)
−0.707543 + 0.706670i \(0.750197\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 1031.60i 1.18986i
\(868\) 0 0
\(869\) 1963.86i 2.25990i
\(870\) 0 0
\(871\) 808.696 0.928468
\(872\) 0 0
\(873\) 59.9032i 0.0686176i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 1096.08i 1.24981i 0.780702 + 0.624904i \(0.214862\pi\)
−0.780702 + 0.624904i \(0.785138\pi\)
\(878\) 0 0
\(879\) −59.6455 −0.0678561
\(880\) 0 0
\(881\) −175.525 −0.199234 −0.0996170 0.995026i \(-0.531762\pi\)
−0.0996170 + 0.995026i \(0.531762\pi\)
\(882\) 0 0
\(883\) −1733.12 −1.96277 −0.981384 0.192055i \(-0.938485\pi\)
−0.981384 + 0.192055i \(0.938485\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 134.522i 0.151660i 0.997121 + 0.0758298i \(0.0241606\pi\)
−0.997121 + 0.0758298i \(0.975839\pi\)
\(888\) 0 0
\(889\) 523.568i 0.588940i
\(890\) 0 0
\(891\) 1347.50 1.51234
\(892\) 0 0
\(893\) −101.212 + 732.711i −0.113339 + 0.820505i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 416.502 0.464328
\(898\) 0 0
\(899\) −221.430 −0.246307
\(900\) 0 0
\(901\) 2074.99i 2.30298i
\(902\) 0 0
\(903\) 462.913i 0.512638i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 293.274i 0.323345i −0.986844 0.161672i \(-0.948311\pi\)
0.986844 0.161672i \(-0.0516888\pi\)
\(908\) 0 0
\(909\) 14.2020 0.0156238
\(910\) 0 0
\(911\) 303.681i 0.333349i 0.986012 + 0.166674i \(0.0533029\pi\)
−0.986012 + 0.166674i \(0.946697\pi\)
\(912\) 0 0
\(913\) −735.531 −0.805620
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1166.27 1.27184
\(918\) 0 0
\(919\) 1466.07 1.59529 0.797644 0.603128i \(-0.206079\pi\)
0.797644 + 0.603128i \(0.206079\pi\)
\(920\) 0 0
\(921\) −924.125 −1.00339
\(922\) 0 0
\(923\) −424.398 −0.459803
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 25.4448i 0.0274486i
\(928\) 0 0
\(929\) −1278.74 −1.37647 −0.688234 0.725489i \(-0.741614\pi\)
−0.688234 + 0.725489i \(0.741614\pi\)
\(930\) 0 0
\(931\) 45.0718 326.292i 0.0484122 0.350475i
\(932\) 0 0
\(933\) 552.953i 0.592661i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −746.023 −0.796182 −0.398091 0.917346i \(-0.630327\pi\)
−0.398091 + 0.917346i \(0.630327\pi\)
\(938\) 0 0
\(939\) 451.599i 0.480936i
\(940\) 0 0
\(941\) 1753.70i 1.86365i 0.362905 + 0.931826i \(0.381785\pi\)
−0.362905 + 0.931826i \(0.618215\pi\)
\(942\) 0 0
\(943\) 314.227i 0.333220i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1195.95 1.26288 0.631440 0.775425i \(-0.282464\pi\)
0.631440 + 0.775425i \(0.282464\pi\)
\(948\) 0 0
\(949\) 268.092i 0.282500i
\(950\) 0 0
\(951\) 11.7603 0.0123662
\(952\) 0 0
\(953\) 667.620i 0.700546i −0.936648 0.350273i \(-0.886089\pi\)
0.936648 0.350273i \(-0.113911\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 250.586 0.261845
\(958\) 0 0
\(959\) 806.781 0.841273
\(960\) 0 0
\(961\) −1083.37 −1.12734
\(962\) 0 0
\(963\) 79.5824i 0.0826401i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1708.02 1.76630 0.883152 0.469086i \(-0.155417\pi\)
0.883152 + 0.469086i \(0.155417\pi\)
\(968\) 0 0
\(969\) −1397.05 192.979i −1.44174 0.199153i
\(970\) 0 0
\(971\) 216.028i 0.222480i 0.993794 + 0.111240i \(0.0354822\pi\)
−0.993794 + 0.111240i \(0.964518\pi\)
\(972\) 0 0
\(973\) 889.776 0.914466
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 57.4013i 0.0587526i 0.999568 + 0.0293763i \(0.00935211\pi\)
−0.999568 + 0.0293763i \(0.990648\pi\)
\(978\) 0 0
\(979\) 1762.90i 1.80072i
\(980\) 0 0
\(981\) 72.1889i 0.0735870i
\(982\) 0 0
\(983\) 207.431i 0.211019i −0.994418 0.105509i \(-0.966353\pi\)
0.994418 0.105509i \(-0.0336473\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 642.331i 0.650792i
\(988\) 0 0
\(989\) 541.780 0.547805
\(990\) 0 0
\(991\) 828.905i 0.836432i −0.908348 0.418216i \(-0.862655\pi\)
0.908348 0.418216i \(-0.137345\pi\)
\(992\) 0 0
\(993\) 284.764 0.286771
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1735.54 −1.74076 −0.870380 0.492381i \(-0.836127\pi\)
−0.870380 + 0.492381i \(0.836127\pi\)
\(998\) 0 0
\(999\) 697.459 0.698157
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.1101.11 yes 14
5.2 odd 4 1900.3.g.d.949.21 28
5.3 odd 4 1900.3.g.d.949.8 28
5.4 even 2 1900.3.e.h.1101.4 yes 14
19.18 odd 2 inner 1900.3.e.g.1101.4 14
95.18 even 4 1900.3.g.d.949.22 28
95.37 even 4 1900.3.g.d.949.7 28
95.94 odd 2 1900.3.e.h.1101.11 yes 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1900.3.e.g.1101.4 14 19.18 odd 2 inner
1900.3.e.g.1101.11 yes 14 1.1 even 1 trivial
1900.3.e.h.1101.4 yes 14 5.4 even 2
1900.3.e.h.1101.11 yes 14 95.94 odd 2
1900.3.g.d.949.7 28 95.37 even 4
1900.3.g.d.949.8 28 5.3 odd 4
1900.3.g.d.949.21 28 5.2 odd 4
1900.3.g.d.949.22 28 95.18 even 4