Properties

Label 4600.2.a.q.1.2
Level $4600$
Weight $2$
Character 4600.1
Self dual yes
Analytic conductor $36.731$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4600,2,Mod(1,4600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4600.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4600.a (trivial)

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: yes
Analytic conductor: \(36.7311849298\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 4600.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.23607 q^{3} -0.236068 q^{7} -1.47214 q^{9} +1.00000 q^{11} -2.23607 q^{13} +2.47214 q^{17} +1.00000 q^{19} -0.291796 q^{21} +1.00000 q^{23} -5.52786 q^{27} -6.23607 q^{29} -8.47214 q^{31} +1.23607 q^{33} -6.76393 q^{37} -2.76393 q^{39} +11.9443 q^{41} -11.4721 q^{43} +1.70820 q^{47} -6.94427 q^{49} +3.05573 q^{51} +3.23607 q^{53} +1.23607 q^{57} -1.23607 q^{59} -2.76393 q^{61} +0.347524 q^{63} +4.94427 q^{67} +1.23607 q^{69} +10.0000 q^{71} +0.527864 q^{73} -0.236068 q^{77} -7.18034 q^{79} -2.41641 q^{81} -9.00000 q^{83} -7.70820 q^{87} +2.00000 q^{89} +0.527864 q^{91} -10.4721 q^{93} +16.1803 q^{97} -1.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} + 4 q^{7} + 6 q^{9} + 2 q^{11} - 4 q^{17} + 2 q^{19} - 14 q^{21} + 2 q^{23} - 20 q^{27} - 8 q^{29} - 8 q^{31} - 2 q^{33} - 18 q^{37} - 10 q^{39} + 6 q^{41} - 14 q^{43} - 10 q^{47} + 4 q^{49}+ \cdots + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 1.23607 0.713644 0.356822 0.934172i \(-0.383860\pi\)
0.356822 + 0.934172i \(0.383860\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.236068 −0.0892253 −0.0446127 0.999004i \(-0.514205\pi\)
−0.0446127 + 0.999004i \(0.514205\pi\)
\(8\) 0 0
\(9\) −1.47214 −0.490712
\(10\) 0 0
\(11\) 1.00000 0.301511 0.150756 0.988571i \(-0.451829\pi\)
0.150756 + 0.988571i \(0.451829\pi\)
\(12\) 0 0
\(13\) −2.23607 −0.620174 −0.310087 0.950708i \(-0.600358\pi\)
−0.310087 + 0.950708i \(0.600358\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.47214 0.599581 0.299791 0.954005i \(-0.403083\pi\)
0.299791 + 0.954005i \(0.403083\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) −0.291796 −0.0636751
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −5.52786 −1.06384
\(28\) 0 0
\(29\) −6.23607 −1.15801 −0.579004 0.815324i \(-0.696559\pi\)
−0.579004 + 0.815324i \(0.696559\pi\)
\(30\) 0 0
\(31\) −8.47214 −1.52164 −0.760820 0.648963i \(-0.775203\pi\)
−0.760820 + 0.648963i \(0.775203\pi\)
\(32\) 0 0
\(33\) 1.23607 0.215172
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −6.76393 −1.11198 −0.555992 0.831188i \(-0.687661\pi\)
−0.555992 + 0.831188i \(0.687661\pi\)
\(38\) 0 0
\(39\) −2.76393 −0.442583
\(40\) 0 0
\(41\) 11.9443 1.86538 0.932691 0.360677i \(-0.117454\pi\)
0.932691 + 0.360677i \(0.117454\pi\)
\(42\) 0 0
\(43\) −11.4721 −1.74948 −0.874742 0.484589i \(-0.838969\pi\)
−0.874742 + 0.484589i \(0.838969\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.70820 0.249167 0.124584 0.992209i \(-0.460241\pi\)
0.124584 + 0.992209i \(0.460241\pi\)
\(48\) 0 0
\(49\) −6.94427 −0.992039
\(50\) 0 0
\(51\) 3.05573 0.427888
\(52\) 0 0
\(53\) 3.23607 0.444508 0.222254 0.974989i \(-0.428659\pi\)
0.222254 + 0.974989i \(0.428659\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.23607 0.163721
\(58\) 0 0
\(59\) −1.23607 −0.160922 −0.0804612 0.996758i \(-0.525639\pi\)
−0.0804612 + 0.996758i \(0.525639\pi\)
\(60\) 0 0
\(61\) −2.76393 −0.353885 −0.176943 0.984221i \(-0.556621\pi\)
−0.176943 + 0.984221i \(0.556621\pi\)
\(62\) 0 0
\(63\) 0.347524 0.0437839
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.94427 0.604039 0.302019 0.953302i \(-0.402339\pi\)
0.302019 + 0.953302i \(0.402339\pi\)
\(68\) 0 0
\(69\) 1.23607 0.148805
\(70\) 0 0
\(71\) 10.0000 1.18678 0.593391 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) 0 0
\(73\) 0.527864 0.0617818 0.0308909 0.999523i \(-0.490166\pi\)
0.0308909 + 0.999523i \(0.490166\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.236068 −0.0269024
\(78\) 0 0
\(79\) −7.18034 −0.807851 −0.403926 0.914792i \(-0.632355\pi\)
−0.403926 + 0.914792i \(0.632355\pi\)
\(80\) 0 0
\(81\) −2.41641 −0.268490
\(82\) 0 0
\(83\) −9.00000 −0.987878 −0.493939 0.869496i \(-0.664443\pi\)
−0.493939 + 0.869496i \(0.664443\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −7.70820 −0.826406
\(88\) 0 0
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 0 0
\(91\) 0.527864 0.0553352
\(92\) 0 0
\(93\) −10.4721 −1.08591
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 16.1803 1.64286 0.821432 0.570306i \(-0.193175\pi\)
0.821432 + 0.570306i \(0.193175\pi\)
\(98\) 0 0
\(99\) −1.47214 −0.147955
\(100\) 0 0
\(101\) −1.05573 −0.105049 −0.0525244 0.998620i \(-0.516727\pi\)
−0.0525244 + 0.998620i \(0.516727\pi\)
\(102\) 0 0
\(103\) −2.23607 −0.220326 −0.110163 0.993914i \(-0.535137\pi\)
−0.110163 + 0.993914i \(0.535137\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.41641 −0.716971 −0.358486 0.933535i \(-0.616707\pi\)
−0.358486 + 0.933535i \(0.616707\pi\)
\(108\) 0 0
\(109\) −17.2361 −1.65092 −0.825458 0.564464i \(-0.809083\pi\)
−0.825458 + 0.564464i \(0.809083\pi\)
\(110\) 0 0
\(111\) −8.36068 −0.793561
\(112\) 0 0
\(113\) −11.2361 −1.05700 −0.528500 0.848933i \(-0.677245\pi\)
−0.528500 + 0.848933i \(0.677245\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 3.29180 0.304327
\(118\) 0 0
\(119\) −0.583592 −0.0534978
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 0 0
\(123\) 14.7639 1.33122
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −18.1803 −1.61324 −0.806622 0.591067i \(-0.798707\pi\)
−0.806622 + 0.591067i \(0.798707\pi\)
\(128\) 0 0
\(129\) −14.1803 −1.24851
\(130\) 0 0
\(131\) 2.94427 0.257242 0.128621 0.991694i \(-0.458945\pi\)
0.128621 + 0.991694i \(0.458945\pi\)
\(132\) 0 0
\(133\) −0.236068 −0.0204697
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −20.4721 −1.74905 −0.874526 0.484978i \(-0.838828\pi\)
−0.874526 + 0.484978i \(0.838828\pi\)
\(138\) 0 0
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 0 0
\(141\) 2.11146 0.177817
\(142\) 0 0
\(143\) −2.23607 −0.186989
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −8.58359 −0.707963
\(148\) 0 0
\(149\) −6.94427 −0.568897 −0.284448 0.958691i \(-0.591810\pi\)
−0.284448 + 0.958691i \(0.591810\pi\)
\(150\) 0 0
\(151\) 20.4721 1.66600 0.832999 0.553274i \(-0.186622\pi\)
0.832999 + 0.553274i \(0.186622\pi\)
\(152\) 0 0
\(153\) −3.63932 −0.294222
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −13.7082 −1.09403 −0.547017 0.837122i \(-0.684237\pi\)
−0.547017 + 0.837122i \(0.684237\pi\)
\(158\) 0 0
\(159\) 4.00000 0.317221
\(160\) 0 0
\(161\) −0.236068 −0.0186048
\(162\) 0 0
\(163\) −1.70820 −0.133797 −0.0668984 0.997760i \(-0.521310\pi\)
−0.0668984 + 0.997760i \(0.521310\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −21.4164 −1.65725 −0.828626 0.559803i \(-0.810877\pi\)
−0.828626 + 0.559803i \(0.810877\pi\)
\(168\) 0 0
\(169\) −8.00000 −0.615385
\(170\) 0 0
\(171\) −1.47214 −0.112577
\(172\) 0 0
\(173\) −9.76393 −0.742338 −0.371169 0.928565i \(-0.621043\pi\)
−0.371169 + 0.928565i \(0.621043\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1.52786 −0.114841
\(178\) 0 0
\(179\) −2.29180 −0.171297 −0.0856484 0.996325i \(-0.527296\pi\)
−0.0856484 + 0.996325i \(0.527296\pi\)
\(180\) 0 0
\(181\) 16.9443 1.25946 0.629729 0.776815i \(-0.283166\pi\)
0.629729 + 0.776815i \(0.283166\pi\)
\(182\) 0 0
\(183\) −3.41641 −0.252548
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2.47214 0.180780
\(188\) 0 0
\(189\) 1.30495 0.0949213
\(190\) 0 0
\(191\) 3.18034 0.230121 0.115061 0.993358i \(-0.463294\pi\)
0.115061 + 0.993358i \(0.463294\pi\)
\(192\) 0 0
\(193\) 14.9443 1.07571 0.537856 0.843037i \(-0.319234\pi\)
0.537856 + 0.843037i \(0.319234\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3.76393 0.268169 0.134085 0.990970i \(-0.457191\pi\)
0.134085 + 0.990970i \(0.457191\pi\)
\(198\) 0 0
\(199\) −0.708204 −0.0502032 −0.0251016 0.999685i \(-0.507991\pi\)
−0.0251016 + 0.999685i \(0.507991\pi\)
\(200\) 0 0
\(201\) 6.11146 0.431069
\(202\) 0 0
\(203\) 1.47214 0.103324
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.47214 −0.102321
\(208\) 0 0
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) 2.94427 0.202692 0.101346 0.994851i \(-0.467685\pi\)
0.101346 + 0.994851i \(0.467685\pi\)
\(212\) 0 0
\(213\) 12.3607 0.846940
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 2.00000 0.135769
\(218\) 0 0
\(219\) 0.652476 0.0440902
\(220\) 0 0
\(221\) −5.52786 −0.371844
\(222\) 0 0
\(223\) −8.76393 −0.586876 −0.293438 0.955978i \(-0.594799\pi\)
−0.293438 + 0.955978i \(0.594799\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 4.94427 0.328163 0.164081 0.986447i \(-0.447534\pi\)
0.164081 + 0.986447i \(0.447534\pi\)
\(228\) 0 0
\(229\) −10.9443 −0.723218 −0.361609 0.932330i \(-0.617772\pi\)
−0.361609 + 0.932330i \(0.617772\pi\)
\(230\) 0 0
\(231\) −0.291796 −0.0191988
\(232\) 0 0
\(233\) −13.4721 −0.882589 −0.441294 0.897362i \(-0.645481\pi\)
−0.441294 + 0.897362i \(0.645481\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −8.87539 −0.576518
\(238\) 0 0
\(239\) 11.2361 0.726801 0.363400 0.931633i \(-0.381616\pi\)
0.363400 + 0.931633i \(0.381616\pi\)
\(240\) 0 0
\(241\) 16.7639 1.07986 0.539930 0.841710i \(-0.318451\pi\)
0.539930 + 0.841710i \(0.318451\pi\)
\(242\) 0 0
\(243\) 13.5967 0.872232
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −2.23607 −0.142278
\(248\) 0 0
\(249\) −11.1246 −0.704994
\(250\) 0 0
\(251\) −14.4721 −0.913473 −0.456737 0.889602i \(-0.650982\pi\)
−0.456737 + 0.889602i \(0.650982\pi\)
\(252\) 0 0
\(253\) 1.00000 0.0628695
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 14.0000 0.873296 0.436648 0.899632i \(-0.356166\pi\)
0.436648 + 0.899632i \(0.356166\pi\)
\(258\) 0 0
\(259\) 1.59675 0.0992171
\(260\) 0 0
\(261\) 9.18034 0.568249
\(262\) 0 0
\(263\) −8.00000 −0.493301 −0.246651 0.969104i \(-0.579330\pi\)
−0.246651 + 0.969104i \(0.579330\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 2.47214 0.151292
\(268\) 0 0
\(269\) −2.81966 −0.171918 −0.0859589 0.996299i \(-0.527395\pi\)
−0.0859589 + 0.996299i \(0.527395\pi\)
\(270\) 0 0
\(271\) 26.0689 1.58357 0.791786 0.610799i \(-0.209152\pi\)
0.791786 + 0.610799i \(0.209152\pi\)
\(272\) 0 0
\(273\) 0.652476 0.0394896
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −9.76393 −0.586658 −0.293329 0.956012i \(-0.594763\pi\)
−0.293329 + 0.956012i \(0.594763\pi\)
\(278\) 0 0
\(279\) 12.4721 0.746687
\(280\) 0 0
\(281\) 0.180340 0.0107582 0.00537909 0.999986i \(-0.498288\pi\)
0.00537909 + 0.999986i \(0.498288\pi\)
\(282\) 0 0
\(283\) 16.3607 0.972541 0.486271 0.873808i \(-0.338357\pi\)
0.486271 + 0.873808i \(0.338357\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.81966 −0.166439
\(288\) 0 0
\(289\) −10.8885 −0.640503
\(290\) 0 0
\(291\) 20.0000 1.17242
\(292\) 0 0
\(293\) 5.52786 0.322941 0.161471 0.986878i \(-0.448376\pi\)
0.161471 + 0.986878i \(0.448376\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −5.52786 −0.320759
\(298\) 0 0
\(299\) −2.23607 −0.129315
\(300\) 0 0
\(301\) 2.70820 0.156098
\(302\) 0 0
\(303\) −1.30495 −0.0749675
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −24.0000 −1.36975 −0.684876 0.728659i \(-0.740144\pi\)
−0.684876 + 0.728659i \(0.740144\pi\)
\(308\) 0 0
\(309\) −2.76393 −0.157235
\(310\) 0 0
\(311\) 1.23607 0.0700910 0.0350455 0.999386i \(-0.488842\pi\)
0.0350455 + 0.999386i \(0.488842\pi\)
\(312\) 0 0
\(313\) −20.6525 −1.16735 −0.583673 0.811988i \(-0.698385\pi\)
−0.583673 + 0.811988i \(0.698385\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −18.1246 −1.01798 −0.508990 0.860773i \(-0.669981\pi\)
−0.508990 + 0.860773i \(0.669981\pi\)
\(318\) 0 0
\(319\) −6.23607 −0.349153
\(320\) 0 0
\(321\) −9.16718 −0.511662
\(322\) 0 0
\(323\) 2.47214 0.137553
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −21.3050 −1.17817
\(328\) 0 0
\(329\) −0.403252 −0.0222320
\(330\) 0 0
\(331\) 13.0557 0.717608 0.358804 0.933413i \(-0.383185\pi\)
0.358804 + 0.933413i \(0.383185\pi\)
\(332\) 0 0
\(333\) 9.95743 0.545664
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −6.65248 −0.362383 −0.181192 0.983448i \(-0.557995\pi\)
−0.181192 + 0.983448i \(0.557995\pi\)
\(338\) 0 0
\(339\) −13.8885 −0.754322
\(340\) 0 0
\(341\) −8.47214 −0.458792
\(342\) 0 0
\(343\) 3.29180 0.177740
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −20.9443 −1.12435 −0.562174 0.827019i \(-0.690035\pi\)
−0.562174 + 0.827019i \(0.690035\pi\)
\(348\) 0 0
\(349\) 17.1803 0.919643 0.459821 0.888011i \(-0.347913\pi\)
0.459821 + 0.888011i \(0.347913\pi\)
\(350\) 0 0
\(351\) 12.3607 0.659764
\(352\) 0 0
\(353\) −30.8885 −1.64403 −0.822016 0.569465i \(-0.807150\pi\)
−0.822016 + 0.569465i \(0.807150\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −0.721360 −0.0381784
\(358\) 0 0
\(359\) 24.2361 1.27913 0.639565 0.768737i \(-0.279114\pi\)
0.639565 + 0.768737i \(0.279114\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) −12.3607 −0.648767
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −7.65248 −0.399456 −0.199728 0.979851i \(-0.564006\pi\)
−0.199728 + 0.979851i \(0.564006\pi\)
\(368\) 0 0
\(369\) −17.5836 −0.915365
\(370\) 0 0
\(371\) −0.763932 −0.0396614
\(372\) 0 0
\(373\) 12.0000 0.621336 0.310668 0.950518i \(-0.399447\pi\)
0.310668 + 0.950518i \(0.399447\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 13.9443 0.718167
\(378\) 0 0
\(379\) 20.9443 1.07583 0.537917 0.842997i \(-0.319211\pi\)
0.537917 + 0.842997i \(0.319211\pi\)
\(380\) 0 0
\(381\) −22.4721 −1.15128
\(382\) 0 0
\(383\) −4.23607 −0.216453 −0.108226 0.994126i \(-0.534517\pi\)
−0.108226 + 0.994126i \(0.534517\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 16.8885 0.858493
\(388\) 0 0
\(389\) −16.1803 −0.820376 −0.410188 0.912001i \(-0.634537\pi\)
−0.410188 + 0.912001i \(0.634537\pi\)
\(390\) 0 0
\(391\) 2.47214 0.125021
\(392\) 0 0
\(393\) 3.63932 0.183579
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 22.3607 1.12225 0.561125 0.827731i \(-0.310369\pi\)
0.561125 + 0.827731i \(0.310369\pi\)
\(398\) 0 0
\(399\) −0.291796 −0.0146081
\(400\) 0 0
\(401\) 27.1246 1.35454 0.677269 0.735735i \(-0.263163\pi\)
0.677269 + 0.735735i \(0.263163\pi\)
\(402\) 0 0
\(403\) 18.9443 0.943681
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −6.76393 −0.335276
\(408\) 0 0
\(409\) 0.416408 0.0205900 0.0102950 0.999947i \(-0.496723\pi\)
0.0102950 + 0.999947i \(0.496723\pi\)
\(410\) 0 0
\(411\) −25.3050 −1.24820
\(412\) 0 0
\(413\) 0.291796 0.0143583
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 24.7214 1.21061
\(418\) 0 0
\(419\) 34.7771 1.69897 0.849486 0.527611i \(-0.176912\pi\)
0.849486 + 0.527611i \(0.176912\pi\)
\(420\) 0 0
\(421\) −19.8885 −0.969308 −0.484654 0.874706i \(-0.661055\pi\)
−0.484654 + 0.874706i \(0.661055\pi\)
\(422\) 0 0
\(423\) −2.51471 −0.122269
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.652476 0.0315755
\(428\) 0 0
\(429\) −2.76393 −0.133444
\(430\) 0 0
\(431\) −4.94427 −0.238157 −0.119079 0.992885i \(-0.537994\pi\)
−0.119079 + 0.992885i \(0.537994\pi\)
\(432\) 0 0
\(433\) −11.1246 −0.534615 −0.267307 0.963611i \(-0.586134\pi\)
−0.267307 + 0.963611i \(0.586134\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.00000 0.0478365
\(438\) 0 0
\(439\) −32.3607 −1.54449 −0.772245 0.635324i \(-0.780866\pi\)
−0.772245 + 0.635324i \(0.780866\pi\)
\(440\) 0 0
\(441\) 10.2229 0.486805
\(442\) 0 0
\(443\) 10.0000 0.475114 0.237557 0.971374i \(-0.423653\pi\)
0.237557 + 0.971374i \(0.423653\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −8.58359 −0.405990
\(448\) 0 0
\(449\) 16.8328 0.794390 0.397195 0.917734i \(-0.369984\pi\)
0.397195 + 0.917734i \(0.369984\pi\)
\(450\) 0 0
\(451\) 11.9443 0.562434
\(452\) 0 0
\(453\) 25.3050 1.18893
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −10.6525 −0.498302 −0.249151 0.968465i \(-0.580152\pi\)
−0.249151 + 0.968465i \(0.580152\pi\)
\(458\) 0 0
\(459\) −13.6656 −0.637857
\(460\) 0 0
\(461\) 2.34752 0.109335 0.0546676 0.998505i \(-0.482590\pi\)
0.0546676 + 0.998505i \(0.482590\pi\)
\(462\) 0 0
\(463\) 17.5279 0.814589 0.407294 0.913297i \(-0.366472\pi\)
0.407294 + 0.913297i \(0.366472\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 17.0000 0.786666 0.393333 0.919396i \(-0.371322\pi\)
0.393333 + 0.919396i \(0.371322\pi\)
\(468\) 0 0
\(469\) −1.16718 −0.0538956
\(470\) 0 0
\(471\) −16.9443 −0.780751
\(472\) 0 0
\(473\) −11.4721 −0.527489
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −4.76393 −0.218125
\(478\) 0 0
\(479\) 28.1246 1.28505 0.642523 0.766266i \(-0.277888\pi\)
0.642523 + 0.766266i \(0.277888\pi\)
\(480\) 0 0
\(481\) 15.1246 0.689623
\(482\) 0 0
\(483\) −0.291796 −0.0132772
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −1.12461 −0.0509610 −0.0254805 0.999675i \(-0.508112\pi\)
−0.0254805 + 0.999675i \(0.508112\pi\)
\(488\) 0 0
\(489\) −2.11146 −0.0954833
\(490\) 0 0
\(491\) 1.23607 0.0557830 0.0278915 0.999611i \(-0.491121\pi\)
0.0278915 + 0.999611i \(0.491121\pi\)
\(492\) 0 0
\(493\) −15.4164 −0.694320
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.36068 −0.105891
\(498\) 0 0
\(499\) 24.5410 1.09861 0.549303 0.835623i \(-0.314893\pi\)
0.549303 + 0.835623i \(0.314893\pi\)
\(500\) 0 0
\(501\) −26.4721 −1.18269
\(502\) 0 0
\(503\) 32.5967 1.45342 0.726709 0.686946i \(-0.241049\pi\)
0.726709 + 0.686946i \(0.241049\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −9.88854 −0.439166
\(508\) 0 0
\(509\) −14.3607 −0.636526 −0.318263 0.948002i \(-0.603099\pi\)
−0.318263 + 0.948002i \(0.603099\pi\)
\(510\) 0 0
\(511\) −0.124612 −0.00551250
\(512\) 0 0
\(513\) −5.52786 −0.244061
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 1.70820 0.0751267
\(518\) 0 0
\(519\) −12.0689 −0.529765
\(520\) 0 0
\(521\) 40.6525 1.78102 0.890509 0.454966i \(-0.150349\pi\)
0.890509 + 0.454966i \(0.150349\pi\)
\(522\) 0 0
\(523\) −16.8885 −0.738484 −0.369242 0.929333i \(-0.620383\pi\)
−0.369242 + 0.929333i \(0.620383\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −20.9443 −0.912347
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 1.81966 0.0789665
\(532\) 0 0
\(533\) −26.7082 −1.15686
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −2.83282 −0.122245
\(538\) 0 0
\(539\) −6.94427 −0.299111
\(540\) 0 0
\(541\) −4.70820 −0.202421 −0.101211 0.994865i \(-0.532272\pi\)
−0.101211 + 0.994865i \(0.532272\pi\)
\(542\) 0 0
\(543\) 20.9443 0.898805
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 2.29180 0.0979901 0.0489951 0.998799i \(-0.484398\pi\)
0.0489951 + 0.998799i \(0.484398\pi\)
\(548\) 0 0
\(549\) 4.06888 0.173656
\(550\) 0 0
\(551\) −6.23607 −0.265665
\(552\) 0 0
\(553\) 1.69505 0.0720808
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −13.8197 −0.585558 −0.292779 0.956180i \(-0.594580\pi\)
−0.292779 + 0.956180i \(0.594580\pi\)
\(558\) 0 0
\(559\) 25.6525 1.08498
\(560\) 0 0
\(561\) 3.05573 0.129013
\(562\) 0 0
\(563\) −5.36068 −0.225926 −0.112963 0.993599i \(-0.536034\pi\)
−0.112963 + 0.993599i \(0.536034\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.570437 0.0239561
\(568\) 0 0
\(569\) 39.4164 1.65242 0.826211 0.563361i \(-0.190492\pi\)
0.826211 + 0.563361i \(0.190492\pi\)
\(570\) 0 0
\(571\) 24.0000 1.00437 0.502184 0.864761i \(-0.332530\pi\)
0.502184 + 0.864761i \(0.332530\pi\)
\(572\) 0 0
\(573\) 3.93112 0.164225
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −9.00000 −0.374675 −0.187337 0.982296i \(-0.559986\pi\)
−0.187337 + 0.982296i \(0.559986\pi\)
\(578\) 0 0
\(579\) 18.4721 0.767676
\(580\) 0 0
\(581\) 2.12461 0.0881437
\(582\) 0 0
\(583\) 3.23607 0.134024
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 21.5967 0.891393 0.445697 0.895184i \(-0.352956\pi\)
0.445697 + 0.895184i \(0.352956\pi\)
\(588\) 0 0
\(589\) −8.47214 −0.349088
\(590\) 0 0
\(591\) 4.65248 0.191377
\(592\) 0 0
\(593\) −9.11146 −0.374163 −0.187081 0.982344i \(-0.559903\pi\)
−0.187081 + 0.982344i \(0.559903\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −0.875388 −0.0358273
\(598\) 0 0
\(599\) −36.8328 −1.50495 −0.752474 0.658622i \(-0.771140\pi\)
−0.752474 + 0.658622i \(0.771140\pi\)
\(600\) 0 0
\(601\) 2.94427 0.120099 0.0600497 0.998195i \(-0.480874\pi\)
0.0600497 + 0.998195i \(0.480874\pi\)
\(602\) 0 0
\(603\) −7.27864 −0.296409
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 17.1246 0.695067 0.347533 0.937668i \(-0.387019\pi\)
0.347533 + 0.937668i \(0.387019\pi\)
\(608\) 0 0
\(609\) 1.81966 0.0737363
\(610\) 0 0
\(611\) −3.81966 −0.154527
\(612\) 0 0
\(613\) −40.0689 −1.61837 −0.809183 0.587556i \(-0.800090\pi\)
−0.809183 + 0.587556i \(0.800090\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 37.3050 1.50184 0.750920 0.660393i \(-0.229610\pi\)
0.750920 + 0.660393i \(0.229610\pi\)
\(618\) 0 0
\(619\) −18.4721 −0.742458 −0.371229 0.928541i \(-0.621063\pi\)
−0.371229 + 0.928541i \(0.621063\pi\)
\(620\) 0 0
\(621\) −5.52786 −0.221826
\(622\) 0 0
\(623\) −0.472136 −0.0189157
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 1.23607 0.0493638
\(628\) 0 0
\(629\) −16.7214 −0.666724
\(630\) 0 0
\(631\) 16.1246 0.641911 0.320955 0.947094i \(-0.395996\pi\)
0.320955 + 0.947094i \(0.395996\pi\)
\(632\) 0 0
\(633\) 3.63932 0.144650
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 15.5279 0.615236
\(638\) 0 0
\(639\) −14.7214 −0.582368
\(640\) 0 0
\(641\) −43.7771 −1.72909 −0.864546 0.502555i \(-0.832394\pi\)
−0.864546 + 0.502555i \(0.832394\pi\)
\(642\) 0 0
\(643\) 15.9443 0.628781 0.314390 0.949294i \(-0.398200\pi\)
0.314390 + 0.949294i \(0.398200\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 12.1803 0.478859 0.239429 0.970914i \(-0.423040\pi\)
0.239429 + 0.970914i \(0.423040\pi\)
\(648\) 0 0
\(649\) −1.23607 −0.0485199
\(650\) 0 0
\(651\) 2.47214 0.0968906
\(652\) 0 0
\(653\) −27.5410 −1.07776 −0.538882 0.842381i \(-0.681153\pi\)
−0.538882 + 0.842381i \(0.681153\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −0.777088 −0.0303171
\(658\) 0 0
\(659\) 4.52786 0.176381 0.0881903 0.996104i \(-0.471892\pi\)
0.0881903 + 0.996104i \(0.471892\pi\)
\(660\) 0 0
\(661\) −44.1803 −1.71842 −0.859208 0.511626i \(-0.829043\pi\)
−0.859208 + 0.511626i \(0.829043\pi\)
\(662\) 0 0
\(663\) −6.83282 −0.265365
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −6.23607 −0.241462
\(668\) 0 0
\(669\) −10.8328 −0.418821
\(670\) 0 0
\(671\) −2.76393 −0.106700
\(672\) 0 0
\(673\) 14.3050 0.551415 0.275708 0.961242i \(-0.411088\pi\)
0.275708 + 0.961242i \(0.411088\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.29180 0.164947 0.0824736 0.996593i \(-0.473718\pi\)
0.0824736 + 0.996593i \(0.473718\pi\)
\(678\) 0 0
\(679\) −3.81966 −0.146585
\(680\) 0 0
\(681\) 6.11146 0.234192
\(682\) 0 0
\(683\) 29.7771 1.13939 0.569694 0.821857i \(-0.307062\pi\)
0.569694 + 0.821857i \(0.307062\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −13.5279 −0.516120
\(688\) 0 0
\(689\) −7.23607 −0.275672
\(690\) 0 0
\(691\) −33.5279 −1.27546 −0.637730 0.770260i \(-0.720126\pi\)
−0.637730 + 0.770260i \(0.720126\pi\)
\(692\) 0 0
\(693\) 0.347524 0.0132014
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 29.5279 1.11845
\(698\) 0 0
\(699\) −16.6525 −0.629854
\(700\) 0 0
\(701\) −46.4721 −1.75523 −0.877614 0.479368i \(-0.840866\pi\)
−0.877614 + 0.479368i \(0.840866\pi\)
\(702\) 0 0
\(703\) −6.76393 −0.255107
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0.249224 0.00937302
\(708\) 0 0
\(709\) −17.4164 −0.654087 −0.327043 0.945009i \(-0.606052\pi\)
−0.327043 + 0.945009i \(0.606052\pi\)
\(710\) 0 0
\(711\) 10.5704 0.396422
\(712\) 0 0
\(713\) −8.47214 −0.317284
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 13.8885 0.518677
\(718\) 0 0
\(719\) 24.2918 0.905931 0.452966 0.891528i \(-0.350366\pi\)
0.452966 + 0.891528i \(0.350366\pi\)
\(720\) 0 0
\(721\) 0.527864 0.0196587
\(722\) 0 0
\(723\) 20.7214 0.770636
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 44.7214 1.65862 0.829312 0.558786i \(-0.188733\pi\)
0.829312 + 0.558786i \(0.188733\pi\)
\(728\) 0 0
\(729\) 24.0557 0.890953
\(730\) 0 0
\(731\) −28.3607 −1.04896
\(732\) 0 0
\(733\) 48.4721 1.79036 0.895180 0.445706i \(-0.147047\pi\)
0.895180 + 0.445706i \(0.147047\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.94427 0.182125
\(738\) 0 0
\(739\) 26.9443 0.991161 0.495581 0.868562i \(-0.334955\pi\)
0.495581 + 0.868562i \(0.334955\pi\)
\(740\) 0 0
\(741\) −2.76393 −0.101536
\(742\) 0 0
\(743\) −16.8197 −0.617053 −0.308527 0.951216i \(-0.599836\pi\)
−0.308527 + 0.951216i \(0.599836\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 13.2492 0.484764
\(748\) 0 0
\(749\) 1.75078 0.0639720
\(750\) 0 0
\(751\) 26.5967 0.970529 0.485265 0.874367i \(-0.338723\pi\)
0.485265 + 0.874367i \(0.338723\pi\)
\(752\) 0 0
\(753\) −17.8885 −0.651895
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 21.2361 0.771838 0.385919 0.922533i \(-0.373884\pi\)
0.385919 + 0.922533i \(0.373884\pi\)
\(758\) 0 0
\(759\) 1.23607 0.0448664
\(760\) 0 0
\(761\) −17.1115 −0.620290 −0.310145 0.950689i \(-0.600378\pi\)
−0.310145 + 0.950689i \(0.600378\pi\)
\(762\) 0 0
\(763\) 4.06888 0.147303
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.76393 0.0997998
\(768\) 0 0
\(769\) 12.0689 0.435215 0.217608 0.976036i \(-0.430175\pi\)
0.217608 + 0.976036i \(0.430175\pi\)
\(770\) 0 0
\(771\) 17.3050 0.623223
\(772\) 0 0
\(773\) 9.23607 0.332198 0.166099 0.986109i \(-0.446883\pi\)
0.166099 + 0.986109i \(0.446883\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.97369 0.0708057
\(778\) 0 0
\(779\) 11.9443 0.427948
\(780\) 0 0
\(781\) 10.0000 0.357828
\(782\) 0 0
\(783\) 34.4721 1.23193
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 49.7214 1.77238 0.886188 0.463327i \(-0.153344\pi\)
0.886188 + 0.463327i \(0.153344\pi\)
\(788\) 0 0
\(789\) −9.88854 −0.352041
\(790\) 0 0
\(791\) 2.65248 0.0943112
\(792\) 0 0
\(793\) 6.18034 0.219470
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −10.7639 −0.381278 −0.190639 0.981660i \(-0.561056\pi\)
−0.190639 + 0.981660i \(0.561056\pi\)
\(798\) 0 0
\(799\) 4.22291 0.149396
\(800\) 0 0
\(801\) −2.94427 −0.104031
\(802\) 0 0
\(803\) 0.527864 0.0186279
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −3.48529 −0.122688
\(808\) 0 0
\(809\) −44.8885 −1.57820 −0.789099 0.614267i \(-0.789452\pi\)
−0.789099 + 0.614267i \(0.789452\pi\)
\(810\) 0 0
\(811\) −11.4164 −0.400884 −0.200442 0.979706i \(-0.564238\pi\)
−0.200442 + 0.979706i \(0.564238\pi\)
\(812\) 0 0
\(813\) 32.2229 1.13011
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −11.4721 −0.401359
\(818\) 0 0
\(819\) −0.777088 −0.0271536
\(820\) 0 0
\(821\) −17.7639 −0.619966 −0.309983 0.950742i \(-0.600323\pi\)
−0.309983 + 0.950742i \(0.600323\pi\)
\(822\) 0 0
\(823\) 8.94427 0.311778 0.155889 0.987775i \(-0.450176\pi\)
0.155889 + 0.987775i \(0.450176\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −3.00000 −0.104320 −0.0521601 0.998639i \(-0.516611\pi\)
−0.0521601 + 0.998639i \(0.516611\pi\)
\(828\) 0 0
\(829\) 0.236068 0.00819898 0.00409949 0.999992i \(-0.498695\pi\)
0.00409949 + 0.999992i \(0.498695\pi\)
\(830\) 0 0
\(831\) −12.0689 −0.418665
\(832\) 0 0
\(833\) −17.1672 −0.594808
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 46.8328 1.61878
\(838\) 0 0
\(839\) −40.5967 −1.40156 −0.700778 0.713380i \(-0.747164\pi\)
−0.700778 + 0.713380i \(0.747164\pi\)
\(840\) 0 0
\(841\) 9.88854 0.340984
\(842\) 0 0
\(843\) 0.222912 0.00767751
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 2.36068 0.0811139
\(848\) 0 0
\(849\) 20.2229 0.694049
\(850\) 0 0
\(851\) −6.76393 −0.231865
\(852\) 0 0
\(853\) −23.7639 −0.813662 −0.406831 0.913504i \(-0.633366\pi\)
−0.406831 + 0.913504i \(0.633366\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −27.3050 −0.932719 −0.466360 0.884595i \(-0.654435\pi\)
−0.466360 + 0.884595i \(0.654435\pi\)
\(858\) 0 0
\(859\) −8.29180 −0.282912 −0.141456 0.989945i \(-0.545178\pi\)
−0.141456 + 0.989945i \(0.545178\pi\)
\(860\) 0 0
\(861\) −3.48529 −0.118778
\(862\) 0 0
\(863\) −32.5410 −1.10771 −0.553855 0.832613i \(-0.686844\pi\)
−0.553855 + 0.832613i \(0.686844\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −13.4590 −0.457091
\(868\) 0 0
\(869\) −7.18034 −0.243576
\(870\) 0 0
\(871\) −11.0557 −0.374609
\(872\) 0 0
\(873\) −23.8197 −0.806173
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 29.4164 0.993322 0.496661 0.867945i \(-0.334559\pi\)
0.496661 + 0.867945i \(0.334559\pi\)
\(878\) 0 0
\(879\) 6.83282 0.230465
\(880\) 0 0
\(881\) 24.2918 0.818411 0.409206 0.912442i \(-0.365806\pi\)
0.409206 + 0.912442i \(0.365806\pi\)
\(882\) 0 0
\(883\) 20.9443 0.704831 0.352415 0.935844i \(-0.385360\pi\)
0.352415 + 0.935844i \(0.385360\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −32.3607 −1.08657 −0.543283 0.839550i \(-0.682819\pi\)
−0.543283 + 0.839550i \(0.682819\pi\)
\(888\) 0 0
\(889\) 4.29180 0.143942
\(890\) 0 0
\(891\) −2.41641 −0.0809527
\(892\) 0 0
\(893\) 1.70820 0.0571629
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −2.76393 −0.0922850
\(898\) 0 0
\(899\) 52.8328 1.76207
\(900\) 0 0
\(901\) 8.00000 0.266519
\(902\) 0 0
\(903\) 3.34752 0.111399
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 32.4164 1.07637 0.538185 0.842827i \(-0.319110\pi\)
0.538185 + 0.842827i \(0.319110\pi\)
\(908\) 0 0
\(909\) 1.55418 0.0515487
\(910\) 0 0
\(911\) 27.0689 0.896832 0.448416 0.893825i \(-0.351988\pi\)
0.448416 + 0.893825i \(0.351988\pi\)
\(912\) 0 0
\(913\) −9.00000 −0.297857
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −0.695048 −0.0229525
\(918\) 0 0
\(919\) −27.7771 −0.916282 −0.458141 0.888880i \(-0.651484\pi\)
−0.458141 + 0.888880i \(0.651484\pi\)
\(920\) 0 0
\(921\) −29.6656 −0.977516
\(922\) 0 0
\(923\) −22.3607 −0.736011
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 3.29180 0.108117
\(928\) 0 0
\(929\) 31.0000 1.01708 0.508539 0.861039i \(-0.330186\pi\)
0.508539 + 0.861039i \(0.330186\pi\)
\(930\) 0 0
\(931\) −6.94427 −0.227589
\(932\) 0 0
\(933\) 1.52786 0.0500200
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 33.1246 1.08213 0.541067 0.840980i \(-0.318021\pi\)
0.541067 + 0.840980i \(0.318021\pi\)
\(938\) 0 0
\(939\) −25.5279 −0.833070
\(940\) 0 0
\(941\) −8.76393 −0.285696 −0.142848 0.989745i \(-0.545626\pi\)
−0.142848 + 0.989745i \(0.545626\pi\)
\(942\) 0 0
\(943\) 11.9443 0.388959
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 53.1935 1.72856 0.864278 0.503014i \(-0.167776\pi\)
0.864278 + 0.503014i \(0.167776\pi\)
\(948\) 0 0
\(949\) −1.18034 −0.0383155
\(950\) 0 0
\(951\) −22.4033 −0.726475
\(952\) 0 0
\(953\) −36.6525 −1.18729 −0.593645 0.804727i \(-0.702312\pi\)
−0.593645 + 0.804727i \(0.702312\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −7.70820 −0.249171
\(958\) 0 0
\(959\) 4.83282 0.156060
\(960\) 0 0
\(961\) 40.7771 1.31539
\(962\) 0 0
\(963\) 10.9180 0.351826
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 29.8885 0.961151 0.480575 0.876953i \(-0.340428\pi\)
0.480575 + 0.876953i \(0.340428\pi\)
\(968\) 0 0
\(969\) 3.05573 0.0981641
\(970\) 0 0
\(971\) −43.2492 −1.38793 −0.693967 0.720007i \(-0.744139\pi\)
−0.693967 + 0.720007i \(0.744139\pi\)
\(972\) 0 0
\(973\) −4.72136 −0.151360
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 44.5410 1.42499 0.712497 0.701675i \(-0.247564\pi\)
0.712497 + 0.701675i \(0.247564\pi\)
\(978\) 0 0
\(979\) 2.00000 0.0639203
\(980\) 0 0
\(981\) 25.3738 0.810124
\(982\) 0 0
\(983\) 3.65248 0.116496 0.0582479 0.998302i \(-0.481449\pi\)
0.0582479 + 0.998302i \(0.481449\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −0.498447 −0.0158657
\(988\) 0 0
\(989\) −11.4721 −0.364793
\(990\) 0 0
\(991\) 7.59675 0.241319 0.120659 0.992694i \(-0.461499\pi\)
0.120659 + 0.992694i \(0.461499\pi\)
\(992\) 0 0
\(993\) 16.1378 0.512117
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −38.1246 −1.20742 −0.603709 0.797205i \(-0.706311\pi\)
−0.603709 + 0.797205i \(0.706311\pi\)
\(998\) 0 0
\(999\) 37.3901 1.18297
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 4600.2.a.q.1.2 2
4.3 odd 2 9200.2.a.bz.1.1 2
5.2 odd 4 4600.2.e.l.4049.2 4
5.3 odd 4 4600.2.e.l.4049.3 4
5.4 even 2 4600.2.a.u.1.1 yes 2
20.19 odd 2 9200.2.a.bn.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4600.2.a.q.1.2 2 1.1 even 1 trivial
4600.2.a.u.1.1 yes 2 5.4 even 2
4600.2.e.l.4049.2 4 5.2 odd 4
4600.2.e.l.4049.3 4 5.3 odd 4
9200.2.a.bn.1.2 2 20.19 odd 2
9200.2.a.bz.1.1 2 4.3 odd 2