Properties

Label 4600.2.a.q.1.1
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 1.1
Root \(1.61803\) 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)
 
\(f(q)\) \(=\) \(q-3.23607 q^{3} +4.23607 q^{7} +7.47214 q^{9} +1.00000 q^{11} +2.23607 q^{13} -6.47214 q^{17} +1.00000 q^{19} -13.7082 q^{21} +1.00000 q^{23} -14.4721 q^{27} -1.76393 q^{29} +0.472136 q^{31} -3.23607 q^{33} -11.2361 q^{37} -7.23607 q^{39} -5.94427 q^{41} -2.52786 q^{43} -11.7082 q^{47} +10.9443 q^{49} +20.9443 q^{51} -1.23607 q^{53} -3.23607 q^{57} +3.23607 q^{59} -7.23607 q^{61} +31.6525 q^{63} -12.9443 q^{67} -3.23607 q^{69} +10.0000 q^{71} +9.47214 q^{73} +4.23607 q^{77} +15.1803 q^{79} +24.4164 q^{81} -9.00000 q^{83} +5.70820 q^{87} +2.00000 q^{89} +9.47214 q^{91} -1.52786 q^{93} -6.18034 q^{97} +7.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} + 4 q^{7} + 6 q^{9} + 2 q^{11} - 4 q^{17} + 2 q^{19} - 14 q^{21} + 2 q^{23} - 20 q^{27} - 8 q^{29} - 8 q^{31} - 2 q^{33} - 18 q^{37} - 10 q^{39} + 6 q^{41} - 14 q^{43} - 10 q^{47} + 4 q^{49}+ \cdots + 6 q^{99}+O(q^{100}) \) 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
\(3\) −3.23607 −1.86834 −0.934172 0.356822i \(-0.883860\pi\)
−0.934172 + 0.356822i \(0.883860\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.23607 1.60108 0.800542 0.599277i \(-0.204545\pi\)
0.800542 + 0.599277i \(0.204545\pi\)
\(8\) 0 0
\(9\) 7.47214 2.49071
\(10\) 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 \(-0.399642\pi\)
0.310087 + 0.950708i \(0.399642\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.47214 −1.56972 −0.784862 0.619671i \(-0.787266\pi\)
−0.784862 + 0.619671i \(0.787266\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416 0.114708 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) −13.7082 −2.99138
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −14.4721 −2.78516
\(28\) 0 0
\(29\) −1.76393 −0.327554 −0.163777 0.986497i \(-0.552368\pi\)
−0.163777 + 0.986497i \(0.552368\pi\)
\(30\) 0 0
\(31\) 0.472136 0.0847981 0.0423991 0.999101i \(-0.486500\pi\)
0.0423991 + 0.999101i \(0.486500\pi\)
\(32\) 0 0
\(33\) −3.23607 −0.563327
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −11.2361 −1.84720 −0.923599 0.383360i \(-0.874767\pi\)
−0.923599 + 0.383360i \(0.874767\pi\)
\(38\) 0 0
\(39\) −7.23607 −1.15870
\(40\) 0 0
\(41\) −5.94427 −0.928339 −0.464170 0.885746i \(-0.653647\pi\)
−0.464170 + 0.885746i \(0.653647\pi\)
\(42\) 0 0
\(43\) −2.52786 −0.385496 −0.192748 0.981248i \(-0.561740\pi\)
−0.192748 + 0.981248i \(0.561740\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −11.7082 −1.70782 −0.853909 0.520423i \(-0.825774\pi\)
−0.853909 + 0.520423i \(0.825774\pi\)
\(48\) 0 0
\(49\) 10.9443 1.56347
\(50\) 0 0
\(51\) 20.9443 2.93278
\(52\) 0 0
\(53\) −1.23607 −0.169787 −0.0848935 0.996390i \(-0.527055\pi\)
−0.0848935 + 0.996390i \(0.527055\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −3.23607 −0.428628
\(58\) 0 0
\(59\) 3.23607 0.421300 0.210650 0.977562i \(-0.432442\pi\)
0.210650 + 0.977562i \(0.432442\pi\)
\(60\) 0 0
\(61\) −7.23607 −0.926484 −0.463242 0.886232i \(-0.653314\pi\)
−0.463242 + 0.886232i \(0.653314\pi\)
\(62\) 0 0
\(63\) 31.6525 3.98784
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −12.9443 −1.58139 −0.790697 0.612207i \(-0.790282\pi\)
−0.790697 + 0.612207i \(0.790282\pi\)
\(68\) 0 0
\(69\) −3.23607 −0.389577
\(70\) 0 0
\(71\) 10.0000 1.18678 0.593391 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) 0 0
\(73\) 9.47214 1.10863 0.554315 0.832307i \(-0.312980\pi\)
0.554315 + 0.832307i \(0.312980\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.23607 0.482745
\(78\) 0 0
\(79\) 15.1803 1.70792 0.853961 0.520337i \(-0.174194\pi\)
0.853961 + 0.520337i \(0.174194\pi\)
\(80\) 0 0
\(81\) 24.4164 2.71293
\(82\) 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
\(87\) 5.70820 0.611984
\(88\) 0 0
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 0 0
\(91\) 9.47214 0.992950
\(92\) 0 0
\(93\) −1.52786 −0.158432
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −6.18034 −0.627518 −0.313759 0.949503i \(-0.601588\pi\)
−0.313759 + 0.949503i \(0.601588\pi\)
\(98\) 0 0
\(99\) 7.47214 0.750978
\(100\) 0 0
\(101\) −18.9443 −1.88503 −0.942513 0.334170i \(-0.891544\pi\)
−0.942513 + 0.334170i \(0.891544\pi\)
\(102\) 0 0
\(103\) 2.23607 0.220326 0.110163 0.993914i \(-0.464863\pi\)
0.110163 + 0.993914i \(0.464863\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 19.4164 1.87705 0.938527 0.345204i \(-0.112190\pi\)
0.938527 + 0.345204i \(0.112190\pi\)
\(108\) 0 0
\(109\) −12.7639 −1.22256 −0.611281 0.791413i \(-0.709346\pi\)
−0.611281 + 0.791413i \(0.709346\pi\)
\(110\) 0 0
\(111\) 36.3607 3.45120
\(112\) 0 0
\(113\) −6.76393 −0.636297 −0.318149 0.948041i \(-0.603061\pi\)
−0.318149 + 0.948041i \(0.603061\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 16.7082 1.54467
\(118\) 0 0
\(119\) −27.4164 −2.51326
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 0 0
\(123\) 19.2361 1.73446
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 4.18034 0.370945 0.185473 0.982649i \(-0.440618\pi\)
0.185473 + 0.982649i \(0.440618\pi\)
\(128\) 0 0
\(129\) 8.18034 0.720239
\(130\) 0 0
\(131\) −14.9443 −1.30569 −0.652844 0.757493i \(-0.726424\pi\)
−0.652844 + 0.757493i \(0.726424\pi\)
\(132\) 0 0
\(133\) 4.23607 0.367314
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −11.5279 −0.984892 −0.492446 0.870343i \(-0.663897\pi\)
−0.492446 + 0.870343i \(0.663897\pi\)
\(138\) 0 0
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 0 0
\(141\) 37.8885 3.19079
\(142\) 0 0
\(143\) 2.23607 0.186989
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −35.4164 −2.92110
\(148\) 0 0
\(149\) 10.9443 0.896590 0.448295 0.893886i \(-0.352031\pi\)
0.448295 + 0.893886i \(0.352031\pi\)
\(150\) 0 0
\(151\) 11.5279 0.938124 0.469062 0.883165i \(-0.344592\pi\)
0.469062 + 0.883165i \(0.344592\pi\)
\(152\) 0 0
\(153\) −48.3607 −3.90973
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.291796 −0.0232879 −0.0116439 0.999932i \(-0.503706\pi\)
−0.0116439 + 0.999932i \(0.503706\pi\)
\(158\) 0 0
\(159\) 4.00000 0.317221
\(160\) 0 0
\(161\) 4.23607 0.333849
\(162\) 0 0
\(163\) 11.7082 0.917057 0.458529 0.888680i \(-0.348377\pi\)
0.458529 + 0.888680i \(0.348377\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 5.41641 0.419134 0.209567 0.977794i \(-0.432795\pi\)
0.209567 + 0.977794i \(0.432795\pi\)
\(168\) 0 0
\(169\) −8.00000 −0.615385
\(170\) 0 0
\(171\) 7.47214 0.571409
\(172\) 0 0
\(173\) −14.2361 −1.08235 −0.541174 0.840911i \(-0.682020\pi\)
−0.541174 + 0.840911i \(0.682020\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −10.4721 −0.787134
\(178\) 0 0
\(179\) −15.7082 −1.17409 −0.587043 0.809556i \(-0.699708\pi\)
−0.587043 + 0.809556i \(0.699708\pi\)
\(180\) 0 0
\(181\) −0.944272 −0.0701872 −0.0350936 0.999384i \(-0.511173\pi\)
−0.0350936 + 0.999384i \(0.511173\pi\)
\(182\) 0 0
\(183\) 23.4164 1.73099
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −6.47214 −0.473289
\(188\) 0 0
\(189\) −61.3050 −4.45928
\(190\) 0 0
\(191\) −19.1803 −1.38784 −0.693920 0.720052i \(-0.744118\pi\)
−0.693920 + 0.720052i \(0.744118\pi\)
\(192\) 0 0
\(193\) −2.94427 −0.211933 −0.105967 0.994370i \(-0.533794\pi\)
−0.105967 + 0.994370i \(0.533794\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 8.23607 0.586796 0.293398 0.955990i \(-0.405214\pi\)
0.293398 + 0.955990i \(0.405214\pi\)
\(198\) 0 0
\(199\) 12.7082 0.900861 0.450430 0.892812i \(-0.351271\pi\)
0.450430 + 0.892812i \(0.351271\pi\)
\(200\) 0 0
\(201\) 41.8885 2.95459
\(202\) 0 0
\(203\) −7.47214 −0.524441
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 7.47214 0.519349
\(208\) 0 0
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) −14.9443 −1.02881 −0.514403 0.857549i \(-0.671986\pi\)
−0.514403 + 0.857549i \(0.671986\pi\)
\(212\) 0 0
\(213\) −32.3607 −2.21732
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 2.00000 0.135769
\(218\) 0 0
\(219\) −30.6525 −2.07130
\(220\) 0 0
\(221\) −14.4721 −0.973501
\(222\) 0 0
\(223\) −13.2361 −0.886353 −0.443176 0.896434i \(-0.646148\pi\)
−0.443176 + 0.896434i \(0.646148\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −12.9443 −0.859142 −0.429571 0.903033i \(-0.641335\pi\)
−0.429571 + 0.903033i \(0.641335\pi\)
\(228\) 0 0
\(229\) 6.94427 0.458890 0.229445 0.973322i \(-0.426309\pi\)
0.229445 + 0.973322i \(0.426309\pi\)
\(230\) 0 0
\(231\) −13.7082 −0.901934
\(232\) 0 0
\(233\) −4.52786 −0.296630 −0.148315 0.988940i \(-0.547385\pi\)
−0.148315 + 0.988940i \(0.547385\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −49.1246 −3.19099
\(238\) 0 0
\(239\) 6.76393 0.437522 0.218761 0.975778i \(-0.429798\pi\)
0.218761 + 0.975778i \(0.429798\pi\)
\(240\) 0 0
\(241\) 21.2361 1.36794 0.683968 0.729512i \(-0.260253\pi\)
0.683968 + 0.729512i \(0.260253\pi\)
\(242\) 0 0
\(243\) −35.5967 −2.28353
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.23607 0.142278
\(248\) 0 0
\(249\) 29.1246 1.84570
\(250\) 0 0
\(251\) −5.52786 −0.348916 −0.174458 0.984665i \(-0.555817\pi\)
−0.174458 + 0.984665i \(0.555817\pi\)
\(252\) 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
\(259\) −47.5967 −2.95752
\(260\) 0 0
\(261\) −13.1803 −0.815843
\(262\) 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
\(267\) −6.47214 −0.396088
\(268\) 0 0
\(269\) −25.1803 −1.53527 −0.767636 0.640886i \(-0.778567\pi\)
−0.767636 + 0.640886i \(0.778567\pi\)
\(270\) 0 0
\(271\) −32.0689 −1.94805 −0.974023 0.226449i \(-0.927288\pi\)
−0.974023 + 0.226449i \(0.927288\pi\)
\(272\) 0 0
\(273\) −30.6525 −1.85517
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −14.2361 −0.855362 −0.427681 0.903930i \(-0.640669\pi\)
−0.427681 + 0.903930i \(0.640669\pi\)
\(278\) 0 0
\(279\) 3.52786 0.211208
\(280\) 0 0
\(281\) −22.1803 −1.32317 −0.661584 0.749871i \(-0.730116\pi\)
−0.661584 + 0.749871i \(0.730116\pi\)
\(282\) 0 0
\(283\) −28.3607 −1.68587 −0.842934 0.538017i \(-0.819173\pi\)
−0.842934 + 0.538017i \(0.819173\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −25.1803 −1.48635
\(288\) 0 0
\(289\) 24.8885 1.46403
\(290\) 0 0
\(291\) 20.0000 1.17242
\(292\) 0 0
\(293\) 14.4721 0.845471 0.422736 0.906253i \(-0.361070\pi\)
0.422736 + 0.906253i \(0.361070\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −14.4721 −0.839759
\(298\) 0 0
\(299\) 2.23607 0.129315
\(300\) 0 0
\(301\) −10.7082 −0.617211
\(302\) 0 0
\(303\) 61.3050 3.52188
\(304\) 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
\(309\) −7.23607 −0.411646
\(310\) 0 0
\(311\) −3.23607 −0.183501 −0.0917503 0.995782i \(-0.529246\pi\)
−0.0917503 + 0.995782i \(0.529246\pi\)
\(312\) 0 0
\(313\) 10.6525 0.602114 0.301057 0.953606i \(-0.402661\pi\)
0.301057 + 0.953606i \(0.402661\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 22.1246 1.24264 0.621321 0.783556i \(-0.286596\pi\)
0.621321 + 0.783556i \(0.286596\pi\)
\(318\) 0 0
\(319\) −1.76393 −0.0987612
\(320\) 0 0
\(321\) −62.8328 −3.50699
\(322\) 0 0
\(323\) −6.47214 −0.360119
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 41.3050 2.28417
\(328\) 0 0
\(329\) −49.5967 −2.73436
\(330\) 0 0
\(331\) 30.9443 1.70085 0.850426 0.526095i \(-0.176345\pi\)
0.850426 + 0.526095i \(0.176345\pi\)
\(332\) 0 0
\(333\) −83.9574 −4.60084
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 24.6525 1.34291 0.671453 0.741047i \(-0.265671\pi\)
0.671453 + 0.741047i \(0.265671\pi\)
\(338\) 0 0
\(339\) 21.8885 1.18882
\(340\) 0 0
\(341\) 0.472136 0.0255676
\(342\) 0 0
\(343\) 16.7082 0.902158
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.05573 −0.164040 −0.0820200 0.996631i \(-0.526137\pi\)
−0.0820200 + 0.996631i \(0.526137\pi\)
\(348\) 0 0
\(349\) −5.18034 −0.277297 −0.138649 0.990342i \(-0.544276\pi\)
−0.138649 + 0.990342i \(0.544276\pi\)
\(350\) 0 0
\(351\) −32.3607 −1.72729
\(352\) 0 0
\(353\) 4.88854 0.260191 0.130095 0.991501i \(-0.458472\pi\)
0.130095 + 0.991501i \(0.458472\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 88.7214 4.69563
\(358\) 0 0
\(359\) 19.7639 1.04310 0.521550 0.853221i \(-0.325354\pi\)
0.521550 + 0.853221i \(0.325354\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) 32.3607 1.69850
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 23.6525 1.23465 0.617325 0.786709i \(-0.288217\pi\)
0.617325 + 0.786709i \(0.288217\pi\)
\(368\) 0 0
\(369\) −44.4164 −2.31223
\(370\) 0 0
\(371\) −5.23607 −0.271843
\(372\) 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
\(377\) −3.94427 −0.203140
\(378\) 0 0
\(379\) 3.05573 0.156962 0.0784811 0.996916i \(-0.474993\pi\)
0.0784811 + 0.996916i \(0.474993\pi\)
\(380\) 0 0
\(381\) −13.5279 −0.693053
\(382\) 0 0
\(383\) 0.236068 0.0120625 0.00603126 0.999982i \(-0.498080\pi\)
0.00603126 + 0.999982i \(0.498080\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −18.8885 −0.960159
\(388\) 0 0
\(389\) 6.18034 0.313356 0.156678 0.987650i \(-0.449922\pi\)
0.156678 + 0.987650i \(0.449922\pi\)
\(390\) 0 0
\(391\) −6.47214 −0.327310
\(392\) 0 0
\(393\) 48.3607 2.43947
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −22.3607 −1.12225 −0.561125 0.827731i \(-0.689631\pi\)
−0.561125 + 0.827731i \(0.689631\pi\)
\(398\) 0 0
\(399\) −13.7082 −0.686269
\(400\) 0 0
\(401\) −13.1246 −0.655412 −0.327706 0.944780i \(-0.606276\pi\)
−0.327706 + 0.944780i \(0.606276\pi\)
\(402\) 0 0
\(403\) 1.05573 0.0525896
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −11.2361 −0.556951
\(408\) 0 0
\(409\) −26.4164 −1.30621 −0.653104 0.757269i \(-0.726533\pi\)
−0.653104 + 0.757269i \(0.726533\pi\)
\(410\) 0 0
\(411\) 37.3050 1.84012
\(412\) 0 0
\(413\) 13.7082 0.674537
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −64.7214 −3.16942
\(418\) 0 0
\(419\) −36.7771 −1.79668 −0.898339 0.439303i \(-0.855226\pi\)
−0.898339 + 0.439303i \(0.855226\pi\)
\(420\) 0 0
\(421\) 15.8885 0.774360 0.387180 0.922004i \(-0.373449\pi\)
0.387180 + 0.922004i \(0.373449\pi\)
\(422\) 0 0
\(423\) −87.4853 −4.25368
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −30.6525 −1.48338
\(428\) 0 0
\(429\) −7.23607 −0.349361
\(430\) 0 0
\(431\) 12.9443 0.623504 0.311752 0.950164i \(-0.399084\pi\)
0.311752 + 0.950164i \(0.399084\pi\)
\(432\) 0 0
\(433\) 29.1246 1.39964 0.699820 0.714319i \(-0.253264\pi\)
0.699820 + 0.714319i \(0.253264\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.00000 0.0478365
\(438\) 0 0
\(439\) 12.3607 0.589943 0.294972 0.955506i \(-0.404690\pi\)
0.294972 + 0.955506i \(0.404690\pi\)
\(440\) 0 0
\(441\) 81.7771 3.89415
\(442\) 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
\(447\) −35.4164 −1.67514
\(448\) 0 0
\(449\) −36.8328 −1.73825 −0.869124 0.494594i \(-0.835317\pi\)
−0.869124 + 0.494594i \(0.835317\pi\)
\(450\) 0 0
\(451\) −5.94427 −0.279905
\(452\) 0 0
\(453\) −37.3050 −1.75274
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 20.6525 0.966082 0.483041 0.875598i \(-0.339532\pi\)
0.483041 + 0.875598i \(0.339532\pi\)
\(458\) 0 0
\(459\) 93.6656 4.37194
\(460\) 0 0
\(461\) 33.6525 1.56735 0.783676 0.621170i \(-0.213342\pi\)
0.783676 + 0.621170i \(0.213342\pi\)
\(462\) 0 0
\(463\) 26.4721 1.23026 0.615132 0.788424i \(-0.289103\pi\)
0.615132 + 0.788424i \(0.289103\pi\)
\(464\) 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
\(469\) −54.8328 −2.53194
\(470\) 0 0
\(471\) 0.944272 0.0435098
\(472\) 0 0
\(473\) −2.52786 −0.116231
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −9.23607 −0.422891
\(478\) 0 0
\(479\) −12.1246 −0.553988 −0.276994 0.960872i \(-0.589338\pi\)
−0.276994 + 0.960872i \(0.589338\pi\)
\(480\) 0 0
\(481\) −25.1246 −1.14558
\(482\) 0 0
\(483\) −13.7082 −0.623745
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 39.1246 1.77291 0.886453 0.462819i \(-0.153162\pi\)
0.886453 + 0.462819i \(0.153162\pi\)
\(488\) 0 0
\(489\) −37.8885 −1.71338
\(490\) 0 0
\(491\) −3.23607 −0.146042 −0.0730209 0.997330i \(-0.523264\pi\)
−0.0730209 + 0.997330i \(0.523264\pi\)
\(492\) 0 0
\(493\) 11.4164 0.514169
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 42.3607 1.90014
\(498\) 0 0
\(499\) −42.5410 −1.90440 −0.952199 0.305479i \(-0.901183\pi\)
−0.952199 + 0.305479i \(0.901183\pi\)
\(500\) 0 0
\(501\) −17.5279 −0.783087
\(502\) 0 0
\(503\) −16.5967 −0.740012 −0.370006 0.929029i \(-0.620644\pi\)
−0.370006 + 0.929029i \(0.620644\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 25.8885 1.14975
\(508\) 0 0
\(509\) 30.3607 1.34571 0.672857 0.739773i \(-0.265067\pi\)
0.672857 + 0.739773i \(0.265067\pi\)
\(510\) 0 0
\(511\) 40.1246 1.77501
\(512\) 0 0
\(513\) −14.4721 −0.638960
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −11.7082 −0.514926
\(518\) 0 0
\(519\) 46.0689 2.02220
\(520\) 0 0
\(521\) 9.34752 0.409522 0.204761 0.978812i \(-0.434358\pi\)
0.204761 + 0.978812i \(0.434358\pi\)
\(522\) 0 0
\(523\) 18.8885 0.825938 0.412969 0.910745i \(-0.364492\pi\)
0.412969 + 0.910745i \(0.364492\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.05573 −0.133110
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 24.1803 1.04934
\(532\) 0 0
\(533\) −13.2918 −0.575732
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 50.8328 2.19360
\(538\) 0 0
\(539\) 10.9443 0.471403
\(540\) 0 0
\(541\) 8.70820 0.374395 0.187197 0.982322i \(-0.440060\pi\)
0.187197 + 0.982322i \(0.440060\pi\)
\(542\) 0 0
\(543\) 3.05573 0.131134
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 15.7082 0.671634 0.335817 0.941927i \(-0.390988\pi\)
0.335817 + 0.941927i \(0.390988\pi\)
\(548\) 0 0
\(549\) −54.0689 −2.30760
\(550\) 0 0
\(551\) −1.76393 −0.0751460
\(552\) 0 0
\(553\) 64.3050 2.73452
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −36.1803 −1.53301 −0.766505 0.642238i \(-0.778006\pi\)
−0.766505 + 0.642238i \(0.778006\pi\)
\(558\) 0 0
\(559\) −5.65248 −0.239074
\(560\) 0 0
\(561\) 20.9443 0.884268
\(562\) 0 0
\(563\) 39.3607 1.65885 0.829427 0.558614i \(-0.188667\pi\)
0.829427 + 0.558614i \(0.188667\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 103.430 4.34363
\(568\) 0 0
\(569\) 12.5836 0.527532 0.263766 0.964587i \(-0.415035\pi\)
0.263766 + 0.964587i \(0.415035\pi\)
\(570\) 0 0
\(571\) 24.0000 1.00437 0.502184 0.864761i \(-0.332530\pi\)
0.502184 + 0.864761i \(0.332530\pi\)
\(572\) 0 0
\(573\) 62.0689 2.59296
\(574\) 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
\(579\) 9.52786 0.395965
\(580\) 0 0
\(581\) −38.1246 −1.58168
\(582\) 0 0
\(583\) −1.23607 −0.0511927
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −27.5967 −1.13904 −0.569520 0.821978i \(-0.692871\pi\)
−0.569520 + 0.821978i \(0.692871\pi\)
\(588\) 0 0
\(589\) 0.472136 0.0194540
\(590\) 0 0
\(591\) −26.6525 −1.09634
\(592\) 0 0
\(593\) −44.8885 −1.84335 −0.921676 0.387961i \(-0.873180\pi\)
−0.921676 + 0.387961i \(0.873180\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −41.1246 −1.68312
\(598\) 0 0
\(599\) 16.8328 0.687770 0.343885 0.939012i \(-0.388257\pi\)
0.343885 + 0.939012i \(0.388257\pi\)
\(600\) 0 0
\(601\) −14.9443 −0.609590 −0.304795 0.952418i \(-0.598588\pi\)
−0.304795 + 0.952418i \(0.598588\pi\)
\(602\) 0 0
\(603\) −96.7214 −3.93880
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −23.1246 −0.938599 −0.469300 0.883039i \(-0.655494\pi\)
−0.469300 + 0.883039i \(0.655494\pi\)
\(608\) 0 0
\(609\) 24.1803 0.979837
\(610\) 0 0
\(611\) −26.1803 −1.05914
\(612\) 0 0
\(613\) 18.0689 0.729795 0.364898 0.931048i \(-0.381104\pi\)
0.364898 + 0.931048i \(0.381104\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −25.3050 −1.01874 −0.509369 0.860548i \(-0.670121\pi\)
−0.509369 + 0.860548i \(0.670121\pi\)
\(618\) 0 0
\(619\) −9.52786 −0.382957 −0.191479 0.981497i \(-0.561328\pi\)
−0.191479 + 0.981497i \(0.561328\pi\)
\(620\) 0 0
\(621\) −14.4721 −0.580747
\(622\) 0 0
\(623\) 8.47214 0.339429
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −3.23607 −0.129236
\(628\) 0 0
\(629\) 72.7214 2.89959
\(630\) 0 0
\(631\) −24.1246 −0.960386 −0.480193 0.877163i \(-0.659433\pi\)
−0.480193 + 0.877163i \(0.659433\pi\)
\(632\) 0 0
\(633\) 48.3607 1.92216
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 24.4721 0.969621
\(638\) 0 0
\(639\) 74.7214 2.95593
\(640\) 0 0
\(641\) 27.7771 1.09713 0.548564 0.836108i \(-0.315175\pi\)
0.548564 + 0.836108i \(0.315175\pi\)
\(642\) 0 0
\(643\) −1.94427 −0.0766746 −0.0383373 0.999265i \(-0.512206\pi\)
−0.0383373 + 0.999265i \(0.512206\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10.1803 −0.400230 −0.200115 0.979772i \(-0.564132\pi\)
−0.200115 + 0.979772i \(0.564132\pi\)
\(648\) 0 0
\(649\) 3.23607 0.127027
\(650\) 0 0
\(651\) −6.47214 −0.253663
\(652\) 0 0
\(653\) 39.5410 1.54736 0.773680 0.633577i \(-0.218414\pi\)
0.773680 + 0.633577i \(0.218414\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 70.7771 2.76128
\(658\) 0 0
\(659\) 13.4721 0.524800 0.262400 0.964959i \(-0.415486\pi\)
0.262400 + 0.964959i \(0.415486\pi\)
\(660\) 0 0
\(661\) −21.8197 −0.848686 −0.424343 0.905501i \(-0.639495\pi\)
−0.424343 + 0.905501i \(0.639495\pi\)
\(662\) 0 0
\(663\) 46.8328 1.81884
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.76393 −0.0682997
\(668\) 0 0
\(669\) 42.8328 1.65601
\(670\) 0 0
\(671\) −7.23607 −0.279345
\(672\) 0 0
\(673\) −48.3050 −1.86202 −0.931010 0.364995i \(-0.881071\pi\)
−0.931010 + 0.364995i \(0.881071\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 17.7082 0.680582 0.340291 0.940320i \(-0.389474\pi\)
0.340291 + 0.940320i \(0.389474\pi\)
\(678\) 0 0
\(679\) −26.1803 −1.00471
\(680\) 0 0
\(681\) 41.8885 1.60517
\(682\) 0 0
\(683\) −41.7771 −1.59856 −0.799278 0.600962i \(-0.794784\pi\)
−0.799278 + 0.600962i \(0.794784\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −22.4721 −0.857365
\(688\) 0 0
\(689\) −2.76393 −0.105297
\(690\) 0 0
\(691\) −42.4721 −1.61572 −0.807858 0.589377i \(-0.799373\pi\)
−0.807858 + 0.589377i \(0.799373\pi\)
\(692\) 0 0
\(693\) 31.6525 1.20238
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 38.4721 1.45724
\(698\) 0 0
\(699\) 14.6525 0.554208
\(700\) 0 0
\(701\) −37.5279 −1.41741 −0.708704 0.705506i \(-0.750720\pi\)
−0.708704 + 0.705506i \(0.750720\pi\)
\(702\) 0 0
\(703\) −11.2361 −0.423776
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −80.2492 −3.01808
\(708\) 0 0
\(709\) 9.41641 0.353641 0.176820 0.984243i \(-0.443419\pi\)
0.176820 + 0.984243i \(0.443419\pi\)
\(710\) 0 0
\(711\) 113.430 4.25394
\(712\) 0 0
\(713\) 0.472136 0.0176816
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −21.8885 −0.817443
\(718\) 0 0
\(719\) 37.7082 1.40628 0.703139 0.711052i \(-0.251781\pi\)
0.703139 + 0.711052i \(0.251781\pi\)
\(720\) 0 0
\(721\) 9.47214 0.352761
\(722\) 0 0
\(723\) −68.7214 −2.55577
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −44.7214 −1.65862 −0.829312 0.558786i \(-0.811267\pi\)
−0.829312 + 0.558786i \(0.811267\pi\)
\(728\) 0 0
\(729\) 41.9443 1.55349
\(730\) 0 0
\(731\) 16.3607 0.605122
\(732\) 0 0
\(733\) 39.5279 1.45999 0.729997 0.683450i \(-0.239521\pi\)
0.729997 + 0.683450i \(0.239521\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −12.9443 −0.476808
\(738\) 0 0
\(739\) 9.05573 0.333120 0.166560 0.986031i \(-0.446734\pi\)
0.166560 + 0.986031i \(0.446734\pi\)
\(740\) 0 0
\(741\) −7.23607 −0.265824
\(742\) 0 0
\(743\) −39.1803 −1.43739 −0.718694 0.695327i \(-0.755260\pi\)
−0.718694 + 0.695327i \(0.755260\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −67.2492 −2.46052
\(748\) 0 0
\(749\) 82.2492 3.00532
\(750\) 0 0
\(751\) −22.5967 −0.824567 −0.412284 0.911056i \(-0.635269\pi\)
−0.412284 + 0.911056i \(0.635269\pi\)
\(752\) 0 0
\(753\) 17.8885 0.651895
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 16.7639 0.609295 0.304648 0.952465i \(-0.401461\pi\)
0.304648 + 0.952465i \(0.401461\pi\)
\(758\) 0 0
\(759\) −3.23607 −0.117462
\(760\) 0 0
\(761\) −52.8885 −1.91721 −0.958604 0.284742i \(-0.908092\pi\)
−0.958604 + 0.284742i \(0.908092\pi\)
\(762\) 0 0
\(763\) −54.0689 −1.95743
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 7.23607 0.261279
\(768\) 0 0
\(769\) −46.0689 −1.66129 −0.830643 0.556805i \(-0.812027\pi\)
−0.830643 + 0.556805i \(0.812027\pi\)
\(770\) 0 0
\(771\) −45.3050 −1.63162
\(772\) 0 0
\(773\) 4.76393 0.171347 0.0856734 0.996323i \(-0.472696\pi\)
0.0856734 + 0.996323i \(0.472696\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 154.026 5.52566
\(778\) 0 0
\(779\) −5.94427 −0.212976
\(780\) 0 0
\(781\) 10.0000 0.357828
\(782\) 0 0
\(783\) 25.5279 0.912291
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −39.7214 −1.41591 −0.707957 0.706256i \(-0.750383\pi\)
−0.707957 + 0.706256i \(0.750383\pi\)
\(788\) 0 0
\(789\) 25.8885 0.921657
\(790\) 0 0
\(791\) −28.6525 −1.01876
\(792\) 0 0
\(793\) −16.1803 −0.574581
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −15.2361 −0.539689 −0.269845 0.962904i \(-0.586972\pi\)
−0.269845 + 0.962904i \(0.586972\pi\)
\(798\) 0 0
\(799\) 75.7771 2.68080
\(800\) 0 0
\(801\) 14.9443 0.528030
\(802\) 0 0
\(803\) 9.47214 0.334264
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 81.4853 2.86842
\(808\) 0 0
\(809\) −9.11146 −0.320342 −0.160171 0.987089i \(-0.551205\pi\)
−0.160171 + 0.987089i \(0.551205\pi\)
\(810\) 0 0
\(811\) 15.4164 0.541343 0.270672 0.962672i \(-0.412754\pi\)
0.270672 + 0.962672i \(0.412754\pi\)
\(812\) 0 0
\(813\) 103.777 3.63962
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −2.52786 −0.0884388
\(818\) 0 0
\(819\) 70.7771 2.47315
\(820\) 0 0
\(821\) −22.2361 −0.776044 −0.388022 0.921650i \(-0.626842\pi\)
−0.388022 + 0.921650i \(0.626842\pi\)
\(822\) 0 0
\(823\) −8.94427 −0.311778 −0.155889 0.987775i \(-0.549824\pi\)
−0.155889 + 0.987775i \(0.549824\pi\)
\(824\) 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
\(829\) −4.23607 −0.147125 −0.0735624 0.997291i \(-0.523437\pi\)
−0.0735624 + 0.997291i \(0.523437\pi\)
\(830\) 0 0
\(831\) 46.0689 1.59811
\(832\) 0 0
\(833\) −70.8328 −2.45421
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −6.83282 −0.236177
\(838\) 0 0
\(839\) 8.59675 0.296793 0.148396 0.988928i \(-0.452589\pi\)
0.148396 + 0.988928i \(0.452589\pi\)
\(840\) 0 0
\(841\) −25.8885 −0.892708
\(842\) 0 0
\(843\) 71.7771 2.47213
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −42.3607 −1.45553
\(848\) 0 0
\(849\) 91.7771 3.14978
\(850\) 0 0
\(851\) −11.2361 −0.385167
\(852\) 0 0
\(853\) −28.2361 −0.966785 −0.483392 0.875404i \(-0.660596\pi\)
−0.483392 + 0.875404i \(0.660596\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 35.3050 1.20599 0.602997 0.797743i \(-0.293973\pi\)
0.602997 + 0.797743i \(0.293973\pi\)
\(858\) 0 0
\(859\) −21.7082 −0.740674 −0.370337 0.928897i \(-0.620758\pi\)
−0.370337 + 0.928897i \(0.620758\pi\)
\(860\) 0 0
\(861\) 81.4853 2.77701
\(862\) 0 0
\(863\) 34.5410 1.17579 0.587895 0.808937i \(-0.299957\pi\)
0.587895 + 0.808937i \(0.299957\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −80.5410 −2.73532
\(868\) 0 0
\(869\) 15.1803 0.514958
\(870\) 0 0
\(871\) −28.9443 −0.980739
\(872\) 0 0
\(873\) −46.1803 −1.56297
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 2.58359 0.0872417 0.0436209 0.999048i \(-0.486111\pi\)
0.0436209 + 0.999048i \(0.486111\pi\)
\(878\) 0 0
\(879\) −46.8328 −1.57963
\(880\) 0 0
\(881\) 37.7082 1.27042 0.635211 0.772339i \(-0.280913\pi\)
0.635211 + 0.772339i \(0.280913\pi\)
\(882\) 0 0
\(883\) 3.05573 0.102833 0.0514167 0.998677i \(-0.483626\pi\)
0.0514167 + 0.998677i \(0.483626\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 12.3607 0.415031 0.207516 0.978232i \(-0.433462\pi\)
0.207516 + 0.978232i \(0.433462\pi\)
\(888\) 0 0
\(889\) 17.7082 0.593914
\(890\) 0 0
\(891\) 24.4164 0.817980
\(892\) 0 0
\(893\) −11.7082 −0.391800
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −7.23607 −0.241605
\(898\) 0 0
\(899\) −0.832816 −0.0277760
\(900\) 0 0
\(901\) 8.00000 0.266519
\(902\) 0 0
\(903\) 34.6525 1.15316
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 5.58359 0.185400 0.0927001 0.995694i \(-0.470450\pi\)
0.0927001 + 0.995694i \(0.470450\pi\)
\(908\) 0 0
\(909\) −141.554 −4.69506
\(910\) 0 0
\(911\) −31.0689 −1.02936 −0.514679 0.857383i \(-0.672089\pi\)
−0.514679 + 0.857383i \(0.672089\pi\)
\(912\) 0 0
\(913\) −9.00000 −0.297857
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −63.3050 −2.09051
\(918\) 0 0
\(919\) 43.7771 1.44407 0.722036 0.691855i \(-0.243206\pi\)
0.722036 + 0.691855i \(0.243206\pi\)
\(920\) 0 0
\(921\) 77.6656 2.55917
\(922\) 0 0
\(923\) 22.3607 0.736011
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 16.7082 0.548769
\(928\) 0 0
\(929\) 31.0000 1.01708 0.508539 0.861039i \(-0.330186\pi\)
0.508539 + 0.861039i \(0.330186\pi\)
\(930\) 0 0
\(931\) 10.9443 0.358684
\(932\) 0 0
\(933\) 10.4721 0.342842
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −7.12461 −0.232751 −0.116375 0.993205i \(-0.537128\pi\)
−0.116375 + 0.993205i \(0.537128\pi\)
\(938\) 0 0
\(939\) −34.4721 −1.12496
\(940\) 0 0
\(941\) −13.2361 −0.431483 −0.215742 0.976450i \(-0.569217\pi\)
−0.215742 + 0.976450i \(0.569217\pi\)
\(942\) 0 0
\(943\) −5.94427 −0.193572
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −45.1935 −1.46859 −0.734296 0.678830i \(-0.762487\pi\)
−0.734296 + 0.678830i \(0.762487\pi\)
\(948\) 0 0
\(949\) 21.1803 0.687543
\(950\) 0 0
\(951\) −71.5967 −2.32168
\(952\) 0 0
\(953\) −5.34752 −0.173223 −0.0866116 0.996242i \(-0.527604\pi\)
−0.0866116 + 0.996242i \(0.527604\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 5.70820 0.184520
\(958\) 0 0
\(959\) −48.8328 −1.57689
\(960\) 0 0
\(961\) −30.7771 −0.992809
\(962\) 0 0
\(963\) 145.082 4.67520
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −5.88854 −0.189363 −0.0946814 0.995508i \(-0.530183\pi\)
−0.0946814 + 0.995508i \(0.530183\pi\)
\(968\) 0 0
\(969\) 20.9443 0.672827
\(970\) 0 0
\(971\) 37.2492 1.19538 0.597692 0.801726i \(-0.296084\pi\)
0.597692 + 0.801726i \(0.296084\pi\)
\(972\) 0 0
\(973\) 84.7214 2.71604
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −22.5410 −0.721151 −0.360576 0.932730i \(-0.617420\pi\)
−0.360576 + 0.932730i \(0.617420\pi\)
\(978\) 0 0
\(979\) 2.00000 0.0639203
\(980\) 0 0
\(981\) −95.3738 −3.04505
\(982\) 0 0
\(983\) −27.6525 −0.881977 −0.440989 0.897513i \(-0.645372\pi\)
−0.440989 + 0.897513i \(0.645372\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 160.498 5.10872
\(988\) 0 0
\(989\) −2.52786 −0.0803814
\(990\) 0 0
\(991\) −41.5967 −1.32136 −0.660682 0.750666i \(-0.729733\pi\)
−0.660682 + 0.750666i \(0.729733\pi\)
\(992\) 0 0
\(993\) −100.138 −3.17778
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 2.12461 0.0672871 0.0336436 0.999434i \(-0.489289\pi\)
0.0336436 + 0.999434i \(0.489289\pi\)
\(998\) 0 0
\(999\) 162.610 5.14475
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.1.1 2
4.3 odd 2 9200.2.a.bz.1.2 2
5.2 odd 4 4600.2.e.l.4049.4 4
5.3 odd 4 4600.2.e.l.4049.1 4
5.4 even 2 4600.2.a.u.1.2 yes 2
20.19 odd 2 9200.2.a.bn.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4600.2.a.q.1.1 2 1.1 even 1 trivial
4600.2.a.u.1.2 yes 2 5.4 even 2
4600.2.e.l.4049.1 4 5.3 odd 4
4600.2.e.l.4049.4 4 5.2 odd 4
9200.2.a.bn.1.1 2 20.19 odd 2
9200.2.a.bz.1.2 2 4.3 odd 2