Properties

Label 7600.2.a.bp.1.1
Level $7600$
Weight $2$
Character 7600.1
Self dual yes
Analytic conductor $60.686$
Analytic rank $1$
Dimension $3$
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] = [7600,2,Mod(1,7600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7600, 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("7600.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7600.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: \(60.6863055362\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.316.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 760)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.34292\) of defining polynomial
Character \(\chi\) \(=\) 7600.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.34292 q^{3} +1.19656 q^{7} +2.48929 q^{9} +O(q^{10})\) \(q-2.34292 q^{3} +1.19656 q^{7} +2.48929 q^{9} -4.97858 q^{11} +6.63565 q^{13} -1.48929 q^{17} -1.00000 q^{19} -2.80344 q^{21} -0.510711 q^{23} +1.19656 q^{27} -7.88240 q^{29} +2.97858 q^{31} +11.6644 q^{33} +7.14637 q^{37} -15.5468 q^{39} +1.66442 q^{41} -6.39312 q^{43} -9.95715 q^{47} -5.56825 q^{49} +3.48929 q^{51} +11.4219 q^{53} +2.34292 q^{57} +11.8396 q^{59} +3.66442 q^{61} +2.97858 q^{63} +7.61423 q^{67} +1.19656 q^{69} -13.8396 q^{73} -5.95715 q^{77} -12.6858 q^{79} -10.2713 q^{81} -8.68585 q^{83} +18.4679 q^{87} -4.87819 q^{89} +7.93994 q^{91} -6.97858 q^{93} +6.81079 q^{97} -12.3931 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{3} - q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{3} - q^{7} + 11 q^{13} + 3 q^{17} - 3 q^{19} - 13 q^{21} - 9 q^{23} - q^{27} - 7 q^{29} - 6 q^{31} + 8 q^{33} + 20 q^{37} - 3 q^{39} - 22 q^{41} - 10 q^{43} + 12 q^{49} + 3 q^{51} + 7 q^{53} + q^{57} - 11 q^{59} - 16 q^{61} - 6 q^{63} - q^{67} - q^{69} + 5 q^{73} + 12 q^{77} - 26 q^{79} - 13 q^{81} - 14 q^{83} + 33 q^{87} - 6 q^{89} - 29 q^{91} - 6 q^{93} - 8 q^{97} - 28 q^{99}+O(q^{100}) \) 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
\(3\) −2.34292 −1.35269 −0.676344 0.736586i \(-0.736437\pi\)
−0.676344 + 0.736586i \(0.736437\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.19656 0.452256 0.226128 0.974098i \(-0.427393\pi\)
0.226128 + 0.974098i \(0.427393\pi\)
\(8\) 0 0
\(9\) 2.48929 0.829763
\(10\) 0 0
\(11\) −4.97858 −1.50110 −0.750549 0.660815i \(-0.770211\pi\)
−0.750549 + 0.660815i \(0.770211\pi\)
\(12\) 0 0
\(13\) 6.63565 1.84040 0.920200 0.391449i \(-0.128026\pi\)
0.920200 + 0.391449i \(0.128026\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.48929 −0.361206 −0.180603 0.983556i \(-0.557805\pi\)
−0.180603 + 0.983556i \(0.557805\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −2.80344 −0.611761
\(22\) 0 0
\(23\) −0.510711 −0.106491 −0.0532453 0.998581i \(-0.516957\pi\)
−0.0532453 + 0.998581i \(0.516957\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.19656 0.230278
\(28\) 0 0
\(29\) −7.88240 −1.46373 −0.731863 0.681452i \(-0.761349\pi\)
−0.731863 + 0.681452i \(0.761349\pi\)
\(30\) 0 0
\(31\) 2.97858 0.534968 0.267484 0.963562i \(-0.413808\pi\)
0.267484 + 0.963562i \(0.413808\pi\)
\(32\) 0 0
\(33\) 11.6644 2.03052
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 7.14637 1.17486 0.587428 0.809277i \(-0.300141\pi\)
0.587428 + 0.809277i \(0.300141\pi\)
\(38\) 0 0
\(39\) −15.5468 −2.48948
\(40\) 0 0
\(41\) 1.66442 0.259939 0.129970 0.991518i \(-0.458512\pi\)
0.129970 + 0.991518i \(0.458512\pi\)
\(42\) 0 0
\(43\) −6.39312 −0.974941 −0.487470 0.873139i \(-0.662080\pi\)
−0.487470 + 0.873139i \(0.662080\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −9.95715 −1.45240 −0.726200 0.687483i \(-0.758715\pi\)
−0.726200 + 0.687483i \(0.758715\pi\)
\(48\) 0 0
\(49\) −5.56825 −0.795464
\(50\) 0 0
\(51\) 3.48929 0.488598
\(52\) 0 0
\(53\) 11.4219 1.56892 0.784458 0.620182i \(-0.212941\pi\)
0.784458 + 0.620182i \(0.212941\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 2.34292 0.310328
\(58\) 0 0
\(59\) 11.8396 1.54138 0.770690 0.637211i \(-0.219912\pi\)
0.770690 + 0.637211i \(0.219912\pi\)
\(60\) 0 0
\(61\) 3.66442 0.469181 0.234591 0.972094i \(-0.424625\pi\)
0.234591 + 0.972094i \(0.424625\pi\)
\(62\) 0 0
\(63\) 2.97858 0.375265
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 7.61423 0.930226 0.465113 0.885251i \(-0.346014\pi\)
0.465113 + 0.885251i \(0.346014\pi\)
\(68\) 0 0
\(69\) 1.19656 0.144049
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −13.8396 −1.61980 −0.809899 0.586570i \(-0.800478\pi\)
−0.809899 + 0.586570i \(0.800478\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −5.95715 −0.678881
\(78\) 0 0
\(79\) −12.6858 −1.42727 −0.713635 0.700518i \(-0.752952\pi\)
−0.713635 + 0.700518i \(0.752952\pi\)
\(80\) 0 0
\(81\) −10.2713 −1.14126
\(82\) 0 0
\(83\) −8.68585 −0.953395 −0.476698 0.879067i \(-0.658166\pi\)
−0.476698 + 0.879067i \(0.658166\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 18.4679 1.97996
\(88\) 0 0
\(89\) −4.87819 −0.517087 −0.258544 0.966000i \(-0.583243\pi\)
−0.258544 + 0.966000i \(0.583243\pi\)
\(90\) 0 0
\(91\) 7.93994 0.832332
\(92\) 0 0
\(93\) −6.97858 −0.723645
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 6.81079 0.691531 0.345765 0.938321i \(-0.387619\pi\)
0.345765 + 0.938321i \(0.387619\pi\)
\(98\) 0 0
\(99\) −12.3931 −1.24555
\(100\) 0 0
\(101\) −2.29273 −0.228135 −0.114068 0.993473i \(-0.536388\pi\)
−0.114068 + 0.993473i \(0.536388\pi\)
\(102\) 0 0
\(103\) −6.51806 −0.642243 −0.321122 0.947038i \(-0.604060\pi\)
−0.321122 + 0.947038i \(0.604060\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.71462 0.745800 0.372900 0.927872i \(-0.378363\pi\)
0.372900 + 0.927872i \(0.378363\pi\)
\(108\) 0 0
\(109\) 15.5468 1.48912 0.744558 0.667558i \(-0.232660\pi\)
0.744558 + 0.667558i \(0.232660\pi\)
\(110\) 0 0
\(111\) −16.7434 −1.58921
\(112\) 0 0
\(113\) 0.753250 0.0708598 0.0354299 0.999372i \(-0.488720\pi\)
0.0354299 + 0.999372i \(0.488720\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 16.5181 1.52709
\(118\) 0 0
\(119\) −1.78202 −0.163357
\(120\) 0 0
\(121\) 13.7862 1.25329
\(122\) 0 0
\(123\) −3.89962 −0.351617
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 10.4177 0.924419 0.462210 0.886771i \(-0.347057\pi\)
0.462210 + 0.886771i \(0.347057\pi\)
\(128\) 0 0
\(129\) 14.9786 1.31879
\(130\) 0 0
\(131\) 17.9572 1.56892 0.784462 0.620177i \(-0.212939\pi\)
0.784462 + 0.620177i \(0.212939\pi\)
\(132\) 0 0
\(133\) −1.19656 −0.103755
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.83956 0.840650 0.420325 0.907374i \(-0.361916\pi\)
0.420325 + 0.907374i \(0.361916\pi\)
\(138\) 0 0
\(139\) 0.978577 0.0830018 0.0415009 0.999138i \(-0.486786\pi\)
0.0415009 + 0.999138i \(0.486786\pi\)
\(140\) 0 0
\(141\) 23.3288 1.96464
\(142\) 0 0
\(143\) −33.0361 −2.76262
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 13.0460 1.07601
\(148\) 0 0
\(149\) −8.24989 −0.675857 −0.337928 0.941172i \(-0.609726\pi\)
−0.337928 + 0.941172i \(0.609726\pi\)
\(150\) 0 0
\(151\) −13.8568 −1.12765 −0.563824 0.825895i \(-0.690670\pi\)
−0.563824 + 0.825895i \(0.690670\pi\)
\(152\) 0 0
\(153\) −3.70727 −0.299715
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 15.7073 1.25358 0.626788 0.779190i \(-0.284369\pi\)
0.626788 + 0.779190i \(0.284369\pi\)
\(158\) 0 0
\(159\) −26.7606 −2.12225
\(160\) 0 0
\(161\) −0.611096 −0.0481611
\(162\) 0 0
\(163\) 5.80765 0.454891 0.227445 0.973791i \(-0.426963\pi\)
0.227445 + 0.973791i \(0.426963\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −13.8322 −1.07037 −0.535184 0.844735i \(-0.679758\pi\)
−0.535184 + 0.844735i \(0.679758\pi\)
\(168\) 0 0
\(169\) 31.0319 2.38707
\(170\) 0 0
\(171\) −2.48929 −0.190361
\(172\) 0 0
\(173\) −14.8108 −1.12604 −0.563022 0.826442i \(-0.690361\pi\)
−0.563022 + 0.826442i \(0.690361\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −27.7392 −2.08500
\(178\) 0 0
\(179\) −15.6644 −1.17081 −0.585407 0.810740i \(-0.699065\pi\)
−0.585407 + 0.810740i \(0.699065\pi\)
\(180\) 0 0
\(181\) −14.7862 −1.09905 −0.549526 0.835477i \(-0.685192\pi\)
−0.549526 + 0.835477i \(0.685192\pi\)
\(182\) 0 0
\(183\) −8.58546 −0.634656
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 7.41454 0.542205
\(188\) 0 0
\(189\) 1.43175 0.104144
\(190\) 0 0
\(191\) 6.36748 0.460735 0.230367 0.973104i \(-0.426007\pi\)
0.230367 + 0.973104i \(0.426007\pi\)
\(192\) 0 0
\(193\) 19.5970 1.41062 0.705312 0.708897i \(-0.250807\pi\)
0.705312 + 0.708897i \(0.250807\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −10.7862 −0.768487 −0.384244 0.923232i \(-0.625538\pi\)
−0.384244 + 0.923232i \(0.625538\pi\)
\(198\) 0 0
\(199\) −2.80344 −0.198731 −0.0993654 0.995051i \(-0.531681\pi\)
−0.0993654 + 0.995051i \(0.531681\pi\)
\(200\) 0 0
\(201\) −17.8396 −1.25831
\(202\) 0 0
\(203\) −9.43175 −0.661979
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −1.27131 −0.0883620
\(208\) 0 0
\(209\) 4.97858 0.344375
\(210\) 0 0
\(211\) 11.2541 0.774764 0.387382 0.921919i \(-0.373379\pi\)
0.387382 + 0.921919i \(0.373379\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 3.56404 0.241943
\(218\) 0 0
\(219\) 32.4250 2.19108
\(220\) 0 0
\(221\) −9.88240 −0.664762
\(222\) 0 0
\(223\) 17.4966 1.17166 0.585831 0.810433i \(-0.300768\pi\)
0.585831 + 0.810433i \(0.300768\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3.84942 −0.255495 −0.127748 0.991807i \(-0.540775\pi\)
−0.127748 + 0.991807i \(0.540775\pi\)
\(228\) 0 0
\(229\) −14.6430 −0.967637 −0.483818 0.875168i \(-0.660750\pi\)
−0.483818 + 0.875168i \(0.660750\pi\)
\(230\) 0 0
\(231\) 13.9572 0.918313
\(232\) 0 0
\(233\) −11.9572 −0.783339 −0.391670 0.920106i \(-0.628102\pi\)
−0.391670 + 0.920106i \(0.628102\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 29.7220 1.93065
\(238\) 0 0
\(239\) −15.5897 −1.00841 −0.504206 0.863583i \(-0.668215\pi\)
−0.504206 + 0.863583i \(0.668215\pi\)
\(240\) 0 0
\(241\) −16.0575 −1.03436 −0.517178 0.855878i \(-0.673018\pi\)
−0.517178 + 0.855878i \(0.673018\pi\)
\(242\) 0 0
\(243\) 20.4752 1.31349
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.63565 −0.422217
\(248\) 0 0
\(249\) 20.3503 1.28965
\(250\) 0 0
\(251\) −23.9143 −1.50946 −0.754729 0.656037i \(-0.772232\pi\)
−0.754729 + 0.656037i \(0.772232\pi\)
\(252\) 0 0
\(253\) 2.54262 0.159853
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 24.4324 1.52405 0.762025 0.647548i \(-0.224206\pi\)
0.762025 + 0.647548i \(0.224206\pi\)
\(258\) 0 0
\(259\) 8.55104 0.531336
\(260\) 0 0
\(261\) −19.6216 −1.21455
\(262\) 0 0
\(263\) −14.4935 −0.893707 −0.446854 0.894607i \(-0.647456\pi\)
−0.446854 + 0.894607i \(0.647456\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 11.4292 0.699458
\(268\) 0 0
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 0 0
\(271\) 6.76060 0.410677 0.205339 0.978691i \(-0.434170\pi\)
0.205339 + 0.978691i \(0.434170\pi\)
\(272\) 0 0
\(273\) −18.6027 −1.12589
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 25.4292 1.52789 0.763947 0.645279i \(-0.223259\pi\)
0.763947 + 0.645279i \(0.223259\pi\)
\(278\) 0 0
\(279\) 7.41454 0.443897
\(280\) 0 0
\(281\) 9.07896 0.541605 0.270803 0.962635i \(-0.412711\pi\)
0.270803 + 0.962635i \(0.412711\pi\)
\(282\) 0 0
\(283\) 12.0147 0.714199 0.357100 0.934066i \(-0.383766\pi\)
0.357100 + 0.934066i \(0.383766\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.99158 0.117559
\(288\) 0 0
\(289\) −14.7820 −0.869531
\(290\) 0 0
\(291\) −15.9572 −0.935425
\(292\) 0 0
\(293\) −23.6718 −1.38292 −0.691460 0.722415i \(-0.743032\pi\)
−0.691460 + 0.722415i \(0.743032\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −5.95715 −0.345669
\(298\) 0 0
\(299\) −3.38890 −0.195985
\(300\) 0 0
\(301\) −7.64973 −0.440923
\(302\) 0 0
\(303\) 5.37169 0.308596
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −16.0246 −0.914570 −0.457285 0.889320i \(-0.651178\pi\)
−0.457285 + 0.889320i \(0.651178\pi\)
\(308\) 0 0
\(309\) 15.2713 0.868754
\(310\) 0 0
\(311\) 27.5468 1.56204 0.781019 0.624508i \(-0.214700\pi\)
0.781019 + 0.624508i \(0.214700\pi\)
\(312\) 0 0
\(313\) −10.1751 −0.575133 −0.287566 0.957761i \(-0.592846\pi\)
−0.287566 + 0.957761i \(0.592846\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −29.6289 −1.66413 −0.832063 0.554681i \(-0.812840\pi\)
−0.832063 + 0.554681i \(0.812840\pi\)
\(318\) 0 0
\(319\) 39.2432 2.19719
\(320\) 0 0
\(321\) −18.0748 −1.00883
\(322\) 0 0
\(323\) 1.48929 0.0828662
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −36.4250 −2.01431
\(328\) 0 0
\(329\) −11.9143 −0.656857
\(330\) 0 0
\(331\) −30.4679 −1.67467 −0.837333 0.546694i \(-0.815886\pi\)
−0.837333 + 0.546694i \(0.815886\pi\)
\(332\) 0 0
\(333\) 17.7894 0.974851
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −26.1396 −1.42392 −0.711958 0.702222i \(-0.752192\pi\)
−0.711958 + 0.702222i \(0.752192\pi\)
\(338\) 0 0
\(339\) −1.76481 −0.0958512
\(340\) 0 0
\(341\) −14.8291 −0.803039
\(342\) 0 0
\(343\) −15.0386 −0.812010
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −7.31415 −0.392644 −0.196322 0.980539i \(-0.562900\pi\)
−0.196322 + 0.980539i \(0.562900\pi\)
\(348\) 0 0
\(349\) 0.628308 0.0336325 0.0168163 0.999859i \(-0.494647\pi\)
0.0168163 + 0.999859i \(0.494647\pi\)
\(350\) 0 0
\(351\) 7.93994 0.423803
\(352\) 0 0
\(353\) 8.23267 0.438181 0.219090 0.975705i \(-0.429691\pi\)
0.219090 + 0.975705i \(0.429691\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 4.17513 0.220972
\(358\) 0 0
\(359\) −12.1323 −0.640318 −0.320159 0.947364i \(-0.603736\pi\)
−0.320159 + 0.947364i \(0.603736\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −32.3001 −1.69531
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 17.9572 0.937356 0.468678 0.883369i \(-0.344730\pi\)
0.468678 + 0.883369i \(0.344730\pi\)
\(368\) 0 0
\(369\) 4.14323 0.215688
\(370\) 0 0
\(371\) 13.6669 0.709552
\(372\) 0 0
\(373\) −29.6289 −1.53413 −0.767064 0.641571i \(-0.778283\pi\)
−0.767064 + 0.641571i \(0.778283\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −52.3049 −2.69384
\(378\) 0 0
\(379\) 6.80344 0.349469 0.174735 0.984616i \(-0.444093\pi\)
0.174735 + 0.984616i \(0.444093\pi\)
\(380\) 0 0
\(381\) −24.4078 −1.25045
\(382\) 0 0
\(383\) −20.2253 −1.03347 −0.516733 0.856147i \(-0.672852\pi\)
−0.516733 + 0.856147i \(0.672852\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −15.9143 −0.808970
\(388\) 0 0
\(389\) 0.393115 0.0199317 0.00996587 0.999950i \(-0.496828\pi\)
0.00996587 + 0.999950i \(0.496828\pi\)
\(390\) 0 0
\(391\) 0.760597 0.0384650
\(392\) 0 0
\(393\) −42.0722 −2.12226
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −17.4292 −0.874748 −0.437374 0.899280i \(-0.644091\pi\)
−0.437374 + 0.899280i \(0.644091\pi\)
\(398\) 0 0
\(399\) 2.80344 0.140348
\(400\) 0 0
\(401\) 13.1281 0.655585 0.327792 0.944750i \(-0.393695\pi\)
0.327792 + 0.944750i \(0.393695\pi\)
\(402\) 0 0
\(403\) 19.7648 0.984555
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −35.5787 −1.76357
\(408\) 0 0
\(409\) −18.7862 −0.928919 −0.464460 0.885594i \(-0.653751\pi\)
−0.464460 + 0.885594i \(0.653751\pi\)
\(410\) 0 0
\(411\) −23.0533 −1.13714
\(412\) 0 0
\(413\) 14.1667 0.697098
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −2.29273 −0.112276
\(418\) 0 0
\(419\) 5.22219 0.255121 0.127560 0.991831i \(-0.459285\pi\)
0.127560 + 0.991831i \(0.459285\pi\)
\(420\) 0 0
\(421\) −7.68164 −0.374380 −0.187190 0.982324i \(-0.559938\pi\)
−0.187190 + 0.982324i \(0.559938\pi\)
\(422\) 0 0
\(423\) −24.7862 −1.20515
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 4.38469 0.212190
\(428\) 0 0
\(429\) 77.4011 3.73696
\(430\) 0 0
\(431\) 17.7073 0.852929 0.426465 0.904504i \(-0.359759\pi\)
0.426465 + 0.904504i \(0.359759\pi\)
\(432\) 0 0
\(433\) −17.9901 −0.864551 −0.432275 0.901742i \(-0.642289\pi\)
−0.432275 + 0.901742i \(0.642289\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.510711 0.0244306
\(438\) 0 0
\(439\) −14.8438 −0.708454 −0.354227 0.935159i \(-0.615256\pi\)
−0.354227 + 0.935159i \(0.615256\pi\)
\(440\) 0 0
\(441\) −13.8610 −0.660047
\(442\) 0 0
\(443\) 22.4078 1.06463 0.532314 0.846547i \(-0.321323\pi\)
0.532314 + 0.846547i \(0.321323\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 19.3288 0.914223
\(448\) 0 0
\(449\) −40.7434 −1.92280 −0.961400 0.275156i \(-0.911271\pi\)
−0.961400 + 0.275156i \(0.911271\pi\)
\(450\) 0 0
\(451\) −8.28646 −0.390194
\(452\) 0 0
\(453\) 32.4653 1.52536
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −8.01721 −0.375029 −0.187515 0.982262i \(-0.560043\pi\)
−0.187515 + 0.982262i \(0.560043\pi\)
\(458\) 0 0
\(459\) −1.78202 −0.0831775
\(460\) 0 0
\(461\) −25.1281 −1.17033 −0.585166 0.810914i \(-0.698971\pi\)
−0.585166 + 0.810914i \(0.698971\pi\)
\(462\) 0 0
\(463\) −31.7795 −1.47692 −0.738459 0.674298i \(-0.764446\pi\)
−0.738459 + 0.674298i \(0.764446\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 20.9210 0.968110 0.484055 0.875038i \(-0.339163\pi\)
0.484055 + 0.875038i \(0.339163\pi\)
\(468\) 0 0
\(469\) 9.11087 0.420701
\(470\) 0 0
\(471\) −36.8009 −1.69570
\(472\) 0 0
\(473\) 31.8286 1.46348
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 28.4324 1.30183
\(478\) 0 0
\(479\) −27.7220 −1.26665 −0.633324 0.773886i \(-0.718310\pi\)
−0.633324 + 0.773886i \(0.718310\pi\)
\(480\) 0 0
\(481\) 47.4208 2.16220
\(482\) 0 0
\(483\) 1.43175 0.0651469
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 3.20390 0.145183 0.0725914 0.997362i \(-0.476873\pi\)
0.0725914 + 0.997362i \(0.476873\pi\)
\(488\) 0 0
\(489\) −13.6069 −0.615325
\(490\) 0 0
\(491\) 21.5212 0.971238 0.485619 0.874171i \(-0.338594\pi\)
0.485619 + 0.874171i \(0.338594\pi\)
\(492\) 0 0
\(493\) 11.7392 0.528706
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 23.1709 1.03727 0.518637 0.854995i \(-0.326440\pi\)
0.518637 + 0.854995i \(0.326440\pi\)
\(500\) 0 0
\(501\) 32.4078 1.44787
\(502\) 0 0
\(503\) −1.88240 −0.0839322 −0.0419661 0.999119i \(-0.513362\pi\)
−0.0419661 + 0.999119i \(0.513362\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −72.7054 −3.22896
\(508\) 0 0
\(509\) 5.46365 0.242172 0.121086 0.992642i \(-0.461362\pi\)
0.121086 + 0.992642i \(0.461362\pi\)
\(510\) 0 0
\(511\) −16.5598 −0.732564
\(512\) 0 0
\(513\) −1.19656 −0.0528293
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 49.5725 2.18019
\(518\) 0 0
\(519\) 34.7005 1.52318
\(520\) 0 0
\(521\) 11.2222 0.491653 0.245827 0.969314i \(-0.420941\pi\)
0.245827 + 0.969314i \(0.420941\pi\)
\(522\) 0 0
\(523\) −29.1867 −1.27624 −0.638122 0.769935i \(-0.720289\pi\)
−0.638122 + 0.769935i \(0.720289\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −4.43596 −0.193233
\(528\) 0 0
\(529\) −22.7392 −0.988660
\(530\) 0 0
\(531\) 29.4721 1.27898
\(532\) 0 0
\(533\) 11.0445 0.478392
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 36.7005 1.58375
\(538\) 0 0
\(539\) 27.7220 1.19407
\(540\) 0 0
\(541\) 20.2499 0.870611 0.435305 0.900283i \(-0.356640\pi\)
0.435305 + 0.900283i \(0.356640\pi\)
\(542\) 0 0
\(543\) 34.6430 1.48667
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 42.8830 1.83355 0.916773 0.399409i \(-0.130785\pi\)
0.916773 + 0.399409i \(0.130785\pi\)
\(548\) 0 0
\(549\) 9.12181 0.389309
\(550\) 0 0
\(551\) 7.88240 0.335802
\(552\) 0 0
\(553\) −15.1793 −0.645491
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −28.2583 −1.19734 −0.598671 0.800995i \(-0.704304\pi\)
−0.598671 + 0.800995i \(0.704304\pi\)
\(558\) 0 0
\(559\) −42.4225 −1.79428
\(560\) 0 0
\(561\) −17.3717 −0.733433
\(562\) 0 0
\(563\) −20.2253 −0.852396 −0.426198 0.904630i \(-0.640147\pi\)
−0.426198 + 0.904630i \(0.640147\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −12.2902 −0.516140
\(568\) 0 0
\(569\) −31.1365 −1.30531 −0.652655 0.757655i \(-0.726345\pi\)
−0.652655 + 0.757655i \(0.726345\pi\)
\(570\) 0 0
\(571\) −27.4868 −1.15029 −0.575143 0.818053i \(-0.695053\pi\)
−0.575143 + 0.818053i \(0.695053\pi\)
\(572\) 0 0
\(573\) −14.9185 −0.623230
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −23.7820 −0.990058 −0.495029 0.868876i \(-0.664843\pi\)
−0.495029 + 0.868876i \(0.664843\pi\)
\(578\) 0 0
\(579\) −45.9143 −1.90813
\(580\) 0 0
\(581\) −10.3931 −0.431179
\(582\) 0 0
\(583\) −56.8647 −2.35510
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 24.0147 0.991192 0.495596 0.868553i \(-0.334950\pi\)
0.495596 + 0.868553i \(0.334950\pi\)
\(588\) 0 0
\(589\) −2.97858 −0.122730
\(590\) 0 0
\(591\) 25.2713 1.03952
\(592\) 0 0
\(593\) −46.6148 −1.91424 −0.957121 0.289688i \(-0.906449\pi\)
−0.957121 + 0.289688i \(0.906449\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 6.56825 0.268821
\(598\) 0 0
\(599\) 44.6002 1.82231 0.911156 0.412061i \(-0.135191\pi\)
0.911156 + 0.412061i \(0.135191\pi\)
\(600\) 0 0
\(601\) −17.5787 −0.717051 −0.358526 0.933520i \(-0.616720\pi\)
−0.358526 + 0.933520i \(0.616720\pi\)
\(602\) 0 0
\(603\) 18.9540 0.771867
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 37.2467 1.51180 0.755899 0.654688i \(-0.227200\pi\)
0.755899 + 0.654688i \(0.227200\pi\)
\(608\) 0 0
\(609\) 22.0979 0.895451
\(610\) 0 0
\(611\) −66.0722 −2.67300
\(612\) 0 0
\(613\) 14.8866 0.601265 0.300632 0.953740i \(-0.402802\pi\)
0.300632 + 0.953740i \(0.402802\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −3.70727 −0.149249 −0.0746245 0.997212i \(-0.523776\pi\)
−0.0746245 + 0.997212i \(0.523776\pi\)
\(618\) 0 0
\(619\) −17.7648 −0.714028 −0.357014 0.934099i \(-0.616205\pi\)
−0.357014 + 0.934099i \(0.616205\pi\)
\(620\) 0 0
\(621\) −0.611096 −0.0245224
\(622\) 0 0
\(623\) −5.83704 −0.233856
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −11.6644 −0.465832
\(628\) 0 0
\(629\) −10.6430 −0.424364
\(630\) 0 0
\(631\) −40.3074 −1.60461 −0.802307 0.596912i \(-0.796394\pi\)
−0.802307 + 0.596912i \(0.796394\pi\)
\(632\) 0 0
\(633\) −26.3675 −1.04801
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −36.9490 −1.46397
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −27.6728 −1.09301 −0.546506 0.837455i \(-0.684042\pi\)
−0.546506 + 0.837455i \(0.684042\pi\)
\(642\) 0 0
\(643\) 19.0277 0.750379 0.375190 0.926948i \(-0.377578\pi\)
0.375190 + 0.926948i \(0.377578\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −32.0403 −1.25964 −0.629818 0.776743i \(-0.716870\pi\)
−0.629818 + 0.776743i \(0.716870\pi\)
\(648\) 0 0
\(649\) −58.9442 −2.31376
\(650\) 0 0
\(651\) −8.35027 −0.327273
\(652\) 0 0
\(653\) −25.3142 −0.990619 −0.495310 0.868716i \(-0.664945\pi\)
−0.495310 + 0.868716i \(0.664945\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −34.4507 −1.34405
\(658\) 0 0
\(659\) 0.860981 0.0335391 0.0167695 0.999859i \(-0.494662\pi\)
0.0167695 + 0.999859i \(0.494662\pi\)
\(660\) 0 0
\(661\) 4.55356 0.177113 0.0885564 0.996071i \(-0.471775\pi\)
0.0885564 + 0.996071i \(0.471775\pi\)
\(662\) 0 0
\(663\) 23.1537 0.899216
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 4.02563 0.155873
\(668\) 0 0
\(669\) −40.9933 −1.58489
\(670\) 0 0
\(671\) −18.2436 −0.704287
\(672\) 0 0
\(673\) 11.7465 0.452795 0.226398 0.974035i \(-0.427305\pi\)
0.226398 + 0.974035i \(0.427305\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 22.2854 0.856497 0.428248 0.903661i \(-0.359131\pi\)
0.428248 + 0.903661i \(0.359131\pi\)
\(678\) 0 0
\(679\) 8.14950 0.312749
\(680\) 0 0
\(681\) 9.01890 0.345605
\(682\) 0 0
\(683\) −7.23833 −0.276967 −0.138483 0.990365i \(-0.544223\pi\)
−0.138483 + 0.990365i \(0.544223\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 34.3074 1.30891
\(688\) 0 0
\(689\) 75.7917 2.88743
\(690\) 0 0
\(691\) −32.7434 −1.24562 −0.622809 0.782374i \(-0.714008\pi\)
−0.622809 + 0.782374i \(0.714008\pi\)
\(692\) 0 0
\(693\) −14.8291 −0.563310
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −2.47881 −0.0938915
\(698\) 0 0
\(699\) 28.0147 1.05961
\(700\) 0 0
\(701\) −29.4208 −1.11121 −0.555604 0.831447i \(-0.687513\pi\)
−0.555604 + 0.831447i \(0.687513\pi\)
\(702\) 0 0
\(703\) −7.14637 −0.269530
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.74338 −0.103176
\(708\) 0 0
\(709\) −5.32885 −0.200129 −0.100065 0.994981i \(-0.531905\pi\)
−0.100065 + 0.994981i \(0.531905\pi\)
\(710\) 0 0
\(711\) −31.5787 −1.18429
\(712\) 0 0
\(713\) −1.52119 −0.0569691
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 36.5254 1.36407
\(718\) 0 0
\(719\) −8.45317 −0.315250 −0.157625 0.987499i \(-0.550384\pi\)
−0.157625 + 0.987499i \(0.550384\pi\)
\(720\) 0 0
\(721\) −7.79923 −0.290459
\(722\) 0 0
\(723\) 37.6216 1.39916
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 2.56825 0.0952511 0.0476256 0.998865i \(-0.484835\pi\)
0.0476256 + 0.998865i \(0.484835\pi\)
\(728\) 0 0
\(729\) −17.1579 −0.635479
\(730\) 0 0
\(731\) 9.52119 0.352154
\(732\) 0 0
\(733\) −35.5212 −1.31201 −0.656003 0.754759i \(-0.727754\pi\)
−0.656003 + 0.754759i \(0.727754\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −37.9080 −1.39636
\(738\) 0 0
\(739\) 37.0508 1.36294 0.681468 0.731848i \(-0.261342\pi\)
0.681468 + 0.731848i \(0.261342\pi\)
\(740\) 0 0
\(741\) 15.5468 0.571127
\(742\) 0 0
\(743\) 23.2039 0.851269 0.425634 0.904895i \(-0.360051\pi\)
0.425634 + 0.904895i \(0.360051\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −21.6216 −0.791092
\(748\) 0 0
\(749\) 9.23098 0.337293
\(750\) 0 0
\(751\) −51.2285 −1.86935 −0.934677 0.355499i \(-0.884311\pi\)
−0.934677 + 0.355499i \(0.884311\pi\)
\(752\) 0 0
\(753\) 56.0294 2.04182
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 43.3717 1.57637 0.788185 0.615438i \(-0.211021\pi\)
0.788185 + 0.615438i \(0.211021\pi\)
\(758\) 0 0
\(759\) −5.95715 −0.216231
\(760\) 0 0
\(761\) 24.7753 0.898104 0.449052 0.893506i \(-0.351762\pi\)
0.449052 + 0.893506i \(0.351762\pi\)
\(762\) 0 0
\(763\) 18.6027 0.673462
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 78.5632 2.83675
\(768\) 0 0
\(769\) −11.4893 −0.414314 −0.207157 0.978308i \(-0.566421\pi\)
−0.207157 + 0.978308i \(0.566421\pi\)
\(770\) 0 0
\(771\) −57.2432 −2.06156
\(772\) 0 0
\(773\) −27.0863 −0.974227 −0.487113 0.873339i \(-0.661950\pi\)
−0.487113 + 0.873339i \(0.661950\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −20.0344 −0.718731
\(778\) 0 0
\(779\) −1.66442 −0.0596342
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −9.43175 −0.337063
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 13.4563 0.479666 0.239833 0.970814i \(-0.422907\pi\)
0.239833 + 0.970814i \(0.422907\pi\)
\(788\) 0 0
\(789\) 33.9572 1.20891
\(790\) 0 0
\(791\) 0.901307 0.0320468
\(792\) 0 0
\(793\) 24.3158 0.863481
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −30.4496 −1.07858 −0.539290 0.842120i \(-0.681307\pi\)
−0.539290 + 0.842120i \(0.681307\pi\)
\(798\) 0 0
\(799\) 14.8291 0.524615
\(800\) 0 0
\(801\) −12.1432 −0.429060
\(802\) 0 0
\(803\) 68.9013 2.43147
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 32.8009 1.15465
\(808\) 0 0
\(809\) −29.7047 −1.04436 −0.522182 0.852834i \(-0.674882\pi\)
−0.522182 + 0.852834i \(0.674882\pi\)
\(810\) 0 0
\(811\) −32.2902 −1.13386 −0.566931 0.823765i \(-0.691870\pi\)
−0.566931 + 0.823765i \(0.691870\pi\)
\(812\) 0 0
\(813\) −15.8396 −0.555518
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 6.39312 0.223667
\(818\) 0 0
\(819\) 19.7648 0.690638
\(820\) 0 0
\(821\) 9.06427 0.316345 0.158173 0.987411i \(-0.449440\pi\)
0.158173 + 0.987411i \(0.449440\pi\)
\(822\) 0 0
\(823\) −7.35448 −0.256361 −0.128181 0.991751i \(-0.540914\pi\)
−0.128181 + 0.991751i \(0.540914\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.02204 0.0703132 0.0351566 0.999382i \(-0.488807\pi\)
0.0351566 + 0.999382i \(0.488807\pi\)
\(828\) 0 0
\(829\) −36.3675 −1.26309 −0.631547 0.775337i \(-0.717580\pi\)
−0.631547 + 0.775337i \(0.717580\pi\)
\(830\) 0 0
\(831\) −59.5787 −2.06676
\(832\) 0 0
\(833\) 8.29273 0.287326
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 3.56404 0.123191
\(838\) 0 0
\(839\) −25.8223 −0.891486 −0.445743 0.895161i \(-0.647061\pi\)
−0.445743 + 0.895161i \(0.647061\pi\)
\(840\) 0 0
\(841\) 33.1323 1.14249
\(842\) 0 0
\(843\) −21.2713 −0.732623
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 16.4960 0.566810
\(848\) 0 0
\(849\) −28.1495 −0.966088
\(850\) 0 0
\(851\) −3.64973 −0.125111
\(852\) 0 0
\(853\) −8.54262 −0.292494 −0.146247 0.989248i \(-0.546719\pi\)
−0.146247 + 0.989248i \(0.546719\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −27.8322 −0.950730 −0.475365 0.879789i \(-0.657684\pi\)
−0.475365 + 0.879789i \(0.657684\pi\)
\(858\) 0 0
\(859\) −33.4868 −1.14255 −0.571277 0.820757i \(-0.693552\pi\)
−0.571277 + 0.820757i \(0.693552\pi\)
\(860\) 0 0
\(861\) −4.66611 −0.159021
\(862\) 0 0
\(863\) −29.2614 −0.996071 −0.498036 0.867157i \(-0.665945\pi\)
−0.498036 + 0.867157i \(0.665945\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 34.6331 1.17620
\(868\) 0 0
\(869\) 63.1575 2.14247
\(870\) 0 0
\(871\) 50.5254 1.71199
\(872\) 0 0
\(873\) 16.9540 0.573807
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 46.7852 1.57982 0.789911 0.613221i \(-0.210127\pi\)
0.789911 + 0.613221i \(0.210127\pi\)
\(878\) 0 0
\(879\) 55.4611 1.87066
\(880\) 0 0
\(881\) −30.7581 −1.03627 −0.518133 0.855300i \(-0.673373\pi\)
−0.518133 + 0.855300i \(0.673373\pi\)
\(882\) 0 0
\(883\) 0.435961 0.0146713 0.00733563 0.999973i \(-0.497665\pi\)
0.00733563 + 0.999973i \(0.497665\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.15310 −0.0722939 −0.0361469 0.999346i \(-0.511508\pi\)
−0.0361469 + 0.999346i \(0.511508\pi\)
\(888\) 0 0
\(889\) 12.4653 0.418074
\(890\) 0 0
\(891\) 51.1365 1.71314
\(892\) 0 0
\(893\) 9.95715 0.333203
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 7.93994 0.265107
\(898\) 0 0
\(899\) −23.4783 −0.783047
\(900\) 0 0
\(901\) −17.0105 −0.566701
\(902\) 0 0
\(903\) 17.9227 0.596431
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −36.9002 −1.22525 −0.612626 0.790373i \(-0.709887\pi\)
−0.612626 + 0.790373i \(0.709887\pi\)
\(908\) 0 0
\(909\) −5.70727 −0.189298
\(910\) 0 0
\(911\) 36.9504 1.22422 0.612111 0.790772i \(-0.290321\pi\)
0.612111 + 0.790772i \(0.290321\pi\)
\(912\) 0 0
\(913\) 43.2432 1.43114
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 21.4868 0.709556
\(918\) 0 0
\(919\) −19.1537 −0.631823 −0.315911 0.948789i \(-0.602310\pi\)
−0.315911 + 0.948789i \(0.602310\pi\)
\(920\) 0 0
\(921\) 37.5443 1.23713
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −16.2253 −0.532910
\(928\) 0 0
\(929\) −56.9185 −1.86744 −0.933718 0.358009i \(-0.883456\pi\)
−0.933718 + 0.358009i \(0.883456\pi\)
\(930\) 0 0
\(931\) 5.56825 0.182492
\(932\) 0 0
\(933\) −64.5401 −2.11295
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 24.1176 0.787888 0.393944 0.919135i \(-0.371110\pi\)
0.393944 + 0.919135i \(0.371110\pi\)
\(938\) 0 0
\(939\) 23.8396 0.777975
\(940\) 0 0
\(941\) 3.19656 0.104205 0.0521024 0.998642i \(-0.483408\pi\)
0.0521024 + 0.998642i \(0.483408\pi\)
\(942\) 0 0
\(943\) −0.850040 −0.0276811
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.63504 0.118123 0.0590614 0.998254i \(-0.481189\pi\)
0.0590614 + 0.998254i \(0.481189\pi\)
\(948\) 0 0
\(949\) −91.8345 −2.98107
\(950\) 0 0
\(951\) 69.4183 2.25104
\(952\) 0 0
\(953\) 48.0821 1.55753 0.778766 0.627315i \(-0.215846\pi\)
0.778766 + 0.627315i \(0.215846\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −91.9437 −2.97212
\(958\) 0 0
\(959\) 11.7736 0.380189
\(960\) 0 0
\(961\) −22.1281 −0.713809
\(962\) 0 0
\(963\) 19.2039 0.618837
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −23.4637 −0.754540 −0.377270 0.926103i \(-0.623137\pi\)
−0.377270 + 0.926103i \(0.623137\pi\)
\(968\) 0 0
\(969\) −3.48929 −0.112092
\(970\) 0 0
\(971\) −17.4868 −0.561177 −0.280589 0.959828i \(-0.590530\pi\)
−0.280589 + 0.959828i \(0.590530\pi\)
\(972\) 0 0
\(973\) 1.17092 0.0375381
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −20.2316 −0.647266 −0.323633 0.946183i \(-0.604904\pi\)
−0.323633 + 0.946183i \(0.604904\pi\)
\(978\) 0 0
\(979\) 24.2865 0.776199
\(980\) 0 0
\(981\) 38.7005 1.23561
\(982\) 0 0
\(983\) 28.1249 0.897046 0.448523 0.893771i \(-0.351950\pi\)
0.448523 + 0.893771i \(0.351950\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 27.9143 0.888522
\(988\) 0 0
\(989\) 3.26504 0.103822
\(990\) 0 0
\(991\) 33.9718 1.07915 0.539576 0.841937i \(-0.318585\pi\)
0.539576 + 0.841937i \(0.318585\pi\)
\(992\) 0 0
\(993\) 71.3839 2.26530
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 23.8223 0.754461 0.377231 0.926119i \(-0.376876\pi\)
0.377231 + 0.926119i \(0.376876\pi\)
\(998\) 0 0
\(999\) 8.55104 0.270543
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 7600.2.a.bp.1.1 3
4.3 odd 2 3800.2.a.w.1.3 3
5.4 even 2 1520.2.a.q.1.3 3
20.3 even 4 3800.2.d.n.3649.6 6
20.7 even 4 3800.2.d.n.3649.1 6
20.19 odd 2 760.2.a.i.1.1 3
40.19 odd 2 6080.2.a.bx.1.3 3
40.29 even 2 6080.2.a.br.1.1 3
60.59 even 2 6840.2.a.bm.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
760.2.a.i.1.1 3 20.19 odd 2
1520.2.a.q.1.3 3 5.4 even 2
3800.2.a.w.1.3 3 4.3 odd 2
3800.2.d.n.3649.1 6 20.7 even 4
3800.2.d.n.3649.6 6 20.3 even 4
6080.2.a.br.1.1 3 40.29 even 2
6080.2.a.bx.1.3 3 40.19 odd 2
6840.2.a.bm.1.2 3 60.59 even 2
7600.2.a.bp.1.1 3 1.1 even 1 trivial