Properties

Label 1805.2.b.h.1084.1
Level $1805$
Weight $2$
Character 1805.1084
Analytic conductor $14.413$
Analytic rank $0$
Dimension $8$
CM discriminant -95
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1805,2,Mod(1084,1805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1805.1084");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.b (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(14.4129975648\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.280944640000.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 16x^{6} + 80x^{4} + 128x^{2} + 19 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 1084.1
Root \(-2.79913i\) of defining polynomial
Character \(\chi\) \(=\) 1805.1084
Dual form 1805.2.b.h.1084.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.79913i q^{2} -1.12228i q^{3} -5.83513 q^{4} +2.23607 q^{5} -3.14142 q^{6} +10.7350i q^{8} +1.74048 q^{9} +O(q^{10})\) \(q-2.79913i q^{2} -1.12228i q^{3} -5.83513 q^{4} +2.23607 q^{5} -3.14142 q^{6} +10.7350i q^{8} +1.74048 q^{9} -6.25904i q^{10} +2.92978 q^{11} +6.54867i q^{12} +3.08876i q^{13} -2.50950i q^{15} +18.3785 q^{16} -4.87183i q^{18} -13.0477 q^{20} -8.20083i q^{22} +12.0477 q^{24} +5.00000 q^{25} +8.64583 q^{26} -5.32016i q^{27} -7.02443 q^{30} -29.9737i q^{32} -3.28804i q^{33} -10.1559 q^{36} -9.15124i q^{37} +3.46646 q^{39} +24.0042i q^{40} -17.0956 q^{44} +3.89183 q^{45} -20.6259i q^{48} +7.00000 q^{49} -13.9956i q^{50} -18.0233i q^{52} -13.6404i q^{53} -14.8918 q^{54} +6.55118 q^{55} +14.6433i q^{60} +1.11908 q^{61} -47.1432 q^{64} +6.90667i q^{65} -9.20366 q^{66} +13.7060i q^{67} +18.6841i q^{72} -25.6155 q^{74} -5.61142i q^{75} -9.70308i q^{78} +41.0955 q^{80} -0.749299 q^{81} +31.4512i q^{88} -10.8937i q^{90} -33.6390 q^{96} -15.8849i q^{97} -19.5939i q^{98} +5.09921 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 16 q^{4} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 16 q^{4} - 24 q^{9} + 32 q^{16} - 8 q^{24} + 40 q^{25} + 24 q^{26} - 40 q^{30} - 8 q^{36} - 72 q^{44} + 56 q^{49} - 88 q^{54} - 64 q^{64} + 104 q^{66} + 120 q^{80} + 72 q^{81} - 120 q^{96} - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).

\(n\) \(362\) \(1446\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) − 2.79913i − 1.97928i −0.143559 0.989642i \(-0.545855\pi\)
0.143559 0.989642i \(-0.454145\pi\)
\(3\) − 1.12228i − 0.647951i −0.946065 0.323976i \(-0.894980\pi\)
0.946065 0.323976i \(-0.105020\pi\)
\(4\) −5.83513 −2.91756
\(5\) 2.23607 1.00000
\(6\) −3.14142 −1.28248
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 10.7350i 3.79540i
\(9\) 1.74048 0.580159
\(10\) − 6.25904i − 1.97928i
\(11\) 2.92978 0.883361 0.441680 0.897172i \(-0.354382\pi\)
0.441680 + 0.897172i \(0.354382\pi\)
\(12\) 6.54867i 1.89044i
\(13\) 3.08876i 0.856667i 0.903621 + 0.428333i \(0.140899\pi\)
−0.903621 + 0.428333i \(0.859101\pi\)
\(14\) 0 0
\(15\) − 2.50950i − 0.647951i
\(16\) 18.3785 4.59461
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) − 4.87183i − 1.14830i
\(19\) 0 0
\(20\) −13.0477 −2.91756
\(21\) 0 0
\(22\) − 8.20083i − 1.74842i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 12.0477 2.45924
\(25\) 5.00000 1.00000
\(26\) 8.64583 1.69559
\(27\) − 5.32016i − 1.02387i
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −7.02443 −1.28248
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) − 29.9737i − 5.29864i
\(33\) − 3.28804i − 0.572375i
\(34\) 0 0
\(35\) 0 0
\(36\) −10.1559 −1.69265
\(37\) − 9.15124i − 1.50445i −0.658904 0.752227i \(-0.728980\pi\)
0.658904 0.752227i \(-0.271020\pi\)
\(38\) 0 0
\(39\) 3.46646 0.555078
\(40\) 24.0042i 3.79540i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) −17.0956 −2.57726
\(45\) 3.89183 0.580159
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) − 20.6259i − 2.97709i
\(49\) 7.00000 1.00000
\(50\) − 13.9956i − 1.97928i
\(51\) 0 0
\(52\) − 18.0233i − 2.49938i
\(53\) − 13.6404i − 1.87365i −0.349799 0.936825i \(-0.613750\pi\)
0.349799 0.936825i \(-0.386250\pi\)
\(54\) −14.8918 −2.02652
\(55\) 6.55118 0.883361
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 14.6433i 1.89044i
\(61\) 1.11908 0.143283 0.0716414 0.997430i \(-0.477176\pi\)
0.0716414 + 0.997430i \(0.477176\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −47.1432 −5.89290
\(65\) 6.90667i 0.856667i
\(66\) −9.20366 −1.13289
\(67\) 13.7060i 1.67446i 0.546853 + 0.837229i \(0.315826\pi\)
−0.546853 + 0.837229i \(0.684174\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 18.6841i 2.20194i
\(73\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(74\) −25.6155 −2.97774
\(75\) − 5.61142i − 0.647951i
\(76\) 0 0
\(77\) 0 0
\(78\) − 9.70308i − 1.09866i
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 41.0955 4.59461
\(81\) −0.749299 −0.0832555
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 31.4512i 3.35271i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) − 10.8937i − 1.14830i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) −33.6390 −3.43326
\(97\) − 15.8849i − 1.61287i −0.591322 0.806436i \(-0.701394\pi\)
0.591322 0.806436i \(-0.298606\pi\)
\(98\) − 19.5939i − 1.97928i
\(99\) 5.09921 0.512490
\(100\) −29.1756 −2.91756
\(101\) 20.0810 1.99813 0.999067 0.0431977i \(-0.0137545\pi\)
0.999067 + 0.0431977i \(0.0137545\pi\)
\(102\) 0 0
\(103\) 19.8835i 1.95918i 0.200999 + 0.979591i \(0.435581\pi\)
−0.200999 + 0.979591i \(0.564419\pi\)
\(104\) −33.1579 −3.25140
\(105\) 0 0
\(106\) −38.1812 −3.70848
\(107\) − 3.66801i − 0.354600i −0.984157 0.177300i \(-0.943264\pi\)
0.984157 0.177300i \(-0.0567363\pi\)
\(108\) 31.0438i 2.98719i
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) − 18.3376i − 1.74842i
\(111\) −10.2703 −0.974813
\(112\) 0 0
\(113\) − 1.93025i − 0.181583i −0.995870 0.0907914i \(-0.971060\pi\)
0.995870 0.0907914i \(-0.0289396\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 5.37591i 0.497003i
\(118\) 0 0
\(119\) 0 0
\(120\) 26.9396 2.45924
\(121\) −2.41641 −0.219673
\(122\) − 3.13244i − 0.283597i
\(123\) 0 0
\(124\) 0 0
\(125\) 11.1803 1.00000
\(126\) 0 0
\(127\) 21.6693i 1.92284i 0.275082 + 0.961421i \(0.411295\pi\)
−0.275082 + 0.961421i \(0.588705\pi\)
\(128\) 72.0127i 6.36508i
\(129\) 0 0
\(130\) 19.3327 1.69559
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 19.1861i 1.66994i
\(133\) 0 0
\(134\) 38.3649 3.31423
\(135\) − 11.8962i − 1.02387i
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) −21.8917 −1.85683 −0.928414 0.371546i \(-0.878828\pi\)
−0.928414 + 0.371546i \(0.878828\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 9.04937i 0.756746i
\(144\) 31.9873 2.66561
\(145\) 0 0
\(146\) 0 0
\(147\) − 7.85599i − 0.647951i
\(148\) 53.3986i 4.38934i
\(149\) −8.36188 −0.685032 −0.342516 0.939512i \(-0.611279\pi\)
−0.342516 + 0.939512i \(0.611279\pi\)
\(150\) −15.7071 −1.28248
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −20.2272 −1.61948
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0 0
\(159\) −15.3084 −1.21403
\(160\) − 67.0231i − 5.29864i
\(161\) 0 0
\(162\) 2.09739i 0.164786i
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) − 7.35229i − 0.572375i
\(166\) 0 0
\(167\) − 17.1802i − 1.32944i −0.747091 0.664721i \(-0.768550\pi\)
0.747091 0.664721i \(-0.231450\pi\)
\(168\) 0 0
\(169\) 3.45959 0.266122
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 13.1268i − 0.998010i −0.866599 0.499005i \(-0.833699\pi\)
0.866599 0.499005i \(-0.166301\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 53.8448 4.05870
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −22.7093 −1.69265
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) − 1.25592i − 0.0928403i
\(184\) 0 0
\(185\) − 20.4628i − 1.50445i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.94427 −0.647185 −0.323592 0.946197i \(-0.604891\pi\)
−0.323592 + 0.946197i \(0.604891\pi\)
\(192\) 52.9081i 3.81831i
\(193\) 2.41753i 0.174018i 0.996208 + 0.0870089i \(0.0277309\pi\)
−0.996208 + 0.0870089i \(0.972269\pi\)
\(194\) −44.4640 −3.19233
\(195\) 7.75124 0.555078
\(196\) −40.8459 −2.91756
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) − 14.2734i − 1.01436i
\(199\) 26.8328 1.90213 0.951064 0.308994i \(-0.0999924\pi\)
0.951064 + 0.308994i \(0.0999924\pi\)
\(200\) 53.6751i 3.79540i
\(201\) 15.3821 1.08497
\(202\) − 56.2093i − 3.95487i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 55.6566 3.87778
\(207\) 0 0
\(208\) 56.7666i 3.93605i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 79.5933i 5.46649i
\(213\) 0 0
\(214\) −10.2672 −0.701854
\(215\) 0 0
\(216\) 57.1121 3.88598
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −38.2270 −2.57726
\(221\) 0 0
\(222\) 28.7479i 1.92943i
\(223\) − 14.9356i − 1.00016i −0.865978 0.500082i \(-0.833303\pi\)
0.865978 0.500082i \(-0.166697\pi\)
\(224\) 0 0
\(225\) 8.70239 0.580159
\(226\) −5.40302 −0.359404
\(227\) 18.7250i 1.24282i 0.783484 + 0.621412i \(0.213441\pi\)
−0.783484 + 0.621412i \(0.786559\pi\)
\(228\) 0 0
\(229\) −29.5619 −1.95351 −0.976754 0.214362i \(-0.931233\pi\)
−0.976754 + 0.214362i \(0.931233\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 15.0479 0.983711
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) − 46.1208i − 2.97709i
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 6.76384i 0.434796i
\(243\) − 15.1196i − 0.969920i
\(244\) −6.52995 −0.418037
\(245\) 15.6525 1.00000
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) − 31.2952i − 1.97928i
\(251\) 17.8885 1.12911 0.564557 0.825394i \(-0.309047\pi\)
0.564557 + 0.825394i \(0.309047\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 60.6553 3.80585
\(255\) 0 0
\(256\) 107.286 6.70540
\(257\) 20.3741i 1.27090i 0.772142 + 0.635450i \(0.219185\pi\)
−0.772142 + 0.635450i \(0.780815\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) − 40.3013i − 2.49938i
\(261\) 0 0
\(262\) − 33.5896i − 2.07517i
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 35.2972 2.17239
\(265\) − 30.5008i − 1.87365i
\(266\) 0 0
\(267\) 0 0
\(268\) − 79.9764i − 4.88534i
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) −33.2991 −2.02652
\(271\) −24.1298 −1.46578 −0.732892 0.680345i \(-0.761830\pi\)
−0.732892 + 0.680345i \(0.761830\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 14.6489 0.883361
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 61.2777i 3.67519i
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 25.3304 1.49781
\(287\) 0 0
\(288\) − 52.1685i − 3.07406i
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) −17.8274 −1.04506
\(292\) 0 0
\(293\) − 0.172964i − 0.0101047i −0.999987 0.00505234i \(-0.998392\pi\)
0.999987 0.00505234i \(-0.00160822\pi\)
\(294\) −21.9899 −1.28248
\(295\) 0 0
\(296\) 98.2387 5.71001
\(297\) − 15.5869i − 0.904443i
\(298\) 23.4060i 1.35587i
\(299\) 0 0
\(300\) 32.7434i 1.89044i
\(301\) 0 0
\(302\) 0 0
\(303\) − 22.5366i − 1.29469i
\(304\) 0 0
\(305\) 2.50233 0.143283
\(306\) 0 0
\(307\) − 1.35100i − 0.0771055i −0.999257 0.0385528i \(-0.987725\pi\)
0.999257 0.0385528i \(-0.0122748\pi\)
\(308\) 0 0
\(309\) 22.3150 1.26945
\(310\) 0 0
\(311\) −31.3726 −1.77898 −0.889490 0.456955i \(-0.848940\pi\)
−0.889490 + 0.456955i \(0.848940\pi\)
\(312\) 37.2125i 2.10675i
\(313\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 31.6593i 1.77816i 0.457748 + 0.889082i \(0.348656\pi\)
−0.457748 + 0.889082i \(0.651344\pi\)
\(318\) 42.8501i 2.40292i
\(319\) 0 0
\(320\) −105.415 −5.89290
\(321\) −4.11655 −0.229763
\(322\) 0 0
\(323\) 0 0
\(324\) 4.37226 0.242903
\(325\) 15.4438i 0.856667i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) −20.5800 −1.13289
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 0 0
\(333\) − 15.9275i − 0.872823i
\(334\) −48.0896 −2.63134
\(335\) 30.6476i 1.67446i
\(336\) 0 0
\(337\) 36.6783i 1.99800i 0.0447653 + 0.998998i \(0.485746\pi\)
−0.0447653 + 0.998998i \(0.514254\pi\)
\(338\) − 9.68383i − 0.526731i
\(339\) −2.16629 −0.117657
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −36.7435 −1.97534
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −13.4164 −0.718164 −0.359082 0.933306i \(-0.616910\pi\)
−0.359082 + 0.933306i \(0.616910\pi\)
\(350\) 0 0
\(351\) 16.4327 0.877112
\(352\) − 87.8161i − 4.68061i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −25.5131 −1.34653 −0.673265 0.739401i \(-0.735109\pi\)
−0.673265 + 0.739401i \(0.735109\pi\)
\(360\) 41.7789i 2.20194i
\(361\) 0 0
\(362\) 0 0
\(363\) 2.71190i 0.142338i
\(364\) 0 0
\(365\) 0 0
\(366\) −3.51548 −0.183757
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −57.2780 −2.97774
\(371\) 0 0
\(372\) 0 0
\(373\) − 22.6186i − 1.17115i −0.810619 0.585575i \(-0.800869\pi\)
0.810619 0.585575i \(-0.199131\pi\)
\(374\) 0 0
\(375\) − 12.5475i − 0.647951i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 24.3191 1.24591
\(382\) 25.0362i 1.28096i
\(383\) − 29.9215i − 1.52892i −0.644671 0.764460i \(-0.723006\pi\)
0.644671 0.764460i \(-0.276994\pi\)
\(384\) 80.8187 4.12426
\(385\) 0 0
\(386\) 6.76699 0.344431
\(387\) 0 0
\(388\) 92.6907i 4.70566i
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) − 21.6967i − 1.09866i
\(391\) 0 0
\(392\) 75.1451i 3.79540i
\(393\) − 13.4674i − 0.679341i
\(394\) 0 0
\(395\) 0 0
\(396\) −29.7546 −1.49522
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) − 75.1085i − 3.76485i
\(399\) 0 0
\(400\) 91.8923 4.59461
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) − 43.0564i − 2.14746i
\(403\) 0 0
\(404\) −117.175 −5.82968
\(405\) −1.67548 −0.0832555
\(406\) 0 0
\(407\) − 26.8111i − 1.32898i
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) − 116.023i − 5.71604i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 92.5813 4.53917
\(417\) 24.5687i 1.20313i
\(418\) 0 0
\(419\) −36.0000 −1.75872 −0.879358 0.476162i \(-0.842028\pi\)
−0.879358 + 0.476162i \(0.842028\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 146.430 7.11125
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 21.4033i 1.03457i
\(429\) 10.1560 0.490334
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) − 97.7764i − 4.70427i
\(433\) 18.1458i 0.872030i 0.899939 + 0.436015i \(0.143611\pi\)
−0.899939 + 0.436015i \(0.856389\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 70.3270i 3.35271i
\(441\) 12.1833 0.580159
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 59.9284 2.84408
\(445\) 0 0
\(446\) −41.8067 −1.97961
\(447\) 9.38441i 0.443867i
\(448\) 0 0
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) − 24.3591i − 1.14830i
\(451\) 0 0
\(452\) 11.2633i 0.529779i
\(453\) 0 0
\(454\) 52.4138 2.45990
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 82.7477i 3.86655i
\(459\) 0 0
\(460\) 0 0
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) − 31.3691i − 1.45004i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) − 23.7408i − 1.08702i
\(478\) 67.1791i 3.07270i
\(479\) 43.0918 1.96891 0.984456 0.175630i \(-0.0561962\pi\)
0.984456 + 0.175630i \(0.0561962\pi\)
\(480\) −75.2190 −3.43326
\(481\) 28.2659 1.28882
\(482\) 0 0
\(483\) 0 0
\(484\) 14.1000 0.640911
\(485\) − 35.5198i − 1.61287i
\(486\) −42.3216 −1.91975
\(487\) − 32.2386i − 1.46087i −0.682983 0.730434i \(-0.739318\pi\)
0.682983 0.730434i \(-0.260682\pi\)
\(488\) 12.0133i 0.543816i
\(489\) 0 0
\(490\) − 43.8133i − 1.97928i
\(491\) −35.7771 −1.61460 −0.807299 0.590143i \(-0.799071\pi\)
−0.807299 + 0.590143i \(0.799071\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 11.4022 0.512490
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −4.31303 −0.193078 −0.0965389 0.995329i \(-0.530777\pi\)
−0.0965389 + 0.995329i \(0.530777\pi\)
\(500\) −65.2387 −2.91756
\(501\) −19.2811 −0.861414
\(502\) − 50.0724i − 2.23484i
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 44.9025 1.99813
\(506\) 0 0
\(507\) − 3.88264i − 0.172434i
\(508\) − 126.443i − 5.61001i
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) − 156.283i − 6.90681i
\(513\) 0 0
\(514\) 57.0297 2.51547
\(515\) 44.4609i 1.95918i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −14.7320 −0.646661
\(520\) −74.1432 −3.25140
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) − 39.9718i − 1.74784i −0.486066 0.873922i \(-0.661568\pi\)
0.486066 0.873922i \(-0.338432\pi\)
\(524\) −70.0215 −3.05890
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) − 60.4291i − 2.62984i
\(529\) 23.0000 1.00000
\(530\) −85.3757 −3.70848
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) − 8.20192i − 0.354600i
\(536\) −147.134 −6.35524
\(537\) 0 0
\(538\) 0 0
\(539\) 20.5084 0.883361
\(540\) 69.4161i 2.98719i
\(541\) −27.3238 −1.17474 −0.587371 0.809318i \(-0.699837\pi\)
−0.587371 + 0.809318i \(0.699837\pi\)
\(542\) 67.5426i 2.90120i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 46.7055i 1.99698i 0.0549052 + 0.998492i \(0.482514\pi\)
−0.0549052 + 0.998492i \(0.517486\pi\)
\(548\) 0 0
\(549\) 1.94773 0.0831269
\(550\) − 41.0041i − 1.74842i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −22.9651 −0.974813
\(556\) 127.741 5.41742
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 37.7272i 1.59001i 0.606601 + 0.795007i \(0.292533\pi\)
−0.606601 + 0.795007i \(0.707467\pi\)
\(564\) 0 0
\(565\) − 4.31617i − 0.181583i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) −39.4704 −1.65178 −0.825891 0.563829i \(-0.809328\pi\)
−0.825891 + 0.563829i \(0.809328\pi\)
\(572\) − 52.8042i − 2.20785i
\(573\) 10.0380i 0.419344i
\(574\) 0 0
\(575\) 0 0
\(576\) −82.0518 −3.41882
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) − 47.5852i − 1.97928i
\(579\) 2.71316 0.112755
\(580\) 0 0
\(581\) 0 0
\(582\) 49.9013i 2.06847i
\(583\) − 39.9632i − 1.65511i
\(584\) 0 0
\(585\) 12.0209i 0.497003i
\(586\) −0.484149 −0.0200000
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 45.8407i 1.89044i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) − 168.186i − 6.91239i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) −43.6297 −1.79015
\(595\) 0 0
\(596\) 48.7926 1.99862
\(597\) − 30.1140i − 1.23249i
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 60.2387 2.45924
\(601\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 0 0
\(603\) 23.8550i 0.971452i
\(604\) 0 0
\(605\) −5.40325 −0.219673
\(606\) −63.0828 −2.56256
\(607\) 47.2956i 1.91967i 0.280568 + 0.959834i \(0.409477\pi\)
−0.280568 + 0.959834i \(0.590523\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) − 7.00434i − 0.283597i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) −3.78162 −0.152614
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) − 62.4625i − 2.51261i
\(619\) 34.9941 1.40653 0.703265 0.710928i \(-0.251725\pi\)
0.703265 + 0.710928i \(0.251725\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 87.8161i 3.52111i
\(623\) 0 0
\(624\) 63.7082 2.55037
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 11.0275 0.438997 0.219499 0.975613i \(-0.429558\pi\)
0.219499 + 0.975613i \(0.429558\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 88.6185 3.51949
\(635\) 48.4541i 1.92284i
\(636\) 89.3263 3.54202
\(637\) 21.6213i 0.856667i
\(638\) 0 0
\(639\) 0 0
\(640\) 161.025i 6.36508i
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 11.5228i 0.454767i
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) − 8.04374i − 0.315988i
\(649\) 0 0
\(650\) 43.2291 1.69559
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 26.8328 1.04844
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 42.9015i 1.66994i
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −44.5832 −1.72756
\(667\) 0 0
\(668\) 100.249i 3.87873i
\(669\) −16.7620 −0.648057
\(670\) 85.7866 3.31423
\(671\) 3.27864 0.126571
\(672\) 0 0
\(673\) 11.9683i 0.461343i 0.973032 + 0.230671i \(0.0740922\pi\)
−0.973032 + 0.230671i \(0.925908\pi\)
\(674\) 102.667 3.95460
\(675\) − 26.6008i − 1.02387i
\(676\) −20.1871 −0.776428
\(677\) 27.1078i 1.04184i 0.853607 + 0.520918i \(0.174410\pi\)
−0.853607 + 0.520918i \(0.825590\pi\)
\(678\) 6.06373i 0.232876i
\(679\) 0 0
\(680\) 0 0
\(681\) 21.0148 0.805289
\(682\) 0 0
\(683\) 51.1946i 1.95891i 0.201667 + 0.979454i \(0.435364\pi\)
−0.201667 + 0.979454i \(0.564636\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 33.1769i 1.26578i
\(688\) 0 0
\(689\) 42.1318 1.60509
\(690\) 0 0
\(691\) 52.5727 1.99996 0.999980 0.00630823i \(-0.00200798\pi\)
0.999980 + 0.00630823i \(0.00200798\pi\)
\(692\) 76.5964i 2.91176i
\(693\) 0 0
\(694\) 0 0
\(695\) −48.9513 −1.85683
\(696\) 0 0
\(697\) 0 0
\(698\) 37.5543i 1.42145i
\(699\) 0 0
\(700\) 0 0
\(701\) 48.5239 1.83272 0.916360 0.400354i \(-0.131113\pi\)
0.916360 + 0.400354i \(0.131113\pi\)
\(702\) − 45.9972i − 1.73605i
\(703\) 0 0
\(704\) −138.119 −5.20556
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 40.2492 1.51159 0.755796 0.654808i \(-0.227250\pi\)
0.755796 + 0.654808i \(0.227250\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 20.2350i 0.756746i
\(716\) 0 0
\(717\) 26.9348i 1.00590i
\(718\) 71.4145i 2.66516i
\(719\) 13.7940 0.514429 0.257214 0.966354i \(-0.417195\pi\)
0.257214 + 0.966354i \(0.417195\pi\)
\(720\) 71.5258 2.66561
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 7.59095 0.281727
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −19.2163 −0.711716
\(730\) 0 0
\(731\) 0 0
\(732\) 7.32845i 0.270867i
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) − 17.5665i − 0.647951i
\(736\) 0 0
\(737\) 40.1556i 1.47915i
\(738\) 0 0
\(739\) −53.6656 −1.97412 −0.987061 0.160345i \(-0.948739\pi\)
−0.987061 + 0.160345i \(0.948739\pi\)
\(740\) 119.403i 4.38934i
\(741\) 0 0
\(742\) 0 0
\(743\) 37.3813i 1.37139i 0.727890 + 0.685693i \(0.240501\pi\)
−0.727890 + 0.685693i \(0.759499\pi\)
\(744\) 0 0
\(745\) −18.6977 −0.685032
\(746\) −63.3125 −2.31804
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) −35.1221 −1.28248
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) − 20.0760i − 0.731611i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 54.3834 1.97140 0.985699 0.168518i \(-0.0538981\pi\)
0.985699 + 0.168518i \(0.0538981\pi\)
\(762\) − 68.0724i − 2.46600i
\(763\) 0 0
\(764\) 52.1910 1.88820
\(765\) 0 0
\(766\) −83.7543 −3.02617
\(767\) 0 0
\(768\) − 120.406i − 4.34477i
\(769\) −47.1406 −1.69993 −0.849967 0.526836i \(-0.823378\pi\)
−0.849967 + 0.526836i \(0.823378\pi\)
\(770\) 0 0
\(771\) 22.8655 0.823481
\(772\) − 14.1066i − 0.507708i
\(773\) − 54.0523i − 1.94413i −0.234717 0.972064i \(-0.575416\pi\)
0.234717 0.972064i \(-0.424584\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 170.525 6.12150
\(777\) 0 0
\(778\) 16.7948i 0.602122i
\(779\) 0 0
\(780\) −45.2295 −1.61948
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 128.649 4.59461
\(785\) 0 0
\(786\) −37.6970 −1.34461
\(787\) − 53.4392i − 1.90490i −0.304692 0.952451i \(-0.598553\pi\)
0.304692 0.952451i \(-0.401447\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 54.7402i 1.94511i
\(793\) 3.45655i 0.122746i
\(794\) 0 0
\(795\) −34.2306 −1.21403
\(796\) −156.573 −5.54958
\(797\) 54.7345i 1.93879i 0.245499 + 0.969397i \(0.421048\pi\)
−0.245499 + 0.969397i \(0.578952\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) − 149.868i − 5.29864i
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) −89.7562 −3.16546
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 215.570i 7.58372i
\(809\) 22.3607 0.786160 0.393080 0.919504i \(-0.371410\pi\)
0.393080 + 0.919504i \(0.371410\pi\)
\(810\) 4.68990i 0.164786i
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 27.0805i 0.949756i
\(814\) −75.0477 −2.63042
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −42.0000 −1.46581 −0.732905 0.680331i \(-0.761836\pi\)
−0.732905 + 0.680331i \(0.761836\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(824\) −213.450 −7.43589
\(825\) − 16.4402i − 0.572375i
\(826\) 0 0
\(827\) 30.9935i 1.07775i 0.842386 + 0.538875i \(0.181151\pi\)
−0.842386 + 0.538875i \(0.818849\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) − 145.614i − 5.04825i
\(833\) 0 0
\(834\) 68.7710 2.38134
\(835\) − 38.4161i − 1.32944i
\(836\) 0 0
\(837\) 0 0
\(838\) 100.769i 3.48100i
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 7.73587 0.266122
\(846\) 0 0
\(847\) 0 0
\(848\) − 250.689i − 8.60870i
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 39.3761 1.34585
\(857\) 48.0008i 1.63967i 0.572597 + 0.819837i \(0.305936\pi\)
−0.572597 + 0.819837i \(0.694064\pi\)
\(858\) − 28.4278i − 0.970511i
\(859\) −4.00000 −0.136478 −0.0682391 0.997669i \(-0.521738\pi\)
−0.0682391 + 0.997669i \(0.521738\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) − 3.71278i − 0.126385i −0.998001 0.0631923i \(-0.979872\pi\)
0.998001 0.0631923i \(-0.0201281\pi\)
\(864\) −159.465 −5.42510
\(865\) − 29.3524i − 0.998010i
\(866\) 50.7924 1.72600
\(867\) − 19.0788i − 0.647951i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) −42.3346 −1.43445
\(872\) 0 0
\(873\) − 27.6474i − 0.935723i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 59.2236i 1.99984i 0.0127028 + 0.999919i \(0.495956\pi\)
−0.0127028 + 0.999919i \(0.504044\pi\)
\(878\) 0 0
\(879\) −0.194115 −0.00654733
\(880\) 120.401 4.05870
\(881\) −9.21678 −0.310521 −0.155261 0.987874i \(-0.549622\pi\)
−0.155261 + 0.987874i \(0.549622\pi\)
\(882\) − 34.1028i − 1.14830i
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 52.3146i 1.75655i 0.478154 + 0.878276i \(0.341306\pi\)
−0.478154 + 0.878276i \(0.658694\pi\)
\(888\) − 110.252i − 3.69981i
\(889\) 0 0
\(890\) 0 0
\(891\) −2.19528 −0.0735446
\(892\) 87.1513i 2.91804i
\(893\) 0 0
\(894\) 26.2682 0.878539
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −50.7796 −1.69265
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 20.7213 0.689180
\(905\) 0 0
\(906\) 0 0
\(907\) 28.7630i 0.955061i 0.878615 + 0.477531i \(0.158468\pi\)
−0.878615 + 0.477531i \(0.841532\pi\)
\(908\) − 109.263i − 3.62602i
\(909\) 34.9505 1.15924
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) − 2.80832i − 0.0928403i
\(916\) 172.498 5.69949
\(917\) 0 0
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) −1.51620 −0.0499606
\(922\) − 50.3843i − 1.65932i
\(923\) 0 0
\(924\) 0 0
\(925\) − 45.7562i − 1.50445i
\(926\) 0 0
\(927\) 34.6069i 1.13664i
\(928\) 0 0
\(929\) 31.3050 1.02708 0.513541 0.858065i \(-0.328333\pi\)
0.513541 + 0.858065i \(0.328333\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 35.2090i 1.15269i
\(934\) 0 0
\(935\) 0 0
\(936\) −57.7105 −1.88633
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 35.5307 1.15216
\(952\) 0 0
\(953\) − 61.4682i − 1.99115i −0.0939754 0.995575i \(-0.529957\pi\)
0.0939754 0.995575i \(-0.470043\pi\)
\(954\) −66.4535 −2.15151
\(955\) −20.0000 −0.647185
\(956\) 140.043 4.52932
\(957\) 0 0
\(958\) − 120.619i − 3.89704i
\(959\) 0 0
\(960\) 118.306i 3.81831i
\(961\) −31.0000 −1.00000
\(962\) − 79.1200i − 2.55093i
\(963\) − 6.38409i − 0.205724i
\(964\) 0 0
\(965\) 5.40577i 0.174018i
\(966\) 0 0
\(967\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(968\) − 25.9402i − 0.833749i
\(969\) 0 0
\(970\) −99.4246 −3.19233
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 88.2246i 2.82980i
\(973\) 0 0
\(974\) −90.2399 −2.89147
\(975\) 17.3323 0.555078
\(976\) 20.5669 0.658330
\(977\) − 16.6023i − 0.531154i −0.964090 0.265577i \(-0.914438\pi\)
0.964090 0.265577i \(-0.0855625\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −91.3342 −2.91756
\(981\) 0 0
\(982\) 100.145i 3.19575i
\(983\) 0.192493i 0.00613957i 0.999995 + 0.00306979i \(0.000977145\pi\)
−0.999995 + 0.00306979i \(0.999023\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) − 31.9162i − 1.01436i
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 60.0000 1.90213
\(996\) 0 0
\(997\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(998\) 12.0727i 0.382156i
\(999\) −48.6861 −1.54036
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 1805.2.b.h.1084.1 8
5.2 odd 4 9025.2.a.cb.1.8 8
5.3 odd 4 9025.2.a.cb.1.1 8
5.4 even 2 inner 1805.2.b.h.1084.8 yes 8
19.18 odd 2 inner 1805.2.b.h.1084.8 yes 8
95.18 even 4 9025.2.a.cb.1.8 8
95.37 even 4 9025.2.a.cb.1.1 8
95.94 odd 2 CM 1805.2.b.h.1084.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.b.h.1084.1 8 1.1 even 1 trivial
1805.2.b.h.1084.1 8 95.94 odd 2 CM
1805.2.b.h.1084.8 yes 8 5.4 even 2 inner
1805.2.b.h.1084.8 yes 8 19.18 odd 2 inner
9025.2.a.cb.1.1 8 5.3 odd 4
9025.2.a.cb.1.1 8 95.37 even 4
9025.2.a.cb.1.8 8 5.2 odd 4
9025.2.a.cb.1.8 8 95.18 even 4