Properties

Label 95.3.d.a.94.2
Level $95$
Weight $3$
Character 95.94
Analytic conductor $2.589$
Analytic rank $0$
Dimension $2$
CM discriminant -19
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,3,Mod(94,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.94");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 95.d (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: \(2.58856251142\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-19}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 5 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 94.2
Root \(0.500000 - 2.17945i\) of defining polynomial
Character \(\chi\) \(=\) 95.94
Dual form 95.3.d.a.94.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000 q^{4} +(-4.50000 + 2.17945i) q^{5} -13.0767i q^{7} -9.00000 q^{9} +O(q^{10})\) \(q-4.00000 q^{4} +(-4.50000 + 2.17945i) q^{5} -13.0767i q^{7} -9.00000 q^{9} -3.00000 q^{11} +16.0000 q^{16} +30.5123i q^{17} -19.0000 q^{19} +(18.0000 - 8.71780i) q^{20} -34.8712i q^{23} +(15.5000 - 19.6150i) q^{25} +52.3068i q^{28} +(28.5000 + 58.8451i) q^{35} +36.0000 q^{36} -13.0767i q^{43} +12.0000 q^{44} +(40.5000 - 19.6150i) q^{45} -56.6657i q^{47} -122.000 q^{49} +(13.5000 - 6.53835i) q^{55} -103.000 q^{61} +117.690i q^{63} -64.0000 q^{64} -122.049i q^{68} -143.844i q^{73} +76.0000 q^{76} +39.2301i q^{77} +(-72.0000 + 34.8712i) q^{80} +81.0000 q^{81} +139.485i q^{83} +(-66.5000 - 137.305i) q^{85} +139.485i q^{92} +(85.5000 - 41.4095i) q^{95} +27.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 8 q^{4} - 9 q^{5} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 8 q^{4} - 9 q^{5} - 18 q^{9} - 6 q^{11} + 32 q^{16} - 38 q^{19} + 36 q^{20} + 31 q^{25} + 57 q^{35} + 72 q^{36} + 24 q^{44} + 81 q^{45} - 244 q^{49} + 27 q^{55} - 206 q^{61} - 128 q^{64} + 152 q^{76} - 144 q^{80} + 162 q^{81} - 133 q^{85} + 171 q^{95} + 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) −4.00000 −1.00000
\(5\) −4.50000 + 2.17945i −0.900000 + 0.435890i
\(6\) 0 0
\(7\) 13.0767i 1.86810i −0.357143 0.934050i \(-0.616249\pi\)
0.357143 0.934050i \(-0.383751\pi\)
\(8\) 0 0
\(9\) −9.00000 −1.00000
\(10\) 0 0
\(11\) −3.00000 −0.272727 −0.136364 0.990659i \(-0.543542\pi\)
−0.136364 + 0.990659i \(0.543542\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 16.0000 1.00000
\(17\) 30.5123i 1.79484i 0.441176 + 0.897420i \(0.354561\pi\)
−0.441176 + 0.897420i \(0.645439\pi\)
\(18\) 0 0
\(19\) −19.0000 −1.00000
\(20\) 18.0000 8.71780i 0.900000 0.435890i
\(21\) 0 0
\(22\) 0 0
\(23\) 34.8712i 1.51614i −0.652174 0.758069i \(-0.726143\pi\)
0.652174 0.758069i \(-0.273857\pi\)
\(24\) 0 0
\(25\) 15.5000 19.6150i 0.620000 0.784602i
\(26\) 0 0
\(27\) 0 0
\(28\) 52.3068i 1.86810i
\(29\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 28.5000 + 58.8451i 0.814286 + 1.68129i
\(36\) 36.0000 1.00000
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 13.0767i 0.304109i −0.988372 0.152055i \(-0.951411\pi\)
0.988372 0.152055i \(-0.0485890\pi\)
\(44\) 12.0000 0.272727
\(45\) 40.5000 19.6150i 0.900000 0.435890i
\(46\) 0 0
\(47\) 56.6657i 1.20565i −0.797872 0.602826i \(-0.794041\pi\)
0.797872 0.602826i \(-0.205959\pi\)
\(48\) 0 0
\(49\) −122.000 −2.48980
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 13.5000 6.53835i 0.245455 0.118879i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −103.000 −1.68852 −0.844262 0.535930i \(-0.819961\pi\)
−0.844262 + 0.535930i \(0.819961\pi\)
\(62\) 0 0
\(63\) 117.690i 1.86810i
\(64\) −64.0000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 122.049i 1.79484i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) 143.844i 1.97046i −0.171233 0.985231i \(-0.554775\pi\)
0.171233 0.985231i \(-0.445225\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 76.0000 1.00000
\(77\) 39.2301i 0.509482i
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −72.0000 + 34.8712i −0.900000 + 0.435890i
\(81\) 81.0000 1.00000
\(82\) 0 0
\(83\) 139.485i 1.68054i 0.542169 + 0.840270i \(0.317603\pi\)
−0.542169 + 0.840270i \(0.682397\pi\)
\(84\) 0 0
\(85\) −66.5000 137.305i −0.782353 1.61536i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 139.485i 1.51614i
\(93\) 0 0
\(94\) 0 0
\(95\) 85.5000 41.4095i 0.900000 0.435890i
\(96\) 0 0
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 0 0
\(99\) 27.0000 0.272727
\(100\) −62.0000 + 78.4602i −0.620000 + 0.784602i
\(101\) 102.000 1.00990 0.504950 0.863148i \(-0.331511\pi\)
0.504950 + 0.863148i \(0.331511\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 209.227i 1.86810i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 0 0
\(115\) 76.0000 + 156.920i 0.660870 + 1.36452i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 399.000 3.35294
\(120\) 0 0
\(121\) −112.000 −0.925620
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −27.0000 + 122.049i −0.216000 + 0.976393i
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −213.000 −1.62595 −0.812977 0.582296i \(-0.802155\pi\)
−0.812977 + 0.582296i \(0.802155\pi\)
\(132\) 0 0
\(133\) 248.457i 1.86810i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 100.255i 0.731786i −0.930657 0.365893i \(-0.880764\pi\)
0.930657 0.365893i \(-0.119236\pi\)
\(138\) 0 0
\(139\) 197.000 1.41727 0.708633 0.705577i \(-0.249312\pi\)
0.708633 + 0.705577i \(0.249312\pi\)
\(140\) −114.000 235.381i −0.814286 1.68129i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −144.000 −1.00000
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 177.000 1.18792 0.593960 0.804495i \(-0.297564\pi\)
0.593960 + 0.804495i \(0.297564\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 274.611i 1.79484i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 313.841i 1.99899i 0.0318471 + 0.999493i \(0.489861\pi\)
−0.0318471 + 0.999493i \(0.510139\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −456.000 −2.83230
\(162\) 0 0
\(163\) 209.227i 1.28360i −0.766871 0.641801i \(-0.778187\pi\)
0.766871 0.641801i \(-0.221813\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(168\) 0 0
\(169\) −169.000 −1.00000
\(170\) 0 0
\(171\) 171.000 1.00000
\(172\) 52.3068i 0.304109i
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) −256.500 202.689i −1.46571 1.15822i
\(176\) −48.0000 −0.272727
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) −162.000 + 78.4602i −0.900000 + 0.435890i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 91.5369i 0.489502i
\(188\) 226.663i 1.20565i
\(189\) 0 0
\(190\) 0 0
\(191\) −93.0000 −0.486911 −0.243455 0.969912i \(-0.578281\pi\)
−0.243455 + 0.969912i \(0.578281\pi\)
\(192\) 0 0
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 488.000 2.48980
\(197\) 383.583i 1.94712i −0.228426 0.973561i \(-0.573358\pi\)
0.228426 0.973561i \(-0.426642\pi\)
\(198\) 0 0
\(199\) 227.000 1.14070 0.570352 0.821401i \(-0.306807\pi\)
0.570352 + 0.821401i \(0.306807\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 313.841i 1.51614i
\(208\) 0 0
\(209\) 57.0000 0.272727
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 28.5000 + 58.8451i 0.132558 + 0.273698i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −54.0000 + 26.1534i −0.245455 + 0.118879i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) −139.500 + 176.535i −0.620000 + 0.784602i
\(226\) 0 0
\(227\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) 0 0
\(229\) 17.0000 0.0742358 0.0371179 0.999311i \(-0.488182\pi\)
0.0371179 + 0.999311i \(0.488182\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 30.5123i 0.130954i 0.997854 + 0.0654770i \(0.0208569\pi\)
−0.997854 + 0.0654770i \(0.979143\pi\)
\(234\) 0 0
\(235\) 123.500 + 254.996i 0.525532 + 1.08509i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −453.000 −1.89540 −0.947699 0.319166i \(-0.896597\pi\)
−0.947699 + 0.319166i \(0.896597\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 412.000 1.68852
\(245\) 549.000 265.893i 2.24082 1.08528i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 27.0000 0.107570 0.0537849 0.998553i \(-0.482871\pi\)
0.0537849 + 0.998553i \(0.482871\pi\)
\(252\) 470.761i 1.86810i
\(253\) 104.614i 0.413492i
\(254\) 0 0
\(255\) 0 0
\(256\) 256.000 1.00000
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 335.635i 1.27618i 0.769962 + 0.638090i \(0.220275\pi\)
−0.769962 + 0.638090i \(0.779725\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 142.000 0.523985 0.261993 0.965070i \(-0.415620\pi\)
0.261993 + 0.965070i \(0.415620\pi\)
\(272\) 488.197i 1.79484i
\(273\) 0 0
\(274\) 0 0
\(275\) −46.5000 + 58.8451i −0.169091 + 0.213982i
\(276\) 0 0
\(277\) 143.844i 0.519291i −0.965704 0.259646i \(-0.916394\pi\)
0.965704 0.259646i \(-0.0836057\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) 405.378i 1.43243i −0.697880 0.716215i \(-0.745873\pi\)
0.697880 0.716215i \(-0.254127\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −642.000 −2.22145
\(290\) 0 0
\(291\) 0 0
\(292\) 575.375i 1.97046i
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −171.000 −0.568106
\(302\) 0 0
\(303\) 0 0
\(304\) −304.000 −1.00000
\(305\) 463.500 224.483i 1.51967 0.736011i
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 156.920i 0.509482i
\(309\) 0 0
\(310\) 0 0
\(311\) −603.000 −1.93891 −0.969453 0.245276i \(-0.921122\pi\)
−0.969453 + 0.245276i \(0.921122\pi\)
\(312\) 0 0
\(313\) 209.227i 0.668457i −0.942492 0.334229i \(-0.891524\pi\)
0.942492 0.334229i \(-0.108476\pi\)
\(314\) 0 0
\(315\) −256.500 529.606i −0.814286 1.68129i
\(316\) 0 0
\(317\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 288.000 139.485i 0.900000 0.435890i
\(321\) 0 0
\(322\) 0 0
\(323\) 579.734i 1.79484i
\(324\) −324.000 −1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −741.000 −2.25228
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 557.939i 1.68054i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 266.000 + 549.221i 0.782353 + 1.61536i
\(341\) 0 0
\(342\) 0 0
\(343\) 954.599i 2.78309i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 161.279i 0.464782i 0.972622 + 0.232391i \(0.0746548\pi\)
−0.972622 + 0.232391i \(0.925345\pi\)
\(348\) 0 0
\(349\) 527.000 1.51003 0.755014 0.655708i \(-0.227630\pi\)
0.755014 + 0.655708i \(0.227630\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 488.197i 1.38299i 0.722380 + 0.691497i \(0.243048\pi\)
−0.722380 + 0.691497i \(0.756952\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −243.000 −0.676880 −0.338440 0.940988i \(-0.609899\pi\)
−0.338440 + 0.940988i \(0.609899\pi\)
\(360\) 0 0
\(361\) 361.000 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 313.500 + 647.296i 0.858904 + 1.77342i
\(366\) 0 0
\(367\) 732.295i 1.99535i −0.0681199 0.997677i \(-0.521700\pi\)
0.0681199 0.997677i \(-0.478300\pi\)
\(368\) 557.939i 1.51614i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) −342.000 + 165.638i −0.900000 + 0.435890i
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) −85.5000 176.535i −0.222078 0.458534i
\(386\) 0 0
\(387\) 117.690i 0.304109i
\(388\) 0 0
\(389\) −153.000 −0.393316 −0.196658 0.980472i \(-0.563009\pi\)
−0.196658 + 0.980472i \(0.563009\pi\)
\(390\) 0 0
\(391\) 1064.00 2.72123
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) −108.000 −0.272727
\(397\) 274.611i 0.691714i −0.938287 0.345857i \(-0.887588\pi\)
0.938287 0.345857i \(-0.112412\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 248.000 313.841i 0.620000 0.784602i
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −408.000 −1.00990
\(405\) −364.500 + 176.535i −0.900000 + 0.435890i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −304.000 627.681i −0.732530 1.51249i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 762.000 1.81862 0.909308 0.416124i \(-0.136612\pi\)
0.909308 + 0.416124i \(0.136612\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 509.991i 1.20565i
\(424\) 0 0
\(425\) 598.500 + 472.941i 1.40824 + 1.11280i
\(426\) 0 0
\(427\) 1346.90i 3.15433i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 662.553i 1.51614i
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 1098.00 2.48980
\(442\) 0 0
\(443\) 884.856i 1.99742i −0.0507901 0.998709i \(-0.516174\pi\)
0.0507901 0.998709i \(-0.483826\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 836.909i 1.86810i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 666.912i 1.45933i −0.683807 0.729663i \(-0.739677\pi\)
0.683807 0.729663i \(-0.260323\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −304.000 627.681i −0.660870 1.36452i
\(461\) 447.000 0.969631 0.484816 0.874616i \(-0.338887\pi\)
0.484816 + 0.874616i \(0.338887\pi\)
\(462\) 0 0
\(463\) 536.145i 1.15798i −0.815335 0.578990i \(-0.803447\pi\)
0.815335 0.578990i \(-0.196553\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 187.433i 0.401355i −0.979657 0.200677i \(-0.935686\pi\)
0.979657 0.200677i \(-0.0643143\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 39.2301i 0.0829389i
\(474\) 0 0
\(475\) −294.500 + 372.686i −0.620000 + 0.784602i
\(476\) −1596.00 −3.35294
\(477\) 0 0
\(478\) 0 0
\(479\) 942.000 1.96660 0.983299 0.182000i \(-0.0582571\pi\)
0.983299 + 0.182000i \(0.0582571\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 448.000 0.925620
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −918.000 −1.86965 −0.934827 0.355104i \(-0.884446\pi\)
−0.934827 + 0.355104i \(0.884446\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −121.500 + 58.8451i −0.245455 + 0.118879i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −523.000 −1.04810 −0.524048 0.851689i \(-0.675579\pi\)
−0.524048 + 0.851689i \(0.675579\pi\)
\(500\) 108.000 488.197i 0.216000 0.976393i
\(501\) 0 0
\(502\) 0 0
\(503\) 383.583i 0.762591i −0.924453 0.381295i \(-0.875478\pi\)
0.924453 0.381295i \(-0.124522\pi\)
\(504\) 0 0
\(505\) −459.000 + 222.304i −0.908911 + 0.440206i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) −1881.00 −3.68102
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 169.997i 0.328814i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 852.000 1.62595
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −687.000 −1.29868
\(530\) 0 0
\(531\) 0 0
\(532\) 993.829i 1.86810i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 366.000 0.679035
\(540\) 0 0
\(541\) 457.000 0.844732 0.422366 0.906425i \(-0.361200\pi\)
0.422366 + 0.906425i \(0.361200\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 401.019i 0.731786i
\(549\) 927.000 1.68852
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −788.000 −1.41727
\(557\) 204.868i 0.367807i 0.982944 + 0.183903i \(0.0588733\pi\)
−0.982944 + 0.183903i \(0.941127\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 456.000 + 941.522i 0.814286 + 1.68129i
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1059.21i 1.86810i
\(568\) 0 0
\(569\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) −458.000 −0.802102 −0.401051 0.916056i \(-0.631355\pi\)
−0.401051 + 0.916056i \(0.631355\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −684.000 540.503i −1.18957 0.940006i
\(576\) 576.000 1.00000
\(577\) 143.844i 0.249296i −0.992201 0.124648i \(-0.960220\pi\)
0.992201 0.124648i \(-0.0397801\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1824.00 3.13941
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 335.635i 0.571781i 0.958262 + 0.285890i \(0.0922893\pi\)
−0.958262 + 0.285890i \(0.907711\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1185.62i 1.99936i 0.0252951 + 0.999680i \(0.491947\pi\)
−0.0252951 + 0.999680i \(0.508053\pi\)
\(594\) 0 0
\(595\) −1795.50 + 869.600i −3.01765 + 1.46151i
\(596\) −708.000 −1.18792
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 504.000 244.098i 0.833058 0.403468i
\(606\) 0 0
\(607\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 1098.44i 1.79484i
\(613\) 1189.98i 1.94124i −0.240620 0.970619i \(-0.577351\pi\)
0.240620 0.970619i \(-0.422649\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 623.323i 1.01025i −0.863047 0.505124i \(-0.831447\pi\)
0.863047 0.505124i \(-0.168553\pi\)
\(618\) 0 0
\(619\) 662.000 1.06947 0.534733 0.845021i \(-0.320412\pi\)
0.534733 + 0.845021i \(0.320412\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −144.500 608.066i −0.231200 0.972906i
\(626\) 0 0
\(627\) 0 0
\(628\) 1255.36i 1.99899i
\(629\) 0 0
\(630\) 0 0
\(631\) 1037.00 1.64342 0.821712 0.569904i \(-0.193019\pi\)
0.821712 + 0.569904i \(0.193019\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(642\) 0 0
\(643\) 640.758i 0.996513i 0.867030 + 0.498257i \(0.166026\pi\)
−0.867030 + 0.498257i \(0.833974\pi\)
\(644\) 1824.00 2.83230
\(645\) 0 0
\(646\) 0 0
\(647\) 815.114i 1.25984i 0.776662 + 0.629918i \(0.216912\pi\)
−0.776662 + 0.629918i \(0.783088\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 836.909i 1.28360i
\(653\) 1251.00i 1.91578i 0.287136 + 0.957890i \(0.407297\pi\)
−0.287136 + 0.957890i \(0.592703\pi\)
\(654\) 0 0
\(655\) 958.500 464.223i 1.46336 0.708737i
\(656\) 0 0
\(657\) 1294.59i 1.97046i
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −541.500 1118.06i −0.814286 1.68129i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 309.000 0.460507
\(672\) 0 0
\(673\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 676.000 1.00000
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) −684.000 −1.00000
\(685\) 218.500 + 451.146i 0.318978 + 0.658607i
\(686\) 0 0
\(687\) 0 0
\(688\) 209.227i 0.304109i
\(689\) 0 0
\(690\) 0 0
\(691\) 157.000 0.227207 0.113603 0.993526i \(-0.463761\pi\)
0.113603 + 0.993526i \(0.463761\pi\)
\(692\) 0 0
\(693\) 353.071i 0.509482i
\(694\) 0 0
\(695\) −886.500 + 429.352i −1.27554 + 0.617772i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 1026.00 + 810.755i 1.46571 + 1.15822i
\(701\) −1098.00 −1.56633 −0.783167 0.621812i \(-0.786397\pi\)
−0.783167 + 0.621812i \(0.786397\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 192.000 0.272727
\(705\) 0 0
\(706\) 0 0
\(707\) 1333.82i 1.88660i
\(708\) 0 0
\(709\) −1318.00 −1.85896 −0.929478 0.368877i \(-0.879742\pi\)
−0.929478 + 0.368877i \(0.879742\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −963.000 −1.33936 −0.669680 0.742650i \(-0.733569\pi\)
−0.669680 + 0.742650i \(0.733569\pi\)
\(720\) 648.000 313.841i 0.900000 0.435890i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1451.51i 1.99658i −0.0584594 0.998290i \(-0.518619\pi\)
0.0584594 0.998290i \(-0.481381\pi\)
\(728\) 0 0
\(729\) −729.000 −1.00000
\(730\) 0 0
\(731\) 399.000 0.545828
\(732\) 0 0
\(733\) 732.295i 0.999038i −0.866303 0.499519i \(-0.833510\pi\)
0.866303 0.499519i \(-0.166490\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 547.000 0.740189 0.370095 0.928994i \(-0.379325\pi\)
0.370095 + 0.928994i \(0.379325\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) −796.500 + 385.763i −1.06913 + 0.517802i
\(746\) 0 0
\(747\) 1255.36i 1.68054i
\(748\) 366.148i 0.489502i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 906.651i 1.20565i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1294.59i 1.71016i 0.518494 + 0.855081i \(0.326493\pi\)
−0.518494 + 0.855081i \(0.673507\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1503.00 −1.97503 −0.987516 0.157516i \(-0.949651\pi\)
−0.987516 + 0.157516i \(0.949651\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 372.000 0.486911
\(765\) 598.500 + 1235.75i 0.782353 + 1.61536i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −1063.00 −1.38231 −0.691157 0.722704i \(-0.742899\pi\)
−0.691157 + 0.722704i \(0.742899\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −1952.00 −2.48980
\(785\) −684.000 1412.28i −0.871338 1.79909i
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 1534.33i 1.94712i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −908.000 −1.14070
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 1729.00 2.16395
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 431.531i 0.537398i
\(804\) 0 0
\(805\) 2052.00 993.829i 2.54907 1.23457i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1593.00 −1.96910 −0.984549 0.175110i \(-0.943972\pi\)
−0.984549 + 0.175110i \(0.943972\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 456.000 + 941.522i 0.559509 + 1.15524i
\(816\) 0 0
\(817\) 248.457i 0.304109i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 1167.00 1.42144 0.710719 0.703476i \(-0.248370\pi\)
0.710719 + 0.703476i \(0.248370\pi\)
\(822\) 0 0
\(823\) 509.991i 0.619673i 0.950790 + 0.309837i \(0.100274\pi\)
−0.950790 + 0.309837i \(0.899726\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 1255.36i 1.51614i
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3722.50i 4.46879i
\(834\) 0 0
\(835\) 0 0
\(836\) −228.000 −0.272727
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) 841.000 1.00000
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 760.500 368.327i 0.900000 0.435890i
\(846\) 0 0
\(847\) 1464.59i 1.72915i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 1359.98i 1.59435i 0.603751 + 0.797173i \(0.293672\pi\)
−0.603751 + 0.797173i \(0.706328\pi\)
\(854\) 0 0
\(855\) −769.500 + 372.686i −0.900000 + 0.435890i
\(856\) 0 0
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) −1493.00 −1.73807 −0.869034 0.494753i \(-0.835259\pi\)
−0.869034 + 0.494753i \(0.835259\pi\)
\(860\) −114.000 235.381i −0.132558 0.273698i
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1596.00 + 353.071i 1.82400 + 0.403510i
\(876\) 0 0
\(877\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 216.000 104.614i 0.245455 0.118879i
\(881\) 537.000 0.609535 0.304767 0.952427i \(-0.401421\pi\)
0.304767 + 0.952427i \(0.401421\pi\)
\(882\) 0 0
\(883\) 1556.13i 1.76232i 0.472820 + 0.881159i \(0.343236\pi\)
−0.472820 + 0.881159i \(0.656764\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −243.000 −0.272727
\(892\) 0 0
\(893\) 1076.65i 1.20565i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 558.000 706.142i 0.620000 0.784602i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 0 0
\(909\) −918.000 −1.00990
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 418.454i 0.458329i
\(914\) 0 0
\(915\) 0 0
\(916\) −68.0000 −0.0742358
\(917\) 2785.34i 3.03744i
\(918\) 0 0
\(919\) 1762.00 1.91730 0.958651 0.284585i \(-0.0918559\pi\)
0.958651 + 0.284585i \(0.0918559\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 642.000 0.691066 0.345533 0.938407i \(-0.387698\pi\)
0.345533 + 0.938407i \(0.387698\pi\)
\(930\) 0 0
\(931\) 2318.00 2.48980
\(932\) 122.049i 0.130954i
\(933\) 0 0
\(934\) 0 0
\(935\) 199.500 + 411.916i 0.213369 + 0.440552i
\(936\) 0 0
\(937\) 1843.81i 1.96778i −0.178762 0.983892i \(-0.557209\pi\)
0.178762 0.983892i \(-0.442791\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −494.000 1019.98i −0.525532 1.08509i
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 488.197i 0.515519i 0.966209 + 0.257760i \(0.0829843\pi\)
−0.966209 + 0.257760i \(0.917016\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) 418.500 202.689i 0.438220 0.212240i
\(956\) 1812.00 1.89540
\(957\) 0 0
\(958\) 0 0
\(959\) −1311.00 −1.36705
\(960\) 0 0
\(961\) 961.000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 732.295i 0.757285i −0.925543 0.378643i \(-0.876391\pi\)
0.925543 0.378643i \(-0.123609\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 2576.11i 2.64759i
\(974\) 0 0
\(975\) 0 0
\(976\) −1648.00 −1.68852
\(977\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −2196.00 + 1063.57i −2.24082 + 1.08528i
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 836.000 + 1726.12i 0.848731 + 1.75241i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −456.000 −0.461072
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1021.50 + 494.735i −1.02663 + 0.497221i
\(996\) 0 0
\(997\) 274.611i 0.275437i −0.990471 0.137718i \(-0.956023\pi\)
0.990471 0.137718i \(-0.0439769\pi\)
\(998\) 0 0
\(999\) 0 0
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 95.3.d.a.94.2 yes 2
3.2 odd 2 855.3.g.a.379.1 2
5.2 odd 4 475.3.c.c.151.2 2
5.3 odd 4 475.3.c.c.151.1 2
5.4 even 2 inner 95.3.d.a.94.1 2
15.14 odd 2 855.3.g.a.379.2 2
19.18 odd 2 CM 95.3.d.a.94.2 yes 2
57.56 even 2 855.3.g.a.379.1 2
95.18 even 4 475.3.c.c.151.1 2
95.37 even 4 475.3.c.c.151.2 2
95.94 odd 2 inner 95.3.d.a.94.1 2
285.284 even 2 855.3.g.a.379.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.3.d.a.94.1 2 5.4 even 2 inner
95.3.d.a.94.1 2 95.94 odd 2 inner
95.3.d.a.94.2 yes 2 1.1 even 1 trivial
95.3.d.a.94.2 yes 2 19.18 odd 2 CM
475.3.c.c.151.1 2 5.3 odd 4
475.3.c.c.151.1 2 95.18 even 4
475.3.c.c.151.2 2 5.2 odd 4
475.3.c.c.151.2 2 95.37 even 4
855.3.g.a.379.1 2 3.2 odd 2
855.3.g.a.379.1 2 57.56 even 2
855.3.g.a.379.2 2 15.14 odd 2
855.3.g.a.379.2 2 285.284 even 2