Properties

Label 95.2.g.a.18.1
Level $95$
Weight $2$
Character 95.18
Analytic conductor $0.759$
Analytic rank $0$
Dimension $4$
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] = [95,2,Mod(18,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.18");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.g (of order \(4\), degree \(2\), 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: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{19})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 9x^{2} + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{4}]$

Embedding invariants

Embedding label 18.1
Root \(2.17945 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 95.18
Dual form 95.2.g.a.37.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000i q^{4} +(0.500000 - 2.17945i) q^{5} +(-0.679449 + 0.679449i) q^{7} +3.00000i q^{9} +O(q^{10})\) \(q-2.00000i q^{4} +(0.500000 - 2.17945i) q^{5} +(-0.679449 + 0.679449i) q^{7} +3.00000i q^{9} +4.35890 q^{11} -4.00000 q^{16} +(-5.67945 + 5.67945i) q^{17} -4.35890i q^{19} +(-4.35890 - 1.00000i) q^{20} +(6.35890 + 6.35890i) q^{23} +(-4.50000 - 2.17945i) q^{25} +(1.35890 + 1.35890i) q^{28} +(1.14110 + 1.82055i) q^{35} +6.00000 q^{36} +(-7.03835 - 7.03835i) q^{43} -8.71780i q^{44} +(6.53835 + 1.50000i) q^{45} +(4.32055 - 4.32055i) q^{47} +6.07670i q^{49} +(2.17945 - 9.50000i) q^{55} +4.35890 q^{61} +(-2.03835 - 2.03835i) q^{63} +8.00000i q^{64} +(11.3589 + 11.3589i) q^{68} +(-12.0383 - 12.0383i) q^{73} -8.71780 q^{76} +(-2.96165 + 2.96165i) q^{77} +(-2.00000 + 8.71780i) q^{80} -9.00000 q^{81} +(-3.64110 - 3.64110i) q^{83} +(9.53835 + 15.2178i) q^{85} +(12.7178 - 12.7178i) q^{92} +(-9.50000 - 2.17945i) q^{95} +13.0767i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{5} + 6 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{5} + 6 q^{7} - 16 q^{16} - 14 q^{17} + 8 q^{23} - 18 q^{25} - 12 q^{28} + 22 q^{35} + 24 q^{36} - 2 q^{43} + 26 q^{47} + 18 q^{63} + 28 q^{68} - 22 q^{73} - 38 q^{77} - 8 q^{80} - 36 q^{81} - 32 q^{83} + 12 q^{85} + 16 q^{92} - 38 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(21\) \(77\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(3\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(4\) 2.00000i 1.00000i
\(5\) 0.500000 2.17945i 0.223607 0.974679i
\(6\) 0 0
\(7\) −0.679449 + 0.679449i −0.256808 + 0.256808i −0.823754 0.566947i \(-0.808125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 0 0
\(9\) 3.00000i 1.00000i
\(10\) 0 0
\(11\) 4.35890 1.31426 0.657129 0.753778i \(-0.271771\pi\)
0.657129 + 0.753778i \(0.271771\pi\)
\(12\) 0 0
\(13\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) −5.67945 + 5.67945i −1.37747 + 1.37747i −0.528594 + 0.848875i \(0.677281\pi\)
−0.848875 + 0.528594i \(0.822719\pi\)
\(18\) 0 0
\(19\) 4.35890i 1.00000i
\(20\) −4.35890 1.00000i −0.974679 0.223607i
\(21\) 0 0
\(22\) 0 0
\(23\) 6.35890 + 6.35890i 1.32592 + 1.32592i 0.908893 + 0.417029i \(0.136929\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 0 0
\(25\) −4.50000 2.17945i −0.900000 0.435890i
\(26\) 0 0
\(27\) 0 0
\(28\) 1.35890 + 1.35890i 0.256808 + 0.256808i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.14110 + 1.82055i 0.192881 + 0.307729i
\(36\) 6.00000 1.00000
\(37\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −7.03835 7.03835i −1.07334 1.07334i −0.997089 0.0762493i \(-0.975706\pi\)
−0.0762493 0.997089i \(-0.524294\pi\)
\(44\) 8.71780i 1.31426i
\(45\) 6.53835 + 1.50000i 0.974679 + 0.223607i
\(46\) 0 0
\(47\) 4.32055 4.32055i 0.630217 0.630217i −0.317905 0.948122i \(-0.602979\pi\)
0.948122 + 0.317905i \(0.102979\pi\)
\(48\) 0 0
\(49\) 6.07670i 0.868100i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(54\) 0 0
\(55\) 2.17945 9.50000i 0.293877 1.28098i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 4.35890 0.558100 0.279050 0.960277i \(-0.409981\pi\)
0.279050 + 0.960277i \(0.409981\pi\)
\(62\) 0 0
\(63\) −2.03835 2.03835i −0.256808 0.256808i
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(68\) 11.3589 + 11.3589i 1.37747 + 1.37747i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −12.0383 12.0383i −1.40898 1.40898i −0.765256 0.643726i \(-0.777388\pi\)
−0.643726 0.765256i \(-0.722612\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −8.71780 −1.00000
\(77\) −2.96165 + 2.96165i −0.337512 + 0.337512i
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −2.00000 + 8.71780i −0.223607 + 0.974679i
\(81\) −9.00000 −1.00000
\(82\) 0 0
\(83\) −3.64110 3.64110i −0.399663 0.399663i 0.478451 0.878114i \(-0.341198\pi\)
−0.878114 + 0.478451i \(0.841198\pi\)
\(84\) 0 0
\(85\) 9.53835 + 15.2178i 1.03458 + 1.65060i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 12.7178 12.7178i 1.32592 1.32592i
\(93\) 0 0
\(94\) 0 0
\(95\) −9.50000 2.17945i −0.974679 0.223607i
\(96\) 0 0
\(97\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(98\) 0 0
\(99\) 13.0767i 1.31426i
\(100\) −4.35890 + 9.00000i −0.435890 + 0.900000i
\(101\) −17.4356 −1.73491 −0.867453 0.497519i \(-0.834245\pi\)
−0.867453 + 0.497519i \(0.834245\pi\)
\(102\) 0 0
\(103\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 2.71780 2.71780i 0.256808 0.256808i
\(113\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(114\) 0 0
\(115\) 17.0383 10.6794i 1.58883 0.995864i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 7.71780i 0.707489i
\(120\) 0 0
\(121\) 8.00000 0.727273
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −7.00000 + 8.71780i −0.626099 + 0.779744i
\(126\) 0 0
\(127\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 7.00000 0.611593 0.305796 0.952097i \(-0.401077\pi\)
0.305796 + 0.952097i \(0.401077\pi\)
\(132\) 0 0
\(133\) 2.96165 + 2.96165i 0.256808 + 0.256808i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.32055 9.32055i 0.796308 0.796308i −0.186203 0.982511i \(-0.559618\pi\)
0.982511 + 0.186203i \(0.0596182\pi\)
\(138\) 0 0
\(139\) 9.00000i 0.763370i −0.924292 0.381685i \(-0.875344\pi\)
0.924292 0.381685i \(-0.124656\pi\)
\(140\) 3.64110 2.28220i 0.307729 0.192881i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 12.0000i 1.00000i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 11.0000i 0.901155i 0.892737 + 0.450578i \(0.148782\pi\)
−0.892737 + 0.450578i \(0.851218\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) −17.0383 17.0383i −1.37747 1.37747i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 17.7178 17.7178i 1.41403 1.41403i 0.695756 0.718278i \(-0.255069\pi\)
0.718278 0.695756i \(-0.244931\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −8.64110 −0.681014
\(162\) 0 0
\(163\) 16.3589 + 16.3589i 1.28133 + 1.28133i 0.939913 + 0.341415i \(0.110906\pi\)
0.341415 + 0.939913i \(0.389094\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(168\) 0 0
\(169\) 13.0000i 1.00000i
\(170\) 0 0
\(171\) 13.0767 1.00000
\(172\) −14.0767 + 14.0767i −1.07334 + 1.07334i
\(173\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(174\) 0 0
\(175\) 4.53835 1.57670i 0.343067 0.119187i
\(176\) −17.4356 −1.31426
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 3.00000 13.0767i 0.223607 0.974679i
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −24.7561 + 24.7561i −1.81035 + 1.81035i
\(188\) −8.64110 8.64110i −0.630217 0.630217i
\(189\) 0 0
\(190\) 0 0
\(191\) 17.0000 1.23008 0.615038 0.788497i \(-0.289140\pi\)
0.615038 + 0.788497i \(0.289140\pi\)
\(192\) 0 0
\(193\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 12.1534 0.868100
\(197\) −2.28220 + 2.28220i −0.162600 + 0.162600i −0.783718 0.621117i \(-0.786679\pi\)
0.621117 + 0.783718i \(0.286679\pi\)
\(198\) 0 0
\(199\) 13.0767i 0.926982i 0.886102 + 0.463491i \(0.153403\pi\)
−0.886102 + 0.463491i \(0.846597\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −19.0767 + 19.0767i −1.32592 + 1.32592i
\(208\) 0 0
\(209\) 19.0000i 1.31426i
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −18.8589 + 11.8206i −1.28617 + 0.806155i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −19.0000 4.35890i −1.28098 0.293877i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(224\) 0 0
\(225\) 6.53835 13.5000i 0.435890 0.900000i
\(226\) 0 0
\(227\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(228\) 0 0
\(229\) 21.0000i 1.38772i 0.720110 + 0.693860i \(0.244091\pi\)
−0.720110 + 0.693860i \(0.755909\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.7561 + 14.7561i 0.966707 + 0.966707i 0.999463 0.0327561i \(-0.0104285\pi\)
−0.0327561 + 0.999463i \(0.510428\pi\)
\(234\) 0 0
\(235\) −7.25615 11.5767i −0.473339 0.755180i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 30.5123i 1.97368i −0.161712 0.986838i \(-0.551701\pi\)
0.161712 0.986838i \(-0.448299\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 8.71780i 0.558100i
\(245\) 13.2439 + 3.03835i 0.846119 + 0.194113i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −23.0000 −1.45175 −0.725874 0.687828i \(-0.758564\pi\)
−0.725874 + 0.687828i \(0.758564\pi\)
\(252\) −4.07670 + 4.07670i −0.256808 + 0.256808i
\(253\) 27.7178 + 27.7178i 1.74260 + 1.74260i
\(254\) 0 0
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 9.75615 + 9.75615i 0.601590 + 0.601590i 0.940734 0.339145i \(-0.110138\pi\)
−0.339145 + 0.940734i \(0.610138\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 26.1534 1.58871 0.794353 0.607457i \(-0.207810\pi\)
0.794353 + 0.607457i \(0.207810\pi\)
\(272\) 22.7178 22.7178i 1.37747 1.37747i
\(273\) 0 0
\(274\) 0 0
\(275\) −19.6150 9.50000i −1.18283 0.572872i
\(276\) 0 0
\(277\) 14.3206 14.3206i 0.860438 0.860438i −0.130950 0.991389i \(-0.541803\pi\)
0.991389 + 0.130950i \(0.0418029\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −22.0383 22.0383i −1.31004 1.31004i −0.921379 0.388664i \(-0.872937\pi\)
−0.388664 0.921379i \(-0.627063\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 47.5123i 2.79484i
\(290\) 0 0
\(291\) 0 0
\(292\) −24.0767 + 24.0767i −1.40898 + 1.40898i
\(293\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 9.56440 0.551283
\(302\) 0 0
\(303\) 0 0
\(304\) 17.4356i 1.00000i
\(305\) 2.17945 9.50000i 0.124795 0.543968i
\(306\) 0 0
\(307\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(308\) 5.92330 + 5.92330i 0.337512 + 0.337512i
\(309\) 0 0
\(310\) 0 0
\(311\) 4.35890 0.247170 0.123585 0.992334i \(-0.460561\pi\)
0.123585 + 0.992334i \(0.460561\pi\)
\(312\) 0 0
\(313\) −20.4356 20.4356i −1.15509 1.15509i −0.985518 0.169570i \(-0.945762\pi\)
−0.169570 0.985518i \(-0.554238\pi\)
\(314\) 0 0
\(315\) −5.46165 + 3.42330i −0.307729 + 0.192881i
\(316\) 0 0
\(317\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 17.4356 + 4.00000i 0.974679 + 0.223607i
\(321\) 0 0
\(322\) 0 0
\(323\) 24.7561 + 24.7561i 1.37747 + 1.37747i
\(324\) 18.0000i 1.00000i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 5.87119i 0.323689i
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) −7.28220 + 7.28220i −0.399663 + 0.399663i
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 30.4356 19.0767i 1.65060 1.03458i
\(341\) 0 0
\(342\) 0 0
\(343\) −8.88495 8.88495i −0.479742 0.479742i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −20.6794 + 20.6794i −1.11013 + 1.11013i −0.116999 + 0.993132i \(0.537327\pi\)
−0.993132 + 0.116999i \(0.962673\pi\)
\(348\) 0 0
\(349\) 13.0767i 0.699980i 0.936754 + 0.349990i \(0.113815\pi\)
−0.936754 + 0.349990i \(0.886185\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −10.4356 10.4356i −0.555431 0.555431i 0.372572 0.928003i \(-0.378476\pi\)
−0.928003 + 0.372572i \(0.878476\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 31.0000i 1.63612i 0.575135 + 0.818059i \(0.304950\pi\)
−0.575135 + 0.818059i \(0.695050\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −32.2561 + 20.2178i −1.68836 + 1.05825i
\(366\) 0 0
\(367\) 0.923303 0.923303i 0.0481960 0.0481960i −0.682598 0.730794i \(-0.739150\pi\)
0.730794 + 0.682598i \(0.239150\pi\)
\(368\) −25.4356 25.4356i −1.32592 1.32592i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) −4.35890 + 19.0000i −0.223607 + 0.974679i
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(384\) 0 0
\(385\) 4.97394 + 7.93560i 0.253496 + 0.404435i
\(386\) 0 0
\(387\) 21.1150 21.1150i 1.07334 1.07334i
\(388\) 0 0
\(389\) 30.5123i 1.54703i −0.633775 0.773517i \(-0.718496\pi\)
0.633775 0.773517i \(-0.281504\pi\)
\(390\) 0 0
\(391\) −72.2301 −3.65283
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 26.1534 1.31426
\(397\) 16.1150 16.1150i 0.808791 0.808791i −0.175660 0.984451i \(-0.556206\pi\)
0.984451 + 0.175660i \(0.0562059\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 18.0000 + 8.71780i 0.900000 + 0.435890i
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 34.8712i 1.73491i
\(405\) −4.50000 + 19.6150i −0.223607 + 0.974679i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −9.75615 + 6.11505i −0.478910 + 0.300176i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 8.71780i 0.425892i −0.977064 0.212946i \(-0.931694\pi\)
0.977064 0.212946i \(-0.0683059\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 12.9617 + 12.9617i 0.630217 + 0.630217i
\(424\) 0 0
\(425\) 37.9356 13.1794i 1.84015 0.639297i
\(426\) 0 0
\(427\) −2.96165 + 2.96165i −0.143324 + 0.143324i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 27.7178 27.7178i 1.32592 1.32592i
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) −18.2301 −0.868100
\(442\) 0 0
\(443\) 29.7561 + 29.7561i 1.41376 + 1.41376i 0.724841 + 0.688916i \(0.241913\pi\)
0.688916 + 0.724841i \(0.258087\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −5.43560 5.43560i −0.256808 0.256808i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 11.1150 11.1150i 0.519940 0.519940i −0.397613 0.917553i \(-0.630161\pi\)
0.917553 + 0.397613i \(0.130161\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −21.3589 34.0767i −0.995864 1.58883i
\(461\) 37.0000 1.72326 0.861631 0.507535i \(-0.169443\pi\)
0.861631 + 0.507535i \(0.169443\pi\)
\(462\) 0 0
\(463\) −27.0383 27.0383i −1.25658 1.25658i −0.952716 0.303863i \(-0.901724\pi\)
−0.303863 0.952716i \(-0.598276\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 19.3206 19.3206i 0.894048 0.894048i −0.100853 0.994901i \(-0.532157\pi\)
0.994901 + 0.100853i \(0.0321571\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −30.6794 30.6794i −1.41064 1.41064i
\(474\) 0 0
\(475\) −9.50000 + 19.6150i −0.435890 + 0.900000i
\(476\) −15.4356 −0.707489
\(477\) 0 0
\(478\) 0 0
\(479\) 4.00000i 0.182765i −0.995816 0.0913823i \(-0.970871\pi\)
0.995816 0.0913823i \(-0.0291285\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 16.0000i 0.727273i
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −8.00000 −0.361035 −0.180517 0.983572i \(-0.557777\pi\)
−0.180517 + 0.983572i \(0.557777\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 28.5000 + 6.53835i 1.28098 + 0.293877i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 39.0000i 1.74588i −0.487828 0.872940i \(-0.662211\pi\)
0.487828 0.872940i \(-0.337789\pi\)
\(500\) 17.4356 + 14.0000i 0.779744 + 0.626099i
\(501\) 0 0
\(502\) 0 0
\(503\) 26.3589 + 26.3589i 1.17529 + 1.17529i 0.980932 + 0.194354i \(0.0622609\pi\)
0.194354 + 0.980932i \(0.437739\pi\)
\(504\) 0 0
\(505\) −8.71780 + 38.0000i −0.387937 + 1.69098i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) 16.3589 0.723675
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 18.8328 18.8328i 0.828267 0.828267i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(524\) 14.0000i 0.611593i
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 57.8712i 2.51614i
\(530\) 0 0
\(531\) 0 0
\(532\) 5.92330 5.92330i 0.256808 0.256808i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 26.4877i 1.14091i
\(540\) 0 0
\(541\) −39.2301 −1.68663 −0.843317 0.537417i \(-0.819400\pi\)
−0.843317 + 0.537417i \(0.819400\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(548\) −18.6411 18.6411i −0.796308 0.796308i
\(549\) 13.0767i 0.558100i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) −18.0000 −0.763370
\(557\) −25.6794 + 25.6794i −1.08807 + 1.08807i −0.0923462 + 0.995727i \(0.529437\pi\)
−0.995727 + 0.0923462i \(0.970563\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −4.56440 7.28220i −0.192881 0.307729i
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 6.11505 6.11505i 0.256808 0.256808i
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 26.1534 1.09449 0.547243 0.836974i \(-0.315677\pi\)
0.547243 + 0.836974i \(0.315677\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −14.7561 42.4739i −0.615374 1.77129i
\(576\) −24.0000 −1.00000
\(577\) −22.4739 + 22.4739i −0.935603 + 0.935603i −0.998048 0.0624458i \(-0.980110\pi\)
0.0624458 + 0.998048i \(0.480110\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4.94789 0.205273
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −27.4739 + 27.4739i −1.13397 + 1.13397i −0.144460 + 0.989511i \(0.546145\pi\)
−0.989511 + 0.144460i \(0.953855\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.435596 0.435596i −0.0178878 0.0178878i 0.698106 0.715994i \(-0.254026\pi\)
−0.715994 + 0.698106i \(0.754026\pi\)
\(594\) 0 0
\(595\) −16.8206 3.85890i −0.689575 0.158199i
\(596\) 22.0000 0.901155
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 4.00000 17.4356i 0.162623 0.708858i
\(606\) 0 0
\(607\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −34.0767 + 34.0767i −1.37747 + 1.37747i
\(613\) 34.7561 + 34.7561i 1.40379 + 1.40379i 0.787598 + 0.616190i \(0.211325\pi\)
0.616190 + 0.787598i \(0.288675\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −17.4739 + 17.4739i −0.703475 + 0.703475i −0.965155 0.261680i \(-0.915723\pi\)
0.261680 + 0.965155i \(0.415723\pi\)
\(618\) 0 0
\(619\) 24.0000i 0.964641i −0.875995 0.482321i \(-0.839794\pi\)
0.875995 0.482321i \(-0.160206\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 15.5000 + 19.6150i 0.620000 + 0.784602i
\(626\) 0 0
\(627\) 0 0
\(628\) −35.4356 35.4356i −1.41403 1.41403i
\(629\) 0 0
\(630\) 0 0
\(631\) 47.9479 1.90878 0.954388 0.298570i \(-0.0965097\pi\)
0.954388 + 0.298570i \(0.0965097\pi\)
\(632\) 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
\(643\) 17.9617 + 17.9617i 0.708338 + 0.708338i 0.966186 0.257847i \(-0.0830131\pi\)
−0.257847 + 0.966186i \(0.583013\pi\)
\(644\) 17.2822i 0.681014i
\(645\) 0 0
\(646\) 0 0
\(647\) −32.4739 + 32.4739i −1.27668 + 1.27668i −0.334169 + 0.942513i \(0.608456\pi\)
−0.942513 + 0.334169i \(0.891544\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 32.7178 32.7178i 1.28133 1.28133i
\(653\) −5.24385 5.24385i −0.205208 0.205208i 0.597019 0.802227i \(-0.296352\pi\)
−0.802227 + 0.597019i \(0.796352\pi\)
\(654\) 0 0
\(655\) 3.50000 15.2561i 0.136756 0.596107i
\(656\) 0 0
\(657\) 36.1150 36.1150i 1.40898 1.40898i
\(658\) 0 0
\(659\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 7.93560 4.97394i 0.307729 0.192881i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 19.0000 0.733487
\(672\) 0 0
\(673\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 26.0000 1.00000
\(677\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(684\) 26.1534i 1.00000i
\(685\) −15.6534 24.9739i −0.598085 0.954205i
\(686\) 0 0
\(687\) 0 0
\(688\) 28.1534 + 28.1534i 1.07334 + 1.07334i
\(689\) 0 0
\(690\) 0 0
\(691\) −39.2301 −1.49238 −0.746191 0.665731i \(-0.768120\pi\)
−0.746191 + 0.665731i \(0.768120\pi\)
\(692\) 0 0
\(693\) −8.88495 8.88495i −0.337512 0.337512i
\(694\) 0 0
\(695\) −19.6150 4.50000i −0.744041 0.170695i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −3.15339 9.07670i −0.119187 0.343067i
\(701\) −17.4356 −0.658533 −0.329267 0.944237i \(-0.606802\pi\)
−0.329267 + 0.944237i \(0.606802\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 34.8712i 1.31426i
\(705\) 0 0
\(706\) 0 0
\(707\) 11.8466 11.8466i 0.445537 0.445537i
\(708\) 0 0
\(709\) 52.3068i 1.96442i −0.187779 0.982211i \(-0.560129\pi\)
0.187779 0.982211i \(-0.439871\pi\)
\(710\) 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
\(719\) 49.0000i 1.82739i −0.406399 0.913696i \(-0.633216\pi\)
0.406399 0.913696i \(-0.366784\pi\)
\(720\) −26.1534 6.00000i −0.974679 0.223607i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 1.11505 1.11505i 0.0413547 0.0413547i −0.686127 0.727482i \(-0.740691\pi\)
0.727482 + 0.686127i \(0.240691\pi\)
\(728\) 0 0
\(729\) 27.0000i 1.00000i
\(730\) 0 0
\(731\) 79.9479 2.95698
\(732\) 0 0
\(733\) 33.1534 + 33.1534i 1.22455 + 1.22455i 0.965998 + 0.258551i \(0.0832450\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 30.5123i 1.12241i −0.827676 0.561206i \(-0.810337\pi\)
0.827676 0.561206i \(-0.189663\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(744\) 0 0
\(745\) 23.9739 + 5.50000i 0.878337 + 0.201504i
\(746\) 0 0
\(747\) 10.9233 10.9233i 0.399663 0.399663i
\(748\) 49.5123 + 49.5123i 1.81035 + 1.81035i
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) −17.2822 + 17.2822i −0.630217 + 0.630217i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −37.4739 + 37.4739i −1.36201 + 1.36201i −0.490666 + 0.871348i \(0.663246\pi\)
−0.871348 + 0.490666i \(0.836754\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 4.35890 0.158010 0.0790050 0.996874i \(-0.474826\pi\)
0.0790050 + 0.996874i \(0.474826\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 34.0000i 1.23008i
\(765\) −45.6534 + 28.6150i −1.65060 + 1.03458i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 51.0000i 1.83911i 0.392965 + 0.919554i \(0.371449\pi\)
−0.392965 + 0.919554i \(0.628551\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(774\) 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
\(784\) 24.3068i 0.868100i
\(785\) −29.7561 47.4739i −1.06204 1.69442i
\(786\) 0 0
\(787\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(788\) 4.56440 + 4.56440i 0.162600 + 0.162600i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 26.1534 0.926982
\(797\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(798\) 0 0
\(799\) 49.0767i 1.73621i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −52.4739 52.4739i −1.85177 1.85177i
\(804\) 0 0
\(805\) −4.32055 + 18.8328i −0.152279 + 0.663771i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 56.6657i 1.99226i 0.0878953 + 0.996130i \(0.471986\pi\)
−0.0878953 + 0.996130i \(0.528014\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 43.8328 27.4739i 1.53540 0.962370i
\(816\) 0 0
\(817\) −30.6794 + 30.6794i −1.07334 + 1.07334i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −53.0000 −1.84971 −0.924856 0.380317i \(-0.875815\pi\)
−0.924856 + 0.380317i \(0.875815\pi\)
\(822\) 0 0
\(823\) −23.8328 23.8328i −0.830761 0.830761i 0.156860 0.987621i \(-0.449863\pi\)
−0.987621 + 0.156860i \(0.949863\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(828\) 38.1534 + 38.1534i 1.32592 + 1.32592i
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −34.5123 34.5123i −1.19578 1.19578i
\(834\) 0 0
\(835\) 0 0
\(836\) −38.0000 −1.31426
\(837\) 0 0
\(838\) 0 0
\(839\) 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
\(845\) 28.3328 + 6.50000i 0.974679 + 0.223607i
\(846\) 0 0
\(847\) −5.43560 + 5.43560i −0.186769 + 0.186769i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 13.1534 + 13.1534i 0.450364 + 0.450364i 0.895475 0.445112i \(-0.146836\pi\)
−0.445112 + 0.895475i \(0.646836\pi\)
\(854\) 0 0
\(855\) 6.53835 28.5000i 0.223607 0.974679i
\(856\) 0 0
\(857\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(858\) 0 0
\(859\) 56.6657i 1.93341i 0.255897 + 0.966704i \(0.417629\pi\)
−0.255897 + 0.966704i \(0.582371\pi\)
\(860\) 23.6411 + 37.7178i 0.806155 + 1.28617i
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(864\) 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
\(875\) −1.16716 10.6794i −0.0394571 0.361031i
\(876\) 0 0
\(877\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) −8.71780 + 38.0000i −0.293877 + 1.28098i
\(881\) 47.9479 1.61541 0.807703 0.589590i \(-0.200711\pi\)
0.807703 + 0.589590i \(0.200711\pi\)
\(882\) 0 0
\(883\) −10.2439 10.2439i −0.344733 0.344733i 0.513410 0.858143i \(-0.328382\pi\)
−0.858143 + 0.513410i \(0.828382\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −39.2301 −1.31426
\(892\) 0 0
\(893\) −18.8328 18.8328i −0.630217 0.630217i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −27.0000 13.0767i −0.900000 0.435890i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(908\) 0 0
\(909\) 52.3068i 1.73491i
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) −15.8712 15.8712i −0.525260 0.525260i
\(914\) 0 0
\(915\) 0 0
\(916\) 42.0000 1.38772
\(917\) −4.75615 + 4.75615i −0.157062 + 0.157062i
\(918\) 0 0
\(919\) 8.71780i 0.287574i −0.989609 0.143787i \(-0.954072\pi\)
0.989609 0.143787i \(-0.0459280\pi\)
\(920\) 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
\(929\) 34.8712i 1.14409i 0.820223 + 0.572043i \(0.193849\pi\)
−0.820223 + 0.572043i \(0.806151\pi\)
\(930\) 0 0
\(931\) 26.4877 0.868100
\(932\) 29.5123 29.5123i 0.966707 0.966707i
\(933\) 0 0
\(934\) 0 0
\(935\) 41.5767 + 66.3328i 1.35970 + 2.16932i
\(936\) 0 0
\(937\) −3.88495 + 3.88495i −0.126916 + 0.126916i −0.767712 0.640796i \(-0.778605\pi\)
0.640796 + 0.767712i \(0.278605\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −23.1534 + 14.5123i −0.755180 + 0.473339i
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 34.5123 34.5123i 1.12150 1.12150i 0.129983 0.991516i \(-0.458508\pi\)
0.991516 0.129983i \(-0.0414921\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(954\) 0 0
\(955\) 8.50000 37.0506i 0.275054 1.19893i
\(956\) −61.0246 −1.97368
\(957\) 0 0
\(958\) 0 0
\(959\) 12.6657i 0.408996i
\(960\) 0 0
\(961\) 31.0000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 24.5123 24.5123i 0.788262 0.788262i −0.192947 0.981209i \(-0.561805\pi\)
0.981209 + 0.192947i \(0.0618045\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(972\) 0 0
\(973\) 6.11505 + 6.11505i 0.196039 + 0.196039i
\(974\) 0 0
\(975\) 0 0
\(976\) −17.4356 −0.558100
\(977\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 6.07670 26.4877i 0.194113 0.846119i
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(984\) 0 0
\(985\) 3.83284 + 6.11505i 0.122125 + 0.194842i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 89.5123i 2.84633i
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 28.5000 + 6.53835i 0.903511 + 0.207280i
\(996\) 0 0
\(997\) 29.3206 29.3206i 0.928591 0.928591i −0.0690239 0.997615i \(-0.521988\pi\)
0.997615 + 0.0690239i \(0.0219885\pi\)
\(998\) 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 95.2.g.a.18.1 4
3.2 odd 2 855.2.p.a.208.2 4
5.2 odd 4 inner 95.2.g.a.37.2 yes 4
5.3 odd 4 475.2.g.a.132.2 4
5.4 even 2 475.2.g.a.18.2 4
15.2 even 4 855.2.p.a.37.1 4
19.18 odd 2 CM 95.2.g.a.18.1 4
57.56 even 2 855.2.p.a.208.2 4
95.18 even 4 475.2.g.a.132.2 4
95.37 even 4 inner 95.2.g.a.37.2 yes 4
95.94 odd 2 475.2.g.a.18.2 4
285.227 odd 4 855.2.p.a.37.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.g.a.18.1 4 1.1 even 1 trivial
95.2.g.a.18.1 4 19.18 odd 2 CM
95.2.g.a.37.2 yes 4 5.2 odd 4 inner
95.2.g.a.37.2 yes 4 95.37 even 4 inner
475.2.g.a.18.2 4 5.4 even 2
475.2.g.a.18.2 4 95.94 odd 2
475.2.g.a.132.2 4 5.3 odd 4
475.2.g.a.132.2 4 95.18 even 4
855.2.p.a.37.1 4 15.2 even 4
855.2.p.a.37.1 4 285.227 odd 4
855.2.p.a.208.2 4 3.2 odd 2
855.2.p.a.208.2 4 57.56 even 2