Properties

Label 1156.1.o.a.319.1
Level $1156$
Weight $1$
Character 1156.319
Analytic conductor $0.577$
Analytic rank $0$
Dimension $32$
Projective image $D_{68}$
CM discriminant -4
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1156,1,Mod(47,1156)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1156, base_ring=CyclotomicField(68))
 
chi = DirichletCharacter(H, H._module([34, 25]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1156.47");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1156 = 2^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1156.o (of order \(68\), degree \(32\), 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: \(0.576919154604\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient field: \(\Q(\zeta_{68})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{32} - x^{30} + x^{28} - x^{26} + x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{68}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{68} - \cdots)\)

Embedding invariants

Embedding label 319.1
Root \(-0.183750 + 0.982973i\) of defining polynomial
Character \(\chi\) \(=\) 1156.319
Dual form 1156.1.o.a.395.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.361242 + 0.932472i) q^{2} +(-0.739009 + 0.673696i) q^{4} +(0.602635 - 1.79802i) q^{5} +(-0.895163 - 0.445738i) q^{8} +(-0.961826 - 0.273663i) q^{9} +O(q^{10})\) \(q+(0.361242 + 0.932472i) q^{2} +(-0.739009 + 0.673696i) q^{4} +(0.602635 - 1.79802i) q^{5} +(-0.895163 - 0.445738i) q^{8} +(-0.961826 - 0.273663i) q^{9} +(1.89430 - 0.0875787i) q^{10} +(0.857445 - 1.72198i) q^{13} +(0.0922684 - 0.995734i) q^{16} +(-0.0922684 + 0.995734i) q^{17} +(-0.0922684 - 0.995734i) q^{18} +(0.765964 + 1.73474i) q^{20} +(-2.07168 - 1.56446i) q^{25} +(1.91545 + 0.177492i) q^{26} +(0.972171 + 0.0449462i) q^{29} +(0.961826 - 0.273663i) q^{32} +(-0.961826 + 0.273663i) q^{34} +(0.895163 - 0.445738i) q^{36} +(0.666468 + 0.456541i) q^{37} +(-1.34090 + 1.34090i) q^{40} +(0.629488 + 0.0878098i) q^{41} +(-1.07168 + 1.56446i) q^{45} +(-0.526432 + 0.850217i) q^{49} +(0.710439 - 2.49693i) q^{50} +(0.526432 + 1.85022i) q^{52} +(1.01267 + 0.288130i) q^{53} +(0.309277 + 0.922758i) q^{58} +(-1.92821 + 0.453510i) q^{61} +(0.602635 + 0.798017i) q^{64} +(-2.57943 - 2.57943i) q^{65} +(-0.602635 - 0.798017i) q^{68} +(0.739009 + 0.673696i) q^{72} +(-1.34421 + 1.11622i) q^{73} +(-0.184956 + 0.786384i) q^{74} +(-1.73474 - 0.765964i) q^{80} +(0.850217 + 0.526432i) q^{81} +(0.145517 + 0.618701i) q^{82} +(1.73474 + 0.765964i) q^{85} +(0.322039 + 0.646741i) q^{89} +(-1.84595 - 0.434164i) q^{90} +(0.0806938 - 0.0449462i) q^{97} +(-0.982973 - 0.183750i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{4} + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{4} + 2 q^{5} - 2 q^{10} - 2 q^{16} + 2 q^{17} + 2 q^{18} - 2 q^{20} - 34 q^{25} - 2 q^{29} + 2 q^{37} + 2 q^{40} - 2 q^{41} - 2 q^{45} + 2 q^{50} + 2 q^{58} + 2 q^{61} + 2 q^{64} - 2 q^{68} - 2 q^{72} - 2 q^{73} - 2 q^{74} + 2 q^{80} + 2 q^{81} - 2 q^{82} - 2 q^{85} - 2 q^{90} + 2 q^{97} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1156\mathbb{Z}\right)^\times\).

\(n\) \(579\) \(581\)
\(\chi(n)\) \(-1\) \(e\left(\frac{37}{68}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.361242 + 0.932472i 0.361242 + 0.932472i
\(3\) 0 0 0.138156 0.990410i \(-0.455882\pi\)
−0.138156 + 0.990410i \(0.544118\pi\)
\(4\) −0.739009 + 0.673696i −0.739009 + 0.673696i
\(5\) 0.602635 1.79802i 0.602635 1.79802i 1.00000i \(-0.5\pi\)
0.602635 0.798017i \(-0.294118\pi\)
\(6\) 0 0
\(7\) 0 0 −0.486604 0.873622i \(-0.661765\pi\)
0.486604 + 0.873622i \(0.338235\pi\)
\(8\) −0.895163 0.445738i −0.895163 0.445738i
\(9\) −0.961826 0.273663i −0.961826 0.273663i
\(10\) 1.89430 0.0875787i 1.89430 0.0875787i
\(11\) 0 0 0.0461835 0.998933i \(-0.485294\pi\)
−0.0461835 + 0.998933i \(0.514706\pi\)
\(12\) 0 0
\(13\) 0.857445 1.72198i 0.857445 1.72198i 0.183750 0.982973i \(-0.441176\pi\)
0.673696 0.739009i \(-0.264706\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.0922684 0.995734i 0.0922684 0.995734i
\(17\) −0.0922684 + 0.995734i −0.0922684 + 0.995734i
\(18\) −0.0922684 0.995734i −0.0922684 0.995734i
\(19\) 0 0 0.361242 0.932472i \(-0.382353\pi\)
−0.361242 + 0.932472i \(0.617647\pi\)
\(20\) 0.765964 + 1.73474i 0.765964 + 1.73474i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.486604 0.873622i \(-0.661765\pi\)
0.486604 + 0.873622i \(0.338235\pi\)
\(24\) 0 0
\(25\) −2.07168 1.56446i −2.07168 1.56446i
\(26\) 1.91545 + 0.177492i 1.91545 + 0.177492i
\(27\) 0 0
\(28\) 0 0
\(29\) 0.972171 + 0.0449462i 0.972171 + 0.0449462i 0.526432 0.850217i \(-0.323529\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(30\) 0 0
\(31\) 0 0 0.948161 0.317791i \(-0.102941\pi\)
−0.948161 + 0.317791i \(0.897059\pi\)
\(32\) 0.961826 0.273663i 0.961826 0.273663i
\(33\) 0 0
\(34\) −0.961826 + 0.273663i −0.961826 + 0.273663i
\(35\) 0 0
\(36\) 0.895163 0.445738i 0.895163 0.445738i
\(37\) 0.666468 + 0.456541i 0.666468 + 0.456541i 0.850217 0.526432i \(-0.176471\pi\)
−0.183750 + 0.982973i \(0.558824\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −1.34090 + 1.34090i −1.34090 + 1.34090i
\(41\) 0.629488 + 0.0878098i 0.629488 + 0.0878098i 0.445738 0.895163i \(-0.352941\pi\)
0.183750 + 0.982973i \(0.441176\pi\)
\(42\) 0 0
\(43\) 0 0 0.995734 0.0922684i \(-0.0294118\pi\)
−0.995734 + 0.0922684i \(0.970588\pi\)
\(44\) 0 0
\(45\) −1.07168 + 1.56446i −1.07168 + 1.56446i
\(46\) 0 0
\(47\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(48\) 0 0
\(49\) −0.526432 + 0.850217i −0.526432 + 0.850217i
\(50\) 0.710439 2.49693i 0.710439 2.49693i
\(51\) 0 0
\(52\) 0.526432 + 1.85022i 0.526432 + 1.85022i
\(53\) 1.01267 + 0.288130i 1.01267 + 0.288130i 0.739009 0.673696i \(-0.235294\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0.309277 + 0.922758i 0.309277 + 0.922758i
\(59\) 0 0 −0.526432 0.850217i \(-0.676471\pi\)
0.526432 + 0.850217i \(0.323529\pi\)
\(60\) 0 0
\(61\) −1.92821 + 0.453510i −1.92821 + 0.453510i −0.932472 + 0.361242i \(0.882353\pi\)
−0.995734 + 0.0922684i \(0.970588\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.602635 + 0.798017i 0.602635 + 0.798017i
\(65\) −2.57943 2.57943i −2.57943 2.57943i
\(66\) 0 0
\(67\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(68\) −0.602635 0.798017i −0.602635 0.798017i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 0.873622 0.486604i \(-0.161765\pi\)
−0.873622 + 0.486604i \(0.838235\pi\)
\(72\) 0.739009 + 0.673696i 0.739009 + 0.673696i
\(73\) −1.34421 + 1.11622i −1.34421 + 1.11622i −0.361242 + 0.932472i \(0.617647\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(74\) −0.184956 + 0.786384i −0.184956 + 0.786384i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.914794 0.403921i \(-0.132353\pi\)
−0.914794 + 0.403921i \(0.867647\pi\)
\(80\) −1.73474 0.765964i −1.73474 0.765964i
\(81\) 0.850217 + 0.526432i 0.850217 + 0.526432i
\(82\) 0.145517 + 0.618701i 0.145517 + 0.618701i
\(83\) 0 0 −0.798017 0.602635i \(-0.794118\pi\)
0.798017 + 0.602635i \(0.205882\pi\)
\(84\) 0 0
\(85\) 1.73474 + 0.765964i 1.73474 + 0.765964i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.322039 + 0.646741i 0.322039 + 0.646741i 0.995734 0.0922684i \(-0.0294118\pi\)
−0.673696 + 0.739009i \(0.735294\pi\)
\(90\) −1.84595 0.434164i −1.84595 0.434164i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.0806938 0.0449462i 0.0806938 0.0449462i −0.445738 0.895163i \(-0.647059\pi\)
0.526432 + 0.850217i \(0.323529\pi\)
\(98\) −0.982973 0.183750i −0.982973 0.183750i
\(99\) 0 0
\(100\) 2.58496 0.239532i 2.58496 0.239532i
\(101\) 1.69318 + 1.04837i 1.69318 + 1.04837i 0.895163 + 0.445738i \(0.147059\pi\)
0.798017 + 0.602635i \(0.205882\pi\)
\(102\) 0 0
\(103\) 0 0 0.850217 0.526432i \(-0.176471\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(104\) −1.53511 + 1.15926i −1.53511 + 1.15926i
\(105\) 0 0
\(106\) 0.0971461 + 1.04837i 0.0971461 + 1.04837i
\(107\) 0 0 −0.403921 0.914794i \(-0.632353\pi\)
0.403921 + 0.914794i \(0.367647\pi\)
\(108\) 0 0
\(109\) −0.252769 1.81204i −0.252769 1.81204i −0.526432 0.850217i \(-0.676471\pi\)
0.273663 0.961826i \(-0.411765\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1.40065 + 0.195383i 1.40065 + 0.195383i 0.798017 0.602635i \(-0.205882\pi\)
0.602635 + 0.798017i \(0.294118\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.748723 + 0.621731i −0.748723 + 0.621731i
\(117\) −1.29596 + 1.42160i −1.29596 + 1.42160i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.995734 0.0922684i −0.995734 0.0922684i
\(122\) −1.11943 1.63417i −1.11943 1.63417i
\(123\) 0 0
\(124\) 0 0
\(125\) −2.49693 + 1.71044i −2.49693 + 1.71044i
\(126\) 0 0
\(127\) 0 0 0.183750 0.982973i \(-0.441176\pi\)
−0.183750 + 0.982973i \(0.558824\pi\)
\(128\) −0.526432 + 0.850217i −0.526432 + 0.850217i
\(129\) 0 0
\(130\) 1.47345 3.33704i 1.47345 3.33704i
\(131\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.526432 0.850217i 0.526432 0.850217i
\(137\) 1.32307 1.20614i 1.32307 1.20614i 0.361242 0.932472i \(-0.382353\pi\)
0.961826 0.273663i \(-0.0882353\pi\)
\(138\) 0 0
\(139\) 0 0 −0.914794 0.403921i \(-0.867647\pi\)
0.914794 + 0.403921i \(0.132353\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −0.361242 + 0.932472i −0.361242 + 0.932472i
\(145\) 0.666678 1.72089i 0.666678 1.72089i
\(146\) −1.52643 0.850217i −1.52643 0.850217i
\(147\) 0 0
\(148\) −0.800095 + 0.111609i −0.800095 + 0.111609i
\(149\) 0.329838 0.436776i 0.329838 0.436776i −0.602635 0.798017i \(-0.705882\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(150\) 0 0
\(151\) 0 0 −0.673696 0.739009i \(-0.735294\pi\)
0.673696 + 0.739009i \(0.264706\pi\)
\(152\) 0 0
\(153\) 0.361242 0.932472i 0.361242 0.932472i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.757949 + 0.469302i −0.757949 + 0.469302i −0.850217 0.526432i \(-0.823529\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.0875787 1.89430i 0.0875787 1.89430i
\(161\) 0 0
\(162\) −0.183750 + 0.982973i −0.183750 + 0.982973i
\(163\) 0 0 0.824997 0.565136i \(-0.191176\pi\)
−0.824997 + 0.565136i \(0.808824\pi\)
\(164\) −0.524354 + 0.359191i −0.524354 + 0.359191i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.565136 0.824997i \(-0.691176\pi\)
0.565136 + 0.824997i \(0.308824\pi\)
\(168\) 0 0
\(169\) −1.62738 2.15499i −1.62738 2.15499i
\(170\) −0.0875787 + 1.89430i −0.0875787 + 1.89430i
\(171\) 0 0
\(172\) 0 0
\(173\) −1.49780 + 1.24376i −1.49780 + 1.24376i −0.602635 + 0.798017i \(0.705882\pi\)
−0.895163 + 0.445738i \(0.852941\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −0.486734 + 0.533922i −0.486734 + 0.533922i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) −0.261989 1.87814i −0.261989 1.87814i
\(181\) 0.0878098 + 0.261989i 0.0878098 + 0.261989i 0.982973 0.183750i \(-0.0588235\pi\)
−0.895163 + 0.445738i \(0.852941\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.22250 0.923193i 1.22250 0.923193i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.982973 0.183750i \(-0.941176\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(192\) 0 0
\(193\) −0.0632619 0.453510i −0.0632619 0.453510i −0.995734 0.0922684i \(-0.970588\pi\)
0.932472 0.361242i \(-0.117647\pi\)
\(194\) 0.0710610 + 0.0590083i 0.0710610 + 0.0590083i
\(195\) 0 0
\(196\) −0.183750 0.982973i −0.183750 0.982973i
\(197\) −1.21146 0.406040i −1.21146 0.406040i −0.361242 0.932472i \(-0.617647\pi\)
−0.850217 + 0.526432i \(0.823529\pi\)
\(198\) 0 0
\(199\) 0 0 −0.973438 0.228951i \(-0.926471\pi\)
0.973438 + 0.228951i \(0.0735294\pi\)
\(200\) 1.15715 + 2.32387i 1.15715 + 2.32387i
\(201\) 0 0
\(202\) −0.365931 + 1.95756i −0.365931 + 1.95756i
\(203\) 0 0
\(204\) 0 0
\(205\) 0.537235 1.07891i 0.537235 1.07891i
\(206\) 0 0
\(207\) 0 0
\(208\) −1.63552 1.01267i −1.63552 1.01267i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 0.228951 0.973438i \(-0.426471\pi\)
−0.228951 + 0.973438i \(0.573529\pi\)
\(212\) −0.942485 + 0.469302i −0.942485 + 0.469302i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 1.59837 0.890286i 1.59837 0.890286i
\(219\) 0 0
\(220\) 0 0
\(221\) 1.63552 + 1.01267i 1.63552 + 1.01267i
\(222\) 0 0
\(223\) 0 0 −0.183750 0.982973i \(-0.558824\pi\)
0.183750 + 0.982973i \(0.441176\pi\)
\(224\) 0 0
\(225\) 1.56446 + 2.07168i 1.56446 + 2.07168i
\(226\) 0.323785 + 1.37665i 0.323785 + 1.37665i
\(227\) 0 0 −0.638847 0.769334i \(-0.720588\pi\)
0.638847 + 0.769334i \(0.279412\pi\)
\(228\) 0 0
\(229\) 1.89090 0.538007i 1.89090 0.538007i 0.895163 0.445738i \(-0.147059\pi\)
0.995734 0.0922684i \(-0.0294118\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.850217 0.473568i −0.850217 0.473568i
\(233\) 0.0590083 + 1.27633i 0.0590083 + 1.27633i 0.798017 + 0.602635i \(0.205882\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(234\) −1.79375 0.694903i −1.79375 0.694903i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(240\) 0 0
\(241\) −0.268973 0.0632619i −0.268973 0.0632619i 0.0922684 0.995734i \(-0.470588\pi\)
−0.361242 + 0.932472i \(0.617647\pi\)
\(242\) −0.273663 0.961826i −0.273663 0.961826i
\(243\) 0 0
\(244\) 1.11943 1.63417i 1.11943 1.63417i
\(245\) 1.21146 + 1.45890i 1.21146 + 1.45890i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −2.49693 1.71044i −2.49693 1.71044i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.982973 0.183750i −0.982973 0.183750i
\(257\) 1.79375 0.510366i 1.79375 0.510366i 0.798017 0.602635i \(-0.205882\pi\)
0.995734 + 0.0922684i \(0.0294118\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 3.64397 + 0.168471i 3.64397 + 0.168471i
\(261\) −0.922758 0.309277i −0.922758 0.309277i
\(262\) 0 0
\(263\) 0 0 −0.995734 0.0922684i \(-0.970588\pi\)
0.995734 + 0.0922684i \(0.0294118\pi\)
\(264\) 0 0
\(265\) 1.12833 1.64716i 1.12833 1.64716i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.621500 1.40756i −0.621500 1.40756i −0.895163 0.445738i \(-0.852941\pi\)
0.273663 0.961826i \(-0.411765\pi\)
\(270\) 0 0
\(271\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(272\) 0.982973 + 0.183750i 0.982973 + 0.183750i
\(273\) 0 0
\(274\) 1.60263 + 0.798017i 1.60263 + 0.798017i
\(275\) 0 0
\(276\) 0 0
\(277\) 1.10025 + 1.60617i 1.10025 + 1.60617i 0.739009 + 0.673696i \(0.235294\pi\)
0.361242 + 0.932472i \(0.382353\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.20614 + 0.600584i 1.20614 + 0.600584i 0.932472 0.361242i \(-0.117647\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(282\) 0 0
\(283\) 0 0 0.973438 0.228951i \(-0.0735294\pi\)
−0.973438 + 0.228951i \(0.926471\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −1.00000
\(289\) −0.982973 0.183750i −0.982973 0.183750i
\(290\) 1.84552 1.84552
\(291\) 0 0
\(292\) 0.241393 1.73049i 0.241393 1.73049i
\(293\) −1.37821 + 1.25640i −1.37821 + 1.25640i −0.445738 + 0.895163i \(0.647059\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.393100 0.705749i −0.393100 0.705749i
\(297\) 0 0
\(298\) 0.526432 + 0.149783i 0.526432 + 0.149783i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.346585 + 3.74025i −0.346585 + 3.74025i
\(306\) 1.00000 1.00000
\(307\) 0 0 −0.0922684 0.995734i \(-0.529412\pi\)
0.0922684 + 0.995734i \(0.470588\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.948161 0.317791i \(-0.102941\pi\)
−0.948161 + 0.317791i \(0.897059\pi\)
\(312\) 0 0
\(313\) −0.869557 + 1.26940i −0.869557 + 1.26940i 0.0922684 + 0.995734i \(0.470588\pi\)
−0.961826 + 0.273663i \(0.911765\pi\)
\(314\) −0.711414 0.537235i −0.711414 0.537235i
\(315\) 0 0
\(316\) 0 0
\(317\) 1.45890 + 0.488975i 1.45890 + 0.488975i 0.932472 0.361242i \(-0.117647\pi\)
0.526432 + 0.850217i \(0.323529\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.79802 0.602635i 1.79802 0.602635i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.982973 + 0.183750i −0.982973 + 0.183750i
\(325\) −4.47032 + 2.22596i −4.47032 + 2.22596i
\(326\) 0 0
\(327\) 0 0
\(328\) −0.524354 0.359191i −0.524354 0.359191i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.673696 0.739009i \(-0.735294\pi\)
0.673696 + 0.739009i \(0.264706\pi\)
\(332\) 0 0
\(333\) −0.516087 0.621500i −0.516087 0.621500i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.10025 + 0.258777i 1.10025 + 0.258777i 0.739009 0.673696i \(-0.235294\pi\)
0.361242 + 0.932472i \(0.382353\pi\)
\(338\) 1.42160 2.29596i 1.42160 2.29596i
\(339\) 0 0
\(340\) −1.79802 + 0.602635i −1.79802 + 0.602635i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −1.70083 0.947359i −1.70083 0.947359i
\(347\) 0 0 −0.317791 0.948161i \(-0.602941\pi\)
0.317791 + 0.948161i \(0.397059\pi\)
\(348\) 0 0
\(349\) 0.353470 0.100571i 0.353470 0.100571i −0.0922684 0.995734i \(-0.529412\pi\)
0.445738 + 0.895163i \(0.352941\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0.111208 + 0.147263i 0.111208 + 0.147263i 0.850217 0.526432i \(-0.176471\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.673696 0.260991i −0.673696 0.260991i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.526432 0.850217i \(-0.676471\pi\)
0.526432 + 0.850217i \(0.323529\pi\)
\(360\) 1.65667 0.922758i 1.65667 0.922758i
\(361\) −0.739009 0.673696i −0.739009 0.673696i
\(362\) −0.212577 + 0.176521i −0.212577 + 0.176521i
\(363\) 0 0
\(364\) 0 0
\(365\) 1.19692 + 3.08960i 1.19692 + 3.08960i
\(366\) 0 0
\(367\) 0 0 0.228951 0.973438i \(-0.426471\pi\)
−0.228951 + 0.973438i \(0.573529\pi\)
\(368\) 0 0
\(369\) −0.581427 0.256725i −0.581427 0.256725i
\(370\) 1.30247 + 0.806456i 1.30247 + 0.806456i
\(371\) 0 0
\(372\) 0 0
\(373\) 0.163808 0.328972i 0.163808 0.328972i −0.798017 0.602635i \(-0.794118\pi\)
0.961826 + 0.273663i \(0.0882353\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.910979 1.63552i 0.910979 1.63552i
\(378\) 0 0
\(379\) 0 0 −0.973438 0.228951i \(-0.926471\pi\)
0.973438 + 0.228951i \(0.0735294\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.798017 0.602635i \(-0.205882\pi\)
−0.798017 + 0.602635i \(0.794118\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.400033 0.222817i 0.400033 0.222817i
\(387\) 0 0
\(388\) −0.0293534 + 0.0875787i −0.0293534 + 0.0875787i
\(389\) −1.69318 + 0.156896i −1.69318 + 0.156896i −0.895163 0.445738i \(-0.852941\pi\)
−0.798017 + 0.602635i \(0.794118\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.850217 0.526432i 0.850217 0.526432i
\(393\) 0 0
\(394\) −0.0590083 1.27633i −0.0590083 1.27633i
\(395\) 0 0
\(396\) 0 0
\(397\) 0.581427 + 1.73474i 0.581427 + 1.73474i 0.673696 + 0.739009i \(0.264706\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −1.74894 + 1.91849i −1.74894 + 1.91849i
\(401\) −1.78099 + 0.786384i −1.78099 + 0.786384i −0.798017 + 0.602635i \(0.794118\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −1.95756 + 0.365931i −1.95756 + 0.365931i
\(405\) 1.45890 1.21146i 1.45890 1.21146i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.726337 0.961826i −0.726337 0.961826i 0.273663 0.961826i \(-0.411765\pi\)
−1.00000 \(\pi\)
\(410\) 1.20013 + 0.111208i 1.20013 + 0.111208i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0.353470 1.89090i 0.353470 1.89090i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.403921 0.914794i \(-0.367647\pi\)
−0.403921 + 0.914794i \(0.632353\pi\)
\(420\) 0 0
\(421\) 1.69318 1.04837i 1.69318 1.04837i 0.798017 0.602635i \(-0.205882\pi\)
0.895163 0.445738i \(-0.147059\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −0.778076 0.709310i −0.778076 0.709310i
\(425\) 1.74894 1.91849i 1.74894 1.91849i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.769334 0.638847i \(-0.779412\pi\)
0.769334 + 0.638847i \(0.220588\pi\)
\(432\) 0 0
\(433\) −0.322039 + 0.831277i −0.322039 + 0.831277i 0.673696 + 0.739009i \(0.264706\pi\)
−0.995734 + 0.0922684i \(0.970588\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.40756 + 1.16883i 1.40756 + 1.16883i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.914794 0.403921i \(-0.867647\pi\)
0.914794 + 0.403921i \(0.132353\pi\)
\(440\) 0 0
\(441\) 0.739009 0.673696i 0.739009 0.673696i
\(442\) −0.353470 + 1.89090i −0.353470 + 1.89090i
\(443\) 0 0 −0.739009 0.673696i \(-0.764706\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(444\) 0 0
\(445\) 1.35692 0.189283i 1.35692 0.189283i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.0211475 0.457413i 0.0211475 0.457413i −0.961826 0.273663i \(-0.911765\pi\)
0.982973 0.183750i \(-0.0588235\pi\)
\(450\) −1.36664 + 2.20719i −1.36664 + 2.20719i
\(451\) 0 0
\(452\) −1.16672 + 0.799224i −1.16672 + 0.799224i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.183750 + 0.0170269i 0.183750 + 0.0170269i 0.183750 0.982973i \(-0.441176\pi\)
1.00000i \(0.5\pi\)
\(458\) 1.18475 + 1.56886i 1.18475 + 1.56886i
\(459\) 0 0
\(460\) 0 0
\(461\) −0.907732 + 0.995734i −0.907732 + 0.995734i 0.0922684 + 0.995734i \(0.470588\pi\)
−1.00000 \(\pi\)
\(462\) 0 0
\(463\) 0 0 0.982973 0.183750i \(-0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(464\) 0.134455 0.963876i 0.134455 0.963876i
\(465\) 0 0
\(466\) −1.16883 + 0.516087i −1.16883 + 0.516087i
\(467\) 0 0 0.673696 0.739009i \(-0.264706\pi\)
−0.673696 + 0.739009i \(0.735294\pi\)
\(468\) 1.92365i 1.92365i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.895163 0.554262i −0.895163 0.554262i
\(478\) 0 0
\(479\) 0 0 0.317791 0.948161i \(-0.397059\pi\)
−0.317791 + 0.948161i \(0.602941\pi\)
\(480\) 0 0
\(481\) 1.35761 0.756186i 1.35761 0.756186i
\(482\) −0.0381744 0.273663i −0.0381744 0.273663i
\(483\) 0 0
\(484\) 0.798017 0.602635i 0.798017 0.602635i
\(485\) −0.0321851 0.172175i −0.0321851 0.172175i
\(486\) 0 0
\(487\) 0 0 0.998933 0.0461835i \(-0.0147059\pi\)
−0.998933 + 0.0461835i \(0.985294\pi\)
\(488\) 1.92821 + 0.453510i 1.92821 + 0.453510i
\(489\) 0 0
\(490\) −0.922758 + 1.65667i −0.922758 + 1.65667i
\(491\) 0 0 0.183750 0.982973i \(-0.441176\pi\)
−0.183750 + 0.982973i \(0.558824\pi\)
\(492\) 0 0
\(493\) −0.134455 + 0.963876i −0.134455 + 0.963876i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 0.914794 0.403921i \(-0.132353\pi\)
−0.914794 + 0.403921i \(0.867647\pi\)
\(500\) 0.692940 2.94620i 0.692940 2.94620i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(504\) 0 0
\(505\) 2.90536 2.41258i 2.90536 2.41258i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.58561 0.614268i 1.58561 0.614268i 0.602635 0.798017i \(-0.294118\pi\)
0.982973 + 0.183750i \(0.0588235\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.183750 0.982973i −0.183750 0.982973i
\(513\) 0 0
\(514\) 1.12388 + 1.48826i 1.12388 + 1.48826i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 1.15926 + 3.45876i 1.15926 + 3.45876i
\(521\) −1.23549 0.688163i −1.23549 0.688163i −0.273663 0.961826i \(-0.588235\pi\)
−0.961826 + 0.273663i \(0.911765\pi\)
\(522\) −0.0449462 0.972171i −0.0449462 0.972171i
\(523\) 0 0 −0.932472 0.361242i \(-0.882353\pi\)
0.932472 + 0.361242i \(0.117647\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.526432 + 0.850217i −0.526432 + 0.850217i
\(530\) 1.94354 + 0.457116i 1.94354 + 0.457116i
\(531\) 0 0
\(532\) 0 0
\(533\) 0.690958 1.00867i 0.690958 1.00867i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 1.08800 1.08800i 1.08800 1.08800i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.227957 + 0.156154i 0.227957 + 0.156154i 0.673696 0.739009i \(-0.264706\pi\)
−0.445738 + 0.895163i \(0.647059\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.183750 + 0.982973i 0.183750 + 0.982973i
\(545\) −3.41041 0.637516i −3.41041 0.637516i
\(546\) 0 0
\(547\) 0 0 0.948161 0.317791i \(-0.102941\pi\)
−0.948161 + 0.317791i \(0.897059\pi\)
\(548\) −0.165190 + 1.78269i −0.165190 + 1.78269i
\(549\) 1.97871 + 0.0914812i 1.97871 + 0.0914812i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −1.10025 + 1.60617i −1.10025 + 1.60617i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.673696 + 0.260991i −0.673696 + 0.260991i −0.673696 0.739009i \(-0.735294\pi\)
1.00000i \(0.5\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.124322 + 1.34164i −0.124322 + 1.34164i
\(563\) 0 0 −0.895163 0.445738i \(-0.852941\pi\)
0.895163 + 0.445738i \(0.147059\pi\)
\(564\) 0 0
\(565\) 1.19538 2.40065i 1.19538 2.40065i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.273663 0.961826i \(-0.411765\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(570\) 0 0
\(571\) 0 0 −0.486604 0.873622i \(-0.661765\pi\)
0.486604 + 0.873622i \(0.338235\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −0.361242 0.932472i −0.361242 0.932472i
\(577\) −0.367499 −0.367499 −0.183750 0.982973i \(-0.558824\pi\)
−0.183750 + 0.982973i \(0.558824\pi\)
\(578\) −0.183750 0.982973i −0.183750 0.982973i
\(579\) 0 0
\(580\) 0.666678 + 1.72089i 0.666678 + 1.72089i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 1.70083 0.400033i 1.70083 0.400033i
\(585\) 1.77507 + 3.18685i 1.77507 + 3.18685i
\(586\) −1.66943 0.831277i −1.66943 0.831277i
\(587\) 0 0 −0.961826 0.273663i \(-0.911765\pi\)
0.961826 + 0.273663i \(0.0882353\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.516087 0.621500i 0.516087 0.621500i
\(593\) 1.60263 + 0.798017i 1.60263 + 0.798017i 1.00000 \(0\)
0.602635 + 0.798017i \(0.294118\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.0505009 + 0.544991i 0.0505009 + 0.544991i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(600\) 0 0
\(601\) −0.850217 1.52643i −0.850217 1.52643i −0.850217 0.526432i \(-0.823529\pi\)
1.00000i \(-0.5\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.765964 + 1.73474i −0.765964 + 1.73474i
\(606\) 0 0
\(607\) 0 0 −0.998933 0.0461835i \(-0.985294\pi\)
0.998933 + 0.0461835i \(0.0147059\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −3.61288 + 1.02795i −3.61288 + 1.02795i
\(611\) 0 0
\(612\) 0.361242 + 0.932472i 0.361242 + 0.932472i
\(613\) −1.45285 + 0.271585i −1.45285 + 0.271585i −0.850217 0.526432i \(-0.823529\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.44147 0.987432i −1.44147 0.987432i −0.995734 0.0922684i \(-0.970588\pi\)
−0.445738 0.895163i \(-0.647059\pi\)
\(618\) 0 0
\(619\) 0 0 −0.990410 0.138156i \(-0.955882\pi\)
0.990410 + 0.138156i \(0.0441176\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.860221 + 3.02336i 0.860221 + 3.02336i
\(626\) −1.49780 0.352279i −1.49780 0.352279i
\(627\) 0 0
\(628\) 0.243964 0.857445i 0.243964 0.857445i
\(629\) −0.516087 + 0.621500i −0.516087 + 0.621500i
\(630\) 0 0
\(631\) 0 0 −0.961826 0.273663i \(-0.911765\pi\)
0.961826 + 0.273663i \(0.0882353\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0.0710610 + 1.53703i 0.0710610 + 1.53703i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.01267 + 1.63552i 1.01267 + 1.63552i
\(638\) 0 0
\(639\) 0 0
\(640\) 1.21146 + 1.45890i 1.21146 + 1.45890i
\(641\) −0.258777 1.10025i −0.258777 1.10025i −0.932472 0.361242i \(-0.882353\pi\)
0.673696 0.739009i \(-0.264706\pi\)
\(642\) 0 0
\(643\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.932472 0.361242i \(-0.117647\pi\)
−0.932472 + 0.361242i \(0.882353\pi\)
\(648\) −0.526432 0.850217i −0.526432 0.850217i
\(649\) 0 0
\(650\) −3.69051 3.36435i −3.69051 3.36435i
\(651\) 0 0
\(652\) 0 0
\(653\) −1.16672 + 1.16672i −1.16672 + 1.16672i −0.183750 + 0.982973i \(0.558824\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.145517 0.618701i 0.145517 0.618701i
\(657\) 1.59837 0.705749i 1.59837 0.705749i
\(658\) 0 0
\(659\) 0 0 −0.850217 0.526432i \(-0.823529\pi\)
0.850217 + 0.526432i \(0.176471\pi\)
\(660\) 0 0
\(661\) 0 0 0.602635 0.798017i \(-0.294118\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0.393100 0.705749i 0.393100 0.705749i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −1.53703 1.27633i −1.53703 1.27633i −0.798017 0.602635i \(-0.794118\pi\)
−0.739009 0.673696i \(-0.764706\pi\)
\(674\) 0.156154 + 1.11943i 0.156154 + 1.11943i
\(675\) 0 0
\(676\) 2.65445 + 0.496203i 2.65445 + 0.496203i
\(677\) −0.634905 + 1.89430i −0.634905 + 1.89430i −0.273663 + 0.961826i \(0.588235\pi\)
−0.361242 + 0.932472i \(0.617647\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −1.21146 1.45890i −1.21146 1.45890i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.0461835 0.998933i \(-0.514706\pi\)
0.0461835 + 0.998933i \(0.485294\pi\)
\(684\) 0 0
\(685\) −1.37133 3.10576i −1.37133 3.10576i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.36447 1.49675i 1.36447 1.49675i
\(690\) 0 0
\(691\) 0 0 −0.990410 0.138156i \(-0.955882\pi\)
0.990410 + 0.138156i \(0.0441176\pi\)
\(692\) 0.268973 1.92821i 0.268973 1.92821i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −0.145517 + 0.618701i −0.145517 + 0.618701i
\(698\) 0.221468 + 0.293271i 0.221468 + 0.293271i
\(699\) 0 0
\(700\) 0 0
\(701\) 0.544991 1.91545i 0.544991 1.91545i 0.183750 0.982973i \(-0.441176\pi\)
0.361242 0.932472i \(-0.382353\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −0.0971461 + 0.156896i −0.0971461 + 0.156896i
\(707\) 0 0
\(708\) 0 0
\(709\) −1.16672 1.16672i −1.16672 1.16672i −0.982973 0.183750i \(-0.941176\pi\)
−0.183750 0.982973i \(-0.558824\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.722483i 0.722483i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.990410 0.138156i \(-0.0441176\pi\)
−0.990410 + 0.138156i \(0.955882\pi\)
\(720\) 1.45890 + 1.21146i 1.45890 + 1.21146i
\(721\) 0 0
\(722\) 0.361242 0.932472i 0.361242 0.932472i
\(723\) 0 0
\(724\) −0.241393 0.134455i −0.241393 0.134455i
\(725\) −1.94371 1.61404i −1.94371 1.61404i
\(726\) 0 0
\(727\) 0 0 0.602635 0.798017i \(-0.294118\pi\)
−0.602635 + 0.798017i \(0.705882\pi\)
\(728\) 0 0
\(729\) −0.673696 0.739009i −0.673696 0.739009i
\(730\) −2.44859 + 2.23218i −2.44859 + 2.23218i
\(731\) 0 0
\(732\) 0 0
\(733\) 1.79033i 1.79033i −0.445738 0.895163i \(-0.647059\pi\)
0.445738 0.895163i \(-0.352941\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0.0293534 0.634905i 0.0293534 0.634905i
\(739\) 0 0 0.526432 0.850217i \(-0.323529\pi\)
−0.526432 + 0.850217i \(0.676471\pi\)
\(740\) −0.281491 + 1.50584i −0.281491 + 1.50584i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.486604 0.873622i \(-0.338235\pi\)
−0.486604 + 0.873622i \(0.661765\pi\)
\(744\) 0 0
\(745\) −0.586558 0.856270i −0.586558 0.856270i
\(746\) 0.365931 + 0.0339085i 0.365931 + 0.0339085i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.769334 0.638847i \(-0.220588\pi\)
−0.769334 + 0.638847i \(0.779412\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 1.85416 + 0.258645i 1.85416 + 0.258645i
\(755\) 0 0
\(756\) 0 0
\(757\) 1.47802i 1.47802i −0.673696 0.739009i \(-0.735294\pi\)
0.673696 0.739009i \(-0.264706\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.165190 1.78269i −0.165190 1.78269i −0.526432 0.850217i \(-0.676471\pi\)
0.361242 0.932472i \(-0.382353\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −1.45890 1.21146i −1.45890 1.21146i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0.710182 + 0.132756i 0.710182 + 0.132756i 0.526432 0.850217i \(-0.323529\pi\)
0.183750 + 0.982973i \(0.441176\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.352279 + 0.292529i 0.352279 + 0.292529i
\(773\) 0.711414 0.537235i 0.711414 0.537235i −0.183750 0.982973i \(-0.558824\pi\)
0.895163 + 0.445738i \(0.147059\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −0.0922684 + 0.00426582i −0.0922684 + 0.00426582i
\(777\) 0 0
\(778\) −0.757949 1.52217i −0.757949 1.52217i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.798017 + 0.602635i 0.798017 + 0.602635i
\(785\) 0.387047 + 1.64562i 0.387047 + 1.64562i
\(786\) 0 0
\(787\) 0 0 −0.914794 0.403921i \(-0.867647\pi\)
0.914794 + 0.403921i \(0.132353\pi\)
\(788\) 1.16883 0.516087i 1.16883 0.516087i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −0.872395 + 3.70920i −0.872395 + 3.70920i
\(794\) −1.40756 + 1.16883i −1.40756 + 1.16883i
\(795\) 0 0
\(796\) 0 0
\(797\) −0.554262 0.895163i −0.554262 0.895163i 0.445738 0.895163i \(-0.352941\pi\)
−1.00000 \(\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −2.42073 0.937796i −2.42073 0.937796i
\(801\) −0.132756 0.710182i −0.132756 0.710182i
\(802\) −1.37665 1.37665i −1.37665 1.37665i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) −1.04837 1.69318i −1.04837 1.69318i
\(809\) −0.406040 1.21146i −0.406040 1.21146i −0.932472 0.361242i \(-0.882353\pi\)
0.526432 0.850217i \(-0.323529\pi\)
\(810\) 1.65667 + 0.922758i 1.65667 + 0.922758i
\(811\) 0 0 −0.0461835 0.998933i \(-0.514706\pi\)
0.0461835 + 0.998933i \(0.485294\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0.634493 1.02474i 0.634493 1.02474i
\(819\) 0 0
\(820\) 0.329838 + 1.15926i 0.329838 + 1.15926i
\(821\) 1.26544 1.52391i 1.26544 1.52391i 0.526432 0.850217i \(-0.323529\pi\)
0.739009 0.673696i \(-0.235294\pi\)
\(822\) 0 0
\(823\) 0 0 −0.638847 0.769334i \(-0.720588\pi\)
0.638847 + 0.769334i \(0.279412\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(828\) 0 0
\(829\) −0.547326 −0.547326 −0.273663 0.961826i \(-0.588235\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 1.89090 0.353470i 1.89090 0.353470i
\(833\) −0.798017 0.602635i −0.798017 0.602635i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.948161 0.317791i \(-0.897059\pi\)
0.948161 + 0.317791i \(0.102941\pi\)
\(840\) 0 0
\(841\) −0.0526388 0.00487770i −0.0526388 0.00487770i
\(842\) 1.58923 + 1.20013i 1.58923 + 1.20013i
\(843\) 0 0
\(844\) 0 0
\(845\) −4.85543 + 1.62738i −4.85543 + 1.62738i
\(846\) 0 0
\(847\) 0 0
\(848\) 0.380338 0.981767i 0.380338 0.981767i
\(849\) 0 0
\(850\) 2.42073 + 0.937796i 2.42073 + 0.937796i
\(851\) 0 0
\(852\) 0 0
\(853\) −0.722071 + 0.869557i −0.722071 + 0.869557i −0.995734 0.0922684i \(-0.970588\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.64823 + 0.0762025i −1.64823 + 0.0762025i −0.850217 0.526432i \(-0.823529\pi\)
−0.798017 + 0.602635i \(0.794118\pi\)
\(858\) 0 0
\(859\) 0 0 −0.895163 0.445738i \(-0.852941\pi\)
0.895163 + 0.445738i \(0.147059\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 0.739009 0.673696i \(-0.235294\pi\)
−0.739009 + 0.673696i \(0.764706\pi\)
\(864\) 0 0
\(865\) 1.33367 + 3.44260i 1.33367 + 3.44260i
\(866\) −0.891477 −0.891477
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −0.581427 + 1.73474i −0.581427 + 1.73474i
\(873\) −0.0899135 + 0.0211475i −0.0899135 + 0.0211475i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 1.74538 0.0806938i 1.74538 0.0806938i 0.850217 0.526432i \(-0.176471\pi\)
0.895163 + 0.445738i \(0.147059\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −0.0590083 + 0.0710610i −0.0590083 + 0.0710610i −0.798017 0.602635i \(-0.794118\pi\)
0.739009 + 0.673696i \(0.235294\pi\)
\(882\) 0.895163 + 0.445738i 0.895163 + 0.445738i
\(883\) 0 0 0.0922684 0.995734i \(-0.470588\pi\)
−0.0922684 + 0.995734i \(0.529412\pi\)
\(884\) −1.89090 + 0.353470i −1.89090 + 0.353470i
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 −0.403921 0.914794i \(-0.632353\pi\)
0.403921 + 0.914794i \(0.367647\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0.666678 + 1.19692i 0.666678 + 1.19692i
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0.434164 0.145517i 0.434164 0.145517i
\(899\) 0 0
\(900\) −2.55183 0.477020i −2.55183 0.477020i
\(901\) −0.380338 + 0.981767i −0.380338 + 0.981767i
\(902\) 0 0
\(903\) 0 0
\(904\) −1.16672 0.799224i −1.16672 0.799224i
\(905\) 0.523978 0.523978
\(906\) 0 0
\(907\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(908\) 0 0
\(909\) −1.34164 1.47171i −1.34164 1.47171i
\(910\) 0 0
\(911\) 0 0 −0.638847 0.769334i \(-0.720588\pi\)
0.638847 + 0.769334i \(0.279412\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.0505009 + 0.177492i 0.0505009 + 0.177492i
\(915\) 0 0
\(916\) −1.03494 + 1.67148i −1.03494 + 1.67148i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.273663 0.961826i \(-0.588235\pi\)
0.273663 + 0.961826i \(0.411765\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −1.25640 0.486734i −1.25640 0.486734i
\(923\) 0 0
\(924\) 0 0
\(925\) −0.666468 1.98847i −0.666468 1.98847i
\(926\) 0 0
\(927\) 0 0
\(928\) 0.947359 0.222817i 0.947359 0.222817i
\(929\) −1.27633 1.53703i −1.27633 1.53703i −0.673696 0.739009i \(-0.735294\pi\)
−0.602635 0.798017i \(-0.705882\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −0.903466 0.903466i −0.903466 0.903466i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 1.79375 0.694903i 1.79375 0.694903i
\(937\) 0.709310 + 1.14558i 0.709310 + 1.14558i 0.982973 + 0.183750i \(0.0588235\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −0.457413 + 1.94480i −0.457413 + 1.94480i −0.183750 + 0.982973i \(0.558824\pi\)
−0.273663 + 0.961826i \(0.588235\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.914794 0.403921i \(-0.867647\pi\)
0.914794 + 0.403921i \(0.132353\pi\)
\(948\) 0 0
\(949\) 0.769523 + 3.27181i 0.769523 + 3.27181i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −0.322039 0.646741i −0.322039 0.646741i 0.673696 0.739009i \(-0.264706\pi\)
−0.995734 + 0.0922684i \(0.970588\pi\)
\(954\) 0.193463 1.03494i 0.193463 1.03494i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 0.798017 0.602635i 0.798017 0.602635i
\(962\) 1.19555 + 0.992772i 1.19555 + 0.992772i
\(963\) 0 0
\(964\) 0.241393 0.134455i 0.241393 0.134455i
\(965\) −0.853543 0.159555i −0.853543 0.159555i
\(966\) 0 0
\(967\) 0 0 0.995734 0.0922684i \(-0.0294118\pi\)
−0.995734 + 0.0922684i \(0.970588\pi\)
\(968\) 0.850217 + 0.526432i 0.850217 + 0.526432i
\(969\) 0 0
\(970\) 0.148922 0.0922085i 0.148922 0.0922085i
\(971\) 0 0 0.798017 0.602635i \(-0.205882\pi\)
−0.798017 + 0.602635i \(0.794118\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0.273663 + 1.96183i 0.273663 + 1.96183i
\(977\) 0.367499i 0.367499i 0.982973 + 0.183750i \(0.0588235\pi\)
−0.982973 + 0.183750i \(0.941176\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −1.87814 0.261989i −1.87814 0.261989i
\(981\) −0.252769 + 1.81204i −0.252769 + 1.81204i
\(982\) 0 0
\(983\) 0 0 0.769334 0.638847i \(-0.220588\pi\)
−0.769334 + 0.638847i \(0.779412\pi\)
\(984\) 0 0
\(985\) −1.46013 + 1.93353i −1.46013 + 1.93353i
\(986\) −0.947359 + 0.222817i −0.947359 + 0.222817i
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 0.486604 0.873622i \(-0.338235\pi\)
−0.486604 + 0.873622i \(0.661765\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −0.184956 + 0.418885i −0.184956 + 0.418885i −0.982973 0.183750i \(-0.941176\pi\)
0.798017 + 0.602635i \(0.205882\pi\)
\(998\) 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 1156.1.o.a.319.1 32
4.3 odd 2 CM 1156.1.o.a.319.1 32
289.106 even 68 inner 1156.1.o.a.395.1 yes 32
1156.395 odd 68 inner 1156.1.o.a.395.1 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1156.1.o.a.319.1 32 1.1 even 1 trivial
1156.1.o.a.319.1 32 4.3 odd 2 CM
1156.1.o.a.395.1 yes 32 289.106 even 68 inner
1156.1.o.a.395.1 yes 32 1156.395 odd 68 inner