Properties

Label 628.1.o.a.67.1
Level $628$
Weight $1$
Character 628.67
Analytic conductor $0.313$
Analytic rank $0$
Dimension $12$
Projective image $D_{13}$
CM discriminant -4
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [628,1,Mod(39,628)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(628, base_ring=CyclotomicField(26))
 
chi = DirichletCharacter(H, H._module([13, 18]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("628.39");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 628 = 2^{2} \cdot 157 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 628.o (of order \(26\), degree \(12\), 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: \(0.313412827934\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\Q(\zeta_{26})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{13}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{13} - \cdots)\)

Embedding invariants

Embedding label 67.1
Root \(0.354605 - 0.935016i\) of defining polynomial
Character \(\chi\) \(=\) 628.67
Dual form 628.1.o.a.75.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.970942 - 0.239316i) q^{2} +(0.885456 + 0.464723i) q^{4} +(0.136945 + 1.12785i) q^{5} +(-0.748511 - 0.663123i) q^{8} +(0.568065 - 0.822984i) q^{9} +O(q^{10})\) \(q+(-0.970942 - 0.239316i) q^{2} +(0.885456 + 0.464723i) q^{4} +(0.136945 + 1.12785i) q^{5} +(-0.748511 - 0.663123i) q^{8} +(0.568065 - 0.822984i) q^{9} +(0.136945 - 1.12785i) q^{10} +0.241073 q^{13} +(0.568065 + 0.822984i) q^{16} +(0.136945 + 1.12785i) q^{17} +(-0.748511 + 0.663123i) q^{18} +(-0.402877 + 1.06230i) q^{20} +(-0.282340 + 0.0695907i) q^{25} +(-0.234068 - 0.0576926i) q^{26} +(-0.234068 + 1.92773i) q^{29} +(-0.354605 - 0.935016i) q^{32} +(0.136945 - 1.12785i) q^{34} +(0.885456 - 0.464723i) q^{36} +(0.0290582 - 0.239316i) q^{37} +(0.645395 - 0.935016i) q^{40} +(0.645395 - 0.935016i) q^{41} +(1.00599 + 0.527986i) q^{45} +(0.568065 - 0.822984i) q^{49} +0.290790 q^{50} +(0.213460 + 0.112032i) q^{52} +(-1.32555 - 1.17433i) q^{53} +(0.688601 - 1.81569i) q^{58} +(0.530851 + 0.470293i) q^{61} +(0.120537 + 0.992709i) q^{64} +(0.0330139 + 0.271894i) q^{65} +(-0.402877 + 1.06230i) q^{68} +(-0.970942 + 0.239316i) q^{72} +(-1.71945 + 0.902438i) q^{73} +(-0.0854858 + 0.225408i) q^{74} +(-0.850405 + 0.753393i) q^{80} +(-0.354605 - 0.935016i) q^{81} +(-0.850405 + 0.753393i) q^{82} +(-1.25328 + 0.308906i) q^{85} +(0.530851 - 1.39974i) q^{89} +(-0.850405 - 0.753393i) q^{90} +(-0.180446 - 1.48611i) q^{97} +(-0.748511 + 0.663123i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - q^{2} - q^{4} - 2 q^{5} - q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - q^{2} - q^{4} - 2 q^{5} - q^{8} - q^{9} - 2 q^{10} - 2 q^{13} - q^{16} - 2 q^{17} - q^{18} - 2 q^{20} - 3 q^{25} - 2 q^{26} - 2 q^{29} - q^{32} - 2 q^{34} - q^{36} + 11 q^{37} + 11 q^{40} + 11 q^{41} - 2 q^{45} - q^{49} + 10 q^{50} - 2 q^{52} - 2 q^{53} - 2 q^{58} - 2 q^{61} - q^{64} - 4 q^{65} - 2 q^{68} - q^{72} - 2 q^{73} - 2 q^{74} - 2 q^{80} - q^{81} - 2 q^{82} - 4 q^{85} - 2 q^{89} - 2 q^{90} - 2 q^{97} - q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/628\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(315\)
\(\chi(n)\) \(e\left(\frac{6}{13}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.970942 0.239316i −0.970942 0.239316i
\(3\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(4\) 0.885456 + 0.464723i 0.885456 + 0.464723i
\(5\) 0.136945 + 1.12785i 0.136945 + 1.12785i 0.885456 + 0.464723i \(0.153846\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(6\) 0 0
\(7\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(8\) −0.748511 0.663123i −0.748511 0.663123i
\(9\) 0.568065 0.822984i 0.568065 0.822984i
\(10\) 0.136945 1.12785i 0.136945 1.12785i
\(11\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(12\) 0 0
\(13\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.568065 + 0.822984i 0.568065 + 0.822984i
\(17\) 0.136945 + 1.12785i 0.136945 + 1.12785i 0.885456 + 0.464723i \(0.153846\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(18\) −0.748511 + 0.663123i −0.748511 + 0.663123i
\(19\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(20\) −0.402877 + 1.06230i −0.402877 + 1.06230i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(24\) 0 0
\(25\) −0.282340 + 0.0695907i −0.282340 + 0.0695907i
\(26\) −0.234068 0.0576926i −0.234068 0.0576926i
\(27\) 0 0
\(28\) 0 0
\(29\) −0.234068 + 1.92773i −0.234068 + 1.92773i 0.120537 + 0.992709i \(0.461538\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(30\) 0 0
\(31\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(32\) −0.354605 0.935016i −0.354605 0.935016i
\(33\) 0 0
\(34\) 0.136945 1.12785i 0.136945 1.12785i
\(35\) 0 0
\(36\) 0.885456 0.464723i 0.885456 0.464723i
\(37\) 0.0290582 0.239316i 0.0290582 0.239316i −0.970942 0.239316i \(-0.923077\pi\)
1.00000 \(0\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.645395 0.935016i 0.645395 0.935016i
\(41\) 0.645395 0.935016i 0.645395 0.935016i −0.354605 0.935016i \(-0.615385\pi\)
1.00000 \(0\)
\(42\) 0 0
\(43\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(44\) 0 0
\(45\) 1.00599 + 0.527986i 1.00599 + 0.527986i
\(46\) 0 0
\(47\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(48\) 0 0
\(49\) 0.568065 0.822984i 0.568065 0.822984i
\(50\) 0.290790 0.290790
\(51\) 0 0
\(52\) 0.213460 + 0.112032i 0.213460 + 0.112032i
\(53\) −1.32555 1.17433i −1.32555 1.17433i −0.970942 0.239316i \(-0.923077\pi\)
−0.354605 0.935016i \(-0.615385\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0.688601 1.81569i 0.688601 1.81569i
\(59\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(60\) 0 0
\(61\) 0.530851 + 0.470293i 0.530851 + 0.470293i 0.885456 0.464723i \(-0.153846\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.120537 + 0.992709i 0.120537 + 0.992709i
\(65\) 0.0330139 + 0.271894i 0.0330139 + 0.271894i
\(66\) 0 0
\(67\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(68\) −0.402877 + 1.06230i −0.402877 + 1.06230i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(72\) −0.970942 + 0.239316i −0.970942 + 0.239316i
\(73\) −1.71945 + 0.902438i −1.71945 + 0.902438i −0.748511 + 0.663123i \(0.769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(74\) −0.0854858 + 0.225408i −0.0854858 + 0.225408i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(80\) −0.850405 + 0.753393i −0.850405 + 0.753393i
\(81\) −0.354605 0.935016i −0.354605 0.935016i
\(82\) −0.850405 + 0.753393i −0.850405 + 0.753393i
\(83\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(84\) 0 0
\(85\) −1.25328 + 0.308906i −1.25328 + 0.308906i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.530851 1.39974i 0.530851 1.39974i −0.354605 0.935016i \(-0.615385\pi\)
0.885456 0.464723i \(-0.153846\pi\)
\(90\) −0.850405 0.753393i −0.850405 0.753393i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.180446 1.48611i −0.180446 1.48611i −0.748511 0.663123i \(-0.769231\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(98\) −0.748511 + 0.663123i −0.748511 + 0.663123i
\(99\) 0 0
\(100\) −0.282340 0.0695907i −0.282340 0.0695907i
\(101\) −0.234068 0.0576926i −0.234068 0.0576926i 0.120537 0.992709i \(-0.461538\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(102\) 0 0
\(103\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(104\) −0.180446 0.159861i −0.180446 0.159861i
\(105\) 0 0
\(106\) 1.00599 + 1.45743i 1.00599 + 1.45743i
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) −1.71945 0.902438i −1.71945 0.902438i −0.970942 0.239316i \(-0.923077\pi\)
−0.748511 0.663123i \(-0.769231\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.71945 0.423807i −1.71945 0.423807i −0.748511 0.663123i \(-0.769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.10312 + 1.59814i −1.10312 + 1.59814i
\(117\) 0.136945 0.198399i 0.136945 0.198399i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.885456 0.464723i 0.885456 0.464723i
\(122\) −0.402877 0.583668i −0.402877 0.583668i
\(123\) 0 0
\(124\) 0 0
\(125\) 0.285724 + 0.753393i 0.285724 + 0.753393i
\(126\) 0 0
\(127\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(128\) 0.120537 0.992709i 0.120537 0.992709i
\(129\) 0 0
\(130\) 0.0330139 0.271894i 0.0330139 0.271894i
\(131\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.645395 0.935016i 0.645395 0.935016i
\(137\) −0.0854858 + 0.225408i −0.0854858 + 0.225408i −0.970942 0.239316i \(-0.923077\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(138\) 0 0
\(139\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 1.00000 1.00000
\(145\) −2.20623 −2.20623
\(146\) 1.88546 0.464723i 1.88546 0.464723i
\(147\) 0 0
\(148\) 0.136945 0.198399i 0.136945 0.198399i
\(149\) −1.32555 1.17433i −1.32555 1.17433i −0.970942 0.239316i \(-0.923077\pi\)
−0.354605 0.935016i \(-0.615385\pi\)
\(150\) 0 0
\(151\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(152\) 0 0
\(153\) 1.00599 + 0.527986i 1.00599 + 0.527986i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1.00000 1.00000
\(158\) 0 0
\(159\) 0 0
\(160\) 1.00599 0.527986i 1.00599 0.527986i
\(161\) 0 0
\(162\) 0.120537 + 0.992709i 0.120537 + 0.992709i
\(163\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(164\) 1.00599 0.527986i 1.00599 0.527986i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(168\) 0 0
\(169\) −0.941884 −0.941884
\(170\) 1.29079 1.29079
\(171\) 0 0
\(172\) 0 0
\(173\) 1.13613 + 1.64597i 1.13613 + 1.64597i 0.568065 + 0.822984i \(0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −0.850405 + 1.23202i −0.850405 + 1.23202i
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0.645395 + 0.935016i 0.645395 + 0.935016i
\(181\) 1.45352 + 0.358261i 1.45352 + 0.358261i 0.885456 0.464723i \(-0.153846\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.273891 0.273891
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(192\) 0 0
\(193\) −1.32555 + 0.695701i −1.32555 + 0.695701i −0.970942 0.239316i \(-0.923077\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(194\) −0.180446 + 1.48611i −0.180446 + 1.48611i
\(195\) 0 0
\(196\) 0.885456 0.464723i 0.885456 0.464723i
\(197\) 1.00599 1.45743i 1.00599 1.45743i 0.120537 0.992709i \(-0.461538\pi\)
0.885456 0.464723i \(-0.153846\pi\)
\(198\) 0 0
\(199\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(200\) 0.257482 + 0.135137i 0.257482 + 0.135137i
\(201\) 0 0
\(202\) 0.213460 + 0.112032i 0.213460 + 0.112032i
\(203\) 0 0
\(204\) 0 0
\(205\) 1.14294 + 0.599860i 1.14294 + 0.599860i
\(206\) 0 0
\(207\) 0 0
\(208\) 0.136945 + 0.198399i 0.136945 + 0.198399i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(212\) −0.627974 1.65583i −0.627974 1.65583i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 1.45352 + 1.28771i 1.45352 + 1.28771i
\(219\) 0 0
\(220\) 0 0
\(221\) 0.0330139 + 0.271894i 0.0330139 + 0.271894i
\(222\) 0 0
\(223\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(224\) 0 0
\(225\) −0.103116 + 0.271894i −0.103116 + 0.271894i
\(226\) 1.56806 + 0.822984i 1.56806 + 0.822984i
\(227\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(228\) 0 0
\(229\) −0.234068 + 0.0576926i −0.234068 + 0.0576926i −0.354605 0.935016i \(-0.615385\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.45352 1.28771i 1.45352 1.28771i
\(233\) −0.627974 1.65583i −0.627974 1.65583i −0.748511 0.663123i \(-0.769231\pi\)
0.120537 0.992709i \(-0.461538\pi\)
\(234\) −0.180446 + 0.159861i −0.180446 + 0.159861i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(240\) 0 0
\(241\) −1.71945 + 0.902438i −1.71945 + 0.902438i −0.748511 + 0.663123i \(0.769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(242\) −0.970942 + 0.239316i −0.970942 + 0.239316i
\(243\) 0 0
\(244\) 0.251489 + 0.663123i 0.251489 + 0.663123i
\(245\) 1.00599 + 0.527986i 1.00599 + 0.527986i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −0.0971229 0.799879i −0.0971229 0.799879i
\(251\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.354605 + 0.935016i −0.354605 + 0.935016i
\(257\) 1.88546 + 0.464723i 1.88546 + 0.464723i 1.00000 \(0\)
0.885456 + 0.464723i \(0.153846\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −0.0971229 + 0.256092i −0.0971229 + 0.256092i
\(261\) 1.45352 + 1.28771i 1.45352 + 1.28771i
\(262\) 0 0
\(263\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(264\) 0 0
\(265\) 1.14294 1.65583i 1.14294 1.65583i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.32555 0.695701i −1.32555 0.695701i −0.354605 0.935016i \(-0.615385\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(270\) 0 0
\(271\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(272\) −0.850405 + 0.753393i −0.850405 + 0.753393i
\(273\) 0 0
\(274\) 0.136945 0.198399i 0.136945 0.198399i
\(275\) 0 0
\(276\) 0 0
\(277\) −0.180446 + 1.48611i −0.180446 + 1.48611i 0.568065 + 0.822984i \(0.307692\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.12054 0.992709i 1.12054 0.992709i 0.120537 0.992709i \(-0.461538\pi\)
1.00000 \(0\)
\(282\) 0 0
\(283\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.970942 0.239316i −0.970942 0.239316i
\(289\) −0.282340 + 0.0695907i −0.282340 + 0.0695907i
\(290\) 2.14212 + 0.527986i 2.14212 + 0.527986i
\(291\) 0 0
\(292\) −1.94188 −1.94188
\(293\) 1.13613 1.64597i 1.13613 1.64597i 0.568065 0.822984i \(-0.307692\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.180446 + 0.159861i −0.180446 + 0.159861i
\(297\) 0 0
\(298\) 1.00599 + 1.45743i 1.00599 + 1.45743i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −0.457721 + 0.663123i −0.457721 + 0.663123i
\(306\) −0.850405 0.753393i −0.850405 0.753393i
\(307\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(312\) 0 0
\(313\) −0.709210 −0.709210 −0.354605 0.935016i \(-0.615385\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(314\) −0.970942 0.239316i −0.970942 0.239316i
\(315\) 0 0
\(316\) 0 0
\(317\) −0.627974 + 0.329586i −0.627974 + 0.329586i −0.748511 0.663123i \(-0.769231\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.10312 + 0.271894i −1.10312 + 0.271894i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.120537 0.992709i 0.120537 0.992709i
\(325\) −0.0680647 + 0.0167765i −0.0680647 + 0.0167765i
\(326\) 0 0
\(327\) 0 0
\(328\) −1.10312 + 0.271894i −1.10312 + 0.271894i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(332\) 0 0
\(333\) −0.180446 0.159861i −0.180446 0.159861i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.136945 + 0.198399i 0.136945 + 0.198399i 0.885456 0.464723i \(-0.153846\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(338\) 0.914514 + 0.225408i 0.914514 + 0.225408i
\(339\) 0 0
\(340\) −1.25328 0.308906i −1.25328 0.308906i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −0.709210 1.87003i −0.709210 1.87003i
\(347\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(348\) 0 0
\(349\) 0.645395 + 0.935016i 0.645395 + 0.935016i 1.00000 \(0\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.56806 0.822984i 1.56806 0.822984i 0.568065 0.822984i \(-0.307692\pi\)
1.00000 \(0\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.12054 0.992709i 1.12054 0.992709i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(360\) −0.402877 1.06230i −0.402877 1.06230i
\(361\) 0.120537 + 0.992709i 0.120537 + 0.992709i
\(362\) −1.32555 0.695701i −1.32555 0.695701i
\(363\) 0 0
\(364\) 0 0
\(365\) −1.25328 1.81569i −1.25328 1.81569i
\(366\) 0 0
\(367\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(368\) 0 0
\(369\) −0.402877 1.06230i −0.402877 1.06230i
\(370\) −0.265932 0.0655463i −0.265932 0.0655463i
\(371\) 0 0
\(372\) 0 0
\(373\) 0.530851 0.470293i 0.530851 0.470293i −0.354605 0.935016i \(-0.615385\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.0564276 + 0.464723i −0.0564276 + 0.464723i
\(378\) 0 0
\(379\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1.45352 0.358261i 1.45352 0.358261i
\(387\) 0 0
\(388\) 0.530851 1.39974i 0.530851 1.39974i
\(389\) −1.32555 + 1.17433i −1.32555 + 1.17433i −0.354605 + 0.935016i \(0.615385\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.970942 + 0.239316i −0.970942 + 0.239316i
\(393\) 0 0
\(394\) −1.32555 + 1.17433i −1.32555 + 1.17433i
\(395\) 0 0
\(396\) 0 0
\(397\) −0.627974 + 1.65583i −0.627974 + 1.65583i 0.120537 + 0.992709i \(0.461538\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.217660 0.192830i −0.217660 0.192830i
\(401\) 0.688601 + 1.81569i 0.688601 + 1.81569i 0.568065 + 0.822984i \(0.307692\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.180446 0.159861i −0.180446 0.159861i
\(405\) 1.00599 0.527986i 1.00599 0.527986i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −0.850405 + 1.23202i −0.850405 + 1.23202i 0.120537 + 0.992709i \(0.461538\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(410\) −0.966170 0.855952i −0.966170 0.855952i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −0.0854858 0.225408i −0.0854858 0.225408i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(420\) 0 0
\(421\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0.213460 + 1.75800i 0.213460 + 1.75800i
\(425\) −0.117153 0.308906i −0.117153 0.308906i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(432\) 0 0
\(433\) −0.402877 0.583668i −0.402877 0.583668i 0.568065 0.822984i \(-0.307692\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.10312 1.59814i −1.10312 1.59814i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(440\) 0 0
\(441\) −0.354605 0.935016i −0.354605 0.935016i
\(442\) 0.0330139 0.271894i 0.0330139 0.271894i
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 1.65139 + 0.407031i 1.65139 + 0.407031i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.241073 0.241073 0.120537 0.992709i \(-0.461538\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(450\) 0.165188 0.239316i 0.165188 0.239316i
\(451\) 0 0
\(452\) −1.32555 1.17433i −1.32555 1.17433i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.45352 0.358261i 1.45352 0.358261i 0.568065 0.822984i \(-0.307692\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(458\) 0.241073 0.241073
\(459\) 0 0
\(460\) 0 0
\(461\) −0.234068 + 1.92773i −0.234068 + 1.92773i 0.120537 + 0.992709i \(0.461538\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(462\) 0 0
\(463\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(464\) −1.71945 + 0.902438i −1.71945 + 0.902438i
\(465\) 0 0
\(466\) 0.213460 + 1.75800i 0.213460 + 1.75800i
\(467\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(468\) 0.213460 0.112032i 0.213460 0.112032i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.71945 + 0.423807i −1.71945 + 0.423807i
\(478\) 0 0
\(479\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(480\) 0 0
\(481\) 0.00700515 0.0576926i 0.00700515 0.0576926i
\(482\) 1.88546 0.464723i 1.88546 0.464723i
\(483\) 0 0
\(484\) 1.00000 1.00000
\(485\) 1.65139 0.407031i 1.65139 0.407031i
\(486\) 0 0
\(487\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(488\) −0.0854858 0.704039i −0.0854858 0.704039i
\(489\) 0 0
\(490\) −0.850405 0.753393i −0.850405 0.753393i
\(491\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(492\) 0 0
\(493\) −2.20623 −2.20623
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) −0.0971229 + 0.799879i −0.0971229 + 0.799879i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(504\) 0 0
\(505\) 0.0330139 0.271894i 0.0330139 0.271894i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −0.402877 0.583668i −0.402877 0.583668i 0.568065 0.822984i \(-0.307692\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.568065 0.822984i 0.568065 0.822984i
\(513\) 0 0
\(514\) −1.71945 0.902438i −1.71945 0.902438i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0.155588 0.225408i 0.155588 0.225408i
\(521\) 1.77091 1.77091 0.885456 0.464723i \(-0.153846\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(522\) −1.10312 1.59814i −1.10312 1.59814i
\(523\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.354605 + 0.935016i −0.354605 + 0.935016i
\(530\) −1.50599 + 1.33419i −1.50599 + 1.33419i
\(531\) 0 0
\(532\) 0 0
\(533\) 0.155588 0.225408i 0.155588 0.225408i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 1.12054 + 0.992709i 1.12054 + 0.992709i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.251489 + 0.663123i 0.251489 + 0.663123i 1.00000 \(0\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 1.00599 0.527986i 1.00599 0.527986i
\(545\) 0.782340 2.06286i 0.782340 2.06286i
\(546\) 0 0
\(547\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(548\) −0.180446 + 0.159861i −0.180446 + 0.159861i
\(549\) 0.688601 0.169725i 0.688601 0.169725i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0.530851 1.39974i 0.530851 1.39974i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.850405 0.753393i −0.850405 0.753393i 0.120537 0.992709i \(-0.461538\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.32555 + 0.695701i −1.32555 + 0.695701i
\(563\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(564\) 0 0
\(565\) 0.242518 1.99732i 0.242518 1.99732i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.49702 + 1.32625i −1.49702 + 1.32625i −0.748511 + 0.663123i \(0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(570\) 0 0
\(571\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.885456 + 0.464723i 0.885456 + 0.464723i
\(577\) 1.13613 + 1.64597i 1.13613 + 1.64597i 0.568065 + 0.822984i \(0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(578\) 0.290790 0.290790
\(579\) 0 0
\(580\) −1.95352 1.02529i −1.95352 1.02529i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 1.88546 + 0.464723i 1.88546 + 0.464723i
\(585\) 0.242518 + 0.127283i 0.242518 + 0.127283i
\(586\) −1.49702 + 1.32625i −1.49702 + 1.32625i
\(587\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.213460 0.112032i 0.213460 0.112032i
\(593\) 1.00599 + 1.45743i 1.00599 + 1.45743i 0.885456 + 0.464723i \(0.153846\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.627974 1.65583i −0.627974 1.65583i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(600\) 0 0
\(601\) 0.213460 1.75800i 0.213460 1.75800i −0.354605 0.935016i \(-0.615385\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.645395 + 0.935016i 0.645395 + 0.935016i
\(606\) 0 0
\(607\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0.603116 0.534314i 0.603116 0.534314i
\(611\) 0 0
\(612\) 0.645395 + 0.935016i 0.645395 + 0.935016i
\(613\) 0.645395 + 0.935016i 0.645395 + 0.935016i 1.00000 \(0\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.688601 0.169725i 0.688601 0.169725i 0.120537 0.992709i \(-0.461538\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(618\) 0 0
\(619\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −1.06806 + 0.560564i −1.06806 + 0.560564i
\(626\) 0.688601 + 0.169725i 0.688601 + 0.169725i
\(627\) 0 0
\(628\) 0.885456 + 0.464723i 0.885456 + 0.464723i
\(629\) 0.273891 0.273891
\(630\) 0 0
\(631\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0.688601 0.169725i 0.688601 0.169725i
\(635\) 0 0
\(636\) 0 0
\(637\) 0.136945 0.198399i 0.136945 0.198399i
\(638\) 0 0
\(639\) 0 0
\(640\) 1.13613 1.13613
\(641\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(642\) 0 0
\(643\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(648\) −0.354605 + 0.935016i −0.354605 + 0.935016i
\(649\) 0 0
\(650\) 0.0701018 0.0701018
\(651\) 0 0
\(652\) 0 0
\(653\) 1.88546 0.464723i 1.88546 0.464723i 0.885456 0.464723i \(-0.153846\pi\)
1.00000 \(0\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.13613 1.13613
\(657\) −0.234068 + 1.92773i −0.234068 + 1.92773i
\(658\) 0 0
\(659\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(660\) 0 0
\(661\) 1.45352 1.28771i 1.45352 1.28771i 0.568065 0.822984i \(-0.307692\pi\)
0.885456 0.464723i \(-0.153846\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0.136945 + 0.198399i 0.136945 + 0.198399i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.56806 + 0.822984i 1.56806 + 0.822984i 1.00000 \(0\)
0.568065 + 0.822984i \(0.307692\pi\)
\(674\) −0.0854858 0.225408i −0.0854858 0.225408i
\(675\) 0 0
\(676\) −0.833997 0.437715i −0.833997 0.437715i
\(677\) 0.136945 0.198399i 0.136945 0.198399i −0.748511 0.663123i \(-0.769231\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 1.14294 + 0.599860i 1.14294 + 0.599860i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(684\) 0 0
\(685\) −0.265932 0.0655463i −0.265932 0.0655463i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −0.319554 0.283100i −0.319554 0.283100i
\(690\) 0 0
\(691\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(692\) 0.241073 + 1.98542i 0.241073 + 1.98542i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 1.14294 + 0.599860i 1.14294 + 0.599860i
\(698\) −0.402877 1.06230i −0.402877 1.06230i
\(699\) 0 0
\(700\) 0 0
\(701\) 0.213460 0.112032i 0.213460 0.112032i −0.354605 0.935016i \(-0.615385\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −1.71945 + 0.423807i −1.71945 + 0.423807i
\(707\) 0 0
\(708\) 0 0
\(709\) −0.402877 1.06230i −0.402877 1.06230i −0.970942 0.239316i \(-0.923077\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −1.32555 + 0.695701i −1.32555 + 0.695701i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(720\) 0.136945 + 1.12785i 0.136945 + 1.12785i
\(721\) 0 0
\(722\) 0.120537 0.992709i 0.120537 0.992709i
\(723\) 0 0
\(724\) 1.12054 + 0.992709i 1.12054 + 0.992709i
\(725\) −0.0680647 0.560564i −0.0680647 0.560564i
\(726\) 0 0
\(727\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(728\) 0 0
\(729\) −0.970942 0.239316i −0.970942 0.239316i
\(730\) 0.782340 + 2.06286i 0.782340 + 2.06286i
\(731\) 0 0
\(732\) 0 0
\(733\) −1.71945 0.902438i −1.71945 0.902438i −0.970942 0.239316i \(-0.923077\pi\)
−0.748511 0.663123i \(-0.769231\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0.136945 + 1.12785i 0.136945 + 1.12785i
\(739\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(740\) 0.242518 + 0.127283i 0.242518 + 0.127283i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(744\) 0 0
\(745\) 1.14294 1.65583i 1.14294 1.65583i
\(746\) −0.627974 + 0.329586i −0.627974 + 0.329586i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0.166003 0.437715i 0.166003 0.437715i
\(755\) 0 0
\(756\) 0 0
\(757\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.10312 0.271894i −1.10312 0.271894i −0.354605 0.935016i \(-0.615385\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −0.457721 + 1.20691i −0.457721 + 1.20691i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −0.402877 0.583668i −0.402877 0.583668i 0.568065 0.822984i \(-0.307692\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.49702 −1.49702
\(773\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −0.850405 + 1.23202i −0.850405 + 1.23202i
\(777\) 0 0
\(778\) 1.56806 0.822984i 1.56806 0.822984i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) 0.136945 + 1.12785i 0.136945 + 1.12785i
\(786\) 0 0
\(787\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(788\) 1.56806 0.822984i 1.56806 0.822984i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0.127974 + 0.113375i 0.127974 + 0.113375i
\(794\) 1.00599 1.45743i 1.00599 1.45743i
\(795\) 0 0
\(796\) 0 0
\(797\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.165188 + 0.239316i 0.165188 + 0.239316i
\(801\) −0.850405 1.23202i −0.850405 1.23202i
\(802\) −0.234068 1.92773i −0.234068 1.92773i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0.136945 + 0.198399i 0.136945 + 0.198399i
\(809\) 1.45352 + 0.358261i 1.45352 + 0.358261i 0.885456 0.464723i \(-0.153846\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(810\) −1.10312 + 0.271894i −1.10312 + 0.271894i
\(811\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 1.12054 0.992709i 1.12054 0.992709i
\(819\) 0 0
\(820\) 0.733252 + 1.06230i 0.733252 + 1.06230i
\(821\) −0.627974 + 0.329586i −0.627974 + 0.329586i −0.748511 0.663123i \(-0.769231\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(822\) 0 0
\(823\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(828\) 0 0
\(829\) 0.688601 + 0.169725i 0.688601 + 0.169725i 0.568065 0.822984i \(-0.307692\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.0290582 + 0.239316i 0.0290582 + 0.239316i
\(833\) 1.00599 + 0.527986i 1.00599 + 0.527986i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(840\) 0 0
\(841\) −2.69039 0.663123i −2.69039 0.663123i
\(842\) 1.88546 + 0.464723i 1.88546 + 0.464723i
\(843\) 0 0
\(844\) 0 0
\(845\) −0.128987 1.06230i −0.128987 1.06230i
\(846\) 0 0
\(847\) 0 0
\(848\) 0.213460 1.75800i 0.213460 1.75800i
\(849\) 0 0
\(850\) 0.0398223 + 0.327967i 0.0398223 + 0.327967i
\(851\) 0 0
\(852\) 0 0
\(853\) −0.0854858 + 0.225408i −0.0854858 + 0.225408i −0.970942 0.239316i \(-0.923077\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.10312 + 0.271894i −1.10312 + 0.271894i −0.748511 0.663123i \(-0.769231\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(858\) 0 0
\(859\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(864\) 0 0
\(865\) −1.70081 + 1.50679i −1.70081 + 1.50679i
\(866\) 0.251489 + 0.663123i 0.251489 + 0.663123i
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0.688601 + 1.81569i 0.688601 + 1.81569i
\(873\) −1.32555 0.695701i −1.32555 0.695701i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −0.234068 1.92773i −0.234068 1.92773i −0.354605 0.935016i \(-0.615385\pi\)
0.120537 0.992709i \(-0.461538\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.45352 + 1.28771i 1.45352 + 1.28771i 0.885456 + 0.464723i \(0.153846\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(882\) 0.120537 + 0.992709i 0.120537 + 0.992709i
\(883\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(884\) −0.0971229 + 0.256092i −0.0971229 + 0.256092i
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 −0.354605 0.935016i \(-0.615385\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −1.50599 0.790406i −1.50599 0.790406i
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −0.234068 0.0576926i −0.234068 0.0576926i
\(899\) 0 0
\(900\) −0.217660 + 0.192830i −0.217660 + 0.192830i
\(901\) 1.14294 1.65583i 1.14294 1.65583i
\(902\) 0 0
\(903\) 0 0
\(904\) 1.00599 + 1.45743i 1.00599 + 1.45743i
\(905\) −0.205010 + 1.68841i −0.205010 + 1.68841i
\(906\) 0 0
\(907\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(908\) 0 0
\(909\) −0.180446 + 0.159861i −0.180446 + 0.159861i
\(910\) 0 0
\(911\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −1.49702 −1.49702
\(915\) 0 0
\(916\) −0.234068 0.0576926i −0.234068 0.0576926i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0.688601 1.81569i 0.688601 1.81569i
\(923\) 0 0
\(924\) 0 0
\(925\) 0.00844984 + 0.0695907i 0.00844984 + 0.0695907i
\(926\) 0 0
\(927\) 0 0
\(928\) 1.88546 0.464723i 1.88546 0.464723i
\(929\) 1.13613 1.13613 0.568065 0.822984i \(-0.307692\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0.213460 1.75800i 0.213460 1.75800i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) −0.234068 + 0.0576926i −0.234068 + 0.0576926i
\(937\) −0.0854858 0.704039i −0.0854858 0.704039i −0.970942 0.239316i \(-0.923077\pi\)
0.885456 0.464723i \(-0.153846\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.94188 −1.94188 −0.970942 0.239316i \(-0.923077\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(948\) 0 0
\(949\) −0.414514 + 0.217554i −0.414514 + 0.217554i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.88546 0.464723i 1.88546 0.464723i 0.885456 0.464723i \(-0.153846\pi\)
1.00000 \(0\)
\(954\) 1.77091 1.77091
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −0.748511 0.663123i −0.748511 0.663123i
\(962\) −0.0206083 + 0.0543397i −0.0206083 + 0.0543397i
\(963\) 0 0
\(964\) −1.94188 −1.94188
\(965\) −0.966170 1.39974i −0.966170 1.39974i
\(966\) 0 0
\(967\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(968\) −0.970942 0.239316i −0.970942 0.239316i
\(969\) 0 0
\(970\) −1.70081 −1.70081
\(971\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −0.0854858 + 0.704039i −0.0854858 + 0.704039i
\(977\) 0.136945 + 0.198399i 0.136945 + 0.198399i 0.885456 0.464723i \(-0.153846\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0.645395 + 0.935016i 0.645395 + 0.935016i
\(981\) −1.71945 + 0.902438i −1.71945 + 0.902438i
\(982\) 0 0
\(983\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(984\) 0 0
\(985\) 1.78152 + 0.935016i 1.78152 + 0.935016i
\(986\) 2.14212 + 0.527986i 2.14212 + 0.527986i
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −0.627974 1.65583i −0.627974 1.65583i −0.748511 0.663123i \(-0.769231\pi\)
0.120537 0.992709i \(-0.461538\pi\)
\(998\) 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 628.1.o.a.67.1 12
4.3 odd 2 CM 628.1.o.a.67.1 12
157.75 even 13 inner 628.1.o.a.75.1 yes 12
628.75 odd 26 inner 628.1.o.a.75.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
628.1.o.a.67.1 12 1.1 even 1 trivial
628.1.o.a.67.1 12 4.3 odd 2 CM
628.1.o.a.75.1 yes 12 157.75 even 13 inner
628.1.o.a.75.1 yes 12 628.75 odd 26 inner