Properties

Label 1169.1.f.c.667.3
Level $1169$
Weight $1$
Character 1169.667
Analytic conductor $0.583$
Analytic rank $0$
Dimension $20$
Projective image $D_{33}$
CM discriminant -167
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1169,1,Mod(333,1169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1169, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1169.333");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1169 = 7 \cdot 167 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1169.f (of order \(6\), 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: \(0.583406999768\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{33})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{33}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{33} - \cdots)\)

Embedding invariants

Embedding label 667.3
Root \(0.981929 - 0.189251i\) of defining polynomial
Character \(\chi\) \(=\) 1169.667
Dual form 1169.1.f.c.333.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.415415 + 0.719520i) q^{2} +(-0.928368 - 1.60798i) q^{3} +(0.154861 + 0.268227i) q^{4} +1.54263 q^{6} +(0.0475819 + 0.998867i) q^{7} -1.08816 q^{8} +(-1.22373 + 2.11957i) q^{9} +O(q^{10})\) \(q+(-0.415415 + 0.719520i) q^{2} +(-0.928368 - 1.60798i) q^{3} +(0.154861 + 0.268227i) q^{4} +1.54263 q^{6} +(0.0475819 + 0.998867i) q^{7} -1.08816 q^{8} +(-1.22373 + 2.11957i) q^{9} +(-0.981929 - 1.70075i) q^{11} +(0.287535 - 0.498026i) q^{12} +(-0.738471 - 0.380708i) q^{14} +(0.297176 - 0.514723i) q^{16} +(-1.01671 - 1.76100i) q^{18} +(0.959493 - 1.66189i) q^{19} +(1.56199 - 1.00383i) q^{21} +1.63163 q^{22} +(1.01021 + 1.74973i) q^{24} +(-0.500000 - 0.866025i) q^{25} +2.68757 q^{27} +(-0.260554 + 0.167448i) q^{28} -1.77767 q^{29} +(-0.580057 - 1.00469i) q^{31} +(-0.297176 - 0.514723i) q^{32} +(-1.82318 + 3.15784i) q^{33} -0.758033 q^{36} +(0.797176 + 1.38075i) q^{38} +(0.0734014 + 1.54088i) q^{42} +(0.304124 - 0.526759i) q^{44} +(-0.235759 + 0.408346i) q^{47} -1.10355 q^{48} +(-0.995472 + 0.0950560i) q^{49} +0.830830 q^{50} +(-1.11646 + 1.93376i) q^{54} +(-0.0517765 - 1.08692i) q^{56} -3.56305 q^{57} +(0.738471 - 1.27907i) q^{58} +(0.142315 - 0.246497i) q^{61} +0.963857 q^{62} +(-2.17540 - 1.12149i) q^{63} +1.08816 q^{64} +(-1.51475 - 2.62363i) q^{66} +(1.33161 - 2.30642i) q^{72} +(-0.928368 + 1.60798i) q^{75} +0.594351 q^{76} +(1.65210 - 1.06174i) q^{77} +(-1.27132 - 2.20198i) q^{81} +(0.511143 + 0.263513i) q^{84} +(1.65033 + 2.85846i) q^{87} +(1.06849 + 1.85068i) q^{88} +(0.786053 - 1.36148i) q^{89} +(-1.07701 + 1.86544i) q^{93} +(-0.195876 - 0.339266i) q^{94} +(-0.551777 + 0.955705i) q^{96} -1.30972 q^{97} +(0.345139 - 0.755750i) q^{98} +4.80648 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 2 q^{2} - q^{3} - 8 q^{4} + 4 q^{6} + q^{7} - 8 q^{8} - 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 2 q^{2} - q^{3} - 8 q^{4} + 4 q^{6} + q^{7} - 8 q^{8} - 11 q^{9} - q^{11} - 3 q^{12} + 2 q^{14} - 6 q^{16} + 2 q^{19} + 2 q^{21} + 4 q^{22} - 4 q^{24} - 10 q^{25} - 2 q^{27} - 6 q^{28} + 2 q^{29} - q^{31} + 6 q^{32} + q^{33} + 22 q^{36} + 4 q^{38} + 20 q^{42} + 8 q^{44} - q^{47} - 12 q^{48} + q^{49} - 4 q^{50} - 20 q^{54} + 4 q^{56} + 4 q^{57} - 2 q^{58} + 2 q^{61} - 18 q^{62} + 8 q^{64} + 2 q^{66} + 11 q^{72} - q^{75} - 12 q^{76} + 2 q^{77} - 12 q^{81} + 19 q^{84} + q^{87} - 4 q^{88} - q^{89} + q^{93} - 2 q^{94} - 6 q^{96} - 4 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1169\mathbb{Z}\right)^\times\).

\(n\) \(673\) \(836\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.415415 + 0.719520i −0.415415 + 0.719520i −0.995472 0.0950560i \(-0.969697\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(3\) −0.928368 1.60798i −0.928368 1.60798i −0.786053 0.618159i \(-0.787879\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(4\) 0.154861 + 0.268227i 0.154861 + 0.268227i
\(5\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(6\) 1.54263 1.54263
\(7\) 0.0475819 + 0.998867i 0.0475819 + 0.998867i
\(8\) −1.08816 −1.08816
\(9\) −1.22373 + 2.11957i −1.22373 + 2.11957i
\(10\) 0 0
\(11\) −0.981929 1.70075i −0.981929 1.70075i −0.654861 0.755750i \(-0.727273\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(12\) 0.287535 0.498026i 0.287535 0.498026i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −0.738471 0.380708i −0.738471 0.380708i
\(15\) 0 0
\(16\) 0.297176 0.514723i 0.297176 0.514723i
\(17\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(18\) −1.01671 1.76100i −1.01671 1.76100i
\(19\) 0.959493 1.66189i 0.959493 1.66189i 0.235759 0.971812i \(-0.424242\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(20\) 0 0
\(21\) 1.56199 1.00383i 1.56199 1.00383i
\(22\) 1.63163 1.63163
\(23\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) 1.01021 + 1.74973i 1.01021 + 1.74973i
\(25\) −0.500000 0.866025i −0.500000 0.866025i
\(26\) 0 0
\(27\) 2.68757 2.68757
\(28\) −0.260554 + 0.167448i −0.260554 + 0.167448i
\(29\) −1.77767 −1.77767 −0.888835 0.458227i \(-0.848485\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(30\) 0 0
\(31\) −0.580057 1.00469i −0.580057 1.00469i −0.995472 0.0950560i \(-0.969697\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(32\) −0.297176 0.514723i −0.297176 0.514723i
\(33\) −1.82318 + 3.15784i −1.82318 + 3.15784i
\(34\) 0 0
\(35\) 0 0
\(36\) −0.758033 −0.758033
\(37\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(38\) 0.797176 + 1.38075i 0.797176 + 1.38075i
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0.0734014 + 1.54088i 0.0734014 + 1.54088i
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0.304124 0.526759i 0.304124 0.526759i
\(45\) 0 0
\(46\) 0 0
\(47\) −0.235759 + 0.408346i −0.235759 + 0.408346i −0.959493 0.281733i \(-0.909091\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(48\) −1.10355 −1.10355
\(49\) −0.995472 + 0.0950560i −0.995472 + 0.0950560i
\(50\) 0.830830 0.830830
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) −1.11646 + 1.93376i −1.11646 + 1.93376i
\(55\) 0 0
\(56\) −0.0517765 1.08692i −0.0517765 1.08692i
\(57\) −3.56305 −3.56305
\(58\) 0.738471 1.27907i 0.738471 1.27907i
\(59\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(60\) 0 0
\(61\) 0.142315 0.246497i 0.142315 0.246497i −0.786053 0.618159i \(-0.787879\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(62\) 0.963857 0.963857
\(63\) −2.17540 1.12149i −2.17540 1.12149i
\(64\) 1.08816 1.08816
\(65\) 0 0
\(66\) −1.51475 2.62363i −1.51475 2.62363i
\(67\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 1.33161 2.30642i 1.33161 2.30642i
\(73\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(74\) 0 0
\(75\) −0.928368 + 1.60798i −0.928368 + 1.60798i
\(76\) 0.594351 0.594351
\(77\) 1.65210 1.06174i 1.65210 1.06174i
\(78\) 0 0
\(79\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(80\) 0 0
\(81\) −1.27132 2.20198i −1.27132 2.20198i
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0.511143 + 0.263513i 0.511143 + 0.263513i
\(85\) 0 0
\(86\) 0 0
\(87\) 1.65033 + 2.85846i 1.65033 + 2.85846i
\(88\) 1.06849 + 1.85068i 1.06849 + 1.85068i
\(89\) 0.786053 1.36148i 0.786053 1.36148i −0.142315 0.989821i \(-0.545455\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −1.07701 + 1.86544i −1.07701 + 1.86544i
\(94\) −0.195876 0.339266i −0.195876 0.339266i
\(95\) 0 0
\(96\) −0.551777 + 0.955705i −0.551777 + 0.955705i
\(97\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(98\) 0.345139 0.755750i 0.345139 0.755750i
\(99\) 4.80648 4.80648
\(100\) 0.154861 0.268227i 0.154861 0.268227i
\(101\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(102\) 0 0
\(103\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.0475819 + 0.0824143i −0.0475819 + 0.0824143i −0.888835 0.458227i \(-0.848485\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(108\) 0.416198 + 0.720877i 0.416198 + 0.720877i
\(109\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.528280 + 0.272347i 0.528280 + 0.272347i
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 1.48014 2.56369i 1.48014 2.56369i
\(115\) 0 0
\(116\) −0.275291 0.476819i −0.275291 0.476819i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1.42837 + 2.47401i −1.42837 + 2.47401i
\(122\) 0.118239 + 0.204797i 0.118239 + 0.204797i
\(123\) 0 0
\(124\) 0.179656 0.311173i 0.179656 0.311173i
\(125\) 0 0
\(126\) 1.71063 1.09936i 1.71063 1.09936i
\(127\) −0.654136 −0.654136 −0.327068 0.945001i \(-0.606061\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(128\) −0.154861 + 0.268227i −0.154861 + 0.268227i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(132\) −1.12936 −1.12936
\(133\) 1.70566 + 0.879330i 1.70566 + 0.879330i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.327068 + 0.566498i 0.327068 + 0.566498i 0.981929 0.189251i \(-0.0606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0.875484 0.875484
\(142\) 0 0
\(143\) 0 0
\(144\) 0.727328 + 1.25977i 0.727328 + 1.25977i
\(145\) 0 0
\(146\) 0 0
\(147\) 1.07701 + 1.51245i 1.07701 + 1.51245i
\(148\) 0 0
\(149\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) −0.771316 1.33596i −0.771316 1.33596i
\(151\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(152\) −1.04408 + 1.80840i −1.04408 + 1.80840i
\(153\) 0 0
\(154\) 0.0776362 + 1.62978i 0.0776362 + 1.62978i
\(155\) 0 0
\(156\) 0 0
\(157\) 0.995472 + 1.72421i 0.995472 + 1.72421i 0.580057 + 0.814576i \(0.303030\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 2.11249 2.11249
\(163\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.00000 1.00000
\(168\) −1.69968 + 1.09232i −1.69968 + 1.09232i
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 2.34833 + 4.06742i 2.34833 + 4.06742i
\(172\) 0 0
\(173\) 0.327068 0.566498i 0.327068 0.566498i −0.654861 0.755750i \(-0.727273\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(174\) −2.74229 −2.74229
\(175\) 0.841254 0.540641i 0.841254 0.540641i
\(176\) −1.16722 −1.16722
\(177\) 0 0
\(178\) 0.653077 + 1.13116i 0.653077 + 1.13116i
\(179\) −0.235759 0.408346i −0.235759 0.408346i 0.723734 0.690079i \(-0.242424\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(180\) 0 0
\(181\) 0.471518 0.471518 0.235759 0.971812i \(-0.424242\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(182\) 0 0
\(183\) −0.528482 −0.528482
\(184\) 0 0
\(185\) 0 0
\(186\) −0.894814 1.54986i −0.894814 1.54986i
\(187\) 0 0
\(188\) −0.146039 −0.146039
\(189\) 0.127880 + 2.68452i 0.127880 + 2.68452i
\(190\) 0 0
\(191\) 0.995472 1.72421i 0.995472 1.72421i 0.415415 0.909632i \(-0.363636\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(192\) −1.01021 1.74973i −1.01021 1.74973i
\(193\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(194\) 0.544078 0.942371i 0.544078 0.942371i
\(195\) 0 0
\(196\) −0.179656 0.252292i −0.179656 0.252292i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −1.99668 + 3.45836i −1.99668 + 3.45836i
\(199\) 0.327068 + 0.566498i 0.327068 + 0.566498i 0.981929 0.189251i \(-0.0606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(200\) 0.544078 + 0.942371i 0.544078 + 0.942371i
\(201\) 0 0
\(202\) 0 0
\(203\) −0.0845850 1.77566i −0.0845850 1.77566i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −3.76861 −3.76861
\(210\) 0 0
\(211\) −1.99094 −1.99094 −0.995472 0.0950560i \(-0.969697\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.0395325 0.0684723i −0.0395325 0.0684723i
\(215\) 0 0
\(216\) −2.92449 −2.92449
\(217\) 0.975950 0.627205i 0.975950 0.627205i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.57211 −1.57211 −0.786053 0.618159i \(-0.787879\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(224\) 0.500000 0.321330i 0.500000 0.321330i
\(225\) 2.44747 2.44747
\(226\) 0 0
\(227\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(228\) −0.551777 0.955705i −0.551777 0.955705i
\(229\) 0.888835 1.53951i 0.888835 1.53951i 0.0475819 0.998867i \(-0.484848\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(230\) 0 0
\(231\) −3.24102 1.67086i −3.24102 1.67086i
\(232\) 1.93438 1.93438
\(233\) −0.580057 + 1.00469i −0.580057 + 1.00469i 0.415415 + 0.909632i \(0.363636\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.85674 1.85674 0.928368 0.371662i \(-0.121212\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(240\) 0 0
\(241\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) −1.18673 2.05548i −1.18673 2.05548i
\(243\) −1.01671 + 1.76100i −1.01671 + 1.76100i
\(244\) 0.0881559 0.0881559
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0.631192 + 1.09326i 0.631192 + 1.09326i
\(249\) 0 0
\(250\) 0 0
\(251\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(252\) −0.0360687 0.757175i −0.0360687 0.757175i
\(253\) 0 0
\(254\) 0.271738 0.470664i 0.271738 0.470664i
\(255\) 0 0
\(256\) 0.415415 + 0.719520i 0.415415 + 0.719520i
\(257\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 2.17540 3.76790i 2.17540 3.76790i
\(262\) 0 0
\(263\) 0.142315 + 0.246497i 0.142315 + 0.246497i 0.928368 0.371662i \(-0.121212\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(264\) 1.98391 3.43623i 1.98391 3.43623i
\(265\) 0 0
\(266\) −1.34125 + 0.861971i −1.34125 + 0.861971i
\(267\) −2.91899 −2.91899
\(268\) 0 0
\(269\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(270\) 0 0
\(271\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −0.543476 −0.543476
\(275\) −0.981929 + 1.70075i −0.981929 + 1.70075i
\(276\) 0 0
\(277\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(278\) 0 0
\(279\) 2.83934 2.83934
\(280\) 0 0
\(281\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(282\) −0.363689 + 0.629928i −0.363689 + 0.629928i
\(283\) −0.981929 1.70075i −0.981929 1.70075i −0.654861 0.755750i \(-0.727273\pi\)
−0.327068 0.945001i \(-0.606061\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.45466 1.45466
\(289\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(290\) 0 0
\(291\) 1.21590 + 2.10601i 1.21590 + 2.10601i
\(292\) 0 0
\(293\) 1.16011 1.16011 0.580057 0.814576i \(-0.303030\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(294\) −1.53565 + 0.146636i −1.53565 + 0.146636i
\(295\) 0 0
\(296\) 0 0
\(297\) −2.63900 4.57088i −2.63900 4.57088i
\(298\) 0 0
\(299\) 0 0
\(300\) −0.575071 −0.575071
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −0.570276 0.987747i −0.570276 0.987747i
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0.540633 + 0.278716i 0.540633 + 0.278716i
\(309\) 0 0
\(310\) 0 0
\(311\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(312\) 0 0
\(313\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) −1.65414 −1.65414
\(315\) 0 0
\(316\) 0 0
\(317\) −0.928368 + 1.60798i −0.928368 + 1.60798i −0.142315 + 0.989821i \(0.545455\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(318\) 0 0
\(319\) 1.74555 + 3.02337i 1.74555 + 3.02337i
\(320\) 0 0
\(321\) 0.176694 0.176694
\(322\) 0 0
\(323\) 0 0
\(324\) 0.393754 0.682002i 0.393754 0.682002i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −0.419102 0.216062i −0.419102 0.216062i
\(330\) 0 0
\(331\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −0.415415 + 0.719520i −0.415415 + 0.719520i
\(335\) 0 0
\(336\) −0.0525092 1.10230i −0.0525092 1.10230i
\(337\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(338\) −0.415415 + 0.719520i −0.415415 + 0.719520i
\(339\) 0 0
\(340\) 0 0
\(341\) −1.13915 + 1.97306i −1.13915 + 1.97306i
\(342\) −3.90212 −3.90212
\(343\) −0.142315 0.989821i −0.142315 0.989821i
\(344\) 0 0
\(345\) 0 0
\(346\) 0.271738 + 0.470664i 0.271738 + 0.470664i
\(347\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(348\) −0.511143 + 0.885326i −0.511143 + 0.885326i
\(349\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0.0395325 + 0.829889i 0.0395325 + 0.829889i
\(351\) 0 0
\(352\) −0.583610 + 1.01084i −0.583610 + 1.01084i
\(353\) −0.0475819 0.0824143i −0.0475819 0.0824143i 0.841254 0.540641i \(-0.181818\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.486915 0.486915
\(357\) 0 0
\(358\) 0.391751 0.391751
\(359\) −0.580057 + 1.00469i −0.580057 + 1.00469i 0.415415 + 0.909632i \(0.363636\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(360\) 0 0
\(361\) −1.34125 2.32312i −1.34125 2.32312i
\(362\) −0.195876 + 0.339266i −0.195876 + 0.339266i
\(363\) 5.30420 5.30420
\(364\) 0 0
\(365\) 0 0
\(366\) 0.219539 0.380253i 0.219539 0.380253i
\(367\) −0.723734 1.25354i −0.723734 1.25354i −0.959493 0.281733i \(-0.909091\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −0.667148 −0.667148
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.256542 0.444345i 0.256542 0.444345i
\(377\) 0 0
\(378\) −1.98469 1.02318i −1.98469 1.02318i
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0.607279 + 1.05184i 0.607279 + 1.05184i
\(382\) 0.827068 + 1.43252i 0.827068 + 1.43252i
\(383\) 0.888835 1.53951i 0.888835 1.53951i 0.0475819 0.998867i \(-0.484848\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(384\) 0.575071 0.575071
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.202824 0.351302i −0.202824 0.351302i
\(389\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.08323 0.103436i 1.08323 0.103436i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0.744335 + 1.28923i 0.744335 + 1.28923i
\(397\) 0.786053 1.36148i 0.786053 1.36148i −0.142315 0.989821i \(-0.545455\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(398\) −0.543476 −0.543476
\(399\) −0.169537 3.55901i −0.169537 3.55901i
\(400\) −0.594351 −0.594351
\(401\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 1.31276 + 0.676774i 1.31276 + 0.676774i
\(407\) 0 0
\(408\) 0 0
\(409\) 0.327068 + 0.566498i 0.327068 + 0.566498i 0.981929 0.189251i \(-0.0606061\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(410\) 0 0
\(411\) 0.607279 1.05184i 0.607279 1.05184i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 1.56554 2.71159i 1.56554 2.71159i
\(419\) −1.99094 −1.99094 −0.995472 0.0950560i \(-0.969697\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(420\) 0 0
\(421\) 0.0951638 0.0951638 0.0475819 0.998867i \(-0.484848\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(422\) 0.827068 1.43252i 0.827068 1.43252i
\(423\) −0.577012 0.999415i −0.577012 0.999415i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0.252989 + 0.130425i 0.252989 + 0.130425i
\(428\) −0.0294743 −0.0294743
\(429\) 0 0
\(430\) 0 0
\(431\) 0.786053 + 1.36148i 0.786053 + 1.36148i 0.928368 + 0.371662i \(0.121212\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(432\) 0.798679 1.38335i 0.798679 1.38335i
\(433\) 1.44747 1.44747 0.723734 0.690079i \(-0.242424\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(434\) 0.0458622 + 0.962766i 0.0458622 + 0.962766i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) 1.01671 2.22630i 1.01671 2.22630i
\(442\) 0 0
\(443\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0.653077 1.13116i 0.653077 1.13116i
\(447\) 0 0
\(448\) 0.0517765 + 1.08692i 0.0517765 + 1.08692i
\(449\) 0.471518 0.471518 0.235759 0.971812i \(-0.424242\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(450\) −1.01671 + 1.76100i −1.01671 + 1.76100i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 3.87715 3.87715
\(457\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(458\) 0.738471 + 1.27907i 0.738471 + 1.27907i
\(459\) 0 0
\(460\) 0 0
\(461\) −1.91899 −1.91899 −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(462\) 2.54859 1.63788i 2.54859 1.63788i
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) −0.528280 + 0.915008i −0.528280 + 0.915008i
\(465\) 0 0
\(466\) −0.481929 0.834725i −0.481929 0.834725i
\(467\) −0.0475819 + 0.0824143i −0.0475819 + 0.0824143i −0.888835 0.458227i \(-0.848485\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 1.84833 3.20140i 1.84833 3.20140i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −1.91899 −1.91899
\(476\) 0 0
\(477\) 0 0
\(478\) −0.771316 + 1.33596i −0.771316 + 1.33596i
\(479\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.884792 −0.884792
\(485\) 0 0
\(486\) −0.844717 1.46309i −0.844717 1.46309i
\(487\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(488\) −0.154861 + 0.268227i −0.154861 + 0.268227i
\(489\) 0 0
\(490\) 0 0
\(491\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.689515 −0.689515
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(500\) 0 0
\(501\) −0.928368 1.60798i −0.928368 1.60798i
\(502\) −0.698939 + 1.21060i −0.698939 + 1.21060i
\(503\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(504\) 2.36717 + 1.22036i 2.36717 + 1.22036i
\(505\) 0 0
\(506\) 0 0
\(507\) −0.928368 1.60798i −0.928368 1.60798i
\(508\) −0.101300 0.175457i −0.101300 0.175457i
\(509\) 0.654861 1.13425i 0.654861 1.13425i −0.327068 0.945001i \(-0.606061\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −1.00000
\(513\) 2.57870 4.46644i 2.57870 4.46644i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0.925994 0.925994
\(518\) 0 0
\(519\) −1.21456 −1.21456
\(520\) 0 0
\(521\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(522\) 1.80738 + 3.13048i 1.80738 + 3.13048i
\(523\) 0.995472 1.72421i 0.995472 1.72421i 0.415415 0.909632i \(-0.363636\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(524\) 0 0
\(525\) −1.65033 0.850806i −1.65033 0.850806i
\(526\) −0.236479 −0.236479
\(527\) 0 0
\(528\) 1.08361 + 1.87687i 1.08361 + 1.87687i
\(529\) −0.500000 0.866025i −0.500000 0.866025i
\(530\) 0 0
\(531\) 0 0
\(532\) 0.0282804 + 0.593678i 0.0282804 + 0.593678i
\(533\) 0 0
\(534\) 1.21259 2.10027i 1.21259 2.10027i
\(535\) 0 0
\(536\) 0 0
\(537\) −0.437742 + 0.758192i −0.437742 + 0.758192i
\(538\) 0 0
\(539\) 1.13915 + 1.59971i 1.13915 + 1.59971i
\(540\) 0 0
\(541\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 0 0
\(543\) −0.437742 0.758192i −0.437742 0.758192i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) −0.101300 + 0.175457i −0.101300 + 0.175457i
\(549\) 0.348311 + 0.603292i 0.348311 + 0.603292i
\(550\) −0.815816 1.41303i −0.815816 1.41303i
\(551\) −1.70566 + 2.95429i −1.70566 + 2.95429i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.654861 + 1.13425i 0.654861 + 1.13425i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(558\) −1.17951 + 2.04296i −1.17951 + 2.04296i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.118239 0.204797i 0.118239 0.204797i
\(563\) −0.723734 1.25354i −0.723734 1.25354i −0.959493 0.281733i \(-0.909091\pi\)
0.235759 0.971812i \(-0.424242\pi\)
\(564\) 0.135578 + 0.234828i 0.135578 + 0.234828i
\(565\) 0 0
\(566\) 1.63163 1.63163
\(567\) 2.13900 1.37465i 2.13900 1.37465i
\(568\) 0 0
\(569\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) 0 0
\(571\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(572\) 0 0
\(573\) −3.69666 −3.69666
\(574\) 0 0
\(575\) 0 0
\(576\) −1.33161 + 2.30642i −1.33161 + 2.30642i
\(577\) −0.415415 0.719520i −0.415415 0.719520i 0.580057 0.814576i \(-0.303030\pi\)
−0.995472 + 0.0950560i \(0.969697\pi\)
\(578\) −0.415415 0.719520i −0.415415 0.719520i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) −2.02042 −2.02042
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −0.481929 + 0.834725i −0.481929 + 0.834725i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) −0.238893 + 0.523103i −0.238893 + 0.523103i
\(589\) −2.22624 −2.22624
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(594\) 4.38512 4.38512
\(595\) 0 0
\(596\) 0 0
\(597\) 0.607279 1.05184i 0.607279 1.05184i
\(598\) 0 0
\(599\) −0.841254 1.45709i −0.841254 1.45709i −0.888835 0.458227i \(-0.848485\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(600\) 1.01021 1.74973i 1.01021 1.74973i
\(601\) 0.0951638 0.0951638 0.0475819 0.998867i \(-0.484848\pi\)
0.0475819 + 0.998867i \(0.484848\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) −1.14055 −1.14055
\(609\) −2.77670 + 1.78447i −2.77670 + 1.78447i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0.995472 + 1.72421i 0.995472 + 1.72421i 0.580057 + 0.814576i \(0.303030\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −1.79774 + 1.15534i −1.79774 + 1.15534i
\(617\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(618\) 0 0
\(619\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −0.830830 −0.830830
\(623\) 1.39734 + 0.720381i 1.39734 + 0.720381i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(626\) 0 0
\(627\) 3.49866 + 6.05986i 3.49866 + 6.05986i
\(628\) −0.308319 + 0.534024i −0.308319 + 0.534024i
\(629\) 0 0
\(630\) 0 0
\(631\) 1.85674 1.85674 0.928368 0.371662i \(-0.121212\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(632\) 0 0
\(633\) 1.84833 + 3.20140i 1.84833 + 3.20140i
\(634\) −0.771316 1.33596i −0.771316 1.33596i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −2.90050 −2.90050
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(642\) −0.0734014 + 0.127135i −0.0734014 + 0.127135i
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(648\) 1.38339 + 2.39610i 1.38339 + 2.39610i
\(649\) 0 0
\(650\) 0 0
\(651\) −1.91457 0.987031i −1.91457 0.987031i
\(652\) 0 0
\(653\) 0.995472 1.72421i 0.995472 1.72421i 0.415415 0.909632i \(-0.363636\pi\)
0.580057 0.814576i \(-0.303030\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0.329562 0.211797i 0.329562 0.211797i
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0.154861 + 0.268227i 0.154861 + 0.268227i
\(669\) 1.45949 + 2.52792i 1.45949 + 2.52792i
\(670\) 0 0
\(671\) −0.558972 −0.558972
\(672\) −0.980877 0.505677i −0.980877 0.505677i
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0.797176 1.38075i 0.797176 1.38075i
\(675\) −1.34378 2.32750i −1.34378 2.32750i
\(676\) 0.154861 + 0.268227i 0.154861 + 0.268227i
\(677\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(678\) 0 0
\(679\) −0.0623191 1.30824i −0.0623191 1.30824i
\(680\) 0 0
\(681\) 0 0
\(682\) −0.946439 1.63928i −0.946439 1.63928i
\(683\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(684\) −0.727328 + 1.25977i −0.727328 + 1.25977i
\(685\) 0 0
\(686\) 0.771316 + 0.308788i 0.771316 + 0.308788i
\(687\) −3.30067 −3.30067
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0.202600 0.202600
\(693\) 0.228701 + 4.80103i 0.228701 + 4.80103i
\(694\) 0 0
\(695\) 0 0
\(696\) −1.79582 3.11045i −1.79582 3.11045i
\(697\) 0 0
\(698\) 0 0
\(699\) 2.15402 2.15402
\(700\) 0.275291 + 0.141923i 0.275291 + 0.141923i
\(701\) −1.57211 −1.57211 −0.786053 0.618159i \(-0.787879\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −1.06849 1.85068i −1.06849 1.85068i
\(705\) 0 0
\(706\) 0.0790650 0.0790650
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −0.855348 + 1.48151i −0.855348 + 1.48151i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0.0730196 0.126474i 0.0730196 0.126474i
\(717\) −1.72373 2.98559i −1.72373 2.98559i
\(718\) −0.481929 0.834725i −0.481929 0.834725i
\(719\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 2.22871 2.22871
\(723\) 0 0
\(724\) 0.0730196 + 0.126474i 0.0730196 + 0.126474i
\(725\) 0.888835 + 1.53951i 0.888835 + 1.53951i
\(726\) −2.20345 + 3.81648i −2.20345 + 3.81648i
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 1.23291 1.23291
\(730\) 0 0
\(731\) 0 0
\(732\) −0.0818411 0.141753i −0.0818411 0.141753i
\(733\) −0.723734 + 1.25354i −0.723734 + 1.25354i 0.235759 + 0.971812i \(0.424242\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(734\) 1.20260 1.20260
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(744\) 1.17196 2.02989i 1.17196 2.02989i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −0.0845850 0.0436066i −0.0845850 0.0436066i
\(750\) 0 0
\(751\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 0.140124 + 0.242701i 0.140124 + 0.242701i
\(753\) −1.56199 2.70544i −1.56199 2.70544i
\(754\) 0 0
\(755\) 0 0
\(756\) −0.700257 + 0.450028i −0.700257 + 0.450028i
\(757\) 1.96386 1.96386 0.981929 0.189251i \(-0.0606061\pi\)
0.981929 + 0.189251i \(0.0606061\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.142315 0.246497i 0.142315 0.246497i −0.786053 0.618159i \(-0.787879\pi\)
0.928368 + 0.371662i \(0.121212\pi\)
\(762\) −1.00909 −1.00909
\(763\) 0 0
\(764\) 0.616638 0.616638
\(765\) 0 0
\(766\) 0.738471 + 1.27907i 0.738471 + 1.27907i
\(767\) 0 0
\(768\) 0.771316 1.33596i 0.771316 1.33596i
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(774\) 0 0
\(775\) −0.580057 + 1.00469i −0.580057 + 1.00469i
\(776\) 1.42518 1.42518
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −4.77761 −4.77761
\(784\) −0.246902 + 0.540641i −0.246902 + 0.540641i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(788\) 0 0
\(789\) 0.264241 0.457679i 0.264241 0.457679i
\(790\) 0 0
\(791\) 0 0
\(792\) −5.23020 −5.23020
\(793\) 0 0
\(794\) 0.653077 + 1.13116i 0.653077 + 1.13116i
\(795\) 0 0
\(796\) −0.101300 + 0.175457i −0.101300 + 0.175457i
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 2.63121 + 1.35648i 2.63121 + 1.35648i
\(799\) 0 0
\(800\) −0.297176 + 0.514723i −0.297176 + 0.514723i
\(801\) 1.92384 + 3.33219i 1.92384 + 3.33219i
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0.654861 + 1.13425i 0.654861 + 1.13425i 0.981929 + 0.189251i \(0.0606061\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0.463180 0.297668i 0.463180 0.297668i
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −0.543476 −0.543476
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(822\) 0.504545 + 0.873898i 0.504545 + 0.873898i
\(823\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(824\) 0 0
\(825\) 3.64636 3.64636
\(826\) 0 0
\(827\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(828\) 0 0
\(829\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) −0.583610 1.01084i −0.583610 1.01084i
\(837\) −1.55894 2.70017i −1.55894 2.70017i
\(838\) 0.827068 1.43252i 0.827068 1.43252i
\(839\) −1.57211 −1.57211 −0.786053 0.618159i \(-0.787879\pi\)
−0.786053 + 0.618159i \(0.787879\pi\)
\(840\) 0 0
\(841\) 2.16011 2.16011
\(842\) −0.0395325 + 0.0684723i −0.0395325 + 0.0684723i
\(843\) 0.264241 + 0.457679i 0.264241 + 0.457679i
\(844\) −0.308319 0.534024i −0.308319 0.534024i
\(845\) 0 0
\(846\) 0.958799 0.958799
\(847\) −2.53917 1.30903i −2.53917 1.30903i
\(848\) 0 0
\(849\) −1.82318 + 3.15784i −1.82318 + 3.15784i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −0.654136 −0.654136 −0.327068 0.945001i \(-0.606061\pi\)
−0.327068 + 0.945001i \(0.606061\pi\)
\(854\) −0.198939 + 0.127850i −0.198939 + 0.127850i
\(855\) 0 0
\(856\) 0.0517765 0.0896796i 0.0517765 0.0896796i
\(857\) 0.959493 + 1.66189i 0.959493 + 1.66189i 0.723734 + 0.690079i \(0.242424\pi\)
0.235759 + 0.971812i \(0.424242\pi\)
\(858\) 0 0
\(859\) −0.841254 + 1.45709i −0.841254 + 1.45709i 0.0475819 + 0.998867i \(0.484848\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −1.30615 −1.30615
\(863\) 0.654861 1.13425i 0.654861 1.13425i −0.327068 0.945001i \(-0.606061\pi\)
0.981929 0.189251i \(-0.0606061\pi\)
\(864\) −0.798679 1.38335i −0.798679 1.38335i
\(865\) 0 0
\(866\) −0.601300 + 1.04148i −0.601300 + 1.04148i
\(867\) 1.85674 1.85674
\(868\) 0.319369 + 0.164646i 0.319369 + 0.164646i
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 1.60275 2.77605i 1.60275 2.77605i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0.959493 1.66189i 0.959493 1.66189i 0.235759 0.971812i \(-0.424242\pi\)
0.723734 0.690079i \(-0.242424\pi\)
\(878\) 0 0
\(879\) −1.07701 1.86544i −1.07701 1.86544i
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 1.17951 + 1.65638i 1.17951 + 1.65638i
\(883\) −1.77767 −1.77767 −0.888835 0.458227i \(-0.848485\pi\)
−0.888835 + 0.458227i \(0.848485\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(888\) 0 0
\(889\) −0.0311250 0.653395i −0.0311250 0.653395i
\(890\) 0 0
\(891\) −2.49668 + 4.32438i −2.49668 + 4.32438i
\(892\) −0.243458 0.421681i −0.243458 0.421681i
\(893\) 0.452418 + 0.783611i 0.452418 + 0.783611i
\(894\) 0 0
\(895\) 0 0
\(896\) −0.275291 0.141923i −0.275291 0.141923i
\(897\) 0 0
\(898\) −0.195876 + 0.339266i −0.195876 + 0.339266i
\(899\) 1.03115 + 1.78600i 1.03115 + 1.78600i
\(900\) 0.379017 + 0.656476i 0.379017 + 0.656476i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −0.928368 1.60798i −0.928368 1.60798i −0.786053 0.618159i \(-0.787879\pi\)
−0.142315 0.989821i \(-0.545455\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.44747 1.44747 0.723734 0.690079i \(-0.242424\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(912\) −1.05885 + 1.83398i −1.05885 + 1.83398i
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0.550583 0.550583
\(917\) 0 0
\(918\) 0 0
\(919\) −0.235759 + 0.408346i −0.235759 + 0.408346i −0.959493 0.281733i \(-0.909091\pi\)
0.723734 + 0.690079i \(0.242424\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0.797176 1.38075i 0.797176 1.38075i
\(923\) 0 0
\(924\) −0.0537370 1.12808i −0.0537370 1.12808i
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0.528280 + 0.915008i 0.528280 + 0.915008i
\(929\) −0.415415 + 0.719520i −0.415415 + 0.719520i −0.995472 0.0950560i \(-0.969697\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(930\) 0 0
\(931\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(932\) −0.359312 −0.359312
\(933\) 0.928368 1.60798i 0.928368 1.60798i
\(934\) −0.0395325 0.0684723i −0.0395325 0.0684723i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(942\) 1.53565 + 2.65982i 1.53565 + 2.65982i
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0.786053 1.36148i 0.786053 1.36148i −0.142315 0.989821i \(-0.545455\pi\)
0.928368 0.371662i \(-0.121212\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0.797176 1.38075i 0.797176 1.38075i
\(951\) 3.44747 3.44747
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0.287535 + 0.498026i 0.287535 + 0.498026i
\(957\) 3.24102 5.61361i 3.24102 5.61361i
\(958\) 0 0
\(959\) −0.550294 + 0.353653i −0.550294 + 0.353653i
\(960\) 0 0
\(961\) −0.172932 + 0.299527i −0.172932 + 0.299527i
\(962\) 0 0
\(963\) −0.116455 0.201706i −0.116455 0.201706i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1.16011 1.16011 0.580057 0.814576i \(-0.303030\pi\)
0.580057 + 0.814576i \(0.303030\pi\)
\(968\) 1.55429 2.69210i 1.55429 2.69210i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(972\) −0.629797 −0.629797
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −0.0845850 0.146505i −0.0845850 0.146505i
\(977\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(978\) 0 0
\(979\) −3.08739 −3.08739
\(980\) 0 0
\(981\) 0 0
\(982\) 0.415415 0.719520i 0.415415 0.719520i
\(983\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0.0416572 + 0.874493i 0.0416572 + 0.874493i
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(992\) −0.344757 + 0.597137i −0.344757 + 0.597137i
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −0.841254 1.45709i −0.841254 1.45709i −0.888835 0.458227i \(-0.848485\pi\)
0.0475819 0.998867i \(-0.484848\pi\)
\(998\) 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 1169.1.f.c.667.3 yes 20
7.4 even 3 inner 1169.1.f.c.333.3 20
167.166 odd 2 CM 1169.1.f.c.667.3 yes 20
1169.333 odd 6 inner 1169.1.f.c.333.3 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1169.1.f.c.333.3 20 7.4 even 3 inner
1169.1.f.c.333.3 20 1169.333 odd 6 inner
1169.1.f.c.667.3 yes 20 1.1 even 1 trivial
1169.1.f.c.667.3 yes 20 167.166 odd 2 CM