Properties

Label 1340.1.bb.b.1019.1
Level $1340$
Weight $1$
Character 1340.1019
Analytic conductor $0.669$
Analytic rank $0$
Dimension $10$
Projective image $D_{11}$
CM discriminant -20
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1340,1,Mod(59,1340)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1340, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 12]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1340.59");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1340.bb (of order \(22\), degree \(10\), 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: \(0.668747116928\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{11}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{11} - \cdots)\)

Embedding invariants

Embedding label 1019.1
Root \(-0.415415 - 0.909632i\) of defining polynomial
Character \(\chi\) \(=\) 1340.1019
Dual form 1340.1.bb.b.359.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.415415 - 0.909632i) q^{2} +(1.10181 + 0.708089i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.186393 - 1.29639i) q^{6} +(-0.698939 - 1.53046i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.297176 + 0.650724i) q^{9} +O(q^{10})\) \(q+(-0.415415 - 0.909632i) q^{2} +(1.10181 + 0.708089i) q^{3} +(-0.654861 + 0.755750i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(0.186393 - 1.29639i) q^{6} +(-0.698939 - 1.53046i) q^{7} +(0.959493 + 0.281733i) q^{8} +(0.297176 + 0.650724i) q^{9} +(-0.841254 + 0.540641i) q^{10} +(-1.25667 + 0.368991i) q^{12} +(-1.10181 + 1.27155i) q^{14} +(0.544078 - 1.19136i) q^{15} +(-0.142315 - 0.989821i) q^{16} +(0.468468 - 0.540641i) q^{18} +(0.841254 + 0.540641i) q^{20} +(0.313607 - 2.18119i) q^{21} +(-1.68251 - 1.08128i) q^{23} +(0.857685 + 0.989821i) q^{24} +(-0.959493 + 0.281733i) q^{25} +(0.0530529 - 0.368991i) q^{27} +(1.61435 + 0.474017i) q^{28} +1.68251 q^{29} -1.30972 q^{30} +(-0.841254 + 0.540641i) q^{32} +(-1.41542 + 0.909632i) q^{35} +(-0.686393 - 0.201543i) q^{36} +(0.142315 - 0.989821i) q^{40} +(1.25667 + 1.45027i) q^{41} +(-2.11435 + 0.620830i) q^{42} +(-0.857685 - 0.989821i) q^{43} +(0.601808 - 0.386758i) q^{45} +(-0.284630 + 1.97964i) q^{46} +(1.61435 + 1.03748i) q^{47} +(0.544078 - 1.19136i) q^{48} +(-1.19894 + 1.38365i) q^{49} +(0.654861 + 0.755750i) q^{50} +(-0.357685 + 0.105026i) q^{54} +(-0.239446 - 1.66538i) q^{56} +(-0.698939 - 1.53046i) q^{58} +(0.544078 + 1.19136i) q^{60} +(0.0405070 - 0.281733i) q^{61} +(0.788201 - 0.909632i) q^{63} +(0.841254 + 0.540641i) q^{64} +(0.654861 - 0.755750i) q^{67} +(-1.08816 - 2.38273i) q^{69} +(1.41542 + 0.909632i) q^{70} +(0.101808 + 0.708089i) q^{72} +(-1.25667 - 0.368991i) q^{75} +(-0.959493 + 0.281733i) q^{80} +(0.788201 - 0.909632i) q^{81} +(0.797176 - 1.74557i) q^{82} +(0.118239 + 0.822373i) q^{83} +(1.44306 + 1.66538i) q^{84} +(-0.544078 + 1.19136i) q^{86} +(1.85380 + 1.19136i) q^{87} +(0.698939 - 0.449181i) q^{89} +(-0.601808 - 0.386758i) q^{90} +(1.91899 - 0.563465i) q^{92} +(0.273100 - 1.89945i) q^{94} -1.30972 q^{96} +(1.75667 + 0.515804i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + q^{2} + 2 q^{3} - q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + q^{2} + 2 q^{3} - q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + q^{8} - 3 q^{9} + q^{10} + 2 q^{12} - 2 q^{14} + 2 q^{15} - q^{16} + 3 q^{18} - q^{20} + 7 q^{21} + 2 q^{23} + 9 q^{24} - q^{25} + 4 q^{27} + 2 q^{28} - 2 q^{29} - 2 q^{30} + q^{32} - 9 q^{35} - 3 q^{36} + q^{40} - 2 q^{41} - 7 q^{42} - 9 q^{43} - 3 q^{45} - 2 q^{46} + 2 q^{47} + 2 q^{48} - 3 q^{49} + q^{50} - 4 q^{54} - 2 q^{56} + 2 q^{58} + 2 q^{60} + 9 q^{61} - 5 q^{63} - q^{64} + q^{67} - 4 q^{69} + 9 q^{70} - 8 q^{72} + 2 q^{75} - q^{80} - 5 q^{81} + 2 q^{82} + 2 q^{83} - 4 q^{84} - 2 q^{86} + 4 q^{87} - 2 q^{89} + 3 q^{90} + 2 q^{92} - 2 q^{94} - 2 q^{96} + 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times\).

\(n\) \(537\) \(671\) \(1141\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{4}{11}\right)\)

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 0.909632i −0.415415 0.909632i
\(3\) 1.10181 + 0.708089i 1.10181 + 0.708089i 0.959493 0.281733i \(-0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(4\) −0.654861 + 0.755750i −0.654861 + 0.755750i
\(5\) −0.142315 0.989821i −0.142315 0.989821i
\(6\) 0.186393 1.29639i 0.186393 1.29639i
\(7\) −0.698939 1.53046i −0.698939 1.53046i −0.841254 0.540641i \(-0.818182\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(8\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(9\) 0.297176 + 0.650724i 0.297176 + 0.650724i
\(10\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(11\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(12\) −1.25667 + 0.368991i −1.25667 + 0.368991i
\(13\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(14\) −1.10181 + 1.27155i −1.10181 + 1.27155i
\(15\) 0.544078 1.19136i 0.544078 1.19136i
\(16\) −0.142315 0.989821i −0.142315 0.989821i
\(17\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(18\) 0.468468 0.540641i 0.468468 0.540641i
\(19\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(20\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(21\) 0.313607 2.18119i 0.313607 2.18119i
\(22\) 0 0
\(23\) −1.68251 1.08128i −1.68251 1.08128i −0.841254 0.540641i \(-0.818182\pi\)
−0.841254 0.540641i \(-0.818182\pi\)
\(24\) 0.857685 + 0.989821i 0.857685 + 0.989821i
\(25\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(26\) 0 0
\(27\) 0.0530529 0.368991i 0.0530529 0.368991i
\(28\) 1.61435 + 0.474017i 1.61435 + 0.474017i
\(29\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(30\) −1.30972 −1.30972
\(31\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(32\) −0.841254 + 0.540641i −0.841254 + 0.540641i
\(33\) 0 0
\(34\) 0 0
\(35\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(36\) −0.686393 0.201543i −0.686393 0.201543i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.142315 0.989821i 0.142315 0.989821i
\(41\) 1.25667 + 1.45027i 1.25667 + 1.45027i 0.841254 + 0.540641i \(0.181818\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(42\) −2.11435 + 0.620830i −2.11435 + 0.620830i
\(43\) −0.857685 0.989821i −0.857685 0.989821i 0.142315 0.989821i \(-0.454545\pi\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0.601808 0.386758i 0.601808 0.386758i
\(46\) −0.284630 + 1.97964i −0.284630 + 1.97964i
\(47\) 1.61435 + 1.03748i 1.61435 + 1.03748i 0.959493 + 0.281733i \(0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(48\) 0.544078 1.19136i 0.544078 1.19136i
\(49\) −1.19894 + 1.38365i −1.19894 + 1.38365i
\(50\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(54\) −0.357685 + 0.105026i −0.357685 + 0.105026i
\(55\) 0 0
\(56\) −0.239446 1.66538i −0.239446 1.66538i
\(57\) 0 0
\(58\) −0.698939 1.53046i −0.698939 1.53046i
\(59\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(60\) 0.544078 + 1.19136i 0.544078 + 1.19136i
\(61\) 0.0405070 0.281733i 0.0405070 0.281733i −0.959493 0.281733i \(-0.909091\pi\)
1.00000 \(0\)
\(62\) 0 0
\(63\) 0.788201 0.909632i 0.788201 0.909632i
\(64\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.654861 0.755750i 0.654861 0.755750i
\(68\) 0 0
\(69\) −1.08816 2.38273i −1.08816 2.38273i
\(70\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(71\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(72\) 0.101808 + 0.708089i 0.101808 + 0.708089i
\(73\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(74\) 0 0
\(75\) −1.25667 0.368991i −1.25667 0.368991i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(80\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(81\) 0.788201 0.909632i 0.788201 0.909632i
\(82\) 0.797176 1.74557i 0.797176 1.74557i
\(83\) 0.118239 + 0.822373i 0.118239 + 0.822373i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(84\) 1.44306 + 1.66538i 1.44306 + 1.66538i
\(85\) 0 0
\(86\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(87\) 1.85380 + 1.19136i 1.85380 + 1.19136i
\(88\) 0 0
\(89\) 0.698939 0.449181i 0.698939 0.449181i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(90\) −0.601808 0.386758i −0.601808 0.386758i
\(91\) 0 0
\(92\) 1.91899 0.563465i 1.91899 0.563465i
\(93\) 0 0
\(94\) 0.273100 1.89945i 0.273100 1.89945i
\(95\) 0 0
\(96\) −1.30972 −1.30972
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 1.75667 + 0.515804i 1.75667 + 0.515804i
\(99\) 0 0
\(100\) 0.415415 0.909632i 0.415415 0.909632i
\(101\) 0.345139 0.755750i 0.345139 0.755750i −0.654861 0.755750i \(-0.727273\pi\)
1.00000 \(0\)
\(102\) 0 0
\(103\) 0.797176 + 0.234072i 0.797176 + 0.234072i 0.654861 0.755750i \(-0.272727\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(104\) 0 0
\(105\) −2.20362 −2.20362
\(106\) 0 0
\(107\) −0.273100 + 1.89945i −0.273100 + 1.89945i 0.142315 + 0.989821i \(0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(108\) 0.244123 + 0.281733i 0.244123 + 0.281733i
\(109\) −0.797176 + 0.234072i −0.797176 + 0.234072i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(113\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(114\) 0 0
\(115\) −0.830830 + 1.81926i −0.830830 + 1.81926i
\(116\) −1.10181 + 1.27155i −1.10181 + 1.27155i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0.857685 0.989821i 0.857685 0.989821i
\(121\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(122\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i
\(123\) 0.357685 + 2.48775i 0.357685 + 2.48775i
\(124\) 0 0
\(125\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(126\) −1.15486 0.339098i −1.15486 0.339098i
\(127\) 0.118239 + 0.258908i 0.118239 + 0.258908i 0.959493 0.281733i \(-0.0909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(128\) 0.142315 0.989821i 0.142315 0.989821i
\(129\) −0.244123 1.69791i −0.244123 1.69791i
\(130\) 0 0
\(131\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.959493 0.281733i −0.959493 0.281733i
\(135\) −0.372786 −0.372786
\(136\) 0 0
\(137\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(138\) −1.71537 + 1.97964i −1.71537 + 1.97964i
\(139\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(140\) 0.239446 1.66538i 0.239446 1.66538i
\(141\) 1.04408 + 2.28621i 1.04408 + 2.28621i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.601808 0.386758i 0.601808 0.386758i
\(145\) −0.239446 1.66538i −0.239446 1.66538i
\(146\) 0 0
\(147\) −2.30075 + 0.675560i −2.30075 + 0.675560i
\(148\) 0 0
\(149\) −0.797176 + 1.74557i −0.797176 + 1.74557i −0.142315 + 0.989821i \(0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(150\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(151\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(161\) −0.478891 + 3.33076i −0.478891 + 3.33076i
\(162\) −1.15486 0.339098i −1.15486 0.339098i
\(163\) 1.30972 1.30972 0.654861 0.755750i \(-0.272727\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(164\) −1.91899 −1.91899
\(165\) 0 0
\(166\) 0.698939 0.449181i 0.698939 0.449181i
\(167\) −0.698939 + 1.53046i −0.698939 + 1.53046i 0.142315 + 0.989821i \(0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(168\) 0.915415 2.00448i 0.915415 2.00448i
\(169\) 0.841254 0.540641i 0.841254 0.540641i
\(170\) 0 0
\(171\) 0 0
\(172\) 1.30972 1.30972
\(173\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(174\) 0.313607 2.18119i 0.313607 2.18119i
\(175\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(176\) 0 0
\(177\) 0 0
\(178\) −0.698939 0.449181i −0.698939 0.449181i
\(179\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(180\) −0.101808 + 0.708089i −0.101808 + 0.708089i
\(181\) −1.10181 0.708089i −1.10181 0.708089i −0.142315 0.989821i \(-0.545455\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(182\) 0 0
\(183\) 0.244123 0.281733i 0.244123 0.281733i
\(184\) −1.30972 1.51150i −1.30972 1.51150i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −1.84125 + 0.540641i −1.84125 + 0.540641i
\(189\) −0.601808 + 0.176707i −0.601808 + 0.176707i
\(190\) 0 0
\(191\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(192\) 0.544078 + 1.19136i 0.544078 + 1.19136i
\(193\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.260554 1.81219i −0.260554 1.81219i
\(197\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(198\) 0 0
\(199\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(200\) −1.00000 −1.00000
\(201\) 1.25667 0.368991i 1.25667 0.368991i
\(202\) −0.830830 −0.830830
\(203\) −1.17597 2.57501i −1.17597 2.57501i
\(204\) 0 0
\(205\) 1.25667 1.45027i 1.25667 1.45027i
\(206\) −0.118239 0.822373i −0.118239 0.822373i
\(207\) 0.203616 1.41618i 0.203616 1.41618i
\(208\) 0 0
\(209\) 0 0
\(210\) 0.915415 + 2.00448i 0.915415 + 2.00448i
\(211\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 1.84125 0.540641i 1.84125 0.540641i
\(215\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(216\) 0.154861 0.339098i 0.154861 0.339098i
\(217\) 0 0
\(218\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0.239446 0.153882i 0.239446 0.153882i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(224\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(225\) −0.468468 0.540641i −0.468468 0.540641i
\(226\) 0 0
\(227\) 0.544078 + 0.627899i 0.544078 + 0.627899i 0.959493 0.281733i \(-0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(228\) 0 0
\(229\) 0.273100 + 0.0801894i 0.273100 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(230\) 2.00000 2.00000
\(231\) 0 0
\(232\) 1.61435 + 0.474017i 1.61435 + 0.474017i
\(233\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(234\) 0 0
\(235\) 0.797176 1.74557i 0.797176 1.74557i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) −1.25667 0.368991i −1.25667 0.368991i
\(241\) −0.118239 + 0.822373i −0.118239 + 0.822373i 0.841254 + 0.540641i \(0.181818\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(242\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(243\) 1.15486 0.339098i 1.15486 0.339098i
\(244\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(245\) 1.54019 + 0.989821i 1.54019 + 0.989821i
\(246\) 2.11435 1.35881i 2.11435 1.35881i
\(247\) 0 0
\(248\) 0 0
\(249\) −0.452036 + 0.989821i −0.452036 + 0.989821i
\(250\) 0.654861 0.755750i 0.654861 0.755750i
\(251\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(252\) 0.171292 + 1.19136i 0.171292 + 1.19136i
\(253\) 0 0
\(254\) 0.186393 0.215109i 0.186393 0.215109i
\(255\) 0 0
\(256\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(257\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(258\) −1.44306 + 0.927399i −1.44306 + 0.927399i
\(259\) 0 0
\(260\) 0 0
\(261\) 0.500000 + 1.09485i 0.500000 + 1.09485i
\(262\) 0 0
\(263\) −0.0405070 0.281733i −0.0405070 0.281733i 0.959493 0.281733i \(-0.0909091\pi\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 1.08816 1.08816
\(268\) 0.142315 + 0.989821i 0.142315 + 0.989821i
\(269\) −1.30972 −1.30972 −0.654861 0.755750i \(-0.727273\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(270\) 0.154861 + 0.339098i 0.154861 + 0.339098i
\(271\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 2.51334 + 0.737982i 2.51334 + 0.737982i
\(277\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(281\) 1.84125 0.540641i 1.84125 0.540641i 0.841254 0.540641i \(-0.181818\pi\)
1.00000 \(0\)
\(282\) 1.64589 1.89945i 1.64589 1.89945i
\(283\) 0.118239 0.258908i 0.118239 0.258908i −0.841254 0.540641i \(-0.818182\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.34125 2.93694i 1.34125 2.93694i
\(288\) −0.601808 0.386758i −0.601808 0.386758i
\(289\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(290\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(294\) 1.57028 + 1.81219i 1.57028 + 1.81219i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 1.91899 1.91899
\(299\) 0 0
\(300\) 1.10181 0.708089i 1.10181 0.708089i
\(301\) −0.915415 + 2.00448i −0.915415 + 2.00448i
\(302\) 0 0
\(303\) 0.915415 0.588302i 0.915415 0.588302i
\(304\) 0 0
\(305\) −0.284630 −0.284630
\(306\) 0 0
\(307\) −1.84125 0.540641i −1.84125 0.540641i −0.841254 0.540641i \(-0.818182\pi\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0.712591 + 0.822373i 0.712591 + 0.822373i
\(310\) 0 0
\(311\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(312\) 0 0
\(313\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(314\) 0 0
\(315\) −1.01255 0.650724i −1.01255 0.650724i
\(316\) 0 0
\(317\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.415415 0.909632i 0.415415 0.909632i
\(321\) −1.64589 + 1.89945i −1.64589 + 1.89945i
\(322\) 3.22871 0.948034i 3.22871 0.948034i
\(323\) 0 0
\(324\) 0.171292 + 1.19136i 0.171292 + 1.19136i
\(325\) 0 0
\(326\) −0.544078 1.19136i −0.544078 1.19136i
\(327\) −1.04408 0.306569i −1.04408 0.306569i
\(328\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(329\) 0.459493 3.19584i 0.459493 3.19584i
\(330\) 0 0
\(331\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(332\) −0.698939 0.449181i −0.698939 0.449181i
\(333\) 0 0
\(334\) 1.68251 1.68251
\(335\) −0.841254 0.540641i −0.841254 0.540641i
\(336\) −2.20362 −2.20362
\(337\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(338\) −0.841254 0.540641i −0.841254 0.540641i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.34125 + 0.393828i 1.34125 + 0.393828i
\(344\) −0.544078 1.19136i −0.544078 1.19136i
\(345\) −2.20362 + 1.41618i −2.20362 + 1.41618i
\(346\) 0 0
\(347\) −0.273100 + 0.0801894i −0.273100 + 0.0801894i −0.415415 0.909632i \(-0.636364\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(348\) −2.11435 + 0.620830i −2.11435 + 0.620830i
\(349\) 0.857685 0.989821i 0.857685 0.989821i −0.142315 0.989821i \(-0.545455\pi\)
1.00000 \(0\)
\(350\) 0.698939 1.53046i 0.698939 1.53046i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(360\) 0.686393 0.201543i 0.686393 0.201543i
\(361\) −0.654861 0.755750i −0.654861 0.755750i
\(362\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(363\) −1.25667 0.368991i −1.25667 0.368991i
\(364\) 0 0
\(365\) 0 0
\(366\) −0.357685 0.105026i −0.357685 0.105026i
\(367\) −0.698939 + 0.449181i −0.698939 + 0.449181i −0.841254 0.540641i \(-0.818182\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(368\) −0.830830 + 1.81926i −0.830830 + 1.81926i
\(369\) −0.570276 + 1.24873i −0.570276 + 1.24873i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) −0.186393 + 1.29639i −0.186393 + 1.29639i
\(376\) 1.25667 + 1.45027i 1.25667 + 1.45027i
\(377\) 0 0
\(378\) 0.410738 + 0.474017i 0.410738 + 0.474017i
\(379\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(380\) 0 0
\(381\) −0.0530529 + 0.368991i −0.0530529 + 0.368991i
\(382\) 0 0
\(383\) 0.797176 1.74557i 0.797176 1.74557i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(384\) 0.857685 0.989821i 0.857685 0.989821i
\(385\) 0 0
\(386\) 0 0
\(387\) 0.389217 0.852267i 0.389217 0.852267i
\(388\) 0 0
\(389\) −0.797176 + 0.234072i −0.797176 + 0.234072i −0.654861 0.755750i \(-0.727273\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −1.54019 + 0.989821i −1.54019 + 0.989821i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(401\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(402\) −0.857685 0.989821i −0.857685 0.989821i
\(403\) 0 0
\(404\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(405\) −1.01255 0.650724i −1.01255 0.650724i
\(406\) −1.85380 + 2.13940i −1.85380 + 2.13940i
\(407\) 0 0
\(408\) 0 0
\(409\) −0.544078 1.19136i −0.544078 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(410\) −1.84125 0.540641i −1.84125 0.540641i
\(411\) 0 0
\(412\) −0.698939 + 0.449181i −0.698939 + 0.449181i
\(413\) 0 0
\(414\) −1.37279 + 0.403086i −1.37279 + 0.403086i
\(415\) 0.797176 0.234072i 0.797176 0.234072i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(420\) 1.44306 1.66538i 1.44306 1.66538i
\(421\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(422\) 0 0
\(423\) −0.195368 + 1.35881i −0.195368 + 1.35881i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.459493 + 0.134919i −0.459493 + 0.134919i
\(428\) −1.25667 1.45027i −1.25667 1.45027i
\(429\) 0 0
\(430\) 1.25667 + 0.368991i 1.25667 + 0.368991i
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) −0.372786 −0.372786
\(433\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(434\) 0 0
\(435\) 0.915415 2.00448i 0.915415 2.00448i
\(436\) 0.345139 0.755750i 0.345139 0.755750i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) −1.25667 0.368991i −1.25667 0.368991i
\(442\) 0 0
\(443\) 1.10181 + 1.27155i 1.10181 + 1.27155i 0.959493 + 0.281733i \(0.0909091\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(444\) 0 0
\(445\) −0.544078 0.627899i −0.544078 0.627899i
\(446\) −0.239446 0.153882i −0.239446 0.153882i
\(447\) −2.11435 + 1.35881i −2.11435 + 1.35881i
\(448\) 0.239446 1.66538i 0.239446 1.66538i
\(449\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(450\) −0.297176 + 0.650724i −0.297176 + 0.650724i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.345139 0.755750i 0.345139 0.755750i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(458\) −0.0405070 0.281733i −0.0405070 0.281733i
\(459\) 0 0
\(460\) −0.830830 1.81926i −0.830830 1.81926i
\(461\) −0.797176 0.234072i −0.797176 0.234072i −0.142315 0.989821i \(-0.545455\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(462\) 0 0
\(463\) −0.186393 + 1.29639i −0.186393 + 1.29639i 0.654861 + 0.755750i \(0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(464\) −0.239446 1.66538i −0.239446 1.66538i
\(465\) 0 0
\(466\) 0 0
\(467\) 0.118239 + 0.258908i 0.118239 + 0.258908i 0.959493 0.281733i \(-0.0909091\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(468\) 0 0
\(469\) −1.61435 0.474017i −1.61435 0.474017i
\(470\) −1.91899 −1.91899
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(480\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(481\) 0 0
\(482\) 0.797176 0.234072i 0.797176 0.234072i
\(483\) −2.88612 + 3.33076i −2.88612 + 3.33076i
\(484\) 0.415415 0.909632i 0.415415 0.909632i
\(485\) 0 0
\(486\) −0.788201 0.909632i −0.788201 0.909632i
\(487\) 0.544078 0.627899i 0.544078 0.627899i −0.415415 0.909632i \(-0.636364\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(488\) 0.118239 0.258908i 0.118239 0.258908i
\(489\) 1.44306 + 0.927399i 1.44306 + 0.927399i
\(490\) 0.260554 1.81219i 0.260554 1.81219i
\(491\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(492\) −2.11435 1.35881i −2.11435 1.35881i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 1.08816 1.08816
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) −0.959493 0.281733i −0.959493 0.281733i
\(501\) −1.85380 + 1.19136i −1.85380 + 1.19136i
\(502\) 0 0
\(503\) 0.797176 1.74557i 0.797176 1.74557i 0.142315 0.989821i \(-0.454545\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(504\) 1.01255 0.650724i 1.01255 0.650724i
\(505\) −0.797176 0.234072i −0.797176 0.234072i
\(506\) 0 0
\(507\) 1.30972 1.30972
\(508\) −0.273100 0.0801894i −0.273100 0.0801894i
\(509\) −0.239446 + 1.66538i −0.239446 + 1.66538i 0.415415 + 0.909632i \(0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.654861 + 0.755750i 0.654861 + 0.755750i
\(513\) 0 0
\(514\) 0 0
\(515\) 0.118239 0.822373i 0.118239 0.822373i
\(516\) 1.44306 + 0.927399i 1.44306 + 0.927399i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0.830830 1.81926i 0.830830 1.81926i 0.415415 0.909632i \(-0.363636\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(522\) 0.788201 0.909632i 0.788201 0.909632i
\(523\) −1.25667 + 0.368991i −1.25667 + 0.368991i −0.841254 0.540641i \(-0.818182\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(524\) 0 0
\(525\) 0.313607 + 2.18119i 0.313607 + 2.18119i
\(526\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(527\) 0 0
\(528\) 0 0
\(529\) 1.24625 + 2.72890i 1.24625 + 2.72890i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.452036 0.989821i −0.452036 0.989821i
\(535\) 1.91899 1.91899
\(536\) 0.841254 0.540641i 0.841254 0.540641i
\(537\) 0 0
\(538\) 0.544078 + 1.19136i 0.544078 + 1.19136i
\(539\) 0 0
\(540\) 0.244123 0.281733i 0.244123 0.281733i
\(541\) 0.186393 + 1.29639i 0.186393 + 1.29639i 0.841254 + 0.540641i \(0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(542\) 0 0
\(543\) −0.712591 1.56036i −0.712591 1.56036i
\(544\) 0 0
\(545\) 0.345139 + 0.755750i 0.345139 + 0.755750i
\(546\) 0 0
\(547\) −0.0405070 0.281733i −0.0405070 0.281733i 0.959493 0.281733i \(-0.0909091\pi\)
−1.00000 \(\pi\)
\(548\) 0 0
\(549\) 0.195368 0.0573652i 0.195368 0.0573652i
\(550\) 0 0
\(551\) 0 0
\(552\) −0.372786 2.59278i −0.372786 2.59278i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(561\) 0 0
\(562\) −1.25667 1.45027i −1.25667 1.45027i
\(563\) −0.186393 + 1.29639i −0.186393 + 1.29639i 0.654861 + 0.755750i \(0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(564\) −2.41153 0.708089i −2.41153 0.708089i
\(565\) 0 0
\(566\) −0.284630 −0.284630
\(567\) −1.94306 0.570534i −1.94306 0.570534i
\(568\) 0 0
\(569\) 0.698939 1.53046i 0.698939 1.53046i −0.142315 0.989821i \(-0.545455\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(570\) 0 0
\(571\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −3.22871 −3.22871
\(575\) 1.91899 + 0.563465i 1.91899 + 0.563465i
\(576\) −0.101808 + 0.708089i −0.101808 + 0.708089i
\(577\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(578\) 0.959493 0.281733i 0.959493 0.281733i
\(579\) 0 0
\(580\) 1.41542 + 0.909632i 1.41542 + 0.909632i
\(581\) 1.17597 0.755750i 1.17597 0.755750i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −0.273100 1.89945i −0.273100 1.89945i −0.415415 0.909632i \(-0.636364\pi\)
0.142315 0.989821i \(-0.454545\pi\)
\(588\) 0.996114 2.18119i 0.996114 2.18119i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.797176 1.74557i −0.797176 1.74557i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(600\) −1.10181 0.708089i −1.10181 0.708089i
\(601\) −0.544078 1.19136i −0.544078 1.19136i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 0.909632i \(-0.363636\pi\)
\(602\) 2.20362 2.20362
\(603\) 0.686393 + 0.201543i 0.686393 + 0.201543i
\(604\) 0 0
\(605\) 0.415415 + 0.909632i 0.415415 + 0.909632i
\(606\) −0.915415 0.588302i −0.915415 0.588302i
\(607\) −1.25667 + 1.45027i −1.25667 + 1.45027i −0.415415 + 0.909632i \(0.636364\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(608\) 0 0
\(609\) 0.527646 3.66986i 0.527646 3.66986i
\(610\) 0.118239 + 0.258908i 0.118239 + 0.258908i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(614\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(615\) 2.41153 0.708089i 2.41153 0.708089i
\(616\) 0 0
\(617\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(618\) 0.452036 0.989821i 0.452036 0.989821i
\(619\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(620\) 0 0
\(621\) −0.488245 + 0.563465i −0.488245 + 0.563465i
\(622\) 0 0
\(623\) −1.17597 0.755750i −1.17597 0.755750i
\(624\) 0 0
\(625\) 0.841254 0.540641i 0.841254 0.540641i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −0.171292 + 1.19136i −0.171292 + 1.19136i
\(631\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0.239446 0.153882i 0.239446 0.153882i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −1.00000 −1.00000
\(641\) −0.284630 −0.284630 −0.142315 0.989821i \(-0.545455\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(642\) 2.41153 + 0.708089i 2.41153 + 0.708089i
\(643\) 0.239446 1.66538i 0.239446 1.66538i −0.415415 0.909632i \(-0.636364\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(644\) −2.20362 2.54311i −2.20362 2.54311i
\(645\) −1.64589 + 0.483276i −1.64589 + 0.483276i
\(646\) 0 0
\(647\) 1.61435 + 1.03748i 1.61435 + 1.03748i 0.959493 + 0.281733i \(0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(648\) 1.01255 0.650724i 1.01255 0.650724i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(653\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(654\) 0.154861 + 1.07708i 0.154861 + 1.07708i
\(655\) 0 0
\(656\) 1.25667 1.45027i 1.25667 1.45027i
\(657\) 0 0
\(658\) −3.09792 + 0.909632i −3.09792 + 0.909632i
\(659\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(660\) 0 0
\(661\) 0.698939 + 1.53046i 0.698939 + 1.53046i 0.841254 + 0.540641i \(0.181818\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) −0.118239 + 0.822373i −0.118239 + 0.822373i
\(665\) 0 0
\(666\) 0 0
\(667\) −2.83083 1.81926i −2.83083 1.81926i
\(668\) −0.698939 1.53046i −0.698939 1.53046i
\(669\) 0.372786 0.372786
\(670\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(671\) 0 0
\(672\) 0.915415 + 2.00448i 0.915415 + 2.00448i
\(673\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(674\) 0 0
\(675\) 0.0530529 + 0.368991i 0.0530529 + 0.368991i
\(676\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(677\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.154861 + 1.07708i 0.154861 + 1.07708i
\(682\) 0 0
\(683\) −1.84125 + 0.540641i −1.84125 + 0.540641i −0.841254 + 0.540641i \(0.818182\pi\)
−1.00000 \(1.00000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.198939 1.38365i −0.198939 1.38365i
\(687\) 0.244123 + 0.281733i 0.244123 + 0.281733i
\(688\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(689\) 0 0
\(690\) 2.20362 + 1.41618i 2.20362 + 1.41618i
\(691\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0.186393 + 0.215109i 0.186393 + 0.215109i
\(695\) 0 0
\(696\) 1.44306 + 1.66538i 1.44306 + 1.66538i
\(697\) 0 0
\(698\) −1.25667 0.368991i −1.25667 0.368991i
\(699\) 0 0
\(700\) −1.68251 −1.68251
\(701\) −1.91899 0.563465i −1.91899 0.563465i −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 0.281733i \(-0.909091\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 2.11435 1.35881i 2.11435 1.35881i
\(706\) 0 0
\(707\) −1.39788 −1.39788
\(708\) 0 0
\(709\) −1.91899 0.563465i −1.91899 0.563465i −0.959493 0.281733i \(-0.909091\pi\)
−0.959493 0.281733i \(-0.909091\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.797176 0.234072i 0.797176 0.234072i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(720\) −0.468468 0.540641i −0.468468 0.540641i
\(721\) −0.198939 1.38365i −0.198939 1.38365i
\(722\) −0.415415 + 0.909632i −0.415415 + 0.909632i
\(723\) −0.712591 + 0.822373i −0.712591 + 0.822373i
\(724\) 1.25667 0.368991i 1.25667 0.368991i
\(725\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(726\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(727\) 1.61435 1.03748i 1.61435 1.03748i 0.654861 0.755750i \(-0.272727\pi\)
0.959493 0.281733i \(-0.0909091\pi\)
\(728\) 0 0
\(729\) 0.357685 + 0.105026i 0.357685 + 0.105026i
\(730\) 0 0
\(731\) 0 0
\(732\) 0.0530529 + 0.368991i 0.0530529 + 0.368991i
\(733\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(734\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(735\) 0.996114 + 2.18119i 0.996114 + 2.18119i
\(736\) 2.00000 2.00000
\(737\) 0 0
\(738\) 1.37279 1.37279
\(739\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.186393 + 1.29639i −0.186393 + 1.29639i 0.654861 + 0.755750i \(0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(744\) 0 0
\(745\) 1.84125 + 0.540641i 1.84125 + 0.540641i
\(746\) 0 0
\(747\) −0.500000 + 0.321330i −0.500000 + 0.321330i
\(748\) 0 0
\(749\) 3.09792 0.909632i 3.09792 0.909632i
\(750\) 1.25667 0.368991i 1.25667 0.368991i
\(751\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(752\) 0.797176 1.74557i 0.797176 1.74557i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0.260554 0.570534i 0.260554 0.570534i
\(757\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.857685 + 0.989821i 0.857685 + 0.989821i 1.00000 \(0\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(762\) 0.357685 0.105026i 0.357685 0.105026i
\(763\) 0.915415 + 1.05645i 0.915415 + 1.05645i
\(764\) 0 0
\(765\) 0 0
\(766\) −1.91899 −1.91899
\(767\) 0 0
\(768\) −1.25667 0.368991i −1.25667 0.368991i
\(769\) −1.10181 + 0.708089i −1.10181 + 0.708089i −0.959493 0.281733i \(-0.909091\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(774\) −0.936936 −0.936936
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.544078 + 0.627899i 0.544078 + 0.627899i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0.0892619 0.620830i 0.0892619 0.620830i
\(784\) 1.54019 + 0.989821i 1.54019 + 0.989821i
\(785\) 0 0
\(786\) 0 0
\(787\) −0.186393 0.215109i −0.186393 0.215109i 0.654861 0.755750i \(-0.272727\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(788\) 0 0
\(789\) 0.154861 0.339098i 0.154861 0.339098i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.654861 0.755750i 0.654861 0.755750i
\(801\) 0.500000 + 0.321330i 0.500000 + 0.321330i
\(802\) −0.698939 1.53046i −0.698939 1.53046i
\(803\) 0 0
\(804\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(805\) 3.36501 3.36501
\(806\) 0 0
\(807\) −1.44306 0.927399i −1.44306 0.927399i
\(808\) 0.544078 0.627899i 0.544078 0.627899i
\(809\) 0.0405070 + 0.281733i 0.0405070 + 0.281733i 1.00000 \(0\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(810\) −0.171292 + 1.19136i −0.171292 + 1.19136i
\(811\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(812\) 2.71616 + 0.797537i 2.71616 + 0.797537i
\(813\) 0 0
\(814\) 0 0
\(815\) −0.186393 1.29639i −0.186393 1.29639i
\(816\) 0 0
\(817\) 0 0
\(818\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(819\) 0 0
\(820\) 0.273100 + 1.89945i 0.273100 + 1.89945i
\(821\) 0.186393 + 0.215109i 0.186393 + 0.215109i 0.841254 0.540641i \(-0.181818\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(822\) 0 0
\(823\) −0.698939 + 1.53046i −0.698939 + 1.53046i 0.142315 + 0.989821i \(0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(824\) 0.698939 + 0.449181i 0.698939 + 0.449181i
\(825\) 0 0
\(826\) 0 0
\(827\) 1.61435 + 1.03748i 1.61435 + 1.03748i 0.959493 + 0.281733i \(0.0909091\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(828\) 0.936936 + 1.08128i 0.936936 + 1.08128i
\(829\) 0.273100 0.0801894i 0.273100 0.0801894i −0.142315 0.989821i \(-0.545455\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(830\) −0.544078 0.627899i −0.544078 0.627899i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 1.61435 + 0.474017i 1.61435 + 0.474017i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(840\) −2.11435 0.620830i −2.11435 0.620830i
\(841\) 1.83083 1.83083
\(842\) −1.68251 −1.68251
\(843\) 2.41153 + 0.708089i 2.41153 + 0.708089i
\(844\) 0 0
\(845\) −0.654861 0.755750i −0.654861 0.755750i
\(846\) 1.31718 0.386758i 1.31718 0.386758i
\(847\) 1.10181 + 1.27155i 1.10181 + 1.27155i
\(848\) 0 0
\(849\) 0.313607 0.201543i 0.313607 0.201543i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(854\) 0.313607 + 0.361922i 0.313607 + 0.361922i
\(855\) 0 0
\(856\) −0.797176 + 1.74557i −0.797176 + 1.74557i
\(857\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(858\) 0 0
\(859\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(860\) −0.186393 1.29639i −0.186393 1.29639i
\(861\) 3.55742 2.28621i 3.55742 2.28621i
\(862\) 0 0
\(863\) −0.273100 0.0801894i −0.273100 0.0801894i 0.142315 0.989821i \(-0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(864\) 0.154861 + 0.339098i 0.154861 + 0.339098i
\(865\) 0 0
\(866\) 0 0
\(867\) −0.857685 + 0.989821i −0.857685 + 0.989821i
\(868\) 0 0
\(869\) 0 0
\(870\) −2.20362 −2.20362
\(871\) 0 0
\(872\) −0.830830 −0.830830
\(873\) 0 0
\(874\) 0 0
\(875\) 1.10181 1.27155i 1.10181 1.27155i
\(876\) 0 0
\(877\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.68251 1.08128i 1.68251 1.08128i 0.841254 0.540641i \(-0.181818\pi\)
0.841254 0.540641i \(-0.181818\pi\)
\(882\) 0.186393 + 1.29639i 0.186393 + 1.29639i
\(883\) −1.84125 + 0.540641i −1.84125 + 0.540641i −0.841254 + 0.540641i \(0.818182\pi\)
−1.00000 \(1.00000\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0.698939 1.53046i 0.698939 1.53046i
\(887\) 0.239446 + 1.66538i 0.239446 + 1.66538i 0.654861 + 0.755750i \(0.272727\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(888\) 0 0
\(889\) 0.313607 0.361922i 0.313607 0.361922i
\(890\) −0.345139 + 0.755750i −0.345139 + 0.755750i
\(891\) 0 0
\(892\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(893\) 0 0
\(894\) 2.11435 + 1.35881i 2.11435 + 1.35881i
\(895\) 0 0
\(896\) −1.61435 + 0.474017i −1.61435 + 0.474017i
\(897\) 0 0
\(898\) −0.273100 + 1.89945i −0.273100 + 1.89945i
\(899\) 0 0
\(900\) 0.715370 0.715370
\(901\) 0 0
\(902\) 0 0
\(903\) −2.42796 + 1.56036i −2.42796 + 1.56036i
\(904\) 0 0
\(905\) −0.544078 + 1.19136i −0.544078 + 1.19136i
\(906\) 0 0
\(907\) −0.273100 0.0801894i −0.273100 0.0801894i 0.142315 0.989821i \(-0.454545\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(908\) −0.830830 −0.830830
\(909\) 0.594351 0.594351
\(910\) 0 0
\(911\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) −0.313607 0.201543i −0.313607 0.201543i
\(916\) −0.239446 + 0.153882i −0.239446 + 0.153882i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(920\) −1.30972 + 1.51150i −1.30972 + 1.51150i
\(921\) −1.64589 1.89945i −1.64589 1.89945i
\(922\) 0.118239 + 0.822373i 0.118239 + 0.822373i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 1.25667 0.368991i 1.25667 0.368991i
\(927\) 0.0845850 + 0.588302i 0.0845850 + 0.588302i
\(928\) −1.41542 + 0.909632i −1.41542 + 0.909632i
\(929\) 0.345139 + 0.755750i 0.345139 + 0.755750i 1.00000 \(0\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0.186393 0.215109i 0.186393 0.215109i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0.239446 + 1.66538i 0.239446 + 1.66538i
\(939\) 0 0
\(940\) 0.797176 + 1.74557i 0.797176 + 1.74557i
\(941\) −1.61435 1.03748i −1.61435 1.03748i −0.959493 0.281733i \(-0.909091\pi\)
−0.654861 0.755750i \(-0.727273\pi\)
\(942\) 0 0
\(943\) −0.546200 3.79891i −0.546200 3.79891i
\(944\) 0 0
\(945\) 0.260554 + 0.570534i 0.260554 + 0.570534i
\(946\) 0 0
\(947\) 0.544078 + 1.19136i 0.544078 + 1.19136i 0.959493 + 0.281733i \(0.0909091\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1.10181 0.708089i 1.10181 0.708089i
\(961\) 0.841254 + 0.540641i 0.841254 + 0.540641i
\(962\) 0 0
\(963\) −1.31718 + 0.386758i −1.31718 + 0.386758i
\(964\) −0.544078 0.627899i −0.544078 0.627899i
\(965\) 0 0
\(966\) 4.22871 + 1.24166i 4.22871 + 1.24166i
\(967\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(968\) −1.00000 −1.00000
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(972\) −0.500000 + 1.09485i −0.500000 + 1.09485i
\(973\) 0 0
\(974\) −0.797176 0.234072i −0.797176 0.234072i
\(975\) 0 0
\(976\) −0.284630 −0.284630
\(977\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(978\) 0.244123 1.69791i 0.244123 1.69791i
\(979\) 0 0
\(980\) −1.75667 + 0.515804i −1.75667 + 0.515804i
\(981\) −0.389217 0.449181i −0.389217 0.449181i
\(982\) 0 0
\(983\) −1.41542 + 0.909632i −1.41542 + 0.909632i −0.415415 + 0.909632i \(0.636364\pi\)
−1.00000 \(\pi\)
\(984\) −0.357685 + 2.48775i −0.357685 + 2.48775i
\(985\) 0 0
\(986\) 0 0
\(987\) 2.76921 3.19584i 2.76921 3.19584i
\(988\) 0 0
\(989\) 0.372786 + 2.59278i 0.372786 + 2.59278i
\(990\) 0 0
\(991\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) −0.452036 0.989821i −0.452036 0.989821i
\(997\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(998\) 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 1340.1.bb.b.1019.1 yes 10
4.3 odd 2 1340.1.bb.a.1019.1 yes 10
5.4 even 2 1340.1.bb.a.1019.1 yes 10
20.19 odd 2 CM 1340.1.bb.b.1019.1 yes 10
67.24 even 11 inner 1340.1.bb.b.359.1 yes 10
268.91 odd 22 1340.1.bb.a.359.1 10
335.24 even 22 1340.1.bb.a.359.1 10
1340.359 odd 22 inner 1340.1.bb.b.359.1 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1340.1.bb.a.359.1 10 268.91 odd 22
1340.1.bb.a.359.1 10 335.24 even 22
1340.1.bb.a.1019.1 yes 10 4.3 odd 2
1340.1.bb.a.1019.1 yes 10 5.4 even 2
1340.1.bb.b.359.1 yes 10 67.24 even 11 inner
1340.1.bb.b.359.1 yes 10 1340.359 odd 22 inner
1340.1.bb.b.1019.1 yes 10 1.1 even 1 trivial
1340.1.bb.b.1019.1 yes 10 20.19 odd 2 CM