Properties

Label 1805.2.a.f.1.3
Level $1805$
Weight $2$
Character 1805.1
Self dual yes
Analytic conductor $14.413$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1805,2,Mod(1,1805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1805.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.a (trivial)

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: yes
Analytic conductor: \(14.4129975648\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.48119\) of defining polynomial
Character \(\chi\) \(=\) 1805.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.48119 q^{2} -0.806063 q^{3} +0.193937 q^{4} +1.00000 q^{5} -1.19394 q^{6} +3.35026 q^{7} -2.67513 q^{8} -2.35026 q^{9} +O(q^{10})\) \(q+1.48119 q^{2} -0.806063 q^{3} +0.193937 q^{4} +1.00000 q^{5} -1.19394 q^{6} +3.35026 q^{7} -2.67513 q^{8} -2.35026 q^{9} +1.48119 q^{10} +0.962389 q^{11} -0.156325 q^{12} -6.15633 q^{13} +4.96239 q^{14} -0.806063 q^{15} -4.35026 q^{16} -6.31265 q^{17} -3.48119 q^{18} +0.193937 q^{20} -2.70052 q^{21} +1.42548 q^{22} -4.96239 q^{23} +2.15633 q^{24} +1.00000 q^{25} -9.11871 q^{26} +4.31265 q^{27} +0.649738 q^{28} +3.61213 q^{29} -1.19394 q^{30} +5.92478 q^{31} -1.09332 q^{32} -0.775746 q^{33} -9.35026 q^{34} +3.35026 q^{35} -0.455802 q^{36} -10.1563 q^{37} +4.96239 q^{39} -2.67513 q^{40} -6.31265 q^{41} -4.00000 q^{42} -4.12601 q^{43} +0.186642 q^{44} -2.35026 q^{45} -7.35026 q^{46} +3.35026 q^{47} +3.50659 q^{48} +4.22425 q^{49} +1.48119 q^{50} +5.08840 q^{51} -1.19394 q^{52} -1.84367 q^{53} +6.38787 q^{54} +0.962389 q^{55} -8.96239 q^{56} +5.35026 q^{58} +6.38787 q^{59} -0.156325 q^{60} -11.2750 q^{61} +8.77575 q^{62} -7.87399 q^{63} +7.08110 q^{64} -6.15633 q^{65} -1.14903 q^{66} +6.73084 q^{67} -1.22425 q^{68} +4.00000 q^{69} +4.96239 q^{70} +0.775746 q^{71} +6.28726 q^{72} +0.387873 q^{73} -15.0435 q^{74} -0.806063 q^{75} +3.22425 q^{77} +7.35026 q^{78} +0.836381 q^{79} -4.35026 q^{80} +3.57452 q^{81} -9.35026 q^{82} -7.03761 q^{83} -0.523730 q^{84} -6.31265 q^{85} -6.11142 q^{86} -2.91160 q^{87} -2.57452 q^{88} -7.08840 q^{89} -3.48119 q^{90} -20.6253 q^{91} -0.962389 q^{92} -4.77575 q^{93} +4.96239 q^{94} +0.881286 q^{96} -10.9927 q^{97} +6.25694 q^{98} -2.26187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{2} - 2 q^{3} + q^{4} + 3 q^{5} - 4 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{2} - 2 q^{3} + q^{4} + 3 q^{5} - 4 q^{6} - 3 q^{8} + 3 q^{9} - q^{10} - 8 q^{11} + 10 q^{12} - 8 q^{13} + 4 q^{14} - 2 q^{15} - 3 q^{16} + 2 q^{17} - 5 q^{18} + q^{20} + 12 q^{21} + 16 q^{22} - 4 q^{23} - 4 q^{24} + 3 q^{25} - 6 q^{26} - 8 q^{27} + 12 q^{28} + 10 q^{29} - 4 q^{30} - 4 q^{31} + 3 q^{32} - 4 q^{33} - 18 q^{34} - 11 q^{36} - 20 q^{37} + 4 q^{39} - 3 q^{40} + 2 q^{41} - 12 q^{42} - 4 q^{43} - 12 q^{44} + 3 q^{45} - 12 q^{46} - 10 q^{48} + 11 q^{49} - q^{50} - 4 q^{51} - 4 q^{52} - 16 q^{53} + 20 q^{54} - 8 q^{55} - 16 q^{56} + 6 q^{58} + 20 q^{59} + 10 q^{60} - 2 q^{61} + 28 q^{62} - 32 q^{63} - 11 q^{64} - 8 q^{65} + 20 q^{66} - 2 q^{67} - 2 q^{68} + 12 q^{69} + 4 q^{70} + 4 q^{71} + 13 q^{72} + 2 q^{73} - 2 q^{74} - 2 q^{75} + 8 q^{77} + 12 q^{78} - 3 q^{80} - q^{81} - 18 q^{82} - 32 q^{83} - 20 q^{84} + 2 q^{85} + 16 q^{86} - 28 q^{87} + 4 q^{88} - 2 q^{89} - 5 q^{90} - 20 q^{91} + 8 q^{92} - 16 q^{93} + 4 q^{94} + 24 q^{96} - 20 q^{97} + 15 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.48119 1.04736 0.523681 0.851914i \(-0.324558\pi\)
0.523681 + 0.851914i \(0.324558\pi\)
\(3\) −0.806063 −0.465381 −0.232690 0.972551i \(-0.574753\pi\)
−0.232690 + 0.972551i \(0.574753\pi\)
\(4\) 0.193937 0.0969683
\(5\) 1.00000 0.447214
\(6\) −1.19394 −0.487423
\(7\) 3.35026 1.26628 0.633140 0.774037i \(-0.281766\pi\)
0.633140 + 0.774037i \(0.281766\pi\)
\(8\) −2.67513 −0.945802
\(9\) −2.35026 −0.783421
\(10\) 1.48119 0.468395
\(11\) 0.962389 0.290171 0.145086 0.989419i \(-0.453654\pi\)
0.145086 + 0.989419i \(0.453654\pi\)
\(12\) −0.156325 −0.0451272
\(13\) −6.15633 −1.70746 −0.853729 0.520718i \(-0.825664\pi\)
−0.853729 + 0.520718i \(0.825664\pi\)
\(14\) 4.96239 1.32625
\(15\) −0.806063 −0.208125
\(16\) −4.35026 −1.08757
\(17\) −6.31265 −1.53104 −0.765521 0.643411i \(-0.777519\pi\)
−0.765521 + 0.643411i \(0.777519\pi\)
\(18\) −3.48119 −0.820525
\(19\) 0 0
\(20\) 0.193937 0.0433655
\(21\) −2.70052 −0.589303
\(22\) 1.42548 0.303914
\(23\) −4.96239 −1.03473 −0.517365 0.855765i \(-0.673087\pi\)
−0.517365 + 0.855765i \(0.673087\pi\)
\(24\) 2.15633 0.440158
\(25\) 1.00000 0.200000
\(26\) −9.11871 −1.78833
\(27\) 4.31265 0.829970
\(28\) 0.649738 0.122789
\(29\) 3.61213 0.670755 0.335378 0.942084i \(-0.391136\pi\)
0.335378 + 0.942084i \(0.391136\pi\)
\(30\) −1.19394 −0.217982
\(31\) 5.92478 1.06412 0.532061 0.846706i \(-0.321418\pi\)
0.532061 + 0.846706i \(0.321418\pi\)
\(32\) −1.09332 −0.193274
\(33\) −0.775746 −0.135040
\(34\) −9.35026 −1.60356
\(35\) 3.35026 0.566298
\(36\) −0.455802 −0.0759669
\(37\) −10.1563 −1.66969 −0.834845 0.550485i \(-0.814443\pi\)
−0.834845 + 0.550485i \(0.814443\pi\)
\(38\) 0 0
\(39\) 4.96239 0.794618
\(40\) −2.67513 −0.422975
\(41\) −6.31265 −0.985870 −0.492935 0.870066i \(-0.664076\pi\)
−0.492935 + 0.870066i \(0.664076\pi\)
\(42\) −4.00000 −0.617213
\(43\) −4.12601 −0.629210 −0.314605 0.949223i \(-0.601872\pi\)
−0.314605 + 0.949223i \(0.601872\pi\)
\(44\) 0.186642 0.0281374
\(45\) −2.35026 −0.350356
\(46\) −7.35026 −1.08374
\(47\) 3.35026 0.488686 0.244343 0.969689i \(-0.421428\pi\)
0.244343 + 0.969689i \(0.421428\pi\)
\(48\) 3.50659 0.506132
\(49\) 4.22425 0.603465
\(50\) 1.48119 0.209473
\(51\) 5.08840 0.712518
\(52\) −1.19394 −0.165569
\(53\) −1.84367 −0.253248 −0.126624 0.991951i \(-0.540414\pi\)
−0.126624 + 0.991951i \(0.540414\pi\)
\(54\) 6.38787 0.869279
\(55\) 0.962389 0.129768
\(56\) −8.96239 −1.19765
\(57\) 0 0
\(58\) 5.35026 0.702524
\(59\) 6.38787 0.831630 0.415815 0.909449i \(-0.363496\pi\)
0.415815 + 0.909449i \(0.363496\pi\)
\(60\) −0.156325 −0.0201815
\(61\) −11.2750 −1.44362 −0.721810 0.692091i \(-0.756690\pi\)
−0.721810 + 0.692091i \(0.756690\pi\)
\(62\) 8.77575 1.11452
\(63\) −7.87399 −0.992030
\(64\) 7.08110 0.885138
\(65\) −6.15633 −0.763598
\(66\) −1.14903 −0.141436
\(67\) 6.73084 0.822303 0.411152 0.911567i \(-0.365127\pi\)
0.411152 + 0.911567i \(0.365127\pi\)
\(68\) −1.22425 −0.148463
\(69\) 4.00000 0.481543
\(70\) 4.96239 0.593119
\(71\) 0.775746 0.0920641 0.0460321 0.998940i \(-0.485342\pi\)
0.0460321 + 0.998940i \(0.485342\pi\)
\(72\) 6.28726 0.740960
\(73\) 0.387873 0.0453971 0.0226986 0.999742i \(-0.492774\pi\)
0.0226986 + 0.999742i \(0.492774\pi\)
\(74\) −15.0435 −1.74877
\(75\) −0.806063 −0.0930762
\(76\) 0 0
\(77\) 3.22425 0.367438
\(78\) 7.35026 0.832253
\(79\) 0.836381 0.0941002 0.0470501 0.998893i \(-0.485018\pi\)
0.0470501 + 0.998893i \(0.485018\pi\)
\(80\) −4.35026 −0.486374
\(81\) 3.57452 0.397168
\(82\) −9.35026 −1.03256
\(83\) −7.03761 −0.772478 −0.386239 0.922399i \(-0.626226\pi\)
−0.386239 + 0.922399i \(0.626226\pi\)
\(84\) −0.523730 −0.0571437
\(85\) −6.31265 −0.684703
\(86\) −6.11142 −0.659011
\(87\) −2.91160 −0.312157
\(88\) −2.57452 −0.274444
\(89\) −7.08840 −0.751369 −0.375684 0.926748i \(-0.622592\pi\)
−0.375684 + 0.926748i \(0.622592\pi\)
\(90\) −3.48119 −0.366950
\(91\) −20.6253 −2.16212
\(92\) −0.962389 −0.100336
\(93\) −4.77575 −0.495222
\(94\) 4.96239 0.511831
\(95\) 0 0
\(96\) 0.881286 0.0899459
\(97\) −10.9927 −1.11614 −0.558070 0.829794i \(-0.688458\pi\)
−0.558070 + 0.829794i \(0.688458\pi\)
\(98\) 6.25694 0.632046
\(99\) −2.26187 −0.227326
\(100\) 0.193937 0.0193937
\(101\) −2.64974 −0.263659 −0.131829 0.991272i \(-0.542085\pi\)
−0.131829 + 0.991272i \(0.542085\pi\)
\(102\) 7.53690 0.746265
\(103\) 10.7308 1.05734 0.528671 0.848827i \(-0.322691\pi\)
0.528671 + 0.848827i \(0.322691\pi\)
\(104\) 16.4690 1.61492
\(105\) −2.70052 −0.263544
\(106\) −2.73084 −0.265243
\(107\) −4.80606 −0.464620 −0.232310 0.972642i \(-0.574628\pi\)
−0.232310 + 0.972642i \(0.574628\pi\)
\(108\) 0.836381 0.0804808
\(109\) 2.77575 0.265868 0.132934 0.991125i \(-0.457560\pi\)
0.132934 + 0.991125i \(0.457560\pi\)
\(110\) 1.42548 0.135915
\(111\) 8.18664 0.777042
\(112\) −14.5745 −1.37716
\(113\) −6.99271 −0.657818 −0.328909 0.944362i \(-0.606681\pi\)
−0.328909 + 0.944362i \(0.606681\pi\)
\(114\) 0 0
\(115\) −4.96239 −0.462745
\(116\) 0.700523 0.0650420
\(117\) 14.4690 1.33766
\(118\) 9.46168 0.871018
\(119\) −21.1490 −1.93873
\(120\) 2.15633 0.196845
\(121\) −10.0738 −0.915801
\(122\) −16.7005 −1.51199
\(123\) 5.08840 0.458805
\(124\) 1.14903 0.103186
\(125\) 1.00000 0.0894427
\(126\) −11.6629 −1.03901
\(127\) −13.4314 −1.19184 −0.595920 0.803043i \(-0.703213\pi\)
−0.595920 + 0.803043i \(0.703213\pi\)
\(128\) 12.6751 1.12033
\(129\) 3.32582 0.292822
\(130\) −9.11871 −0.799764
\(131\) 20.6253 1.80204 0.901020 0.433777i \(-0.142819\pi\)
0.901020 + 0.433777i \(0.142819\pi\)
\(132\) −0.150446 −0.0130946
\(133\) 0 0
\(134\) 9.96968 0.861249
\(135\) 4.31265 0.371174
\(136\) 16.8872 1.44806
\(137\) 20.2374 1.72900 0.864500 0.502633i \(-0.167635\pi\)
0.864500 + 0.502633i \(0.167635\pi\)
\(138\) 5.92478 0.504351
\(139\) −17.5877 −1.49177 −0.745884 0.666076i \(-0.767973\pi\)
−0.745884 + 0.666076i \(0.767973\pi\)
\(140\) 0.649738 0.0549129
\(141\) −2.70052 −0.227425
\(142\) 1.14903 0.0964245
\(143\) −5.92478 −0.495455
\(144\) 10.2243 0.852021
\(145\) 3.61213 0.299971
\(146\) 0.574515 0.0475472
\(147\) −3.40502 −0.280841
\(148\) −1.96968 −0.161907
\(149\) −7.42548 −0.608319 −0.304160 0.952621i \(-0.598376\pi\)
−0.304160 + 0.952621i \(0.598376\pi\)
\(150\) −1.19394 −0.0974845
\(151\) 1.61213 0.131193 0.0655965 0.997846i \(-0.479105\pi\)
0.0655965 + 0.997846i \(0.479105\pi\)
\(152\) 0 0
\(153\) 14.8364 1.19945
\(154\) 4.77575 0.384841
\(155\) 5.92478 0.475890
\(156\) 0.962389 0.0770528
\(157\) 4.38787 0.350190 0.175095 0.984552i \(-0.443977\pi\)
0.175095 + 0.984552i \(0.443977\pi\)
\(158\) 1.23884 0.0985570
\(159\) 1.48612 0.117857
\(160\) −1.09332 −0.0864346
\(161\) −16.6253 −1.31026
\(162\) 5.29455 0.415979
\(163\) −0.649738 −0.0508914 −0.0254457 0.999676i \(-0.508100\pi\)
−0.0254457 + 0.999676i \(0.508100\pi\)
\(164\) −1.22425 −0.0955982
\(165\) −0.775746 −0.0603918
\(166\) −10.4241 −0.809065
\(167\) 15.3561 1.18829 0.594147 0.804357i \(-0.297490\pi\)
0.594147 + 0.804357i \(0.297490\pi\)
\(168\) 7.22425 0.557363
\(169\) 24.9003 1.91541
\(170\) −9.35026 −0.717132
\(171\) 0 0
\(172\) −0.800184 −0.0610134
\(173\) −3.24472 −0.246692 −0.123346 0.992364i \(-0.539362\pi\)
−0.123346 + 0.992364i \(0.539362\pi\)
\(174\) −4.31265 −0.326941
\(175\) 3.35026 0.253256
\(176\) −4.18664 −0.315580
\(177\) −5.14903 −0.387025
\(178\) −10.4993 −0.786955
\(179\) −15.0132 −1.12214 −0.561069 0.827769i \(-0.689610\pi\)
−0.561069 + 0.827769i \(0.689610\pi\)
\(180\) −0.455802 −0.0339735
\(181\) −9.22425 −0.685633 −0.342817 0.939402i \(-0.611381\pi\)
−0.342817 + 0.939402i \(0.611381\pi\)
\(182\) −30.5501 −2.26452
\(183\) 9.08840 0.671834
\(184\) 13.2750 0.978649
\(185\) −10.1563 −0.746708
\(186\) −7.07381 −0.518677
\(187\) −6.07522 −0.444264
\(188\) 0.649738 0.0473870
\(189\) 14.4485 1.05097
\(190\) 0 0
\(191\) −21.7743 −1.57554 −0.787768 0.615972i \(-0.788763\pi\)
−0.787768 + 0.615972i \(0.788763\pi\)
\(192\) −5.70782 −0.411926
\(193\) −12.5442 −0.902951 −0.451476 0.892283i \(-0.649102\pi\)
−0.451476 + 0.892283i \(0.649102\pi\)
\(194\) −16.2823 −1.16900
\(195\) 4.96239 0.355364
\(196\) 0.819237 0.0585169
\(197\) 24.5501 1.74912 0.874560 0.484917i \(-0.161150\pi\)
0.874560 + 0.484917i \(0.161150\pi\)
\(198\) −3.35026 −0.238093
\(199\) 23.0738 1.63566 0.817829 0.575461i \(-0.195177\pi\)
0.817829 + 0.575461i \(0.195177\pi\)
\(200\) −2.67513 −0.189160
\(201\) −5.42548 −0.382684
\(202\) −3.92478 −0.276146
\(203\) 12.1016 0.849364
\(204\) 0.986826 0.0690917
\(205\) −6.31265 −0.440895
\(206\) 15.8945 1.10742
\(207\) 11.6629 0.810628
\(208\) 26.7816 1.85697
\(209\) 0 0
\(210\) −4.00000 −0.276026
\(211\) 20.9380 1.44143 0.720714 0.693233i \(-0.243814\pi\)
0.720714 + 0.693233i \(0.243814\pi\)
\(212\) −0.357556 −0.0245570
\(213\) −0.625301 −0.0428449
\(214\) −7.11871 −0.486625
\(215\) −4.12601 −0.281391
\(216\) −11.5369 −0.784987
\(217\) 19.8496 1.34748
\(218\) 4.11142 0.278460
\(219\) −0.312650 −0.0211270
\(220\) 0.186642 0.0125834
\(221\) 38.8627 2.61419
\(222\) 12.1260 0.813844
\(223\) 0.0303172 0.00203019 0.00101509 0.999999i \(-0.499677\pi\)
0.00101509 + 0.999999i \(0.499677\pi\)
\(224\) −3.66291 −0.244739
\(225\) −2.35026 −0.156684
\(226\) −10.3576 −0.688974
\(227\) −4.80606 −0.318990 −0.159495 0.987199i \(-0.550987\pi\)
−0.159495 + 0.987199i \(0.550987\pi\)
\(228\) 0 0
\(229\) 1.87399 0.123837 0.0619184 0.998081i \(-0.480278\pi\)
0.0619184 + 0.998081i \(0.480278\pi\)
\(230\) −7.35026 −0.484662
\(231\) −2.59895 −0.170999
\(232\) −9.66291 −0.634401
\(233\) −11.1490 −0.730397 −0.365199 0.930930i \(-0.618999\pi\)
−0.365199 + 0.930930i \(0.618999\pi\)
\(234\) 21.4314 1.40101
\(235\) 3.35026 0.218547
\(236\) 1.23884 0.0806418
\(237\) −0.674176 −0.0437924
\(238\) −31.3258 −2.03055
\(239\) 9.29948 0.601533 0.300767 0.953698i \(-0.402757\pi\)
0.300767 + 0.953698i \(0.402757\pi\)
\(240\) 3.50659 0.226349
\(241\) 2.31265 0.148971 0.0744855 0.997222i \(-0.476269\pi\)
0.0744855 + 0.997222i \(0.476269\pi\)
\(242\) −14.9213 −0.959175
\(243\) −15.8192 −1.01480
\(244\) −2.18664 −0.139985
\(245\) 4.22425 0.269878
\(246\) 7.53690 0.480535
\(247\) 0 0
\(248\) −15.8496 −1.00645
\(249\) 5.67276 0.359497
\(250\) 1.48119 0.0936790
\(251\) 24.1016 1.52128 0.760639 0.649175i \(-0.224886\pi\)
0.760639 + 0.649175i \(0.224886\pi\)
\(252\) −1.52705 −0.0961954
\(253\) −4.77575 −0.300249
\(254\) −19.8945 −1.24829
\(255\) 5.08840 0.318648
\(256\) 4.61213 0.288258
\(257\) 13.3199 0.830875 0.415438 0.909622i \(-0.363628\pi\)
0.415438 + 0.909622i \(0.363628\pi\)
\(258\) 4.92619 0.306691
\(259\) −34.0263 −2.11429
\(260\) −1.19394 −0.0740448
\(261\) −8.48944 −0.525483
\(262\) 30.5501 1.88739
\(263\) 12.9624 0.799295 0.399648 0.916669i \(-0.369133\pi\)
0.399648 + 0.916669i \(0.369133\pi\)
\(264\) 2.07522 0.127721
\(265\) −1.84367 −0.113256
\(266\) 0 0
\(267\) 5.71370 0.349673
\(268\) 1.30536 0.0797373
\(269\) 11.4010 0.695134 0.347567 0.937655i \(-0.387008\pi\)
0.347567 + 0.937655i \(0.387008\pi\)
\(270\) 6.38787 0.388754
\(271\) 16.8119 1.02125 0.510626 0.859803i \(-0.329414\pi\)
0.510626 + 0.859803i \(0.329414\pi\)
\(272\) 27.4617 1.66511
\(273\) 16.6253 1.00621
\(274\) 29.9756 1.81089
\(275\) 0.962389 0.0580342
\(276\) 0.775746 0.0466944
\(277\) −29.7889 −1.78984 −0.894921 0.446224i \(-0.852769\pi\)
−0.894921 + 0.446224i \(0.852769\pi\)
\(278\) −26.0508 −1.56242
\(279\) −13.9248 −0.833655
\(280\) −8.96239 −0.535605
\(281\) 11.6121 0.692721 0.346361 0.938101i \(-0.387417\pi\)
0.346361 + 0.938101i \(0.387417\pi\)
\(282\) −4.00000 −0.238197
\(283\) 2.26187 0.134454 0.0672270 0.997738i \(-0.478585\pi\)
0.0672270 + 0.997738i \(0.478585\pi\)
\(284\) 0.150446 0.00892730
\(285\) 0 0
\(286\) −8.77575 −0.518921
\(287\) −21.1490 −1.24839
\(288\) 2.56959 0.151415
\(289\) 22.8496 1.34409
\(290\) 5.35026 0.314178
\(291\) 8.86082 0.519430
\(292\) 0.0752228 0.00440208
\(293\) −1.84367 −0.107709 −0.0538543 0.998549i \(-0.517151\pi\)
−0.0538543 + 0.998549i \(0.517151\pi\)
\(294\) −5.04349 −0.294142
\(295\) 6.38787 0.371916
\(296\) 27.1695 1.57920
\(297\) 4.15045 0.240833
\(298\) −10.9986 −0.637131
\(299\) 30.5501 1.76676
\(300\) −0.156325 −0.00902544
\(301\) −13.8232 −0.796756
\(302\) 2.38787 0.137407
\(303\) 2.13586 0.122702
\(304\) 0 0
\(305\) −11.2750 −0.645607
\(306\) 21.9756 1.25626
\(307\) −26.2071 −1.49572 −0.747859 0.663857i \(-0.768918\pi\)
−0.747859 + 0.663857i \(0.768918\pi\)
\(308\) 0.625301 0.0356298
\(309\) −8.64974 −0.492066
\(310\) 8.77575 0.498429
\(311\) 6.51388 0.369368 0.184684 0.982798i \(-0.440874\pi\)
0.184684 + 0.982798i \(0.440874\pi\)
\(312\) −13.2750 −0.751551
\(313\) 16.0752 0.908625 0.454313 0.890842i \(-0.349885\pi\)
0.454313 + 0.890842i \(0.349885\pi\)
\(314\) 6.49929 0.366776
\(315\) −7.87399 −0.443649
\(316\) 0.162205 0.00912473
\(317\) 5.69323 0.319764 0.159882 0.987136i \(-0.448889\pi\)
0.159882 + 0.987136i \(0.448889\pi\)
\(318\) 2.20123 0.123439
\(319\) 3.47627 0.194634
\(320\) 7.08110 0.395846
\(321\) 3.87399 0.216225
\(322\) −24.6253 −1.37231
\(323\) 0 0
\(324\) 0.693229 0.0385127
\(325\) −6.15633 −0.341491
\(326\) −0.962389 −0.0533018
\(327\) −2.23743 −0.123730
\(328\) 16.8872 0.932438
\(329\) 11.2243 0.618813
\(330\) −1.14903 −0.0632521
\(331\) 12.3127 0.676764 0.338382 0.941009i \(-0.390120\pi\)
0.338382 + 0.941009i \(0.390120\pi\)
\(332\) −1.36485 −0.0749059
\(333\) 23.8700 1.30807
\(334\) 22.7454 1.24457
\(335\) 6.73084 0.367745
\(336\) 11.7480 0.640905
\(337\) −3.76845 −0.205281 −0.102640 0.994719i \(-0.532729\pi\)
−0.102640 + 0.994719i \(0.532729\pi\)
\(338\) 36.8822 2.00613
\(339\) 5.63656 0.306136
\(340\) −1.22425 −0.0663945
\(341\) 5.70194 0.308777
\(342\) 0 0
\(343\) −9.29948 −0.502125
\(344\) 11.0376 0.595108
\(345\) 4.00000 0.215353
\(346\) −4.80606 −0.258376
\(347\) −22.3634 −1.20053 −0.600266 0.799800i \(-0.704939\pi\)
−0.600266 + 0.799800i \(0.704939\pi\)
\(348\) −0.564666 −0.0302693
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 4.96239 0.265251
\(351\) −26.5501 −1.41714
\(352\) −1.05220 −0.0560824
\(353\) 5.53690 0.294700 0.147350 0.989084i \(-0.452926\pi\)
0.147350 + 0.989084i \(0.452926\pi\)
\(354\) −7.62672 −0.405355
\(355\) 0.775746 0.0411723
\(356\) −1.37470 −0.0728589
\(357\) 17.0475 0.902247
\(358\) −22.2374 −1.17528
\(359\) −10.3634 −0.546961 −0.273481 0.961878i \(-0.588175\pi\)
−0.273481 + 0.961878i \(0.588175\pi\)
\(360\) 6.28726 0.331368
\(361\) 0 0
\(362\) −13.6629 −0.718107
\(363\) 8.12013 0.426196
\(364\) −4.00000 −0.209657
\(365\) 0.387873 0.0203022
\(366\) 13.4617 0.703653
\(367\) 3.35026 0.174882 0.0874411 0.996170i \(-0.472131\pi\)
0.0874411 + 0.996170i \(0.472131\pi\)
\(368\) 21.5877 1.12534
\(369\) 14.8364 0.772351
\(370\) −15.0435 −0.782074
\(371\) −6.17679 −0.320683
\(372\) −0.926192 −0.0480208
\(373\) 12.6048 0.652653 0.326327 0.945257i \(-0.394189\pi\)
0.326327 + 0.945257i \(0.394189\pi\)
\(374\) −8.99859 −0.465306
\(375\) −0.806063 −0.0416249
\(376\) −8.96239 −0.462200
\(377\) −22.2374 −1.14529
\(378\) 21.4010 1.10075
\(379\) 37.2506 1.91343 0.956717 0.291018i \(-0.0939941\pi\)
0.956717 + 0.291018i \(0.0939941\pi\)
\(380\) 0 0
\(381\) 10.8265 0.554660
\(382\) −32.2520 −1.65016
\(383\) −30.8324 −1.57546 −0.787731 0.616019i \(-0.788744\pi\)
−0.787731 + 0.616019i \(0.788744\pi\)
\(384\) −10.2170 −0.521382
\(385\) 3.22425 0.164323
\(386\) −18.5804 −0.945717
\(387\) 9.69720 0.492936
\(388\) −2.13189 −0.108230
\(389\) −1.37470 −0.0697000 −0.0348500 0.999393i \(-0.511095\pi\)
−0.0348500 + 0.999393i \(0.511095\pi\)
\(390\) 7.35026 0.372195
\(391\) 31.3258 1.58422
\(392\) −11.3004 −0.570758
\(393\) −16.6253 −0.838635
\(394\) 36.3634 1.83196
\(395\) 0.836381 0.0420829
\(396\) −0.438658 −0.0220434
\(397\) −9.38646 −0.471093 −0.235546 0.971863i \(-0.575688\pi\)
−0.235546 + 0.971863i \(0.575688\pi\)
\(398\) 34.1768 1.71313
\(399\) 0 0
\(400\) −4.35026 −0.217513
\(401\) −14.1016 −0.704199 −0.352099 0.935963i \(-0.614532\pi\)
−0.352099 + 0.935963i \(0.614532\pi\)
\(402\) −8.03620 −0.400809
\(403\) −36.4749 −1.81694
\(404\) −0.513881 −0.0255665
\(405\) 3.57452 0.177619
\(406\) 17.9248 0.889592
\(407\) −9.77433 −0.484496
\(408\) −13.6121 −0.673901
\(409\) −35.1490 −1.73801 −0.869004 0.494805i \(-0.835239\pi\)
−0.869004 + 0.494805i \(0.835239\pi\)
\(410\) −9.35026 −0.461777
\(411\) −16.3127 −0.804644
\(412\) 2.08110 0.102529
\(413\) 21.4010 1.05308
\(414\) 17.2750 0.849022
\(415\) −7.03761 −0.345463
\(416\) 6.73084 0.330007
\(417\) 14.1768 0.694241
\(418\) 0 0
\(419\) 9.02776 0.441035 0.220518 0.975383i \(-0.429225\pi\)
0.220518 + 0.975383i \(0.429225\pi\)
\(420\) −0.523730 −0.0255554
\(421\) −15.2097 −0.741274 −0.370637 0.928778i \(-0.620861\pi\)
−0.370637 + 0.928778i \(0.620861\pi\)
\(422\) 31.0132 1.50970
\(423\) −7.87399 −0.382847
\(424\) 4.93207 0.239523
\(425\) −6.31265 −0.306209
\(426\) −0.926192 −0.0448741
\(427\) −37.7743 −1.82803
\(428\) −0.932071 −0.0450534
\(429\) 4.77575 0.230575
\(430\) −6.11142 −0.294719
\(431\) −16.3127 −0.785753 −0.392876 0.919591i \(-0.628520\pi\)
−0.392876 + 0.919591i \(0.628520\pi\)
\(432\) −18.7612 −0.902647
\(433\) −11.1432 −0.535506 −0.267753 0.963488i \(-0.586281\pi\)
−0.267753 + 0.963488i \(0.586281\pi\)
\(434\) 29.4010 1.41130
\(435\) −2.91160 −0.139601
\(436\) 0.538319 0.0257808
\(437\) 0 0
\(438\) −0.463096 −0.0221276
\(439\) −27.3865 −1.30708 −0.653542 0.756890i \(-0.726718\pi\)
−0.653542 + 0.756890i \(0.726718\pi\)
\(440\) −2.57452 −0.122735
\(441\) −9.92810 −0.472767
\(442\) 57.5633 2.73800
\(443\) 19.5125 0.927065 0.463533 0.886080i \(-0.346582\pi\)
0.463533 + 0.886080i \(0.346582\pi\)
\(444\) 1.58769 0.0753484
\(445\) −7.08840 −0.336022
\(446\) 0.0449056 0.00212634
\(447\) 5.98541 0.283100
\(448\) 23.7235 1.12083
\(449\) 22.1016 1.04304 0.521519 0.853240i \(-0.325366\pi\)
0.521519 + 0.853240i \(0.325366\pi\)
\(450\) −3.48119 −0.164105
\(451\) −6.07522 −0.286071
\(452\) −1.35614 −0.0637875
\(453\) −1.29948 −0.0610547
\(454\) −7.11871 −0.334098
\(455\) −20.6253 −0.966929
\(456\) 0 0
\(457\) −17.8496 −0.834967 −0.417483 0.908685i \(-0.637088\pi\)
−0.417483 + 0.908685i \(0.637088\pi\)
\(458\) 2.77575 0.129702
\(459\) −27.2243 −1.27072
\(460\) −0.962389 −0.0448716
\(461\) −35.2506 −1.64178 −0.820892 0.571083i \(-0.806523\pi\)
−0.820892 + 0.571083i \(0.806523\pi\)
\(462\) −3.84955 −0.179097
\(463\) −26.3634 −1.22521 −0.612606 0.790388i \(-0.709879\pi\)
−0.612606 + 0.790388i \(0.709879\pi\)
\(464\) −15.7137 −0.729490
\(465\) −4.77575 −0.221470
\(466\) −16.5139 −0.764991
\(467\) −6.78560 −0.314000 −0.157000 0.987599i \(-0.550182\pi\)
−0.157000 + 0.987599i \(0.550182\pi\)
\(468\) 2.80606 0.129710
\(469\) 22.5501 1.04127
\(470\) 4.96239 0.228898
\(471\) −3.53690 −0.162972
\(472\) −17.0884 −0.786557
\(473\) −3.97082 −0.182579
\(474\) −0.998585 −0.0458665
\(475\) 0 0
\(476\) −4.10157 −0.187995
\(477\) 4.33312 0.198400
\(478\) 13.7743 0.630023
\(479\) 12.7104 0.580752 0.290376 0.956913i \(-0.406220\pi\)
0.290376 + 0.956913i \(0.406220\pi\)
\(480\) 0.881286 0.0402250
\(481\) 62.5256 2.85092
\(482\) 3.42548 0.156027
\(483\) 13.4010 0.609769
\(484\) −1.95368 −0.0888036
\(485\) −10.9927 −0.499153
\(486\) −23.4314 −1.06287
\(487\) 15.7586 0.714090 0.357045 0.934087i \(-0.383784\pi\)
0.357045 + 0.934087i \(0.383784\pi\)
\(488\) 30.1622 1.36538
\(489\) 0.523730 0.0236839
\(490\) 6.25694 0.282660
\(491\) −14.5501 −0.656636 −0.328318 0.944567i \(-0.606482\pi\)
−0.328318 + 0.944567i \(0.606482\pi\)
\(492\) 0.986826 0.0444896
\(493\) −22.8021 −1.02695
\(494\) 0 0
\(495\) −2.26187 −0.101663
\(496\) −25.7743 −1.15730
\(497\) 2.59895 0.116579
\(498\) 8.40246 0.376523
\(499\) −5.48612 −0.245592 −0.122796 0.992432i \(-0.539186\pi\)
−0.122796 + 0.992432i \(0.539186\pi\)
\(500\) 0.193937 0.00867311
\(501\) −12.3780 −0.553009
\(502\) 35.6991 1.59333
\(503\) −36.6615 −1.63466 −0.817328 0.576173i \(-0.804545\pi\)
−0.817328 + 0.576173i \(0.804545\pi\)
\(504\) 21.0640 0.938263
\(505\) −2.64974 −0.117912
\(506\) −7.07381 −0.314469
\(507\) −20.0713 −0.891396
\(508\) −2.60483 −0.115571
\(509\) −39.1900 −1.73706 −0.868532 0.495632i \(-0.834936\pi\)
−0.868532 + 0.495632i \(0.834936\pi\)
\(510\) 7.53690 0.333740
\(511\) 1.29948 0.0574855
\(512\) −18.5188 −0.818423
\(513\) 0 0
\(514\) 19.7294 0.870228
\(515\) 10.7308 0.472857
\(516\) 0.644999 0.0283945
\(517\) 3.22425 0.141803
\(518\) −50.3996 −2.21443
\(519\) 2.61545 0.114806
\(520\) 16.4690 0.722212
\(521\) 17.7283 0.776690 0.388345 0.921514i \(-0.373047\pi\)
0.388345 + 0.921514i \(0.373047\pi\)
\(522\) −12.5745 −0.550372
\(523\) 40.7572 1.78219 0.891094 0.453819i \(-0.149939\pi\)
0.891094 + 0.453819i \(0.149939\pi\)
\(524\) 4.00000 0.174741
\(525\) −2.70052 −0.117861
\(526\) 19.1998 0.837152
\(527\) −37.4010 −1.62922
\(528\) 3.37470 0.146865
\(529\) 1.62530 0.0706652
\(530\) −2.73084 −0.118620
\(531\) −15.0132 −0.651516
\(532\) 0 0
\(533\) 38.8627 1.68333
\(534\) 8.46310 0.366234
\(535\) −4.80606 −0.207784
\(536\) −18.0059 −0.777736
\(537\) 12.1016 0.522221
\(538\) 16.8872 0.728057
\(539\) 4.06537 0.175108
\(540\) 0.836381 0.0359921
\(541\) 23.9003 1.02756 0.513778 0.857923i \(-0.328246\pi\)
0.513778 + 0.857923i \(0.328246\pi\)
\(542\) 24.9018 1.06962
\(543\) 7.43533 0.319081
\(544\) 6.90175 0.295910
\(545\) 2.77575 0.118900
\(546\) 24.6253 1.05387
\(547\) −8.55405 −0.365745 −0.182872 0.983137i \(-0.558539\pi\)
−0.182872 + 0.983137i \(0.558539\pi\)
\(548\) 3.92478 0.167658
\(549\) 26.4993 1.13096
\(550\) 1.42548 0.0607829
\(551\) 0 0
\(552\) −10.7005 −0.455445
\(553\) 2.80209 0.119157
\(554\) −44.1232 −1.87461
\(555\) 8.18664 0.347504
\(556\) −3.41090 −0.144654
\(557\) −4.23743 −0.179546 −0.0897728 0.995962i \(-0.528614\pi\)
−0.0897728 + 0.995962i \(0.528614\pi\)
\(558\) −20.6253 −0.873139
\(559\) 25.4010 1.07435
\(560\) −14.5745 −0.615886
\(561\) 4.89701 0.206752
\(562\) 17.1998 0.725530
\(563\) −16.4934 −0.695114 −0.347557 0.937659i \(-0.612989\pi\)
−0.347557 + 0.937659i \(0.612989\pi\)
\(564\) −0.523730 −0.0220530
\(565\) −6.99271 −0.294185
\(566\) 3.35026 0.140822
\(567\) 11.9756 0.502926
\(568\) −2.07522 −0.0870744
\(569\) 10.0000 0.419222 0.209611 0.977785i \(-0.432780\pi\)
0.209611 + 0.977785i \(0.432780\pi\)
\(570\) 0 0
\(571\) −26.2619 −1.09902 −0.549512 0.835486i \(-0.685186\pi\)
−0.549512 + 0.835486i \(0.685186\pi\)
\(572\) −1.14903 −0.0480434
\(573\) 17.5515 0.733224
\(574\) −31.3258 −1.30751
\(575\) −4.96239 −0.206946
\(576\) −16.6424 −0.693435
\(577\) 30.1016 1.25314 0.626572 0.779363i \(-0.284457\pi\)
0.626572 + 0.779363i \(0.284457\pi\)
\(578\) 33.8446 1.40775
\(579\) 10.1114 0.420216
\(580\) 0.700523 0.0290877
\(581\) −23.5778 −0.978174
\(582\) 13.1246 0.544032
\(583\) −1.77433 −0.0734853
\(584\) −1.03761 −0.0429367
\(585\) 14.4690 0.598219
\(586\) −2.73084 −0.112810
\(587\) −35.1392 −1.45035 −0.725175 0.688565i \(-0.758241\pi\)
−0.725175 + 0.688565i \(0.758241\pi\)
\(588\) −0.660357 −0.0272327
\(589\) 0 0
\(590\) 9.46168 0.389531
\(591\) −19.7889 −0.814007
\(592\) 44.1827 1.81590
\(593\) 34.3244 1.40953 0.704767 0.709439i \(-0.251051\pi\)
0.704767 + 0.709439i \(0.251051\pi\)
\(594\) 6.14762 0.252240
\(595\) −21.1490 −0.867026
\(596\) −1.44007 −0.0589877
\(597\) −18.5990 −0.761204
\(598\) 45.2506 1.85043
\(599\) −14.6107 −0.596978 −0.298489 0.954413i \(-0.596483\pi\)
−0.298489 + 0.954413i \(0.596483\pi\)
\(600\) 2.15633 0.0880316
\(601\) −23.5633 −0.961165 −0.480583 0.876949i \(-0.659575\pi\)
−0.480583 + 0.876949i \(0.659575\pi\)
\(602\) −20.4749 −0.834493
\(603\) −15.8192 −0.644209
\(604\) 0.312650 0.0127216
\(605\) −10.0738 −0.409559
\(606\) 3.16362 0.128513
\(607\) 8.80606 0.357427 0.178714 0.983901i \(-0.442806\pi\)
0.178714 + 0.983901i \(0.442806\pi\)
\(608\) 0 0
\(609\) −9.75463 −0.395278
\(610\) −16.7005 −0.676184
\(611\) −20.6253 −0.834410
\(612\) 2.87732 0.116309
\(613\) 10.4142 0.420626 0.210313 0.977634i \(-0.432552\pi\)
0.210313 + 0.977634i \(0.432552\pi\)
\(614\) −38.8178 −1.56656
\(615\) 5.08840 0.205184
\(616\) −8.62530 −0.347523
\(617\) −17.2849 −0.695863 −0.347932 0.937520i \(-0.613116\pi\)
−0.347932 + 0.937520i \(0.613116\pi\)
\(618\) −12.8119 −0.515372
\(619\) −10.6351 −0.427463 −0.213731 0.976892i \(-0.568562\pi\)
−0.213731 + 0.976892i \(0.568562\pi\)
\(620\) 1.14903 0.0461462
\(621\) −21.4010 −0.858794
\(622\) 9.64832 0.386863
\(623\) −23.7480 −0.951443
\(624\) −21.5877 −0.864199
\(625\) 1.00000 0.0400000
\(626\) 23.8105 0.951660
\(627\) 0 0
\(628\) 0.850969 0.0339574
\(629\) 64.1133 2.55637
\(630\) −11.6629 −0.464662
\(631\) −16.5599 −0.659240 −0.329620 0.944114i \(-0.606921\pi\)
−0.329620 + 0.944114i \(0.606921\pi\)
\(632\) −2.23743 −0.0890001
\(633\) −16.8773 −0.670813
\(634\) 8.43278 0.334908
\(635\) −13.4314 −0.533007
\(636\) 0.288213 0.0114284
\(637\) −26.0059 −1.03039
\(638\) 5.14903 0.203852
\(639\) −1.82321 −0.0721249
\(640\) 12.6751 0.501029
\(641\) 16.7612 0.662026 0.331013 0.943626i \(-0.392610\pi\)
0.331013 + 0.943626i \(0.392610\pi\)
\(642\) 5.73813 0.226466
\(643\) 5.73813 0.226290 0.113145 0.993578i \(-0.463908\pi\)
0.113145 + 0.993578i \(0.463908\pi\)
\(644\) −3.22425 −0.127053
\(645\) 3.32582 0.130954
\(646\) 0 0
\(647\) −37.2144 −1.46305 −0.731525 0.681815i \(-0.761191\pi\)
−0.731525 + 0.681815i \(0.761191\pi\)
\(648\) −9.56230 −0.375642
\(649\) 6.14762 0.241315
\(650\) −9.11871 −0.357665
\(651\) −16.0000 −0.627089
\(652\) −0.126008 −0.00493485
\(653\) 11.7626 0.460305 0.230153 0.973155i \(-0.426077\pi\)
0.230153 + 0.973155i \(0.426077\pi\)
\(654\) −3.31406 −0.129590
\(655\) 20.6253 0.805897
\(656\) 27.4617 1.07220
\(657\) −0.911603 −0.0355650
\(658\) 16.6253 0.648122
\(659\) −1.23884 −0.0482584 −0.0241292 0.999709i \(-0.507681\pi\)
−0.0241292 + 0.999709i \(0.507681\pi\)
\(660\) −0.150446 −0.00585609
\(661\) 9.53690 0.370943 0.185471 0.982650i \(-0.440619\pi\)
0.185471 + 0.982650i \(0.440619\pi\)
\(662\) 18.2374 0.708818
\(663\) −31.3258 −1.21659
\(664\) 18.8265 0.730611
\(665\) 0 0
\(666\) 35.3561 1.37002
\(667\) −17.9248 −0.694050
\(668\) 2.97812 0.115227
\(669\) −0.0244376 −0.000944811 0
\(670\) 9.96968 0.385162
\(671\) −10.8510 −0.418897
\(672\) 2.95254 0.113897
\(673\) −39.9307 −1.53921 −0.769607 0.638518i \(-0.779548\pi\)
−0.769607 + 0.638518i \(0.779548\pi\)
\(674\) −5.58181 −0.215003
\(675\) 4.31265 0.165994
\(676\) 4.82909 0.185734
\(677\) 3.05334 0.117349 0.0586747 0.998277i \(-0.481313\pi\)
0.0586747 + 0.998277i \(0.481313\pi\)
\(678\) 8.34885 0.320636
\(679\) −36.8284 −1.41335
\(680\) 16.8872 0.647593
\(681\) 3.87399 0.148452
\(682\) 8.44568 0.323402
\(683\) −29.2692 −1.11995 −0.559977 0.828508i \(-0.689190\pi\)
−0.559977 + 0.828508i \(0.689190\pi\)
\(684\) 0 0
\(685\) 20.2374 0.773232
\(686\) −13.7743 −0.525906
\(687\) −1.51056 −0.0576313
\(688\) 17.9492 0.684307
\(689\) 11.3503 0.432411
\(690\) 5.92478 0.225552
\(691\) 2.63515 0.100246 0.0501229 0.998743i \(-0.484039\pi\)
0.0501229 + 0.998743i \(0.484039\pi\)
\(692\) −0.629270 −0.0239213
\(693\) −7.57784 −0.287858
\(694\) −33.1246 −1.25739
\(695\) −17.5877 −0.667139
\(696\) 7.78892 0.295238
\(697\) 39.8496 1.50941
\(698\) −14.8119 −0.560640
\(699\) 8.98683 0.339913
\(700\) 0.649738 0.0245578
\(701\) −25.0494 −0.946102 −0.473051 0.881035i \(-0.656847\pi\)
−0.473051 + 0.881035i \(0.656847\pi\)
\(702\) −39.3258 −1.48426
\(703\) 0 0
\(704\) 6.81477 0.256841
\(705\) −2.70052 −0.101708
\(706\) 8.20123 0.308657
\(707\) −8.87732 −0.333866
\(708\) −0.998585 −0.0375291
\(709\) −41.6991 −1.56604 −0.783021 0.621995i \(-0.786323\pi\)
−0.783021 + 0.621995i \(0.786323\pi\)
\(710\) 1.14903 0.0431224
\(711\) −1.96571 −0.0737200
\(712\) 18.9624 0.710646
\(713\) −29.4010 −1.10108
\(714\) 25.2506 0.944980
\(715\) −5.92478 −0.221574
\(716\) −2.91160 −0.108812
\(717\) −7.49597 −0.279942
\(718\) −15.3503 −0.572867
\(719\) 30.6351 1.14250 0.571249 0.820777i \(-0.306459\pi\)
0.571249 + 0.820777i \(0.306459\pi\)
\(720\) 10.2243 0.381035
\(721\) 35.9511 1.33889
\(722\) 0 0
\(723\) −1.86414 −0.0693282
\(724\) −1.78892 −0.0664847
\(725\) 3.61213 0.134151
\(726\) 12.0275 0.446382
\(727\) 7.50071 0.278186 0.139093 0.990279i \(-0.455581\pi\)
0.139093 + 0.990279i \(0.455581\pi\)
\(728\) 55.1754 2.04494
\(729\) 2.02776 0.0751023
\(730\) 0.574515 0.0212638
\(731\) 26.0460 0.963348
\(732\) 1.76257 0.0651466
\(733\) 9.84955 0.363802 0.181901 0.983317i \(-0.441775\pi\)
0.181901 + 0.983317i \(0.441775\pi\)
\(734\) 4.96239 0.183165
\(735\) −3.40502 −0.125596
\(736\) 5.42548 0.199986
\(737\) 6.47768 0.238609
\(738\) 21.9756 0.808932
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) −1.96968 −0.0724070
\(741\) 0 0
\(742\) −9.14903 −0.335871
\(743\) 15.7177 0.576625 0.288313 0.957536i \(-0.406906\pi\)
0.288313 + 0.957536i \(0.406906\pi\)
\(744\) 12.7757 0.468382
\(745\) −7.42548 −0.272049
\(746\) 18.6702 0.683565
\(747\) 16.5402 0.605175
\(748\) −1.17821 −0.0430795
\(749\) −16.1016 −0.588339
\(750\) −1.19394 −0.0435964
\(751\) 43.7400 1.59610 0.798048 0.602593i \(-0.205866\pi\)
0.798048 + 0.602593i \(0.205866\pi\)
\(752\) −14.5745 −0.531478
\(753\) −19.4274 −0.707974
\(754\) −32.9380 −1.19953
\(755\) 1.61213 0.0586713
\(756\) 2.80209 0.101911
\(757\) −15.7743 −0.573328 −0.286664 0.958031i \(-0.592546\pi\)
−0.286664 + 0.958031i \(0.592546\pi\)
\(758\) 55.1754 2.00406
\(759\) 3.84955 0.139730
\(760\) 0 0
\(761\) 43.2262 1.56695 0.783474 0.621425i \(-0.213446\pi\)
0.783474 + 0.621425i \(0.213446\pi\)
\(762\) 16.0362 0.580930
\(763\) 9.29948 0.336664
\(764\) −4.22284 −0.152777
\(765\) 14.8364 0.536410
\(766\) −45.6688 −1.65008
\(767\) −39.3258 −1.41997
\(768\) −3.71767 −0.134150
\(769\) −19.1246 −0.689650 −0.344825 0.938667i \(-0.612062\pi\)
−0.344825 + 0.938667i \(0.612062\pi\)
\(770\) 4.77575 0.172106
\(771\) −10.7367 −0.386674
\(772\) −2.43278 −0.0875576
\(773\) −25.8846 −0.931005 −0.465502 0.885047i \(-0.654126\pi\)
−0.465502 + 0.885047i \(0.654126\pi\)
\(774\) 14.3634 0.516283
\(775\) 5.92478 0.212824
\(776\) 29.4069 1.05565
\(777\) 27.4274 0.983952
\(778\) −2.03620 −0.0730012
\(779\) 0 0
\(780\) 0.962389 0.0344590
\(781\) 0.746569 0.0267144
\(782\) 46.3996 1.65925
\(783\) 15.5778 0.556707
\(784\) −18.3766 −0.656307
\(785\) 4.38787 0.156610
\(786\) −24.6253 −0.878355
\(787\) −19.9814 −0.712261 −0.356131 0.934436i \(-0.615904\pi\)
−0.356131 + 0.934436i \(0.615904\pi\)
\(788\) 4.76116 0.169609
\(789\) −10.4485 −0.371977
\(790\) 1.23884 0.0440760
\(791\) −23.4274 −0.832982
\(792\) 6.05079 0.215005
\(793\) 69.4128 2.46492
\(794\) −13.9032 −0.493405
\(795\) 1.48612 0.0527072
\(796\) 4.47486 0.158607
\(797\) −28.6458 −1.01469 −0.507343 0.861744i \(-0.669372\pi\)
−0.507343 + 0.861744i \(0.669372\pi\)
\(798\) 0 0
\(799\) −21.1490 −0.748199
\(800\) −1.09332 −0.0386547
\(801\) 16.6596 0.588638
\(802\) −20.8872 −0.737551
\(803\) 0.373285 0.0131729
\(804\) −1.05220 −0.0371082
\(805\) −16.6253 −0.585965
\(806\) −54.0263 −1.90300
\(807\) −9.18997 −0.323502
\(808\) 7.08840 0.249369
\(809\) −17.2243 −0.605573 −0.302786 0.953058i \(-0.597917\pi\)
−0.302786 + 0.953058i \(0.597917\pi\)
\(810\) 5.29455 0.186032
\(811\) 15.6267 0.548728 0.274364 0.961626i \(-0.411533\pi\)
0.274364 + 0.961626i \(0.411533\pi\)
\(812\) 2.34694 0.0823613
\(813\) −13.5515 −0.475272
\(814\) −14.4777 −0.507443
\(815\) −0.649738 −0.0227593
\(816\) −22.1359 −0.774910
\(817\) 0 0
\(818\) −52.0625 −1.82032
\(819\) 48.4749 1.69385
\(820\) −1.22425 −0.0427528
\(821\) 39.2506 1.36986 0.684928 0.728611i \(-0.259834\pi\)
0.684928 + 0.728611i \(0.259834\pi\)
\(822\) −24.1622 −0.842754
\(823\) −45.5271 −1.58697 −0.793487 0.608588i \(-0.791736\pi\)
−0.793487 + 0.608588i \(0.791736\pi\)
\(824\) −28.7064 −1.00003
\(825\) −0.775746 −0.0270080
\(826\) 31.6991 1.10295
\(827\) −17.0698 −0.593576 −0.296788 0.954943i \(-0.595916\pi\)
−0.296788 + 0.954943i \(0.595916\pi\)
\(828\) 2.26187 0.0786052
\(829\) −1.69911 −0.0590125 −0.0295062 0.999565i \(-0.509393\pi\)
−0.0295062 + 0.999565i \(0.509393\pi\)
\(830\) −10.4241 −0.361825
\(831\) 24.0118 0.832959
\(832\) −43.5936 −1.51134
\(833\) −26.6662 −0.923930
\(834\) 20.9986 0.727122
\(835\) 15.3561 0.531421
\(836\) 0 0
\(837\) 25.5515 0.883189
\(838\) 13.3719 0.461924
\(839\) 50.5910 1.74660 0.873298 0.487187i \(-0.161977\pi\)
0.873298 + 0.487187i \(0.161977\pi\)
\(840\) 7.22425 0.249260
\(841\) −15.9525 −0.550088
\(842\) −22.5285 −0.776382
\(843\) −9.36011 −0.322379
\(844\) 4.06063 0.139773
\(845\) 24.9003 0.856598
\(846\) −11.6629 −0.400979
\(847\) −33.7499 −1.15966
\(848\) 8.02047 0.275424
\(849\) −1.82321 −0.0625723
\(850\) −9.35026 −0.320711
\(851\) 50.3996 1.72768
\(852\) −0.121269 −0.00415460
\(853\) −22.5237 −0.771198 −0.385599 0.922667i \(-0.626005\pi\)
−0.385599 + 0.922667i \(0.626005\pi\)
\(854\) −55.9511 −1.91461
\(855\) 0 0
\(856\) 12.8568 0.439438
\(857\) 23.6180 0.806776 0.403388 0.915029i \(-0.367833\pi\)
0.403388 + 0.915029i \(0.367833\pi\)
\(858\) 7.07381 0.241496
\(859\) 15.1754 0.517777 0.258889 0.965907i \(-0.416644\pi\)
0.258889 + 0.965907i \(0.416644\pi\)
\(860\) −0.800184 −0.0272860
\(861\) 17.0475 0.580976
\(862\) −24.1622 −0.822968
\(863\) −30.1055 −1.02480 −0.512402 0.858746i \(-0.671244\pi\)
−0.512402 + 0.858746i \(0.671244\pi\)
\(864\) −4.71511 −0.160411
\(865\) −3.24472 −0.110324
\(866\) −16.5052 −0.560869
\(867\) −18.4182 −0.625515
\(868\) 3.84955 0.130662
\(869\) 0.804923 0.0273051
\(870\) −4.31265 −0.146213
\(871\) −41.4372 −1.40405
\(872\) −7.42548 −0.251459
\(873\) 25.8357 0.874407
\(874\) 0 0
\(875\) 3.35026 0.113260
\(876\) −0.0606343 −0.00204864
\(877\) 5.53102 0.186769 0.0933847 0.995630i \(-0.470231\pi\)
0.0933847 + 0.995630i \(0.470231\pi\)
\(878\) −40.5647 −1.36899
\(879\) 1.48612 0.0501255
\(880\) −4.18664 −0.141132
\(881\) 20.8265 0.701664 0.350832 0.936438i \(-0.385899\pi\)
0.350832 + 0.936438i \(0.385899\pi\)
\(882\) −14.7054 −0.495158
\(883\) 43.1509 1.45214 0.726072 0.687618i \(-0.241344\pi\)
0.726072 + 0.687618i \(0.241344\pi\)
\(884\) 7.53690 0.253494
\(885\) −5.14903 −0.173083
\(886\) 28.9018 0.970973
\(887\) 44.5461 1.49571 0.747856 0.663861i \(-0.231083\pi\)
0.747856 + 0.663861i \(0.231083\pi\)
\(888\) −21.9003 −0.734927
\(889\) −44.9986 −1.50920
\(890\) −10.4993 −0.351937
\(891\) 3.44007 0.115247
\(892\) 0.00587961 0.000196864 0
\(893\) 0 0
\(894\) 8.86556 0.296509
\(895\) −15.0132 −0.501835
\(896\) 42.4650 1.41866
\(897\) −24.6253 −0.822215
\(898\) 32.7367 1.09244
\(899\) 21.4010 0.713765
\(900\) −0.455802 −0.0151934
\(901\) 11.6385 0.387734
\(902\) −8.99859 −0.299620
\(903\) 11.1424 0.370795
\(904\) 18.7064 0.622166
\(905\) −9.22425 −0.306625
\(906\) −1.92478 −0.0639464
\(907\) −53.7558 −1.78493 −0.892466 0.451115i \(-0.851026\pi\)
−0.892466 + 0.451115i \(0.851026\pi\)
\(908\) −0.932071 −0.0309319
\(909\) 6.22758 0.206556
\(910\) −30.5501 −1.01273
\(911\) 2.28630 0.0757486 0.0378743 0.999283i \(-0.487941\pi\)
0.0378743 + 0.999283i \(0.487941\pi\)
\(912\) 0 0
\(913\) −6.77292 −0.224151
\(914\) −26.4387 −0.874513
\(915\) 9.08840 0.300453
\(916\) 0.363436 0.0120082
\(917\) 69.1002 2.28189
\(918\) −40.3244 −1.33090
\(919\) −34.8510 −1.14963 −0.574814 0.818284i \(-0.694925\pi\)
−0.574814 + 0.818284i \(0.694925\pi\)
\(920\) 13.2750 0.437665
\(921\) 21.1246 0.696079
\(922\) −52.2130 −1.71954
\(923\) −4.77575 −0.157196
\(924\) −0.504032 −0.0165814
\(925\) −10.1563 −0.333938
\(926\) −39.0494 −1.28324
\(927\) −25.2203 −0.828343
\(928\) −3.94921 −0.129639
\(929\) 41.6991 1.36810 0.684052 0.729434i \(-0.260216\pi\)
0.684052 + 0.729434i \(0.260216\pi\)
\(930\) −7.07381 −0.231959
\(931\) 0 0
\(932\) −2.16220 −0.0708254
\(933\) −5.25060 −0.171897
\(934\) −10.0508 −0.328872
\(935\) −6.07522 −0.198681
\(936\) −38.7064 −1.26516
\(937\) 21.9102 0.715775 0.357887 0.933765i \(-0.383497\pi\)
0.357887 + 0.933765i \(0.383497\pi\)
\(938\) 33.4010 1.09058
\(939\) −12.9576 −0.422857
\(940\) 0.649738 0.0211921
\(941\) 3.55149 0.115775 0.0578877 0.998323i \(-0.481563\pi\)
0.0578877 + 0.998323i \(0.481563\pi\)
\(942\) −5.23884 −0.170691
\(943\) 31.3258 1.02011
\(944\) −27.7889 −0.904452
\(945\) 14.4485 0.470010
\(946\) −5.88156 −0.191226
\(947\) 38.3634 1.24664 0.623322 0.781965i \(-0.285783\pi\)
0.623322 + 0.781965i \(0.285783\pi\)
\(948\) −0.130747 −0.00424648
\(949\) −2.38787 −0.0775136
\(950\) 0 0
\(951\) −4.58910 −0.148812
\(952\) 56.5764 1.83365
\(953\) 22.8714 0.740879 0.370439 0.928857i \(-0.379207\pi\)
0.370439 + 0.928857i \(0.379207\pi\)
\(954\) 6.41819 0.207797
\(955\) −21.7743 −0.704601
\(956\) 1.80351 0.0583296
\(957\) −2.80209 −0.0905788
\(958\) 18.8265 0.608258
\(959\) 67.8007 2.18940
\(960\) −5.70782 −0.184219
\(961\) 4.10299 0.132354
\(962\) 92.6126 2.98595
\(963\) 11.2955 0.363993
\(964\) 0.448507 0.0144455
\(965\) −12.5442 −0.403812
\(966\) 19.8496 0.638649
\(967\) 27.6629 0.889579 0.444790 0.895635i \(-0.353278\pi\)
0.444790 + 0.895635i \(0.353278\pi\)
\(968\) 26.9488 0.866166
\(969\) 0 0
\(970\) −16.2823 −0.522794
\(971\) 42.1768 1.35352 0.676759 0.736205i \(-0.263384\pi\)
0.676759 + 0.736205i \(0.263384\pi\)
\(972\) −3.06793 −0.0984039
\(973\) −58.9234 −1.88900
\(974\) 23.3416 0.747912
\(975\) 4.96239 0.158924
\(976\) 49.0494 1.57003
\(977\) −0.856849 −0.0274130 −0.0137065 0.999906i \(-0.504363\pi\)
−0.0137065 + 0.999906i \(0.504363\pi\)
\(978\) 0.775746 0.0248056
\(979\) −6.82179 −0.218025
\(980\) 0.819237 0.0261696
\(981\) −6.52373 −0.208287
\(982\) −21.5515 −0.687736
\(983\) −45.2809 −1.44424 −0.722119 0.691769i \(-0.756831\pi\)
−0.722119 + 0.691769i \(0.756831\pi\)
\(984\) −13.6121 −0.433939
\(985\) 24.5501 0.782231
\(986\) −33.7743 −1.07559
\(987\) −9.04746 −0.287984
\(988\) 0 0
\(989\) 20.4749 0.651063
\(990\) −3.35026 −0.106478
\(991\) −47.0132 −1.49342 −0.746711 0.665148i \(-0.768368\pi\)
−0.746711 + 0.665148i \(0.768368\pi\)
\(992\) −6.47768 −0.205667
\(993\) −9.92478 −0.314953
\(994\) 3.84955 0.122100
\(995\) 23.0738 0.731489
\(996\) 1.10016 0.0348598
\(997\) 13.6873 0.433483 0.216741 0.976229i \(-0.430457\pi\)
0.216741 + 0.976229i \(0.430457\pi\)
\(998\) −8.12601 −0.257224
\(999\) −43.8007 −1.38579
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 1805.2.a.f.1.3 3
5.4 even 2 9025.2.a.bb.1.1 3
19.18 odd 2 95.2.a.a.1.1 3
57.56 even 2 855.2.a.i.1.3 3
76.75 even 2 1520.2.a.p.1.2 3
95.18 even 4 475.2.b.d.324.5 6
95.37 even 4 475.2.b.d.324.2 6
95.94 odd 2 475.2.a.f.1.3 3
133.132 even 2 4655.2.a.u.1.1 3
152.37 odd 2 6080.2.a.bo.1.2 3
152.75 even 2 6080.2.a.by.1.2 3
285.284 even 2 4275.2.a.bk.1.1 3
380.379 even 2 7600.2.a.bx.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.a.a.1.1 3 19.18 odd 2
475.2.a.f.1.3 3 95.94 odd 2
475.2.b.d.324.2 6 95.37 even 4
475.2.b.d.324.5 6 95.18 even 4
855.2.a.i.1.3 3 57.56 even 2
1520.2.a.p.1.2 3 76.75 even 2
1805.2.a.f.1.3 3 1.1 even 1 trivial
4275.2.a.bk.1.1 3 285.284 even 2
4655.2.a.u.1.1 3 133.132 even 2
6080.2.a.bo.1.2 3 152.37 odd 2
6080.2.a.by.1.2 3 152.75 even 2
7600.2.a.bx.1.2 3 380.379 even 2
9025.2.a.bb.1.1 3 5.4 even 2