Properties

Label 1805.2.a.i.1.3
Level $1805$
Weight $2$
Character 1805.1
Self dual yes
Analytic conductor $14.413$
Analytic rank $1$
Dimension $4$
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: \(4\)
Coefficient field: 4.4.7537.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 5x^{2} + 4x + 3 \) 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 \(-2.04717\) 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)
 
\(f(q)\) \(=\) \(q+1.19091 q^{2} -3.04717 q^{3} -0.581734 q^{4} +1.00000 q^{5} -3.62891 q^{6} -0.609175 q^{7} -3.07461 q^{8} +6.28525 q^{9} +O(q^{10})\) \(q+1.19091 q^{2} -3.04717 q^{3} -0.581734 q^{4} +1.00000 q^{5} -3.62891 q^{6} -0.609175 q^{7} -3.07461 q^{8} +6.28525 q^{9} +1.19091 q^{10} +4.48517 q^{11} +1.77264 q^{12} -4.43800 q^{13} -0.725473 q^{14} -3.04717 q^{15} -2.49812 q^{16} +2.90343 q^{17} +7.48517 q^{18} -0.581734 q^{20} +1.85626 q^{21} +5.34143 q^{22} -2.84726 q^{23} +9.36887 q^{24} +1.00000 q^{25} -5.28525 q^{26} -10.0107 q^{27} +0.354378 q^{28} -1.11630 q^{29} -3.62891 q^{30} +6.22908 q^{31} +3.17419 q^{32} -13.6671 q^{33} +3.45773 q^{34} -0.609175 q^{35} -3.65635 q^{36} +3.77264 q^{37} +13.5233 q^{39} -3.07461 q^{40} +8.30369 q^{41} +2.21064 q^{42} -9.98877 q^{43} -2.60918 q^{44} +6.28525 q^{45} -3.39082 q^{46} -5.88500 q^{47} +7.61219 q^{48} -6.62891 q^{49} +1.19091 q^{50} -8.84726 q^{51} +2.58173 q^{52} -8.44872 q^{53} -11.9219 q^{54} +4.48517 q^{55} +1.87298 q^{56} -1.32941 q^{58} -10.2359 q^{59} +1.77264 q^{60} -4.98199 q^{61} +7.41827 q^{62} -3.82882 q^{63} +8.77641 q^{64} -4.43800 q^{65} -16.2762 q^{66} -8.47616 q^{67} -1.68903 q^{68} +8.67608 q^{69} -0.725473 q^{70} -11.6199 q^{71} -19.3247 q^{72} +3.72325 q^{73} +4.49288 q^{74} -3.04717 q^{75} -2.73225 q^{77} +16.1051 q^{78} -9.03817 q^{79} -2.49812 q^{80} +11.6486 q^{81} +9.88894 q^{82} -2.12178 q^{83} -1.07985 q^{84} +2.90343 q^{85} -11.8957 q^{86} +3.40155 q^{87} -13.7901 q^{88} -7.93217 q^{89} +7.48517 q^{90} +2.70352 q^{91} +1.65635 q^{92} -18.9811 q^{93} -7.00850 q^{94} -9.67231 q^{96} +9.67256 q^{97} -7.89443 q^{98} +28.1904 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - 3 q^{3} + 5 q^{4} + 4 q^{5} + 2 q^{6} - 4 q^{7} - 12 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} - 3 q^{3} + 5 q^{4} + 4 q^{5} + 2 q^{6} - 4 q^{7} - 12 q^{8} + q^{9} - q^{10} - 2 q^{11} - 6 q^{12} - 7 q^{13} + q^{14} - 3 q^{15} + 7 q^{16} - q^{17} + 10 q^{18} + 5 q^{20} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 23 q^{24} + 4 q^{25} + 3 q^{26} - 12 q^{27} - 19 q^{28} + q^{29} + 2 q^{30} - 30 q^{32} - 19 q^{33} - 15 q^{34} - 4 q^{35} - 7 q^{36} + 2 q^{37} + 15 q^{39} - 12 q^{40} + 8 q^{41} - 15 q^{42} + q^{43} - 12 q^{44} + q^{45} - 12 q^{46} - 12 q^{47} - 23 q^{48} - 10 q^{49} - q^{50} - 22 q^{51} + 3 q^{52} + 5 q^{53} - 34 q^{54} - 2 q^{55} + 41 q^{56} - 27 q^{58} + 5 q^{59} - 6 q^{60} + 37 q^{62} - 3 q^{63} + 56 q^{64} - 7 q^{65} - 31 q^{66} - 4 q^{67} + 16 q^{68} + 9 q^{69} + q^{70} - 20 q^{71} - 17 q^{72} - 20 q^{73} + 25 q^{74} - 3 q^{75} + 14 q^{77} + 18 q^{78} - 17 q^{79} + 7 q^{80} + 12 q^{81} + 21 q^{82} + q^{83} + 20 q^{84} - q^{85} - 8 q^{86} - 16 q^{87} + 7 q^{88} - 11 q^{89} + 10 q^{90} - 6 q^{91} - q^{92} - 8 q^{93} + 31 q^{94} + 21 q^{96} - q^{97} - 9 q^{98} + 38 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.19091 0.842100 0.421050 0.907037i \(-0.361662\pi\)
0.421050 + 0.907037i \(0.361662\pi\)
\(3\) −3.04717 −1.75929 −0.879643 0.475635i \(-0.842218\pi\)
−0.879643 + 0.475635i \(0.842218\pi\)
\(4\) −0.581734 −0.290867
\(5\) 1.00000 0.447214
\(6\) −3.62891 −1.48149
\(7\) −0.609175 −0.230247 −0.115123 0.993351i \(-0.536726\pi\)
−0.115123 + 0.993351i \(0.536726\pi\)
\(8\) −3.07461 −1.08704
\(9\) 6.28525 2.09508
\(10\) 1.19091 0.376599
\(11\) 4.48517 1.35233 0.676164 0.736751i \(-0.263641\pi\)
0.676164 + 0.736751i \(0.263641\pi\)
\(12\) 1.77264 0.511718
\(13\) −4.43800 −1.23088 −0.615439 0.788184i \(-0.711021\pi\)
−0.615439 + 0.788184i \(0.711021\pi\)
\(14\) −0.725473 −0.193891
\(15\) −3.04717 −0.786776
\(16\) −2.49812 −0.624529
\(17\) 2.90343 0.704186 0.352093 0.935965i \(-0.385470\pi\)
0.352093 + 0.935965i \(0.385470\pi\)
\(18\) 7.48517 1.76427
\(19\) 0 0
\(20\) −0.581734 −0.130080
\(21\) 1.85626 0.405069
\(22\) 5.34143 1.13880
\(23\) −2.84726 −0.593694 −0.296847 0.954925i \(-0.595935\pi\)
−0.296847 + 0.954925i \(0.595935\pi\)
\(24\) 9.36887 1.91241
\(25\) 1.00000 0.200000
\(26\) −5.28525 −1.03652
\(27\) −10.0107 −1.92656
\(28\) 0.354378 0.0669712
\(29\) −1.11630 −0.207291 −0.103646 0.994614i \(-0.533051\pi\)
−0.103646 + 0.994614i \(0.533051\pi\)
\(30\) −3.62891 −0.662544
\(31\) 6.22908 1.11877 0.559387 0.828906i \(-0.311036\pi\)
0.559387 + 0.828906i \(0.311036\pi\)
\(32\) 3.17419 0.561123
\(33\) −13.6671 −2.37913
\(34\) 3.45773 0.592995
\(35\) −0.609175 −0.102969
\(36\) −3.65635 −0.609391
\(37\) 3.77264 0.620219 0.310109 0.950701i \(-0.399634\pi\)
0.310109 + 0.950701i \(0.399634\pi\)
\(38\) 0 0
\(39\) 13.5233 2.16547
\(40\) −3.07461 −0.486139
\(41\) 8.30369 1.29682 0.648409 0.761292i \(-0.275435\pi\)
0.648409 + 0.761292i \(0.275435\pi\)
\(42\) 2.21064 0.341109
\(43\) −9.98877 −1.52327 −0.761637 0.648004i \(-0.775604\pi\)
−0.761637 + 0.648004i \(0.775604\pi\)
\(44\) −2.60918 −0.393348
\(45\) 6.28525 0.936950
\(46\) −3.39082 −0.499950
\(47\) −5.88500 −0.858415 −0.429208 0.903206i \(-0.641207\pi\)
−0.429208 + 0.903206i \(0.641207\pi\)
\(48\) 7.61219 1.09872
\(49\) −6.62891 −0.946986
\(50\) 1.19091 0.168420
\(51\) −8.84726 −1.23886
\(52\) 2.58173 0.358022
\(53\) −8.44872 −1.16052 −0.580261 0.814431i \(-0.697049\pi\)
−0.580261 + 0.814431i \(0.697049\pi\)
\(54\) −11.9219 −1.62236
\(55\) 4.48517 0.604780
\(56\) 1.87298 0.250287
\(57\) 0 0
\(58\) −1.32941 −0.174560
\(59\) −10.2359 −1.33259 −0.666297 0.745686i \(-0.732122\pi\)
−0.666297 + 0.745686i \(0.732122\pi\)
\(60\) 1.77264 0.228847
\(61\) −4.98199 −0.637878 −0.318939 0.947775i \(-0.603327\pi\)
−0.318939 + 0.947775i \(0.603327\pi\)
\(62\) 7.41827 0.942121
\(63\) −3.82882 −0.482386
\(64\) 8.77641 1.09705
\(65\) −4.43800 −0.550466
\(66\) −16.2762 −2.00347
\(67\) −8.47616 −1.03553 −0.517764 0.855524i \(-0.673235\pi\)
−0.517764 + 0.855524i \(0.673235\pi\)
\(68\) −1.68903 −0.204825
\(69\) 8.67608 1.04448
\(70\) −0.725473 −0.0867106
\(71\) −11.6199 −1.37903 −0.689514 0.724272i \(-0.742176\pi\)
−0.689514 + 0.724272i \(0.742176\pi\)
\(72\) −19.3247 −2.27744
\(73\) 3.72325 0.435773 0.217887 0.975974i \(-0.430084\pi\)
0.217887 + 0.975974i \(0.430084\pi\)
\(74\) 4.49288 0.522286
\(75\) −3.04717 −0.351857
\(76\) 0 0
\(77\) −2.73225 −0.311369
\(78\) 16.1051 1.82354
\(79\) −9.03817 −1.01687 −0.508437 0.861099i \(-0.669776\pi\)
−0.508437 + 0.861099i \(0.669776\pi\)
\(80\) −2.49812 −0.279298
\(81\) 11.6486 1.29429
\(82\) 9.88894 1.09205
\(83\) −2.12178 −0.232896 −0.116448 0.993197i \(-0.537151\pi\)
−0.116448 + 0.993197i \(0.537151\pi\)
\(84\) −1.07985 −0.117821
\(85\) 2.90343 0.314921
\(86\) −11.8957 −1.28275
\(87\) 3.40155 0.364684
\(88\) −13.7901 −1.47003
\(89\) −7.93217 −0.840808 −0.420404 0.907337i \(-0.638112\pi\)
−0.420404 + 0.907337i \(0.638112\pi\)
\(90\) 7.48517 0.789006
\(91\) 2.70352 0.283406
\(92\) 1.65635 0.172686
\(93\) −18.9811 −1.96824
\(94\) −7.00850 −0.722872
\(95\) 0 0
\(96\) −9.67231 −0.987176
\(97\) 9.67256 0.982099 0.491050 0.871132i \(-0.336613\pi\)
0.491050 + 0.871132i \(0.336613\pi\)
\(98\) −7.89443 −0.797458
\(99\) 28.1904 2.83324
\(100\) −0.581734 −0.0581734
\(101\) −0.971265 −0.0966444 −0.0483222 0.998832i \(-0.515387\pi\)
−0.0483222 + 0.998832i \(0.515387\pi\)
\(102\) −10.5363 −1.04325
\(103\) 3.34143 0.329241 0.164620 0.986357i \(-0.447360\pi\)
0.164620 + 0.986357i \(0.447360\pi\)
\(104\) 13.6451 1.33801
\(105\) 1.85626 0.181153
\(106\) −10.0617 −0.977275
\(107\) −9.51655 −0.920000 −0.460000 0.887919i \(-0.652151\pi\)
−0.460000 + 0.887919i \(0.652151\pi\)
\(108\) 5.82358 0.560374
\(109\) −5.54357 −0.530978 −0.265489 0.964114i \(-0.585533\pi\)
−0.265489 + 0.964114i \(0.585533\pi\)
\(110\) 5.34143 0.509285
\(111\) −11.4959 −1.09114
\(112\) 1.52179 0.143796
\(113\) −1.54134 −0.144997 −0.0724987 0.997369i \(-0.523097\pi\)
−0.0724987 + 0.997369i \(0.523097\pi\)
\(114\) 0 0
\(115\) −2.84726 −0.265508
\(116\) 0.649388 0.0602942
\(117\) −27.8939 −2.57879
\(118\) −12.1900 −1.12218
\(119\) −1.76870 −0.162136
\(120\) 9.36887 0.855257
\(121\) 9.11672 0.828793
\(122\) −5.93310 −0.537158
\(123\) −25.3028 −2.28147
\(124\) −3.62367 −0.325415
\(125\) 1.00000 0.0894427
\(126\) −4.55978 −0.406217
\(127\) −2.30549 −0.204579 −0.102289 0.994755i \(-0.532617\pi\)
−0.102289 + 0.994755i \(0.532617\pi\)
\(128\) 4.10353 0.362704
\(129\) 30.4375 2.67987
\(130\) −5.28525 −0.463547
\(131\) −12.9181 −1.12866 −0.564330 0.825549i \(-0.690865\pi\)
−0.564330 + 0.825549i \(0.690865\pi\)
\(132\) 7.95060 0.692011
\(133\) 0 0
\(134\) −10.0943 −0.872018
\(135\) −10.0107 −0.861586
\(136\) −8.92693 −0.765478
\(137\) −12.7335 −1.08790 −0.543950 0.839118i \(-0.683072\pi\)
−0.543950 + 0.839118i \(0.683072\pi\)
\(138\) 10.3324 0.879554
\(139\) 10.6087 0.899816 0.449908 0.893075i \(-0.351457\pi\)
0.449908 + 0.893075i \(0.351457\pi\)
\(140\) 0.354378 0.0299504
\(141\) 17.9326 1.51020
\(142\) −13.8383 −1.16128
\(143\) −19.9052 −1.66455
\(144\) −15.7013 −1.30844
\(145\) −1.11630 −0.0927035
\(146\) 4.43405 0.366965
\(147\) 20.1994 1.66602
\(148\) −2.19468 −0.180401
\(149\) 3.77307 0.309102 0.154551 0.987985i \(-0.450607\pi\)
0.154551 + 0.987985i \(0.450607\pi\)
\(150\) −3.62891 −0.296299
\(151\) 9.51562 0.774370 0.387185 0.922002i \(-0.373447\pi\)
0.387185 + 0.922002i \(0.373447\pi\)
\(152\) 0 0
\(153\) 18.2488 1.47533
\(154\) −3.25387 −0.262204
\(155\) 6.22908 0.500331
\(156\) −7.86699 −0.629863
\(157\) −3.45643 −0.275853 −0.137927 0.990442i \(-0.544044\pi\)
−0.137927 + 0.990442i \(0.544044\pi\)
\(158\) −10.7636 −0.856309
\(159\) 25.7447 2.04169
\(160\) 3.17419 0.250942
\(161\) 1.73448 0.136696
\(162\) 13.8725 1.08992
\(163\) 6.65283 0.521090 0.260545 0.965462i \(-0.416098\pi\)
0.260545 + 0.965462i \(0.416098\pi\)
\(164\) −4.83054 −0.377202
\(165\) −13.6671 −1.06398
\(166\) −2.52685 −0.196122
\(167\) 16.4555 1.27336 0.636682 0.771126i \(-0.280306\pi\)
0.636682 + 0.771126i \(0.280306\pi\)
\(168\) −5.70728 −0.440327
\(169\) 6.69581 0.515062
\(170\) 3.45773 0.265195
\(171\) 0 0
\(172\) 5.81081 0.443070
\(173\) 22.7824 1.73212 0.866058 0.499943i \(-0.166646\pi\)
0.866058 + 0.499943i \(0.166646\pi\)
\(174\) 4.05094 0.307101
\(175\) −0.609175 −0.0460493
\(176\) −11.2045 −0.844569
\(177\) 31.1904 2.34441
\(178\) −9.44650 −0.708045
\(179\) 2.32916 0.174090 0.0870449 0.996204i \(-0.472258\pi\)
0.0870449 + 0.996204i \(0.472258\pi\)
\(180\) −3.65635 −0.272528
\(181\) 22.3392 1.66046 0.830230 0.557421i \(-0.188209\pi\)
0.830230 + 0.557421i \(0.188209\pi\)
\(182\) 3.21965 0.238656
\(183\) 15.1810 1.12221
\(184\) 8.75421 0.645369
\(185\) 3.77264 0.277370
\(186\) −22.6047 −1.65746
\(187\) 13.0224 0.952291
\(188\) 3.42350 0.249685
\(189\) 6.09829 0.443585
\(190\) 0 0
\(191\) 2.23766 0.161911 0.0809556 0.996718i \(-0.474203\pi\)
0.0809556 + 0.996718i \(0.474203\pi\)
\(192\) −26.7432 −1.93003
\(193\) 4.54306 0.327017 0.163508 0.986542i \(-0.447719\pi\)
0.163508 + 0.986542i \(0.447719\pi\)
\(194\) 11.5191 0.827026
\(195\) 13.5233 0.968426
\(196\) 3.85626 0.275447
\(197\) −19.2236 −1.36962 −0.684812 0.728720i \(-0.740116\pi\)
−0.684812 + 0.728720i \(0.740116\pi\)
\(198\) 33.5722 2.38587
\(199\) −6.15094 −0.436029 −0.218014 0.975946i \(-0.569958\pi\)
−0.218014 + 0.975946i \(0.569958\pi\)
\(200\) −3.07461 −0.217408
\(201\) 25.8283 1.82179
\(202\) −1.15669 −0.0813843
\(203\) 0.680021 0.0477281
\(204\) 5.14675 0.360345
\(205\) 8.30369 0.579955
\(206\) 3.97934 0.277254
\(207\) −17.8957 −1.24384
\(208\) 11.0866 0.768720
\(209\) 0 0
\(210\) 2.21064 0.152549
\(211\) −12.6932 −0.873837 −0.436919 0.899501i \(-0.643930\pi\)
−0.436919 + 0.899501i \(0.643930\pi\)
\(212\) 4.91491 0.337557
\(213\) 35.4078 2.42610
\(214\) −11.3334 −0.774732
\(215\) −9.98877 −0.681228
\(216\) 30.7791 2.09425
\(217\) −3.79460 −0.257594
\(218\) −6.60189 −0.447136
\(219\) −11.3454 −0.766649
\(220\) −2.60918 −0.175911
\(221\) −12.8854 −0.866767
\(222\) −13.6906 −0.918851
\(223\) −22.5376 −1.50923 −0.754614 0.656169i \(-0.772176\pi\)
−0.754614 + 0.656169i \(0.772176\pi\)
\(224\) −1.93364 −0.129197
\(225\) 6.28525 0.419017
\(226\) −1.83560 −0.122102
\(227\) −18.1124 −1.20216 −0.601080 0.799189i \(-0.705263\pi\)
−0.601080 + 0.799189i \(0.705263\pi\)
\(228\) 0 0
\(229\) −9.41604 −0.622229 −0.311115 0.950372i \(-0.600702\pi\)
−0.311115 + 0.950372i \(0.600702\pi\)
\(230\) −3.39082 −0.223584
\(231\) 8.32564 0.547787
\(232\) 3.43218 0.225334
\(233\) 15.7000 1.02854 0.514271 0.857628i \(-0.328063\pi\)
0.514271 + 0.857628i \(0.328063\pi\)
\(234\) −33.2191 −2.17160
\(235\) −5.88500 −0.383895
\(236\) 5.95455 0.387608
\(237\) 27.5408 1.78897
\(238\) −2.10636 −0.136535
\(239\) −23.4610 −1.51757 −0.758783 0.651344i \(-0.774205\pi\)
−0.758783 + 0.651344i \(0.774205\pi\)
\(240\) 7.61219 0.491365
\(241\) −13.1694 −0.848314 −0.424157 0.905589i \(-0.639430\pi\)
−0.424157 + 0.905589i \(0.639430\pi\)
\(242\) 10.8572 0.697927
\(243\) −5.46321 −0.350465
\(244\) 2.89819 0.185538
\(245\) −6.62891 −0.423505
\(246\) −30.1333 −1.92123
\(247\) 0 0
\(248\) −19.1520 −1.21615
\(249\) 6.46544 0.409730
\(250\) 1.19091 0.0753197
\(251\) −17.3251 −1.09355 −0.546776 0.837279i \(-0.684145\pi\)
−0.546776 + 0.837279i \(0.684145\pi\)
\(252\) 2.22736 0.140310
\(253\) −12.7704 −0.802869
\(254\) −2.74563 −0.172276
\(255\) −8.84726 −0.554037
\(256\) −12.6659 −0.791618
\(257\) 5.67960 0.354283 0.177142 0.984185i \(-0.443315\pi\)
0.177142 + 0.984185i \(0.443315\pi\)
\(258\) 36.2483 2.25672
\(259\) −2.29820 −0.142803
\(260\) 2.58173 0.160112
\(261\) −7.01621 −0.434293
\(262\) −15.3843 −0.950445
\(263\) 5.65764 0.348865 0.174433 0.984669i \(-0.444191\pi\)
0.174433 + 0.984669i \(0.444191\pi\)
\(264\) 42.0209 2.58621
\(265\) −8.44872 −0.519001
\(266\) 0 0
\(267\) 24.1707 1.47922
\(268\) 4.93087 0.301201
\(269\) 23.9918 1.46280 0.731402 0.681946i \(-0.238866\pi\)
0.731402 + 0.681946i \(0.238866\pi\)
\(270\) −11.9219 −0.725542
\(271\) −21.2995 −1.29385 −0.646926 0.762553i \(-0.723946\pi\)
−0.646926 + 0.762553i \(0.723946\pi\)
\(272\) −7.25311 −0.439785
\(273\) −8.23808 −0.498591
\(274\) −15.1645 −0.916121
\(275\) 4.48517 0.270466
\(276\) −5.04717 −0.303804
\(277\) −0.821109 −0.0493357 −0.0246678 0.999696i \(-0.507853\pi\)
−0.0246678 + 0.999696i \(0.507853\pi\)
\(278\) 12.6340 0.757735
\(279\) 39.1513 2.34393
\(280\) 1.87298 0.111932
\(281\) 0.587479 0.0350461 0.0175230 0.999846i \(-0.494422\pi\)
0.0175230 + 0.999846i \(0.494422\pi\)
\(282\) 21.3561 1.27174
\(283\) 30.9424 1.83933 0.919667 0.392699i \(-0.128459\pi\)
0.919667 + 0.392699i \(0.128459\pi\)
\(284\) 6.75969 0.401114
\(285\) 0 0
\(286\) −23.7052 −1.40172
\(287\) −5.05840 −0.298588
\(288\) 19.9506 1.17560
\(289\) −8.57008 −0.504122
\(290\) −1.32941 −0.0780656
\(291\) −29.4739 −1.72779
\(292\) −2.16594 −0.126752
\(293\) −3.76271 −0.219820 −0.109910 0.993942i \(-0.535056\pi\)
−0.109910 + 0.993942i \(0.535056\pi\)
\(294\) 24.0557 1.40296
\(295\) −10.2359 −0.595955
\(296\) −11.5994 −0.674202
\(297\) −44.8998 −2.60535
\(298\) 4.49338 0.260295
\(299\) 12.6361 0.730765
\(300\) 1.77264 0.102344
\(301\) 6.08491 0.350728
\(302\) 11.3322 0.652097
\(303\) 2.95961 0.170025
\(304\) 0 0
\(305\) −4.98199 −0.285268
\(306\) 21.7327 1.24237
\(307\) −20.3419 −1.16097 −0.580485 0.814271i \(-0.697137\pi\)
−0.580485 + 0.814271i \(0.697137\pi\)
\(308\) 1.58945 0.0905670
\(309\) −10.1819 −0.579228
\(310\) 7.41827 0.421329
\(311\) −7.67830 −0.435397 −0.217698 0.976016i \(-0.569855\pi\)
−0.217698 + 0.976016i \(0.569855\pi\)
\(312\) −41.5790 −2.35395
\(313\) 23.9927 1.35615 0.678074 0.734993i \(-0.262815\pi\)
0.678074 + 0.734993i \(0.262815\pi\)
\(314\) −4.11630 −0.232296
\(315\) −3.82882 −0.215730
\(316\) 5.25781 0.295775
\(317\) −1.03904 −0.0583580 −0.0291790 0.999574i \(-0.509289\pi\)
−0.0291790 + 0.999574i \(0.509289\pi\)
\(318\) 30.6596 1.71931
\(319\) −5.00678 −0.280326
\(320\) 8.77641 0.490616
\(321\) 28.9986 1.61854
\(322\) 2.06561 0.115112
\(323\) 0 0
\(324\) −6.77641 −0.376467
\(325\) −4.43800 −0.246176
\(326\) 7.92292 0.438810
\(327\) 16.8922 0.934141
\(328\) −25.5306 −1.40969
\(329\) 3.58500 0.197647
\(330\) −16.2762 −0.895978
\(331\) −30.8316 −1.69466 −0.847328 0.531069i \(-0.821790\pi\)
−0.847328 + 0.531069i \(0.821790\pi\)
\(332\) 1.23431 0.0677418
\(333\) 23.7120 1.29941
\(334\) 19.5970 1.07230
\(335\) −8.47616 −0.463102
\(336\) −4.63716 −0.252978
\(337\) −20.7153 −1.12843 −0.564217 0.825627i \(-0.690822\pi\)
−0.564217 + 0.825627i \(0.690822\pi\)
\(338\) 7.97410 0.433734
\(339\) 4.69674 0.255092
\(340\) −1.68903 −0.0916003
\(341\) 27.9384 1.51295
\(342\) 0 0
\(343\) 8.30239 0.448287
\(344\) 30.7116 1.65586
\(345\) 8.67608 0.467104
\(346\) 27.1318 1.45862
\(347\) 8.22136 0.441346 0.220673 0.975348i \(-0.429175\pi\)
0.220673 + 0.975348i \(0.429175\pi\)
\(348\) −1.97880 −0.106075
\(349\) 11.9216 0.638150 0.319075 0.947730i \(-0.396628\pi\)
0.319075 + 0.947730i \(0.396628\pi\)
\(350\) −0.725473 −0.0387782
\(351\) 44.4276 2.37137
\(352\) 14.2368 0.758823
\(353\) −11.7983 −0.627959 −0.313980 0.949430i \(-0.601662\pi\)
−0.313980 + 0.949430i \(0.601662\pi\)
\(354\) 37.1450 1.97423
\(355\) −11.6199 −0.616720
\(356\) 4.61441 0.244563
\(357\) 5.38953 0.285244
\(358\) 2.77382 0.146601
\(359\) 0.110812 0.00584841 0.00292420 0.999996i \(-0.499069\pi\)
0.00292420 + 0.999996i \(0.499069\pi\)
\(360\) −19.3247 −1.01850
\(361\) 0 0
\(362\) 26.6040 1.39827
\(363\) −27.7802 −1.45808
\(364\) −1.57273 −0.0824334
\(365\) 3.72325 0.194884
\(366\) 18.0792 0.945013
\(367\) 11.7397 0.612808 0.306404 0.951902i \(-0.400874\pi\)
0.306404 + 0.951902i \(0.400874\pi\)
\(368\) 7.11278 0.370779
\(369\) 52.1908 2.71694
\(370\) 4.49288 0.233574
\(371\) 5.14675 0.267206
\(372\) 11.0419 0.572498
\(373\) −14.5190 −0.751763 −0.375882 0.926668i \(-0.622660\pi\)
−0.375882 + 0.926668i \(0.622660\pi\)
\(374\) 15.5085 0.801924
\(375\) −3.04717 −0.157355
\(376\) 18.0941 0.933131
\(377\) 4.95412 0.255150
\(378\) 7.26251 0.373543
\(379\) 6.59023 0.338518 0.169259 0.985572i \(-0.445863\pi\)
0.169259 + 0.985572i \(0.445863\pi\)
\(380\) 0 0
\(381\) 7.02522 0.359913
\(382\) 2.66485 0.136345
\(383\) 2.86921 0.146610 0.0733049 0.997310i \(-0.476645\pi\)
0.0733049 + 0.997310i \(0.476645\pi\)
\(384\) −12.5041 −0.638099
\(385\) −2.73225 −0.139249
\(386\) 5.41038 0.275381
\(387\) −62.7819 −3.19138
\(388\) −5.62686 −0.285660
\(389\) −6.33149 −0.321019 −0.160510 0.987034i \(-0.551314\pi\)
−0.160510 + 0.987034i \(0.551314\pi\)
\(390\) 16.1051 0.815512
\(391\) −8.26682 −0.418071
\(392\) 20.3813 1.02941
\(393\) 39.3637 1.98563
\(394\) −22.8936 −1.15336
\(395\) −9.03817 −0.454759
\(396\) −16.3993 −0.824097
\(397\) −30.5498 −1.53325 −0.766626 0.642094i \(-0.778066\pi\)
−0.766626 + 0.642094i \(0.778066\pi\)
\(398\) −7.32522 −0.367180
\(399\) 0 0
\(400\) −2.49812 −0.124906
\(401\) −30.3422 −1.51522 −0.757609 0.652709i \(-0.773633\pi\)
−0.757609 + 0.652709i \(0.773633\pi\)
\(402\) 30.7592 1.53413
\(403\) −27.6446 −1.37708
\(404\) 0.565018 0.0281107
\(405\) 11.6486 0.578825
\(406\) 0.809843 0.0401919
\(407\) 16.9209 0.838740
\(408\) 27.2019 1.34669
\(409\) 14.9726 0.740345 0.370173 0.928963i \(-0.379299\pi\)
0.370173 + 0.928963i \(0.379299\pi\)
\(410\) 9.88894 0.488380
\(411\) 38.8013 1.91393
\(412\) −1.94382 −0.0957653
\(413\) 6.23543 0.306825
\(414\) −21.3122 −1.04744
\(415\) −2.12178 −0.104154
\(416\) −14.0871 −0.690675
\(417\) −32.3264 −1.58303
\(418\) 0 0
\(419\) −6.17419 −0.301629 −0.150815 0.988562i \(-0.548190\pi\)
−0.150815 + 0.988562i \(0.548190\pi\)
\(420\) −1.07985 −0.0526913
\(421\) 27.5428 1.34235 0.671177 0.741297i \(-0.265789\pi\)
0.671177 + 0.741297i \(0.265789\pi\)
\(422\) −15.1165 −0.735858
\(423\) −36.9887 −1.79845
\(424\) 25.9765 1.26153
\(425\) 2.90343 0.140837
\(426\) 42.1675 2.04302
\(427\) 3.03490 0.146869
\(428\) 5.53610 0.267598
\(429\) 60.6544 2.92842
\(430\) −11.8957 −0.573663
\(431\) 15.0588 0.725358 0.362679 0.931914i \(-0.381862\pi\)
0.362679 + 0.931914i \(0.381862\pi\)
\(432\) 25.0080 1.20320
\(433\) 0.970840 0.0466556 0.0233278 0.999728i \(-0.492574\pi\)
0.0233278 + 0.999728i \(0.492574\pi\)
\(434\) −4.51902 −0.216920
\(435\) 3.40155 0.163092
\(436\) 3.22488 0.154444
\(437\) 0 0
\(438\) −13.5113 −0.645596
\(439\) 27.4375 1.30952 0.654760 0.755837i \(-0.272770\pi\)
0.654760 + 0.755837i \(0.272770\pi\)
\(440\) −13.7901 −0.657420
\(441\) −41.6643 −1.98402
\(442\) −15.3454 −0.729905
\(443\) −8.76544 −0.416459 −0.208229 0.978080i \(-0.566770\pi\)
−0.208229 + 0.978080i \(0.566770\pi\)
\(444\) 6.68755 0.317377
\(445\) −7.93217 −0.376021
\(446\) −26.8402 −1.27092
\(447\) −11.4972 −0.543798
\(448\) −5.34637 −0.252592
\(449\) 9.63397 0.454655 0.227327 0.973818i \(-0.427001\pi\)
0.227327 + 0.973818i \(0.427001\pi\)
\(450\) 7.48517 0.352854
\(451\) 37.2434 1.75372
\(452\) 0.896652 0.0421750
\(453\) −28.9957 −1.36234
\(454\) −21.5702 −1.01234
\(455\) 2.70352 0.126743
\(456\) 0 0
\(457\) −10.6708 −0.499161 −0.249580 0.968354i \(-0.580293\pi\)
−0.249580 + 0.968354i \(0.580293\pi\)
\(458\) −11.2137 −0.523980
\(459\) −29.0655 −1.35666
\(460\) 1.65635 0.0772276
\(461\) 5.68680 0.264861 0.132430 0.991192i \(-0.457722\pi\)
0.132430 + 0.991192i \(0.457722\pi\)
\(462\) 9.91509 0.461292
\(463\) 35.3550 1.64309 0.821543 0.570147i \(-0.193114\pi\)
0.821543 + 0.570147i \(0.193114\pi\)
\(464\) 2.78864 0.129459
\(465\) −18.9811 −0.880226
\(466\) 18.6973 0.866135
\(467\) −32.9071 −1.52276 −0.761380 0.648306i \(-0.775478\pi\)
−0.761380 + 0.648306i \(0.775478\pi\)
\(468\) 16.2269 0.750086
\(469\) 5.16347 0.238427
\(470\) −7.00850 −0.323278
\(471\) 10.5323 0.485305
\(472\) 31.4713 1.44858
\(473\) −44.8013 −2.05997
\(474\) 32.7986 1.50649
\(475\) 0 0
\(476\) 1.02891 0.0471602
\(477\) −53.1023 −2.43139
\(478\) −27.9399 −1.27794
\(479\) −9.05721 −0.413835 −0.206917 0.978358i \(-0.566343\pi\)
−0.206917 + 0.978358i \(0.566343\pi\)
\(480\) −9.67231 −0.441479
\(481\) −16.7430 −0.763414
\(482\) −15.6835 −0.714366
\(483\) −5.28525 −0.240487
\(484\) −5.30351 −0.241069
\(485\) 9.67256 0.439208
\(486\) −6.50619 −0.295127
\(487\) 16.5206 0.748620 0.374310 0.927304i \(-0.377880\pi\)
0.374310 + 0.927304i \(0.377880\pi\)
\(488\) 15.3177 0.693399
\(489\) −20.2723 −0.916745
\(490\) −7.89443 −0.356634
\(491\) −1.39125 −0.0627862 −0.0313931 0.999507i \(-0.509994\pi\)
−0.0313931 + 0.999507i \(0.509994\pi\)
\(492\) 14.7195 0.663605
\(493\) −3.24109 −0.145972
\(494\) 0 0
\(495\) 28.1904 1.26706
\(496\) −15.5610 −0.698708
\(497\) 7.07856 0.317517
\(498\) 7.69975 0.345034
\(499\) −16.6651 −0.746033 −0.373016 0.927825i \(-0.621676\pi\)
−0.373016 + 0.927825i \(0.621676\pi\)
\(500\) −0.581734 −0.0260159
\(501\) −50.1427 −2.24021
\(502\) −20.6327 −0.920881
\(503\) 15.6391 0.697314 0.348657 0.937250i \(-0.386638\pi\)
0.348657 + 0.937250i \(0.386638\pi\)
\(504\) 11.7721 0.524373
\(505\) −0.971265 −0.0432207
\(506\) −15.2084 −0.676096
\(507\) −20.4033 −0.906141
\(508\) 1.34118 0.0595053
\(509\) 19.1540 0.848988 0.424494 0.905431i \(-0.360452\pi\)
0.424494 + 0.905431i \(0.360452\pi\)
\(510\) −10.5363 −0.466554
\(511\) −2.26811 −0.100335
\(512\) −23.2910 −1.02933
\(513\) 0 0
\(514\) 6.76389 0.298342
\(515\) 3.34143 0.147241
\(516\) −17.7065 −0.779487
\(517\) −26.3952 −1.16086
\(518\) −2.73695 −0.120255
\(519\) −69.4220 −3.04729
\(520\) 13.6451 0.598378
\(521\) 19.2394 0.842892 0.421446 0.906853i \(-0.361523\pi\)
0.421446 + 0.906853i \(0.361523\pi\)
\(522\) −8.35567 −0.365718
\(523\) −6.63945 −0.290323 −0.145161 0.989408i \(-0.546370\pi\)
−0.145161 + 0.989408i \(0.546370\pi\)
\(524\) 7.51490 0.328290
\(525\) 1.85626 0.0810139
\(526\) 6.73774 0.293779
\(527\) 18.0857 0.787825
\(528\) 34.1419 1.48584
\(529\) −14.8931 −0.647528
\(530\) −10.0617 −0.437051
\(531\) −64.3349 −2.79190
\(532\) 0 0
\(533\) −36.8517 −1.59623
\(534\) 28.7851 1.24565
\(535\) −9.51655 −0.411436
\(536\) 26.0609 1.12566
\(537\) −7.09736 −0.306274
\(538\) 28.5720 1.23183
\(539\) −29.7317 −1.28064
\(540\) 5.82358 0.250607
\(541\) 41.7511 1.79502 0.897510 0.440994i \(-0.145374\pi\)
0.897510 + 0.440994i \(0.145374\pi\)
\(542\) −25.3658 −1.08955
\(543\) −68.0714 −2.92122
\(544\) 9.21606 0.395135
\(545\) −5.54357 −0.237460
\(546\) −9.81081 −0.419864
\(547\) −12.2052 −0.521855 −0.260927 0.965358i \(-0.584028\pi\)
−0.260927 + 0.965358i \(0.584028\pi\)
\(548\) 7.40754 0.316434
\(549\) −31.3131 −1.33641
\(550\) 5.34143 0.227759
\(551\) 0 0
\(552\) −26.6756 −1.13539
\(553\) 5.50583 0.234132
\(554\) −0.977867 −0.0415456
\(555\) −11.4959 −0.487973
\(556\) −6.17143 −0.261727
\(557\) 35.1548 1.48956 0.744779 0.667311i \(-0.232555\pi\)
0.744779 + 0.667311i \(0.232555\pi\)
\(558\) 46.6257 1.97382
\(559\) 44.3301 1.87496
\(560\) 1.52179 0.0643074
\(561\) −39.6814 −1.67535
\(562\) 0.699634 0.0295123
\(563\) −17.8406 −0.751891 −0.375945 0.926642i \(-0.622682\pi\)
−0.375945 + 0.926642i \(0.622682\pi\)
\(564\) −10.4320 −0.439267
\(565\) −1.54134 −0.0648448
\(566\) 36.8496 1.54890
\(567\) −7.09606 −0.298007
\(568\) 35.7267 1.49906
\(569\) −31.6042 −1.32492 −0.662459 0.749098i \(-0.730487\pi\)
−0.662459 + 0.749098i \(0.730487\pi\)
\(570\) 0 0
\(571\) −4.73053 −0.197967 −0.0989833 0.995089i \(-0.531559\pi\)
−0.0989833 + 0.995089i \(0.531559\pi\)
\(572\) 11.5795 0.484164
\(573\) −6.81852 −0.284848
\(574\) −6.02410 −0.251441
\(575\) −2.84726 −0.118739
\(576\) 55.1620 2.29841
\(577\) 24.4074 1.01609 0.508047 0.861330i \(-0.330368\pi\)
0.508047 + 0.861330i \(0.330368\pi\)
\(578\) −10.2062 −0.424522
\(579\) −13.8435 −0.575316
\(580\) 0.649388 0.0269644
\(581\) 1.29254 0.0536235
\(582\) −35.1008 −1.45497
\(583\) −37.8939 −1.56941
\(584\) −11.4475 −0.473703
\(585\) −27.8939 −1.15327
\(586\) −4.48104 −0.185110
\(587\) −28.6154 −1.18109 −0.590543 0.807006i \(-0.701086\pi\)
−0.590543 + 0.807006i \(0.701086\pi\)
\(588\) −11.7507 −0.484590
\(589\) 0 0
\(590\) −12.1900 −0.501853
\(591\) 58.5776 2.40956
\(592\) −9.42450 −0.387345
\(593\) 3.71511 0.152561 0.0762807 0.997086i \(-0.475695\pi\)
0.0762807 + 0.997086i \(0.475695\pi\)
\(594\) −53.4716 −2.19397
\(595\) −1.76870 −0.0725096
\(596\) −2.19492 −0.0899076
\(597\) 18.7430 0.767099
\(598\) 15.0485 0.615378
\(599\) −7.09940 −0.290074 −0.145037 0.989426i \(-0.546330\pi\)
−0.145037 + 0.989426i \(0.546330\pi\)
\(600\) 9.36887 0.382482
\(601\) 11.0596 0.451131 0.225566 0.974228i \(-0.427577\pi\)
0.225566 + 0.974228i \(0.427577\pi\)
\(602\) 7.24658 0.295349
\(603\) −53.2748 −2.16952
\(604\) −5.53556 −0.225239
\(605\) 9.11672 0.370647
\(606\) 3.52463 0.143178
\(607\) −27.1193 −1.10074 −0.550369 0.834921i \(-0.685513\pi\)
−0.550369 + 0.834921i \(0.685513\pi\)
\(608\) 0 0
\(609\) −2.07214 −0.0839673
\(610\) −5.93310 −0.240224
\(611\) 26.1176 1.05660
\(612\) −10.6160 −0.429125
\(613\) 41.8312 1.68954 0.844772 0.535126i \(-0.179736\pi\)
0.844772 + 0.535126i \(0.179736\pi\)
\(614\) −24.2253 −0.977654
\(615\) −25.3028 −1.02031
\(616\) 8.40062 0.338471
\(617\) −17.7052 −0.712786 −0.356393 0.934336i \(-0.615994\pi\)
−0.356393 + 0.934336i \(0.615994\pi\)
\(618\) −12.1257 −0.487768
\(619\) −39.8064 −1.59995 −0.799976 0.600032i \(-0.795155\pi\)
−0.799976 + 0.600032i \(0.795155\pi\)
\(620\) −3.62367 −0.145530
\(621\) 28.5031 1.14379
\(622\) −9.14416 −0.366648
\(623\) 4.83208 0.193593
\(624\) −33.7829 −1.35240
\(625\) 1.00000 0.0400000
\(626\) 28.5732 1.14201
\(627\) 0 0
\(628\) 2.01072 0.0802366
\(629\) 10.9536 0.436749
\(630\) −4.55978 −0.181666
\(631\) 46.1980 1.83911 0.919557 0.392956i \(-0.128547\pi\)
0.919557 + 0.392956i \(0.128547\pi\)
\(632\) 27.7889 1.10538
\(633\) 38.6784 1.53733
\(634\) −1.23740 −0.0491433
\(635\) −2.30549 −0.0914905
\(636\) −14.9766 −0.593860
\(637\) 29.4191 1.16563
\(638\) −5.96262 −0.236062
\(639\) −73.0340 −2.88918
\(640\) 4.10353 0.162206
\(641\) −6.61348 −0.261217 −0.130608 0.991434i \(-0.541693\pi\)
−0.130608 + 0.991434i \(0.541693\pi\)
\(642\) 34.5347 1.36297
\(643\) −30.6152 −1.20735 −0.603673 0.797232i \(-0.706297\pi\)
−0.603673 + 0.797232i \(0.706297\pi\)
\(644\) −1.00901 −0.0397604
\(645\) 30.4375 1.19847
\(646\) 0 0
\(647\) −11.8979 −0.467753 −0.233877 0.972266i \(-0.575141\pi\)
−0.233877 + 0.972266i \(0.575141\pi\)
\(648\) −35.8150 −1.40695
\(649\) −45.9095 −1.80211
\(650\) −5.28525 −0.207305
\(651\) 11.5628 0.453182
\(652\) −3.87018 −0.151568
\(653\) −1.42899 −0.0559207 −0.0279604 0.999609i \(-0.508901\pi\)
−0.0279604 + 0.999609i \(0.508901\pi\)
\(654\) 20.1171 0.786640
\(655\) −12.9181 −0.504752
\(656\) −20.7436 −0.809901
\(657\) 23.4015 0.912981
\(658\) 4.26941 0.166439
\(659\) 24.4970 0.954268 0.477134 0.878831i \(-0.341676\pi\)
0.477134 + 0.878831i \(0.341676\pi\)
\(660\) 7.95060 0.309477
\(661\) 3.22606 0.125479 0.0627396 0.998030i \(-0.480016\pi\)
0.0627396 + 0.998030i \(0.480016\pi\)
\(662\) −36.7176 −1.42707
\(663\) 39.2641 1.52489
\(664\) 6.52366 0.253167
\(665\) 0 0
\(666\) 28.2389 1.09423
\(667\) 3.17838 0.123068
\(668\) −9.57273 −0.370380
\(669\) 68.6759 2.65516
\(670\) −10.0943 −0.389978
\(671\) −22.3451 −0.862621
\(672\) 5.89213 0.227294
\(673\) −37.1424 −1.43173 −0.715866 0.698237i \(-0.753968\pi\)
−0.715866 + 0.698237i \(0.753968\pi\)
\(674\) −24.6700 −0.950254
\(675\) −10.0107 −0.385313
\(676\) −3.89518 −0.149815
\(677\) 24.7550 0.951412 0.475706 0.879604i \(-0.342193\pi\)
0.475706 + 0.879604i \(0.342193\pi\)
\(678\) 5.59339 0.214813
\(679\) −5.89228 −0.226125
\(680\) −8.92693 −0.342332
\(681\) 55.1914 2.11494
\(682\) 33.2722 1.27406
\(683\) −40.1153 −1.53497 −0.767484 0.641068i \(-0.778492\pi\)
−0.767484 + 0.641068i \(0.778492\pi\)
\(684\) 0 0
\(685\) −12.7335 −0.486524
\(686\) 9.88740 0.377503
\(687\) 28.6923 1.09468
\(688\) 24.9531 0.951328
\(689\) 37.4954 1.42846
\(690\) 10.3324 0.393349
\(691\) 39.4963 1.50251 0.751254 0.660013i \(-0.229449\pi\)
0.751254 + 0.660013i \(0.229449\pi\)
\(692\) −13.2533 −0.503816
\(693\) −17.1729 −0.652344
\(694\) 9.79090 0.371658
\(695\) 10.6087 0.402410
\(696\) −10.4584 −0.396426
\(697\) 24.1092 0.913201
\(698\) 14.1976 0.537386
\(699\) −47.8406 −1.80950
\(700\) 0.354378 0.0133942
\(701\) 0.0219552 0.000829236 0 0.000414618 1.00000i \(-0.499868\pi\)
0.000414618 1.00000i \(0.499868\pi\)
\(702\) 52.9092 1.99693
\(703\) 0 0
\(704\) 39.3637 1.48357
\(705\) 17.9326 0.675381
\(706\) −14.0507 −0.528805
\(707\) 0.591670 0.0222521
\(708\) −18.1445 −0.681913
\(709\) −17.8017 −0.668558 −0.334279 0.942474i \(-0.608493\pi\)
−0.334279 + 0.942474i \(0.608493\pi\)
\(710\) −13.8383 −0.519340
\(711\) −56.8071 −2.13043
\(712\) 24.3883 0.913992
\(713\) −17.7358 −0.664210
\(714\) 6.41844 0.240204
\(715\) −19.9052 −0.744410
\(716\) −1.35495 −0.0506370
\(717\) 71.4896 2.66983
\(718\) 0.131967 0.00492495
\(719\) 18.8103 0.701506 0.350753 0.936468i \(-0.385926\pi\)
0.350753 + 0.936468i \(0.385926\pi\)
\(720\) −15.7013 −0.585153
\(721\) −2.03552 −0.0758066
\(722\) 0 0
\(723\) 40.1294 1.49243
\(724\) −12.9955 −0.482973
\(725\) −1.11630 −0.0414582
\(726\) −33.0837 −1.22785
\(727\) 5.00301 0.185552 0.0927758 0.995687i \(-0.470426\pi\)
0.0927758 + 0.995687i \(0.470426\pi\)
\(728\) −8.31227 −0.308073
\(729\) −18.2986 −0.677725
\(730\) 4.43405 0.164112
\(731\) −29.0017 −1.07267
\(732\) −8.83129 −0.326414
\(733\) −23.5259 −0.868950 −0.434475 0.900684i \(-0.643066\pi\)
−0.434475 + 0.900684i \(0.643066\pi\)
\(734\) 13.9809 0.516046
\(735\) 20.1994 0.745066
\(736\) −9.03774 −0.333136
\(737\) −38.0170 −1.40037
\(738\) 62.1545 2.28794
\(739\) −37.3836 −1.37518 −0.687590 0.726099i \(-0.741331\pi\)
−0.687590 + 0.726099i \(0.741331\pi\)
\(740\) −2.19468 −0.0806779
\(741\) 0 0
\(742\) 6.12932 0.225014
\(743\) −10.3886 −0.381121 −0.190560 0.981675i \(-0.561030\pi\)
−0.190560 + 0.981675i \(0.561030\pi\)
\(744\) 58.3594 2.13956
\(745\) 3.77307 0.138235
\(746\) −17.2908 −0.633060
\(747\) −13.3359 −0.487937
\(748\) −7.57556 −0.276990
\(749\) 5.79725 0.211827
\(750\) −3.62891 −0.132509
\(751\) 31.2825 1.14152 0.570758 0.821119i \(-0.306650\pi\)
0.570758 + 0.821119i \(0.306650\pi\)
\(752\) 14.7014 0.536105
\(753\) 52.7927 1.92387
\(754\) 5.89991 0.214862
\(755\) 9.51562 0.346309
\(756\) −3.54758 −0.129024
\(757\) −12.6241 −0.458830 −0.229415 0.973329i \(-0.573681\pi\)
−0.229415 + 0.973329i \(0.573681\pi\)
\(758\) 7.84837 0.285066
\(759\) 38.9137 1.41248
\(760\) 0 0
\(761\) 11.5495 0.418668 0.209334 0.977844i \(-0.432870\pi\)
0.209334 + 0.977844i \(0.432870\pi\)
\(762\) 8.36640 0.303083
\(763\) 3.37701 0.122256
\(764\) −1.30172 −0.0470946
\(765\) 18.2488 0.659787
\(766\) 3.41697 0.123460
\(767\) 45.4267 1.64026
\(768\) 38.5951 1.39268
\(769\) −26.9207 −0.970784 −0.485392 0.874297i \(-0.661323\pi\)
−0.485392 + 0.874297i \(0.661323\pi\)
\(770\) −3.25387 −0.117261
\(771\) −17.3067 −0.623286
\(772\) −2.64286 −0.0951184
\(773\) −21.3331 −0.767299 −0.383649 0.923479i \(-0.625333\pi\)
−0.383649 + 0.923479i \(0.625333\pi\)
\(774\) −74.7676 −2.68747
\(775\) 6.22908 0.223755
\(776\) −29.7394 −1.06758
\(777\) 7.00301 0.251232
\(778\) −7.54024 −0.270331
\(779\) 0 0
\(780\) −7.86699 −0.281683
\(781\) −52.1172 −1.86490
\(782\) −9.84503 −0.352058
\(783\) 11.1749 0.399360
\(784\) 16.5598 0.591421
\(785\) −3.45643 −0.123365
\(786\) 46.8786 1.67210
\(787\) −3.52489 −0.125649 −0.0628243 0.998025i \(-0.520011\pi\)
−0.0628243 + 0.998025i \(0.520011\pi\)
\(788\) 11.1830 0.398379
\(789\) −17.2398 −0.613753
\(790\) −10.7636 −0.382953
\(791\) 0.938948 0.0333852
\(792\) −86.6746 −3.07985
\(793\) 22.1100 0.785151
\(794\) −36.3821 −1.29115
\(795\) 25.7447 0.913070
\(796\) 3.57821 0.126826
\(797\) 39.0084 1.38175 0.690875 0.722974i \(-0.257226\pi\)
0.690875 + 0.722974i \(0.257226\pi\)
\(798\) 0 0
\(799\) −17.0867 −0.604484
\(800\) 3.17419 0.112225
\(801\) −49.8557 −1.76156
\(802\) −36.1348 −1.27597
\(803\) 16.6994 0.589309
\(804\) −15.0252 −0.529899
\(805\) 1.73448 0.0611323
\(806\) −32.9222 −1.15964
\(807\) −73.1071 −2.57349
\(808\) 2.98626 0.105056
\(809\) 50.7196 1.78321 0.891604 0.452816i \(-0.149581\pi\)
0.891604 + 0.452816i \(0.149581\pi\)
\(810\) 13.8725 0.487429
\(811\) −29.0376 −1.01965 −0.509824 0.860279i \(-0.670289\pi\)
−0.509824 + 0.860279i \(0.670289\pi\)
\(812\) −0.395591 −0.0138825
\(813\) 64.9032 2.27625
\(814\) 20.1513 0.706303
\(815\) 6.65283 0.233038
\(816\) 22.1015 0.773706
\(817\) 0 0
\(818\) 17.8310 0.623445
\(819\) 16.9923 0.593759
\(820\) −4.83054 −0.168690
\(821\) 32.9878 1.15128 0.575640 0.817703i \(-0.304753\pi\)
0.575640 + 0.817703i \(0.304753\pi\)
\(822\) 46.2088 1.61172
\(823\) −26.5533 −0.925591 −0.462796 0.886465i \(-0.653154\pi\)
−0.462796 + 0.886465i \(0.653154\pi\)
\(824\) −10.2736 −0.357898
\(825\) −13.6671 −0.475826
\(826\) 7.42583 0.258378
\(827\) 32.7666 1.13941 0.569703 0.821851i \(-0.307058\pi\)
0.569703 + 0.821851i \(0.307058\pi\)
\(828\) 10.4106 0.361792
\(829\) −32.4548 −1.12720 −0.563601 0.826047i \(-0.690584\pi\)
−0.563601 + 0.826047i \(0.690584\pi\)
\(830\) −2.52685 −0.0877083
\(831\) 2.50206 0.0867955
\(832\) −38.9497 −1.35034
\(833\) −19.2466 −0.666854
\(834\) −38.4979 −1.33307
\(835\) 16.4555 0.569466
\(836\) 0 0
\(837\) −62.3576 −2.15539
\(838\) −7.35291 −0.254002
\(839\) 35.2098 1.21558 0.607788 0.794099i \(-0.292057\pi\)
0.607788 + 0.794099i \(0.292057\pi\)
\(840\) −5.70728 −0.196920
\(841\) −27.7539 −0.957030
\(842\) 32.8010 1.13040
\(843\) −1.79015 −0.0616560
\(844\) 7.38408 0.254171
\(845\) 6.69581 0.230343
\(846\) −44.0502 −1.51448
\(847\) −5.55368 −0.190827
\(848\) 21.1059 0.724779
\(849\) −94.2867 −3.23591
\(850\) 3.45773 0.118599
\(851\) −10.7417 −0.368220
\(852\) −20.5979 −0.705674
\(853\) −1.78825 −0.0612286 −0.0306143 0.999531i \(-0.509746\pi\)
−0.0306143 + 0.999531i \(0.509746\pi\)
\(854\) 3.61430 0.123679
\(855\) 0 0
\(856\) 29.2597 1.00008
\(857\) −3.61379 −0.123445 −0.0617224 0.998093i \(-0.519659\pi\)
−0.0617224 + 0.998093i \(0.519659\pi\)
\(858\) 72.2339 2.46603
\(859\) −25.3648 −0.865437 −0.432719 0.901529i \(-0.642446\pi\)
−0.432719 + 0.901529i \(0.642446\pi\)
\(860\) 5.81081 0.198147
\(861\) 15.4138 0.525301
\(862\) 17.9337 0.610824
\(863\) 29.9878 1.02080 0.510398 0.859939i \(-0.329498\pi\)
0.510398 + 0.859939i \(0.329498\pi\)
\(864\) −31.7760 −1.08104
\(865\) 22.7824 0.774626
\(866\) 1.15618 0.0392887
\(867\) 26.1145 0.886895
\(868\) 2.20745 0.0749257
\(869\) −40.5377 −1.37515
\(870\) 4.05094 0.137340
\(871\) 37.6172 1.27461
\(872\) 17.0443 0.577194
\(873\) 60.7945 2.05758
\(874\) 0 0
\(875\) −0.609175 −0.0205939
\(876\) 6.59999 0.222993
\(877\) −10.6478 −0.359550 −0.179775 0.983708i \(-0.557537\pi\)
−0.179775 + 0.983708i \(0.557537\pi\)
\(878\) 32.6756 1.10275
\(879\) 11.4656 0.386726
\(880\) −11.2045 −0.377703
\(881\) −31.5797 −1.06395 −0.531973 0.846761i \(-0.678549\pi\)
−0.531973 + 0.846761i \(0.678549\pi\)
\(882\) −49.6185 −1.67074
\(883\) 17.0174 0.572682 0.286341 0.958128i \(-0.407561\pi\)
0.286341 + 0.958128i \(0.407561\pi\)
\(884\) 7.49589 0.252114
\(885\) 31.1904 1.04845
\(886\) −10.4388 −0.350700
\(887\) 13.2290 0.444187 0.222093 0.975025i \(-0.428711\pi\)
0.222093 + 0.975025i \(0.428711\pi\)
\(888\) 35.3454 1.18611
\(889\) 1.40445 0.0471036
\(890\) −9.44650 −0.316647
\(891\) 52.2461 1.75031
\(892\) 13.1109 0.438985
\(893\) 0 0
\(894\) −13.6921 −0.457933
\(895\) 2.32916 0.0778553
\(896\) −2.49977 −0.0835113
\(897\) −38.5044 −1.28562
\(898\) 11.4732 0.382865
\(899\) −6.95350 −0.231912
\(900\) −3.65635 −0.121878
\(901\) −24.5303 −0.817222
\(902\) 44.3536 1.47681
\(903\) −18.5418 −0.617031
\(904\) 4.73903 0.157618
\(905\) 22.3392 0.742580
\(906\) −34.5313 −1.14723
\(907\) 14.8904 0.494428 0.247214 0.968961i \(-0.420485\pi\)
0.247214 + 0.968961i \(0.420485\pi\)
\(908\) 10.5366 0.349669
\(909\) −6.10464 −0.202478
\(910\) 3.21965 0.106730
\(911\) 49.5480 1.64160 0.820800 0.571216i \(-0.193528\pi\)
0.820800 + 0.571216i \(0.193528\pi\)
\(912\) 0 0
\(913\) −9.51655 −0.314952
\(914\) −12.7080 −0.420343
\(915\) 15.1810 0.501868
\(916\) 5.47763 0.180986
\(917\) 7.86939 0.259870
\(918\) −34.6143 −1.14244
\(919\) 27.3835 0.903300 0.451650 0.892195i \(-0.350836\pi\)
0.451650 + 0.892195i \(0.350836\pi\)
\(920\) 8.75421 0.288618
\(921\) 61.9851 2.04248
\(922\) 6.77247 0.223039
\(923\) 51.5691 1.69742
\(924\) −4.84331 −0.159333
\(925\) 3.77264 0.124044
\(926\) 42.1046 1.38364
\(927\) 21.0017 0.689787
\(928\) −3.54334 −0.116316
\(929\) 52.1894 1.71228 0.856139 0.516745i \(-0.172857\pi\)
0.856139 + 0.516745i \(0.172857\pi\)
\(930\) −22.6047 −0.741238
\(931\) 0 0
\(932\) −9.13323 −0.299169
\(933\) 23.3971 0.765987
\(934\) −39.1894 −1.28232
\(935\) 13.0224 0.425877
\(936\) 85.7630 2.80325
\(937\) 15.5798 0.508968 0.254484 0.967077i \(-0.418094\pi\)
0.254484 + 0.967077i \(0.418094\pi\)
\(938\) 6.14922 0.200779
\(939\) −73.1099 −2.38585
\(940\) 3.42350 0.111662
\(941\) 58.6553 1.91211 0.956055 0.293189i \(-0.0947164\pi\)
0.956055 + 0.293189i \(0.0947164\pi\)
\(942\) 12.5431 0.408675
\(943\) −23.6427 −0.769913
\(944\) 25.5704 0.832244
\(945\) 6.09829 0.198377
\(946\) −53.3543 −1.73470
\(947\) 12.3065 0.399908 0.199954 0.979805i \(-0.435921\pi\)
0.199954 + 0.979805i \(0.435921\pi\)
\(948\) −16.0214 −0.520352
\(949\) −16.5238 −0.536384
\(950\) 0 0
\(951\) 3.16612 0.102668
\(952\) 5.43807 0.176249
\(953\) −8.26997 −0.267891 −0.133945 0.990989i \(-0.542765\pi\)
−0.133945 + 0.990989i \(0.542765\pi\)
\(954\) −63.2401 −2.04747
\(955\) 2.23766 0.0724088
\(956\) 13.6481 0.441410
\(957\) 15.2565 0.493173
\(958\) −10.7863 −0.348490
\(959\) 7.75696 0.250485
\(960\) −26.7432 −0.863134
\(961\) 7.80138 0.251657
\(962\) −19.9394 −0.642871
\(963\) −59.8139 −1.92748
\(964\) 7.66108 0.246747
\(965\) 4.54306 0.146246
\(966\) −6.29426 −0.202514
\(967\) 14.2247 0.457436 0.228718 0.973493i \(-0.426547\pi\)
0.228718 + 0.973493i \(0.426547\pi\)
\(968\) −28.0304 −0.900931
\(969\) 0 0
\(970\) 11.5191 0.369857
\(971\) −9.73861 −0.312527 −0.156263 0.987715i \(-0.549945\pi\)
−0.156263 + 0.987715i \(0.549945\pi\)
\(972\) 3.17814 0.101939
\(973\) −6.46254 −0.207180
\(974\) 19.6745 0.630413
\(975\) 13.5233 0.433093
\(976\) 12.4456 0.398374
\(977\) 6.35308 0.203253 0.101627 0.994823i \(-0.467595\pi\)
0.101627 + 0.994823i \(0.467595\pi\)
\(978\) −24.1425 −0.771991
\(979\) −35.5771 −1.13705
\(980\) 3.85626 0.123184
\(981\) −34.8427 −1.11244
\(982\) −1.65685 −0.0528723
\(983\) −9.88087 −0.315151 −0.157575 0.987507i \(-0.550368\pi\)
−0.157575 + 0.987507i \(0.550368\pi\)
\(984\) 77.7962 2.48005
\(985\) −19.2236 −0.612514
\(986\) −3.85985 −0.122923
\(987\) −10.9241 −0.347718
\(988\) 0 0
\(989\) 28.4406 0.904358
\(990\) 33.5722 1.06700
\(991\) −37.3350 −1.18599 −0.592993 0.805208i \(-0.702054\pi\)
−0.592993 + 0.805208i \(0.702054\pi\)
\(992\) 19.7723 0.627771
\(993\) 93.9491 2.98138
\(994\) 8.42992 0.267381
\(995\) −6.15094 −0.194998
\(996\) −3.76117 −0.119177
\(997\) −43.6948 −1.38383 −0.691914 0.721980i \(-0.743232\pi\)
−0.691914 + 0.721980i \(0.743232\pi\)
\(998\) −19.8466 −0.628234
\(999\) −37.7669 −1.19489
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.i.1.3 4
5.4 even 2 9025.2.a.bp.1.2 4
19.8 odd 6 95.2.e.c.26.3 yes 8
19.12 odd 6 95.2.e.c.11.3 8
19.18 odd 2 1805.2.a.o.1.2 4
57.8 even 6 855.2.k.h.406.2 8
57.50 even 6 855.2.k.h.676.2 8
76.27 even 6 1520.2.q.o.881.4 8
76.31 even 6 1520.2.q.o.961.4 8
95.8 even 12 475.2.j.c.349.6 16
95.12 even 12 475.2.j.c.49.6 16
95.27 even 12 475.2.j.c.349.3 16
95.69 odd 6 475.2.e.e.201.2 8
95.84 odd 6 475.2.e.e.26.2 8
95.88 even 12 475.2.j.c.49.3 16
95.94 odd 2 9025.2.a.bg.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.e.c.11.3 8 19.12 odd 6
95.2.e.c.26.3 yes 8 19.8 odd 6
475.2.e.e.26.2 8 95.84 odd 6
475.2.e.e.201.2 8 95.69 odd 6
475.2.j.c.49.3 16 95.88 even 12
475.2.j.c.49.6 16 95.12 even 12
475.2.j.c.349.3 16 95.27 even 12
475.2.j.c.349.6 16 95.8 even 12
855.2.k.h.406.2 8 57.8 even 6
855.2.k.h.676.2 8 57.50 even 6
1520.2.q.o.881.4 8 76.27 even 6
1520.2.q.o.961.4 8 76.31 even 6
1805.2.a.i.1.3 4 1.1 even 1 trivial
1805.2.a.o.1.2 4 19.18 odd 2
9025.2.a.bg.1.3 4 95.94 odd 2
9025.2.a.bp.1.2 4 5.4 even 2