Properties

Label 245.4.a.p.1.4
Level $245$
Weight $4$
Character 245.1
Self dual yes
Analytic conductor $14.455$
Analytic rank $0$
Dimension $6$
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] = [245,4,Mod(1,245)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(245, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("245.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 245.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: \(14.4554679514\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.1163891200.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} - 23x^{4} + 12x^{3} + 154x^{2} + 152x + 28 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2\cdot 7 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-2.05886\) of defining polynomial
Character \(\chi\) \(=\) 245.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.644648 q^{2} -4.18687 q^{3} -7.58443 q^{4} -5.00000 q^{5} -2.69906 q^{6} -10.0465 q^{8} -9.47008 q^{9} +O(q^{10})\) \(q+0.644648 q^{2} -4.18687 q^{3} -7.58443 q^{4} -5.00000 q^{5} -2.69906 q^{6} -10.0465 q^{8} -9.47008 q^{9} -3.22324 q^{10} -47.7013 q^{11} +31.7550 q^{12} +57.2256 q^{13} +20.9344 q^{15} +54.1990 q^{16} -36.9686 q^{17} -6.10487 q^{18} +30.7659 q^{19} +37.9221 q^{20} -30.7506 q^{22} +53.1282 q^{23} +42.0633 q^{24} +25.0000 q^{25} +36.8904 q^{26} +152.696 q^{27} -195.663 q^{29} +13.4953 q^{30} +257.870 q^{31} +115.311 q^{32} +199.719 q^{33} -23.8317 q^{34} +71.8252 q^{36} +346.423 q^{37} +19.8332 q^{38} -239.596 q^{39} +50.2324 q^{40} +267.050 q^{41} -176.859 q^{43} +361.787 q^{44} +47.3504 q^{45} +34.2490 q^{46} -311.598 q^{47} -226.924 q^{48} +16.1162 q^{50} +154.783 q^{51} -434.024 q^{52} -492.270 q^{53} +98.4349 q^{54} +238.507 q^{55} -128.813 q^{57} -126.134 q^{58} +98.7653 q^{59} -158.775 q^{60} +82.1682 q^{61} +166.235 q^{62} -359.257 q^{64} -286.128 q^{65} +128.749 q^{66} +654.668 q^{67} +280.386 q^{68} -222.441 q^{69} +779.658 q^{71} +95.1409 q^{72} -829.673 q^{73} +223.321 q^{74} -104.672 q^{75} -233.342 q^{76} -154.455 q^{78} -769.426 q^{79} -270.995 q^{80} -383.625 q^{81} +172.153 q^{82} +613.203 q^{83} +184.843 q^{85} -114.012 q^{86} +819.215 q^{87} +479.230 q^{88} -457.666 q^{89} +30.5244 q^{90} -402.947 q^{92} -1079.67 q^{93} -200.871 q^{94} -153.830 q^{95} -482.793 q^{96} -1412.11 q^{97} +451.736 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{2} + 16 q^{3} + 14 q^{4} - 30 q^{5} + 24 q^{6} - 66 q^{8} + 70 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{2} + 16 q^{3} + 14 q^{4} - 30 q^{5} + 24 q^{6} - 66 q^{8} + 70 q^{9} + 10 q^{10} - 16 q^{11} + 160 q^{12} + 168 q^{13} - 80 q^{15} + 298 q^{16} - 4 q^{17} + 354 q^{18} + 308 q^{19} - 70 q^{20} - 236 q^{22} - 336 q^{23} - 92 q^{24} + 150 q^{25} + 56 q^{26} + 964 q^{27} + 176 q^{29} - 120 q^{30} + 392 q^{31} - 770 q^{32} + 188 q^{33} + 812 q^{34} + 230 q^{36} - 140 q^{37} + 20 q^{38} + 140 q^{39} + 330 q^{40} + 656 q^{41} - 388 q^{43} - 160 q^{44} - 350 q^{45} - 388 q^{46} + 628 q^{47} + 1396 q^{48} - 50 q^{50} + 744 q^{51} + 1520 q^{52} - 676 q^{53} + 2284 q^{54} + 80 q^{55} + 1468 q^{57} - 2012 q^{58} + 996 q^{59} - 800 q^{60} + 740 q^{61} - 364 q^{62} + 1426 q^{64} - 840 q^{65} - 3620 q^{66} + 1768 q^{67} - 2940 q^{68} - 1048 q^{69} - 224 q^{71} + 2858 q^{72} + 2640 q^{73} + 928 q^{74} + 400 q^{75} - 1340 q^{76} + 8 q^{78} + 1636 q^{79} - 1490 q^{80} + 4442 q^{81} - 1756 q^{82} + 140 q^{83} + 20 q^{85} + 1180 q^{86} + 1940 q^{87} - 5652 q^{88} - 1904 q^{89} - 1770 q^{90} - 1952 q^{92} - 1592 q^{93} - 3332 q^{94} - 1540 q^{95} - 6460 q^{96} + 516 q^{97} - 2804 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.644648 0.227917 0.113959 0.993485i \(-0.463647\pi\)
0.113959 + 0.993485i \(0.463647\pi\)
\(3\) −4.18687 −0.805764 −0.402882 0.915252i \(-0.631992\pi\)
−0.402882 + 0.915252i \(0.631992\pi\)
\(4\) −7.58443 −0.948054
\(5\) −5.00000 −0.447214
\(6\) −2.69906 −0.183648
\(7\) 0 0
\(8\) −10.0465 −0.443995
\(9\) −9.47008 −0.350744
\(10\) −3.22324 −0.101928
\(11\) −47.7013 −1.30750 −0.653750 0.756711i \(-0.726805\pi\)
−0.653750 + 0.756711i \(0.726805\pi\)
\(12\) 31.7550 0.763908
\(13\) 57.2256 1.22089 0.610443 0.792060i \(-0.290991\pi\)
0.610443 + 0.792060i \(0.290991\pi\)
\(14\) 0 0
\(15\) 20.9344 0.360349
\(16\) 54.1990 0.846859
\(17\) −36.9686 −0.527423 −0.263712 0.964602i \(-0.584947\pi\)
−0.263712 + 0.964602i \(0.584947\pi\)
\(18\) −6.10487 −0.0799407
\(19\) 30.7659 0.371484 0.185742 0.982599i \(-0.440531\pi\)
0.185742 + 0.982599i \(0.440531\pi\)
\(20\) 37.9221 0.423982
\(21\) 0 0
\(22\) −30.7506 −0.298002
\(23\) 53.1282 0.481652 0.240826 0.970568i \(-0.422582\pi\)
0.240826 + 0.970568i \(0.422582\pi\)
\(24\) 42.0633 0.357756
\(25\) 25.0000 0.200000
\(26\) 36.8904 0.278261
\(27\) 152.696 1.08838
\(28\) 0 0
\(29\) −195.663 −1.25288 −0.626442 0.779468i \(-0.715490\pi\)
−0.626442 + 0.779468i \(0.715490\pi\)
\(30\) 13.4953 0.0821298
\(31\) 257.870 1.49403 0.747014 0.664809i \(-0.231487\pi\)
0.747014 + 0.664809i \(0.231487\pi\)
\(32\) 115.311 0.637010
\(33\) 199.719 1.05354
\(34\) −23.8317 −0.120209
\(35\) 0 0
\(36\) 71.8252 0.332524
\(37\) 346.423 1.53923 0.769616 0.638507i \(-0.220447\pi\)
0.769616 + 0.638507i \(0.220447\pi\)
\(38\) 19.8332 0.0846676
\(39\) −239.596 −0.983747
\(40\) 50.2324 0.198561
\(41\) 267.050 1.01722 0.508611 0.860996i \(-0.330159\pi\)
0.508611 + 0.860996i \(0.330159\pi\)
\(42\) 0 0
\(43\) −176.859 −0.627227 −0.313614 0.949551i \(-0.601540\pi\)
−0.313614 + 0.949551i \(0.601540\pi\)
\(44\) 361.787 1.23958
\(45\) 47.3504 0.156857
\(46\) 34.2490 0.109777
\(47\) −311.598 −0.967049 −0.483524 0.875331i \(-0.660644\pi\)
−0.483524 + 0.875331i \(0.660644\pi\)
\(48\) −226.924 −0.682369
\(49\) 0 0
\(50\) 16.1162 0.0455835
\(51\) 154.783 0.424979
\(52\) −434.024 −1.15747
\(53\) −492.270 −1.27582 −0.637910 0.770111i \(-0.720201\pi\)
−0.637910 + 0.770111i \(0.720201\pi\)
\(54\) 98.4349 0.248061
\(55\) 238.507 0.584731
\(56\) 0 0
\(57\) −128.813 −0.299328
\(58\) −126.134 −0.285554
\(59\) 98.7653 0.217935 0.108967 0.994045i \(-0.465246\pi\)
0.108967 + 0.994045i \(0.465246\pi\)
\(60\) −158.775 −0.341630
\(61\) 82.1682 0.172468 0.0862340 0.996275i \(-0.472517\pi\)
0.0862340 + 0.996275i \(0.472517\pi\)
\(62\) 166.235 0.340515
\(63\) 0 0
\(64\) −359.257 −0.701674
\(65\) −286.128 −0.545997
\(66\) 128.749 0.240119
\(67\) 654.668 1.19374 0.596869 0.802339i \(-0.296411\pi\)
0.596869 + 0.802339i \(0.296411\pi\)
\(68\) 280.386 0.500026
\(69\) −222.441 −0.388098
\(70\) 0 0
\(71\) 779.658 1.30322 0.651608 0.758556i \(-0.274095\pi\)
0.651608 + 0.758556i \(0.274095\pi\)
\(72\) 95.1409 0.155729
\(73\) −829.673 −1.33022 −0.665109 0.746747i \(-0.731615\pi\)
−0.665109 + 0.746747i \(0.731615\pi\)
\(74\) 223.321 0.350818
\(75\) −104.672 −0.161153
\(76\) −233.342 −0.352186
\(77\) 0 0
\(78\) −154.455 −0.224213
\(79\) −769.426 −1.09579 −0.547894 0.836548i \(-0.684570\pi\)
−0.547894 + 0.836548i \(0.684570\pi\)
\(80\) −270.995 −0.378727
\(81\) −383.625 −0.526235
\(82\) 172.153 0.231843
\(83\) 613.203 0.810937 0.405469 0.914109i \(-0.367108\pi\)
0.405469 + 0.914109i \(0.367108\pi\)
\(84\) 0 0
\(85\) 184.843 0.235871
\(86\) −114.012 −0.142956
\(87\) 819.215 1.00953
\(88\) 479.230 0.580524
\(89\) −457.666 −0.545084 −0.272542 0.962144i \(-0.587864\pi\)
−0.272542 + 0.962144i \(0.587864\pi\)
\(90\) 30.5244 0.0357506
\(91\) 0 0
\(92\) −402.947 −0.456632
\(93\) −1079.67 −1.20383
\(94\) −200.871 −0.220407
\(95\) −153.830 −0.166132
\(96\) −482.793 −0.513280
\(97\) −1412.11 −1.47813 −0.739063 0.673636i \(-0.764732\pi\)
−0.739063 + 0.673636i \(0.764732\pi\)
\(98\) 0 0
\(99\) 451.736 0.458597
\(100\) −189.611 −0.189611
\(101\) 1823.79 1.79677 0.898386 0.439208i \(-0.144741\pi\)
0.898386 + 0.439208i \(0.144741\pi\)
\(102\) 99.7804 0.0968601
\(103\) 407.775 0.390090 0.195045 0.980794i \(-0.437515\pi\)
0.195045 + 0.980794i \(0.437515\pi\)
\(104\) −574.915 −0.542068
\(105\) 0 0
\(106\) −317.341 −0.290782
\(107\) −370.109 −0.334390 −0.167195 0.985924i \(-0.553471\pi\)
−0.167195 + 0.985924i \(0.553471\pi\)
\(108\) −1158.11 −1.03184
\(109\) 975.570 0.857272 0.428636 0.903477i \(-0.358994\pi\)
0.428636 + 0.903477i \(0.358994\pi\)
\(110\) 153.753 0.133270
\(111\) −1450.43 −1.24026
\(112\) 0 0
\(113\) 1978.85 1.64739 0.823693 0.567036i \(-0.191910\pi\)
0.823693 + 0.567036i \(0.191910\pi\)
\(114\) −83.0391 −0.0682221
\(115\) −265.641 −0.215401
\(116\) 1483.99 1.18780
\(117\) −541.931 −0.428219
\(118\) 63.6689 0.0496711
\(119\) 0 0
\(120\) −210.317 −0.159993
\(121\) 944.416 0.709554
\(122\) 52.9695 0.0393085
\(123\) −1118.10 −0.819642
\(124\) −1955.80 −1.41642
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 1392.38 0.972867 0.486433 0.873718i \(-0.338298\pi\)
0.486433 + 0.873718i \(0.338298\pi\)
\(128\) −1154.08 −0.796933
\(129\) 740.487 0.505397
\(130\) −184.452 −0.124442
\(131\) −1777.02 −1.18518 −0.592591 0.805504i \(-0.701895\pi\)
−0.592591 + 0.805504i \(0.701895\pi\)
\(132\) −1514.76 −0.998809
\(133\) 0 0
\(134\) 422.031 0.272074
\(135\) −763.478 −0.486739
\(136\) 371.404 0.234174
\(137\) −1980.48 −1.23506 −0.617532 0.786545i \(-0.711868\pi\)
−0.617532 + 0.786545i \(0.711868\pi\)
\(138\) −143.396 −0.0884543
\(139\) 2182.09 1.33153 0.665763 0.746163i \(-0.268106\pi\)
0.665763 + 0.746163i \(0.268106\pi\)
\(140\) 0 0
\(141\) 1304.62 0.779213
\(142\) 502.605 0.297026
\(143\) −2729.74 −1.59631
\(144\) −513.269 −0.297031
\(145\) 978.313 0.560307
\(146\) −534.847 −0.303180
\(147\) 0 0
\(148\) −2627.42 −1.45928
\(149\) 670.154 0.368464 0.184232 0.982883i \(-0.441020\pi\)
0.184232 + 0.982883i \(0.441020\pi\)
\(150\) −67.4765 −0.0367296
\(151\) 3348.84 1.80480 0.902401 0.430898i \(-0.141803\pi\)
0.902401 + 0.430898i \(0.141803\pi\)
\(152\) −309.089 −0.164937
\(153\) 350.096 0.184990
\(154\) 0 0
\(155\) −1289.35 −0.668149
\(156\) 1817.20 0.932645
\(157\) 2408.41 1.22428 0.612140 0.790749i \(-0.290309\pi\)
0.612140 + 0.790749i \(0.290309\pi\)
\(158\) −496.009 −0.249749
\(159\) 2061.07 1.02801
\(160\) −576.555 −0.284879
\(161\) 0 0
\(162\) −247.303 −0.119938
\(163\) −3811.03 −1.83131 −0.915654 0.401968i \(-0.868326\pi\)
−0.915654 + 0.401968i \(0.868326\pi\)
\(164\) −2025.42 −0.964382
\(165\) −998.597 −0.471156
\(166\) 395.300 0.184827
\(167\) 1207.15 0.559354 0.279677 0.960094i \(-0.409773\pi\)
0.279677 + 0.960094i \(0.409773\pi\)
\(168\) 0 0
\(169\) 1077.77 0.490564
\(170\) 119.159 0.0537591
\(171\) −291.356 −0.130296
\(172\) 1341.38 0.594645
\(173\) 3243.28 1.42533 0.712665 0.701505i \(-0.247488\pi\)
0.712665 + 0.701505i \(0.247488\pi\)
\(174\) 528.105 0.230089
\(175\) 0 0
\(176\) −2585.36 −1.10727
\(177\) −413.518 −0.175604
\(178\) −295.034 −0.124234
\(179\) 859.728 0.358989 0.179495 0.983759i \(-0.442554\pi\)
0.179495 + 0.983759i \(0.442554\pi\)
\(180\) −359.126 −0.148709
\(181\) −290.504 −0.119298 −0.0596491 0.998219i \(-0.518998\pi\)
−0.0596491 + 0.998219i \(0.518998\pi\)
\(182\) 0 0
\(183\) −344.028 −0.138969
\(184\) −533.751 −0.213851
\(185\) −1732.12 −0.688366
\(186\) −696.007 −0.274375
\(187\) 1763.45 0.689605
\(188\) 2363.30 0.916814
\(189\) 0 0
\(190\) −99.1660 −0.0378645
\(191\) 4895.61 1.85463 0.927315 0.374282i \(-0.122111\pi\)
0.927315 + 0.374282i \(0.122111\pi\)
\(192\) 1504.16 0.565384
\(193\) −3548.73 −1.32354 −0.661770 0.749707i \(-0.730194\pi\)
−0.661770 + 0.749707i \(0.730194\pi\)
\(194\) −910.315 −0.336891
\(195\) 1197.98 0.439945
\(196\) 0 0
\(197\) −650.107 −0.235118 −0.117559 0.993066i \(-0.537507\pi\)
−0.117559 + 0.993066i \(0.537507\pi\)
\(198\) 291.210 0.104522
\(199\) 4055.09 1.44451 0.722256 0.691626i \(-0.243105\pi\)
0.722256 + 0.691626i \(0.243105\pi\)
\(200\) −251.162 −0.0887991
\(201\) −2741.01 −0.961871
\(202\) 1175.70 0.409516
\(203\) 0 0
\(204\) −1173.94 −0.402903
\(205\) −1335.25 −0.454916
\(206\) 262.871 0.0889083
\(207\) −503.128 −0.168936
\(208\) 3101.57 1.03392
\(209\) −1467.58 −0.485714
\(210\) 0 0
\(211\) −1569.67 −0.512134 −0.256067 0.966659i \(-0.582427\pi\)
−0.256067 + 0.966659i \(0.582427\pi\)
\(212\) 3733.59 1.20955
\(213\) −3264.33 −1.05008
\(214\) −238.590 −0.0762134
\(215\) 884.296 0.280504
\(216\) −1534.05 −0.483236
\(217\) 0 0
\(218\) 628.900 0.195387
\(219\) 3473.74 1.07184
\(220\) −1808.94 −0.554357
\(221\) −2115.55 −0.643924
\(222\) −935.017 −0.282677
\(223\) 4723.86 1.41853 0.709267 0.704940i \(-0.249026\pi\)
0.709267 + 0.704940i \(0.249026\pi\)
\(224\) 0 0
\(225\) −236.752 −0.0701488
\(226\) 1275.66 0.375468
\(227\) 3685.02 1.07746 0.538730 0.842479i \(-0.318904\pi\)
0.538730 + 0.842479i \(0.318904\pi\)
\(228\) 976.973 0.283779
\(229\) 3356.78 0.968656 0.484328 0.874887i \(-0.339064\pi\)
0.484328 + 0.874887i \(0.339064\pi\)
\(230\) −171.245 −0.0490937
\(231\) 0 0
\(232\) 1965.72 0.556275
\(233\) 2314.01 0.650627 0.325314 0.945606i \(-0.394530\pi\)
0.325314 + 0.945606i \(0.394530\pi\)
\(234\) −349.355 −0.0975985
\(235\) 1557.99 0.432477
\(236\) −749.079 −0.206614
\(237\) 3221.49 0.882946
\(238\) 0 0
\(239\) 941.179 0.254727 0.127364 0.991856i \(-0.459348\pi\)
0.127364 + 0.991856i \(0.459348\pi\)
\(240\) 1134.62 0.305165
\(241\) 5638.24 1.50702 0.753509 0.657438i \(-0.228360\pi\)
0.753509 + 0.657438i \(0.228360\pi\)
\(242\) 608.816 0.161720
\(243\) −2516.59 −0.664360
\(244\) −623.199 −0.163509
\(245\) 0 0
\(246\) −720.783 −0.186811
\(247\) 1760.60 0.453539
\(248\) −2590.69 −0.663341
\(249\) −2567.40 −0.653424
\(250\) −80.5810 −0.0203856
\(251\) 365.822 0.0919940 0.0459970 0.998942i \(-0.485354\pi\)
0.0459970 + 0.998942i \(0.485354\pi\)
\(252\) 0 0
\(253\) −2534.28 −0.629759
\(254\) 897.598 0.221733
\(255\) −773.914 −0.190056
\(256\) 2130.08 0.520039
\(257\) −6276.46 −1.52340 −0.761702 0.647928i \(-0.775636\pi\)
−0.761702 + 0.647928i \(0.775636\pi\)
\(258\) 477.353 0.115189
\(259\) 0 0
\(260\) 2170.12 0.517635
\(261\) 1852.94 0.439442
\(262\) −1145.55 −0.270124
\(263\) −4225.97 −0.990817 −0.495408 0.868660i \(-0.664982\pi\)
−0.495408 + 0.868660i \(0.664982\pi\)
\(264\) −2006.48 −0.467765
\(265\) 2461.35 0.570564
\(266\) 0 0
\(267\) 1916.19 0.439210
\(268\) −4965.28 −1.13173
\(269\) 981.591 0.222486 0.111243 0.993793i \(-0.464517\pi\)
0.111243 + 0.993793i \(0.464517\pi\)
\(270\) −492.175 −0.110936
\(271\) 3884.42 0.870708 0.435354 0.900259i \(-0.356623\pi\)
0.435354 + 0.900259i \(0.356623\pi\)
\(272\) −2003.66 −0.446653
\(273\) 0 0
\(274\) −1276.71 −0.281493
\(275\) −1192.53 −0.261500
\(276\) 1687.09 0.367938
\(277\) 3614.93 0.784116 0.392058 0.919941i \(-0.371763\pi\)
0.392058 + 0.919941i \(0.371763\pi\)
\(278\) 1406.68 0.303478
\(279\) −2442.05 −0.524021
\(280\) 0 0
\(281\) 72.6835 0.0154304 0.00771518 0.999970i \(-0.497544\pi\)
0.00771518 + 0.999970i \(0.497544\pi\)
\(282\) 841.023 0.177596
\(283\) 1743.04 0.366125 0.183062 0.983101i \(-0.441399\pi\)
0.183062 + 0.983101i \(0.441399\pi\)
\(284\) −5913.26 −1.23552
\(285\) 644.065 0.133864
\(286\) −1759.72 −0.363827
\(287\) 0 0
\(288\) −1092.01 −0.223427
\(289\) −3546.32 −0.721825
\(290\) 630.668 0.127704
\(291\) 5912.34 1.19102
\(292\) 6292.59 1.26112
\(293\) −4989.29 −0.994804 −0.497402 0.867520i \(-0.665713\pi\)
−0.497402 + 0.867520i \(0.665713\pi\)
\(294\) 0 0
\(295\) −493.827 −0.0974634
\(296\) −3480.33 −0.683412
\(297\) −7283.78 −1.42306
\(298\) 432.013 0.0839794
\(299\) 3040.29 0.588042
\(300\) 793.876 0.152782
\(301\) 0 0
\(302\) 2158.82 0.411346
\(303\) −7635.98 −1.44777
\(304\) 1667.48 0.314594
\(305\) −410.841 −0.0771301
\(306\) 225.688 0.0421626
\(307\) 1664.61 0.309461 0.154731 0.987957i \(-0.450549\pi\)
0.154731 + 0.987957i \(0.450549\pi\)
\(308\) 0 0
\(309\) −1707.30 −0.314320
\(310\) −831.177 −0.152283
\(311\) 545.623 0.0994838 0.0497419 0.998762i \(-0.484160\pi\)
0.0497419 + 0.998762i \(0.484160\pi\)
\(312\) 2407.10 0.436779
\(313\) 213.564 0.0385667 0.0192833 0.999814i \(-0.493862\pi\)
0.0192833 + 0.999814i \(0.493862\pi\)
\(314\) 1552.58 0.279035
\(315\) 0 0
\(316\) 5835.66 1.03887
\(317\) −2683.93 −0.475535 −0.237767 0.971322i \(-0.576416\pi\)
−0.237767 + 0.971322i \(0.576416\pi\)
\(318\) 1328.67 0.234302
\(319\) 9333.37 1.63815
\(320\) 1796.28 0.313798
\(321\) 1549.60 0.269440
\(322\) 0 0
\(323\) −1137.37 −0.195929
\(324\) 2909.58 0.498899
\(325\) 1430.64 0.244177
\(326\) −2456.77 −0.417387
\(327\) −4084.59 −0.690760
\(328\) −2682.91 −0.451642
\(329\) 0 0
\(330\) −643.744 −0.107385
\(331\) −5067.52 −0.841500 −0.420750 0.907177i \(-0.638233\pi\)
−0.420750 + 0.907177i \(0.638233\pi\)
\(332\) −4650.80 −0.768812
\(333\) −3280.66 −0.539876
\(334\) 778.187 0.127487
\(335\) −3273.34 −0.533856
\(336\) 0 0
\(337\) −9353.21 −1.51187 −0.755937 0.654644i \(-0.772818\pi\)
−0.755937 + 0.654644i \(0.772818\pi\)
\(338\) 694.782 0.111808
\(339\) −8285.20 −1.32741
\(340\) −1401.93 −0.223618
\(341\) −12300.7 −1.95344
\(342\) −187.822 −0.0296966
\(343\) 0 0
\(344\) 1776.81 0.278486
\(345\) 1112.21 0.173563
\(346\) 2090.77 0.324858
\(347\) 2349.34 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(348\) −6213.28 −0.957088
\(349\) −10472.6 −1.60626 −0.803128 0.595806i \(-0.796833\pi\)
−0.803128 + 0.595806i \(0.796833\pi\)
\(350\) 0 0
\(351\) 8738.10 1.32879
\(352\) −5500.49 −0.832889
\(353\) −7174.63 −1.08178 −0.540888 0.841095i \(-0.681912\pi\)
−0.540888 + 0.841095i \(0.681912\pi\)
\(354\) −266.574 −0.0400232
\(355\) −3898.29 −0.582816
\(356\) 3471.14 0.516769
\(357\) 0 0
\(358\) 554.222 0.0818199
\(359\) −7534.13 −1.10762 −0.553811 0.832643i \(-0.686827\pi\)
−0.553811 + 0.832643i \(0.686827\pi\)
\(360\) −475.705 −0.0696440
\(361\) −5912.46 −0.862000
\(362\) −187.273 −0.0271902
\(363\) −3954.15 −0.571733
\(364\) 0 0
\(365\) 4148.36 0.594891
\(366\) −221.777 −0.0316734
\(367\) 5453.06 0.775606 0.387803 0.921742i \(-0.373234\pi\)
0.387803 + 0.921742i \(0.373234\pi\)
\(368\) 2879.49 0.407891
\(369\) −2528.98 −0.356785
\(370\) −1116.60 −0.156891
\(371\) 0 0
\(372\) 8188.68 1.14130
\(373\) 8231.29 1.14263 0.571314 0.820732i \(-0.306434\pi\)
0.571314 + 0.820732i \(0.306434\pi\)
\(374\) 1136.80 0.157173
\(375\) 523.359 0.0720698
\(376\) 3130.46 0.429365
\(377\) −11196.9 −1.52963
\(378\) 0 0
\(379\) 1670.06 0.226346 0.113173 0.993575i \(-0.463898\pi\)
0.113173 + 0.993575i \(0.463898\pi\)
\(380\) 1166.71 0.157502
\(381\) −5829.74 −0.783901
\(382\) 3155.95 0.422703
\(383\) 3220.14 0.429612 0.214806 0.976657i \(-0.431088\pi\)
0.214806 + 0.976657i \(0.431088\pi\)
\(384\) 4832.00 0.642140
\(385\) 0 0
\(386\) −2287.68 −0.301658
\(387\) 1674.87 0.219996
\(388\) 10710.1 1.40134
\(389\) 3522.23 0.459085 0.229543 0.973299i \(-0.426277\pi\)
0.229543 + 0.973299i \(0.426277\pi\)
\(390\) 772.277 0.100271
\(391\) −1964.07 −0.254034
\(392\) 0 0
\(393\) 7440.15 0.954977
\(394\) −419.090 −0.0535875
\(395\) 3847.13 0.490051
\(396\) −3426.16 −0.434775
\(397\) −5455.16 −0.689639 −0.344819 0.938669i \(-0.612060\pi\)
−0.344819 + 0.938669i \(0.612060\pi\)
\(398\) 2614.11 0.329229
\(399\) 0 0
\(400\) 1354.97 0.169372
\(401\) −1161.80 −0.144682 −0.0723409 0.997380i \(-0.523047\pi\)
−0.0723409 + 0.997380i \(0.523047\pi\)
\(402\) −1766.99 −0.219227
\(403\) 14756.8 1.82404
\(404\) −13832.4 −1.70344
\(405\) 1918.13 0.235339
\(406\) 0 0
\(407\) −16524.8 −2.01255
\(408\) −1555.02 −0.188689
\(409\) −7398.65 −0.894473 −0.447237 0.894416i \(-0.647592\pi\)
−0.447237 + 0.894416i \(0.647592\pi\)
\(410\) −860.765 −0.103683
\(411\) 8292.02 0.995171
\(412\) −3092.74 −0.369826
\(413\) 0 0
\(414\) −324.341 −0.0385036
\(415\) −3066.02 −0.362662
\(416\) 6598.74 0.777716
\(417\) −9136.12 −1.07290
\(418\) −946.069 −0.110703
\(419\) 2134.46 0.248867 0.124433 0.992228i \(-0.460289\pi\)
0.124433 + 0.992228i \(0.460289\pi\)
\(420\) 0 0
\(421\) −3902.36 −0.451756 −0.225878 0.974156i \(-0.572525\pi\)
−0.225878 + 0.974156i \(0.572525\pi\)
\(422\) −1011.88 −0.116724
\(423\) 2950.86 0.339186
\(424\) 4945.58 0.566459
\(425\) −924.214 −0.105485
\(426\) −2104.34 −0.239333
\(427\) 0 0
\(428\) 2807.06 0.317020
\(429\) 11429.1 1.28625
\(430\) 570.059 0.0639319
\(431\) −3618.13 −0.404360 −0.202180 0.979348i \(-0.564803\pi\)
−0.202180 + 0.979348i \(0.564803\pi\)
\(432\) 8275.95 0.921706
\(433\) 4222.37 0.468624 0.234312 0.972161i \(-0.424716\pi\)
0.234312 + 0.972161i \(0.424716\pi\)
\(434\) 0 0
\(435\) −4096.08 −0.451475
\(436\) −7399.14 −0.812740
\(437\) 1634.54 0.178926
\(438\) 2239.34 0.244291
\(439\) 13518.0 1.46965 0.734826 0.678256i \(-0.237264\pi\)
0.734826 + 0.678256i \(0.237264\pi\)
\(440\) −2396.15 −0.259618
\(441\) 0 0
\(442\) −1363.78 −0.146762
\(443\) 16591.2 1.77939 0.889695 0.456555i \(-0.150917\pi\)
0.889695 + 0.456555i \(0.150917\pi\)
\(444\) 11000.7 1.17583
\(445\) 2288.33 0.243769
\(446\) 3045.23 0.323309
\(447\) −2805.85 −0.296895
\(448\) 0 0
\(449\) 8354.32 0.878095 0.439048 0.898464i \(-0.355316\pi\)
0.439048 + 0.898464i \(0.355316\pi\)
\(450\) −152.622 −0.0159881
\(451\) −12738.6 −1.33002
\(452\) −15008.5 −1.56181
\(453\) −14021.2 −1.45424
\(454\) 2375.54 0.245572
\(455\) 0 0
\(456\) 1294.12 0.132900
\(457\) −1280.34 −0.131054 −0.0655269 0.997851i \(-0.520873\pi\)
−0.0655269 + 0.997851i \(0.520873\pi\)
\(458\) 2163.94 0.220774
\(459\) −5644.94 −0.574038
\(460\) 2014.73 0.204212
\(461\) 6986.72 0.705865 0.352932 0.935649i \(-0.385185\pi\)
0.352932 + 0.935649i \(0.385185\pi\)
\(462\) 0 0
\(463\) −5587.32 −0.560831 −0.280416 0.959879i \(-0.590472\pi\)
−0.280416 + 0.959879i \(0.590472\pi\)
\(464\) −10604.7 −1.06102
\(465\) 5398.35 0.538371
\(466\) 1491.73 0.148289
\(467\) 9933.83 0.984332 0.492166 0.870501i \(-0.336205\pi\)
0.492166 + 0.870501i \(0.336205\pi\)
\(468\) 4110.24 0.405974
\(469\) 0 0
\(470\) 1004.36 0.0985691
\(471\) −10083.7 −0.986481
\(472\) −992.243 −0.0967620
\(473\) 8436.41 0.820099
\(474\) 2076.73 0.201239
\(475\) 769.148 0.0742967
\(476\) 0 0
\(477\) 4661.84 0.447486
\(478\) 606.729 0.0580568
\(479\) −5068.62 −0.483489 −0.241744 0.970340i \(-0.577720\pi\)
−0.241744 + 0.970340i \(0.577720\pi\)
\(480\) 2413.96 0.229546
\(481\) 19824.3 1.87923
\(482\) 3634.68 0.343476
\(483\) 0 0
\(484\) −7162.86 −0.672695
\(485\) 7060.56 0.661038
\(486\) −1622.32 −0.151419
\(487\) 264.353 0.0245975 0.0122988 0.999924i \(-0.496085\pi\)
0.0122988 + 0.999924i \(0.496085\pi\)
\(488\) −825.500 −0.0765751
\(489\) 15956.3 1.47560
\(490\) 0 0
\(491\) −7459.47 −0.685623 −0.342812 0.939404i \(-0.611379\pi\)
−0.342812 + 0.939404i \(0.611379\pi\)
\(492\) 8480.17 0.777064
\(493\) 7233.37 0.660800
\(494\) 1134.97 0.103370
\(495\) −2258.68 −0.205091
\(496\) 13976.3 1.26523
\(497\) 0 0
\(498\) −1655.07 −0.148927
\(499\) 7206.67 0.646523 0.323261 0.946310i \(-0.395221\pi\)
0.323261 + 0.946310i \(0.395221\pi\)
\(500\) 948.054 0.0847965
\(501\) −5054.19 −0.450707
\(502\) 235.827 0.0209670
\(503\) −10886.7 −0.965037 −0.482519 0.875886i \(-0.660278\pi\)
−0.482519 + 0.875886i \(0.660278\pi\)
\(504\) 0 0
\(505\) −9118.95 −0.803541
\(506\) −1633.72 −0.143533
\(507\) −4512.49 −0.395279
\(508\) −10560.4 −0.922330
\(509\) −7504.97 −0.653540 −0.326770 0.945104i \(-0.605960\pi\)
−0.326770 + 0.945104i \(0.605960\pi\)
\(510\) −498.902 −0.0433172
\(511\) 0 0
\(512\) 10605.8 0.915459
\(513\) 4697.82 0.404316
\(514\) −4046.11 −0.347210
\(515\) −2038.87 −0.174453
\(516\) −5616.17 −0.479144
\(517\) 14863.7 1.26442
\(518\) 0 0
\(519\) −13579.2 −1.14848
\(520\) 2874.58 0.242420
\(521\) −22264.8 −1.87224 −0.936120 0.351681i \(-0.885610\pi\)
−0.936120 + 0.351681i \(0.885610\pi\)
\(522\) 1194.50 0.100156
\(523\) 11286.7 0.943655 0.471828 0.881691i \(-0.343595\pi\)
0.471828 + 0.881691i \(0.343595\pi\)
\(524\) 13477.7 1.12362
\(525\) 0 0
\(526\) −2724.27 −0.225824
\(527\) −9533.09 −0.787985
\(528\) 10824.6 0.892197
\(529\) −9344.40 −0.768012
\(530\) 1586.70 0.130042
\(531\) −935.316 −0.0764393
\(532\) 0 0
\(533\) 15282.1 1.24191
\(534\) 1235.27 0.100104
\(535\) 1850.54 0.149544
\(536\) −6577.10 −0.530014
\(537\) −3599.57 −0.289261
\(538\) 632.781 0.0507084
\(539\) 0 0
\(540\) 5790.55 0.461455
\(541\) 16406.8 1.30385 0.651924 0.758284i \(-0.273962\pi\)
0.651924 + 0.758284i \(0.273962\pi\)
\(542\) 2504.08 0.198450
\(543\) 1216.30 0.0961263
\(544\) −4262.88 −0.335974
\(545\) −4877.85 −0.383384
\(546\) 0 0
\(547\) −8692.48 −0.679458 −0.339729 0.940523i \(-0.610335\pi\)
−0.339729 + 0.940523i \(0.610335\pi\)
\(548\) 15020.8 1.17091
\(549\) −778.139 −0.0604921
\(550\) −768.764 −0.0596004
\(551\) −6019.74 −0.465426
\(552\) 2234.75 0.172314
\(553\) 0 0
\(554\) 2330.36 0.178714
\(555\) 7252.15 0.554661
\(556\) −16549.9 −1.26236
\(557\) −13935.7 −1.06010 −0.530049 0.847967i \(-0.677826\pi\)
−0.530049 + 0.847967i \(0.677826\pi\)
\(558\) −1574.26 −0.119434
\(559\) −10120.9 −0.765773
\(560\) 0 0
\(561\) −7383.34 −0.555659
\(562\) 46.8553 0.00351685
\(563\) 22263.6 1.66661 0.833304 0.552815i \(-0.186447\pi\)
0.833304 + 0.552815i \(0.186447\pi\)
\(564\) −9894.82 −0.738736
\(565\) −9894.26 −0.736734
\(566\) 1123.65 0.0834462
\(567\) 0 0
\(568\) −7832.81 −0.578622
\(569\) 9525.66 0.701822 0.350911 0.936409i \(-0.385872\pi\)
0.350911 + 0.936409i \(0.385872\pi\)
\(570\) 415.195 0.0305099
\(571\) 7669.99 0.562135 0.281068 0.959688i \(-0.409311\pi\)
0.281068 + 0.959688i \(0.409311\pi\)
\(572\) 20703.5 1.51339
\(573\) −20497.3 −1.49439
\(574\) 0 0
\(575\) 1328.20 0.0963304
\(576\) 3402.19 0.246108
\(577\) −3907.15 −0.281901 −0.140950 0.990017i \(-0.545016\pi\)
−0.140950 + 0.990017i \(0.545016\pi\)
\(578\) −2286.13 −0.164516
\(579\) 14858.1 1.06646
\(580\) −7419.95 −0.531201
\(581\) 0 0
\(582\) 3811.38 0.271455
\(583\) 23481.9 1.66813
\(584\) 8335.28 0.590610
\(585\) 2709.66 0.191505
\(586\) −3216.34 −0.226733
\(587\) 19891.6 1.39866 0.699331 0.714798i \(-0.253481\pi\)
0.699331 + 0.714798i \(0.253481\pi\)
\(588\) 0 0
\(589\) 7933.61 0.555007
\(590\) −318.344 −0.0222136
\(591\) 2721.92 0.189450
\(592\) 18775.8 1.30351
\(593\) −4780.36 −0.331038 −0.165519 0.986207i \(-0.552930\pi\)
−0.165519 + 0.986207i \(0.552930\pi\)
\(594\) −4695.48 −0.324340
\(595\) 0 0
\(596\) −5082.74 −0.349324
\(597\) −16978.2 −1.16394
\(598\) 1959.92 0.134025
\(599\) 11085.6 0.756170 0.378085 0.925771i \(-0.376583\pi\)
0.378085 + 0.925771i \(0.376583\pi\)
\(600\) 1051.58 0.0715511
\(601\) 1573.44 0.106792 0.0533958 0.998573i \(-0.482995\pi\)
0.0533958 + 0.998573i \(0.482995\pi\)
\(602\) 0 0
\(603\) −6199.76 −0.418696
\(604\) −25399.1 −1.71105
\(605\) −4722.08 −0.317322
\(606\) −4922.52 −0.329973
\(607\) −8542.73 −0.571233 −0.285617 0.958344i \(-0.592198\pi\)
−0.285617 + 0.958344i \(0.592198\pi\)
\(608\) 3547.65 0.236639
\(609\) 0 0
\(610\) −264.848 −0.0175793
\(611\) −17831.4 −1.18066
\(612\) −2655.27 −0.175381
\(613\) 15068.2 0.992817 0.496409 0.868089i \(-0.334652\pi\)
0.496409 + 0.868089i \(0.334652\pi\)
\(614\) 1073.09 0.0705316
\(615\) 5590.52 0.366555
\(616\) 0 0
\(617\) 2524.58 0.164725 0.0823627 0.996602i \(-0.473753\pi\)
0.0823627 + 0.996602i \(0.473753\pi\)
\(618\) −1100.61 −0.0716391
\(619\) 21238.9 1.37910 0.689551 0.724237i \(-0.257808\pi\)
0.689551 + 0.724237i \(0.257808\pi\)
\(620\) 9778.99 0.633441
\(621\) 8112.44 0.524221
\(622\) 351.735 0.0226741
\(623\) 0 0
\(624\) −12985.9 −0.833095
\(625\) 625.000 0.0400000
\(626\) 137.674 0.00879002
\(627\) 6144.55 0.391371
\(628\) −18266.4 −1.16068
\(629\) −12806.8 −0.811827
\(630\) 0 0
\(631\) −8885.83 −0.560601 −0.280300 0.959912i \(-0.590434\pi\)
−0.280300 + 0.959912i \(0.590434\pi\)
\(632\) 7730.02 0.486525
\(633\) 6571.99 0.412659
\(634\) −1730.19 −0.108383
\(635\) −6961.92 −0.435079
\(636\) −15632.1 −0.974609
\(637\) 0 0
\(638\) 6016.74 0.373362
\(639\) −7383.42 −0.457095
\(640\) 5770.41 0.356399
\(641\) 3655.63 0.225255 0.112628 0.993637i \(-0.464073\pi\)
0.112628 + 0.993637i \(0.464073\pi\)
\(642\) 998.946 0.0614100
\(643\) −4221.22 −0.258894 −0.129447 0.991586i \(-0.541320\pi\)
−0.129447 + 0.991586i \(0.541320\pi\)
\(644\) 0 0
\(645\) −3702.43 −0.226020
\(646\) −733.205 −0.0446557
\(647\) −103.679 −0.00629989 −0.00314995 0.999995i \(-0.501003\pi\)
−0.00314995 + 0.999995i \(0.501003\pi\)
\(648\) 3854.08 0.233646
\(649\) −4711.24 −0.284949
\(650\) 922.259 0.0556523
\(651\) 0 0
\(652\) 28904.5 1.73618
\(653\) 4476.11 0.268245 0.134122 0.990965i \(-0.457179\pi\)
0.134122 + 0.990965i \(0.457179\pi\)
\(654\) −2633.12 −0.157436
\(655\) 8885.09 0.530029
\(656\) 14473.8 0.861445
\(657\) 7857.07 0.466566
\(658\) 0 0
\(659\) 12022.0 0.710641 0.355321 0.934745i \(-0.384372\pi\)
0.355321 + 0.934745i \(0.384372\pi\)
\(660\) 7573.79 0.446681
\(661\) −13451.0 −0.791504 −0.395752 0.918357i \(-0.629516\pi\)
−0.395752 + 0.918357i \(0.629516\pi\)
\(662\) −3266.77 −0.191792
\(663\) 8857.54 0.518851
\(664\) −6160.53 −0.360053
\(665\) 0 0
\(666\) −2114.87 −0.123047
\(667\) −10395.2 −0.603454
\(668\) −9155.55 −0.530297
\(669\) −19778.2 −1.14300
\(670\) −2110.15 −0.121675
\(671\) −3919.53 −0.225502
\(672\) 0 0
\(673\) 9774.83 0.559869 0.279935 0.960019i \(-0.409687\pi\)
0.279935 + 0.960019i \(0.409687\pi\)
\(674\) −6029.53 −0.344583
\(675\) 3817.39 0.217676
\(676\) −8174.27 −0.465081
\(677\) −23857.4 −1.35438 −0.677190 0.735808i \(-0.736802\pi\)
−0.677190 + 0.735808i \(0.736802\pi\)
\(678\) −5341.04 −0.302539
\(679\) 0 0
\(680\) −1857.02 −0.104726
\(681\) −15428.7 −0.868179
\(682\) −7929.65 −0.445223
\(683\) 11919.4 0.667763 0.333881 0.942615i \(-0.391642\pi\)
0.333881 + 0.942615i \(0.391642\pi\)
\(684\) 2209.77 0.123527
\(685\) 9902.40 0.552338
\(686\) 0 0
\(687\) −14054.4 −0.780508
\(688\) −9585.59 −0.531173
\(689\) −28170.5 −1.55763
\(690\) 716.981 0.0395580
\(691\) 8203.58 0.451634 0.225817 0.974170i \(-0.427495\pi\)
0.225817 + 0.974170i \(0.427495\pi\)
\(692\) −24598.4 −1.35129
\(693\) 0 0
\(694\) 1514.50 0.0828380
\(695\) −10910.4 −0.595477
\(696\) −8230.22 −0.448227
\(697\) −9872.44 −0.536507
\(698\) −6751.12 −0.366094
\(699\) −9688.49 −0.524252
\(700\) 0 0
\(701\) 449.084 0.0241964 0.0120982 0.999927i \(-0.496149\pi\)
0.0120982 + 0.999927i \(0.496149\pi\)
\(702\) 5633.00 0.302855
\(703\) 10658.0 0.571800
\(704\) 17137.0 0.917438
\(705\) −6523.11 −0.348475
\(706\) −4625.11 −0.246556
\(707\) 0 0
\(708\) 3136.30 0.166482
\(709\) 1897.64 0.100518 0.0502590 0.998736i \(-0.483995\pi\)
0.0502590 + 0.998736i \(0.483995\pi\)
\(710\) −2513.02 −0.132834
\(711\) 7286.53 0.384341
\(712\) 4597.93 0.242015
\(713\) 13700.2 0.719601
\(714\) 0 0
\(715\) 13648.7 0.713891
\(716\) −6520.54 −0.340341
\(717\) −3940.60 −0.205250
\(718\) −4856.86 −0.252446
\(719\) −6494.70 −0.336873 −0.168436 0.985713i \(-0.553872\pi\)
−0.168436 + 0.985713i \(0.553872\pi\)
\(720\) 2566.35 0.132836
\(721\) 0 0
\(722\) −3811.45 −0.196465
\(723\) −23606.6 −1.21430
\(724\) 2203.31 0.113101
\(725\) −4891.57 −0.250577
\(726\) −2549.04 −0.130308
\(727\) 18311.2 0.934148 0.467074 0.884218i \(-0.345308\pi\)
0.467074 + 0.884218i \(0.345308\pi\)
\(728\) 0 0
\(729\) 20894.5 1.06155
\(730\) 2674.23 0.135586
\(731\) 6538.23 0.330814
\(732\) 2609.25 0.131750
\(733\) −21233.3 −1.06994 −0.534972 0.844870i \(-0.679678\pi\)
−0.534972 + 0.844870i \(0.679678\pi\)
\(734\) 3515.30 0.176774
\(735\) 0 0
\(736\) 6126.27 0.306817
\(737\) −31228.5 −1.56081
\(738\) −1630.30 −0.0813175
\(739\) −22023.5 −1.09628 −0.548138 0.836388i \(-0.684663\pi\)
−0.548138 + 0.836388i \(0.684663\pi\)
\(740\) 13137.1 0.652608
\(741\) −7371.40 −0.365446
\(742\) 0 0
\(743\) 9436.77 0.465951 0.232975 0.972483i \(-0.425154\pi\)
0.232975 + 0.972483i \(0.425154\pi\)
\(744\) 10846.9 0.534497
\(745\) −3350.77 −0.164782
\(746\) 5306.29 0.260425
\(747\) −5807.09 −0.284431
\(748\) −13374.8 −0.653783
\(749\) 0 0
\(750\) 337.383 0.0164260
\(751\) −39161.8 −1.90284 −0.951421 0.307893i \(-0.900376\pi\)
−0.951421 + 0.307893i \(0.900376\pi\)
\(752\) −16888.3 −0.818954
\(753\) −1531.65 −0.0741255
\(754\) −7218.07 −0.348629
\(755\) −16744.2 −0.807132
\(756\) 0 0
\(757\) 20340.6 0.976607 0.488303 0.872674i \(-0.337616\pi\)
0.488303 + 0.872674i \(0.337616\pi\)
\(758\) 1076.60 0.0515883
\(759\) 10610.7 0.507438
\(760\) 1545.44 0.0737621
\(761\) −3307.90 −0.157570 −0.0787852 0.996892i \(-0.525104\pi\)
−0.0787852 + 0.996892i \(0.525104\pi\)
\(762\) −3758.13 −0.178665
\(763\) 0 0
\(764\) −37130.4 −1.75829
\(765\) −1750.48 −0.0827303
\(766\) 2075.85 0.0979160
\(767\) 5651.91 0.266074
\(768\) −8918.37 −0.419029
\(769\) −17234.0 −0.808159 −0.404079 0.914724i \(-0.632408\pi\)
−0.404079 + 0.914724i \(0.632408\pi\)
\(770\) 0 0
\(771\) 26278.7 1.22750
\(772\) 26915.1 1.25479
\(773\) 8726.33 0.406034 0.203017 0.979175i \(-0.434925\pi\)
0.203017 + 0.979175i \(0.434925\pi\)
\(774\) 1079.70 0.0501409
\(775\) 6446.75 0.298806
\(776\) 14186.7 0.656281
\(777\) 0 0
\(778\) 2270.60 0.104634
\(779\) 8216.03 0.377882
\(780\) −9086.01 −0.417091
\(781\) −37190.7 −1.70395
\(782\) −1266.14 −0.0578989
\(783\) −29876.8 −1.36362
\(784\) 0 0
\(785\) −12042.0 −0.547515
\(786\) 4796.28 0.217656
\(787\) 10642.1 0.482018 0.241009 0.970523i \(-0.422522\pi\)
0.241009 + 0.970523i \(0.422522\pi\)
\(788\) 4930.69 0.222904
\(789\) 17693.6 0.798365
\(790\) 2480.05 0.111691
\(791\) 0 0
\(792\) −4538.35 −0.203615
\(793\) 4702.12 0.210564
\(794\) −3516.66 −0.157181
\(795\) −10305.4 −0.459740
\(796\) −30755.5 −1.36947
\(797\) −29234.1 −1.29928 −0.649640 0.760242i \(-0.725080\pi\)
−0.649640 + 0.760242i \(0.725080\pi\)
\(798\) 0 0
\(799\) 11519.3 0.510044
\(800\) 2882.78 0.127402
\(801\) 4334.14 0.191185
\(802\) −748.950 −0.0329755
\(803\) 39576.5 1.73926
\(804\) 20789.0 0.911906
\(805\) 0 0
\(806\) 9512.93 0.415730
\(807\) −4109.80 −0.179271
\(808\) −18322.7 −0.797758
\(809\) 36211.2 1.57369 0.786846 0.617150i \(-0.211713\pi\)
0.786846 + 0.617150i \(0.211713\pi\)
\(810\) 1236.52 0.0536380
\(811\) 27995.2 1.21214 0.606069 0.795412i \(-0.292746\pi\)
0.606069 + 0.795412i \(0.292746\pi\)
\(812\) 0 0
\(813\) −16263.6 −0.701585
\(814\) −10652.7 −0.458694
\(815\) 19055.2 0.818985
\(816\) 8389.07 0.359897
\(817\) −5441.23 −0.233005
\(818\) −4769.52 −0.203866
\(819\) 0 0
\(820\) 10127.1 0.431285
\(821\) 44805.7 1.90467 0.952333 0.305060i \(-0.0986766\pi\)
0.952333 + 0.305060i \(0.0986766\pi\)
\(822\) 5345.44 0.226817
\(823\) −15850.9 −0.671360 −0.335680 0.941976i \(-0.608966\pi\)
−0.335680 + 0.941976i \(0.608966\pi\)
\(824\) −4096.70 −0.173198
\(825\) 4992.99 0.210707
\(826\) 0 0
\(827\) −45013.9 −1.89273 −0.946363 0.323104i \(-0.895274\pi\)
−0.946363 + 0.323104i \(0.895274\pi\)
\(828\) 3815.94 0.160161
\(829\) −5655.83 −0.236954 −0.118477 0.992957i \(-0.537801\pi\)
−0.118477 + 0.992957i \(0.537801\pi\)
\(830\) −1976.50 −0.0826571
\(831\) −15135.3 −0.631812
\(832\) −20558.7 −0.856664
\(833\) 0 0
\(834\) −5889.58 −0.244532
\(835\) −6035.75 −0.250151
\(836\) 11130.7 0.460483
\(837\) 39375.7 1.62607
\(838\) 1375.97 0.0567211
\(839\) 22037.0 0.906797 0.453398 0.891308i \(-0.350211\pi\)
0.453398 + 0.891308i \(0.350211\pi\)
\(840\) 0 0
\(841\) 13894.9 0.569719
\(842\) −2515.65 −0.102963
\(843\) −304.317 −0.0124332
\(844\) 11905.0 0.485530
\(845\) −5388.85 −0.219387
\(846\) 1902.27 0.0773065
\(847\) 0 0
\(848\) −26680.5 −1.08044
\(849\) −7297.91 −0.295010
\(850\) −595.793 −0.0240418
\(851\) 18404.8 0.741374
\(852\) 24758.1 0.995537
\(853\) 44486.7 1.78569 0.892846 0.450362i \(-0.148705\pi\)
0.892846 + 0.450362i \(0.148705\pi\)
\(854\) 0 0
\(855\) 1456.78 0.0582699
\(856\) 3718.29 0.148468
\(857\) 38559.6 1.53696 0.768478 0.639877i \(-0.221015\pi\)
0.768478 + 0.639877i \(0.221015\pi\)
\(858\) 7367.72 0.293158
\(859\) −8426.01 −0.334682 −0.167341 0.985899i \(-0.553518\pi\)
−0.167341 + 0.985899i \(0.553518\pi\)
\(860\) −6706.88 −0.265933
\(861\) 0 0
\(862\) −2332.42 −0.0921608
\(863\) −20054.3 −0.791029 −0.395514 0.918460i \(-0.629434\pi\)
−0.395514 + 0.918460i \(0.629434\pi\)
\(864\) 17607.5 0.693309
\(865\) −16216.4 −0.637427
\(866\) 2721.94 0.106808
\(867\) 14848.0 0.581621
\(868\) 0 0
\(869\) 36702.6 1.43274
\(870\) −2640.53 −0.102899
\(871\) 37463.8 1.45742
\(872\) −9801.04 −0.380625
\(873\) 13372.8 0.518444
\(874\) 1053.70 0.0407803
\(875\) 0 0
\(876\) −26346.3 −1.01616
\(877\) 47082.1 1.81283 0.906414 0.422391i \(-0.138809\pi\)
0.906414 + 0.422391i \(0.138809\pi\)
\(878\) 8714.32 0.334959
\(879\) 20889.5 0.801577
\(880\) 12926.8 0.495185
\(881\) 9467.24 0.362042 0.181021 0.983479i \(-0.442060\pi\)
0.181021 + 0.983479i \(0.442060\pi\)
\(882\) 0 0
\(883\) −3049.49 −0.116221 −0.0581106 0.998310i \(-0.518508\pi\)
−0.0581106 + 0.998310i \(0.518508\pi\)
\(884\) 16045.2 0.610475
\(885\) 2067.59 0.0785325
\(886\) 10695.5 0.405554
\(887\) 19468.6 0.736968 0.368484 0.929634i \(-0.379877\pi\)
0.368484 + 0.929634i \(0.379877\pi\)
\(888\) 14571.7 0.550669
\(889\) 0 0
\(890\) 1475.17 0.0555592
\(891\) 18299.4 0.688052
\(892\) −35827.8 −1.34485
\(893\) −9586.61 −0.359243
\(894\) −1808.79 −0.0676676
\(895\) −4298.64 −0.160545
\(896\) 0 0
\(897\) −12729.3 −0.473823
\(898\) 5385.60 0.200133
\(899\) −50455.6 −1.87184
\(900\) 1795.63 0.0665048
\(901\) 18198.5 0.672898
\(902\) −8211.92 −0.303134
\(903\) 0 0
\(904\) −19880.5 −0.731432
\(905\) 1452.52 0.0533518
\(906\) −9038.73 −0.331448
\(907\) −32014.2 −1.17201 −0.586006 0.810307i \(-0.699301\pi\)
−0.586006 + 0.810307i \(0.699301\pi\)
\(908\) −27948.8 −1.02149
\(909\) −17271.4 −0.630206
\(910\) 0 0
\(911\) 20921.1 0.760866 0.380433 0.924809i \(-0.375775\pi\)
0.380433 + 0.924809i \(0.375775\pi\)
\(912\) −6981.54 −0.253489
\(913\) −29250.6 −1.06030
\(914\) −825.366 −0.0298694
\(915\) 1720.14 0.0621487
\(916\) −25459.2 −0.918337
\(917\) 0 0
\(918\) −3639.00 −0.130833
\(919\) 43467.4 1.56024 0.780118 0.625632i \(-0.215159\pi\)
0.780118 + 0.625632i \(0.215159\pi\)
\(920\) 2668.75 0.0956372
\(921\) −6969.53 −0.249353
\(922\) 4503.97 0.160879
\(923\) 44616.4 1.59108
\(924\) 0 0
\(925\) 8660.58 0.307847
\(926\) −3601.85 −0.127823
\(927\) −3861.66 −0.136822
\(928\) −22562.1 −0.798099
\(929\) 18542.1 0.654840 0.327420 0.944879i \(-0.393821\pi\)
0.327420 + 0.944879i \(0.393821\pi\)
\(930\) 3480.04 0.122704
\(931\) 0 0
\(932\) −17550.5 −0.616830
\(933\) −2284.46 −0.0801605
\(934\) 6403.82 0.224346
\(935\) −8817.25 −0.308401
\(936\) 5444.50 0.190127
\(937\) −13842.5 −0.482619 −0.241309 0.970448i \(-0.577577\pi\)
−0.241309 + 0.970448i \(0.577577\pi\)
\(938\) 0 0
\(939\) −894.167 −0.0310757
\(940\) −11816.5 −0.410012
\(941\) 53393.2 1.84970 0.924850 0.380333i \(-0.124191\pi\)
0.924850 + 0.380333i \(0.124191\pi\)
\(942\) −6500.44 −0.224836
\(943\) 14187.9 0.489947
\(944\) 5352.98 0.184560
\(945\) 0 0
\(946\) 5438.52 0.186915
\(947\) 22344.2 0.766727 0.383364 0.923598i \(-0.374766\pi\)
0.383364 + 0.923598i \(0.374766\pi\)
\(948\) −24433.2 −0.837081
\(949\) −47478.5 −1.62404
\(950\) 495.830 0.0169335
\(951\) 11237.3 0.383169
\(952\) 0 0
\(953\) −8902.63 −0.302607 −0.151304 0.988487i \(-0.548347\pi\)
−0.151304 + 0.988487i \(0.548347\pi\)
\(954\) 3005.25 0.101990
\(955\) −24478.1 −0.829416
\(956\) −7138.31 −0.241495
\(957\) −39077.6 −1.31996
\(958\) −3267.48 −0.110196
\(959\) 0 0
\(960\) −7520.82 −0.252847
\(961\) 36706.0 1.23212
\(962\) 12779.7 0.428309
\(963\) 3504.96 0.117285
\(964\) −42762.8 −1.42873
\(965\) 17743.6 0.591905
\(966\) 0 0
\(967\) −2225.57 −0.0740119 −0.0370059 0.999315i \(-0.511782\pi\)
−0.0370059 + 0.999315i \(0.511782\pi\)
\(968\) −9488.05 −0.315039
\(969\) 4762.03 0.157873
\(970\) 4551.58 0.150662
\(971\) 11324.8 0.374285 0.187143 0.982333i \(-0.440077\pi\)
0.187143 + 0.982333i \(0.440077\pi\)
\(972\) 19086.9 0.629849
\(973\) 0 0
\(974\) 170.415 0.00560621
\(975\) −5989.91 −0.196749
\(976\) 4453.43 0.146056
\(977\) −57695.9 −1.88931 −0.944654 0.328067i \(-0.893603\pi\)
−0.944654 + 0.328067i \(0.893603\pi\)
\(978\) 10286.2 0.336315
\(979\) 21831.3 0.712697
\(980\) 0 0
\(981\) −9238.73 −0.300683
\(982\) −4808.73 −0.156266
\(983\) −59657.3 −1.93568 −0.967839 0.251570i \(-0.919053\pi\)
−0.967839 + 0.251570i \(0.919053\pi\)
\(984\) 11233.0 0.363917
\(985\) 3250.54 0.105148
\(986\) 4662.98 0.150608
\(987\) 0 0
\(988\) −13353.1 −0.429980
\(989\) −9396.20 −0.302105
\(990\) −1456.05 −0.0467438
\(991\) 2890.60 0.0926568 0.0463284 0.998926i \(-0.485248\pi\)
0.0463284 + 0.998926i \(0.485248\pi\)
\(992\) 29735.3 0.951710
\(993\) 21217.1 0.678050
\(994\) 0 0
\(995\) −20275.5 −0.646005
\(996\) 19472.3 0.619481
\(997\) 10619.6 0.337337 0.168669 0.985673i \(-0.446053\pi\)
0.168669 + 0.985673i \(0.446053\pi\)
\(998\) 4645.77 0.147354
\(999\) 52897.3 1.67527
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 245.4.a.p.1.4 yes 6
3.2 odd 2 2205.4.a.ca.1.3 6
5.4 even 2 1225.4.a.bi.1.3 6
7.2 even 3 245.4.e.p.116.3 12
7.3 odd 6 245.4.e.q.226.3 12
7.4 even 3 245.4.e.p.226.3 12
7.5 odd 6 245.4.e.q.116.3 12
7.6 odd 2 245.4.a.o.1.4 6
21.20 even 2 2205.4.a.bz.1.3 6
35.34 odd 2 1225.4.a.bj.1.3 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
245.4.a.o.1.4 6 7.6 odd 2
245.4.a.p.1.4 yes 6 1.1 even 1 trivial
245.4.e.p.116.3 12 7.2 even 3
245.4.e.p.226.3 12 7.4 even 3
245.4.e.q.116.3 12 7.5 odd 6
245.4.e.q.226.3 12 7.3 odd 6
1225.4.a.bi.1.3 6 5.4 even 2
1225.4.a.bj.1.3 6 35.34 odd 2
2205.4.a.bz.1.3 6 21.20 even 2
2205.4.a.ca.1.3 6 3.2 odd 2