Properties

Label 2401.4.a.d.1.7
Level $2401$
Weight $4$
Character 2401.1
Self dual yes
Analytic conductor $141.664$
Analytic rank $0$
Dimension $39$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2401,4,Mod(1,2401)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2401, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2401.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2401 = 7^{4} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2401.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: \(141.663585924\)
Analytic rank: \(0\)
Dimension: \(39\)
Twist minimal: no (minimal twist has level 49)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 2401.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.93571 q^{2} -3.09696 q^{3} +7.48982 q^{4} -18.2977 q^{5} +12.1887 q^{6} +2.00794 q^{8} -17.4089 q^{9} +O(q^{10})\) \(q-3.93571 q^{2} -3.09696 q^{3} +7.48982 q^{4} -18.2977 q^{5} +12.1887 q^{6} +2.00794 q^{8} -17.4089 q^{9} +72.0144 q^{10} +11.1264 q^{11} -23.1956 q^{12} -32.1274 q^{13} +56.6671 q^{15} -67.8212 q^{16} +68.2593 q^{17} +68.5163 q^{18} +113.492 q^{19} -137.046 q^{20} -43.7905 q^{22} +151.295 q^{23} -6.21849 q^{24} +209.805 q^{25} +126.444 q^{26} +137.532 q^{27} -183.747 q^{29} -223.025 q^{30} +167.796 q^{31} +250.861 q^{32} -34.4581 q^{33} -268.649 q^{34} -130.389 q^{36} +255.519 q^{37} -446.673 q^{38} +99.4970 q^{39} -36.7406 q^{40} -238.493 q^{41} -90.2895 q^{43} +83.3350 q^{44} +318.542 q^{45} -595.452 q^{46} +353.761 q^{47} +210.039 q^{48} -825.732 q^{50} -211.396 q^{51} -240.628 q^{52} +231.242 q^{53} -541.287 q^{54} -203.588 q^{55} -351.481 q^{57} +723.174 q^{58} +238.752 q^{59} +424.426 q^{60} +33.1087 q^{61} -660.396 q^{62} -444.747 q^{64} +587.856 q^{65} +135.617 q^{66} -505.936 q^{67} +511.249 q^{68} -468.553 q^{69} +683.159 q^{71} -34.9559 q^{72} +587.218 q^{73} -1005.65 q^{74} -649.757 q^{75} +850.037 q^{76} -391.592 q^{78} -50.1378 q^{79} +1240.97 q^{80} +44.1082 q^{81} +938.639 q^{82} +559.144 q^{83} -1248.99 q^{85} +355.353 q^{86} +569.055 q^{87} +22.3412 q^{88} -1171.00 q^{89} -1253.69 q^{90} +1133.17 q^{92} -519.656 q^{93} -1392.30 q^{94} -2076.65 q^{95} -776.905 q^{96} +5.56045 q^{97} -193.699 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 39 q + q^{2} + q^{3} + 145 q^{4} + 27 q^{5} + 41 q^{6} - 12 q^{8} + 312 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 39 q + q^{2} + q^{3} + 145 q^{4} + 27 q^{5} + 41 q^{6} - 12 q^{8} + 312 q^{9} + 78 q^{10} + q^{11} - 91 q^{12} + 77 q^{13} - 161 q^{15} + 461 q^{16} + 211 q^{17} + 8 q^{18} + 314 q^{19} + 476 q^{20} - 61 q^{22} - 69 q^{23} + 330 q^{24} + 606 q^{25} + 504 q^{26} - 50 q^{27} + 57 q^{29} + 42 q^{30} + 638 q^{31} - 1600 q^{32} + 1574 q^{33} + 1343 q^{34} + 782 q^{36} + 71 q^{37} + 1359 q^{38} - 84 q^{39} - 155 q^{40} + 1393 q^{41} - 125 q^{43} + 52 q^{44} + 1129 q^{45} - 1454 q^{46} + 1483 q^{47} - 974 q^{48} + 3074 q^{50} - 2044 q^{51} + 3899 q^{52} + 2213 q^{53} + 1142 q^{54} + 1604 q^{55} + 98 q^{57} + 2403 q^{58} + 2073 q^{59} - 1519 q^{60} + 2575 q^{61} + 1742 q^{62} + 1358 q^{64} + 1876 q^{65} - 48 q^{66} + 176 q^{67} + 3038 q^{68} - 638 q^{69} - 1259 q^{71} - 3799 q^{72} - 307 q^{73} + 3845 q^{74} + 131 q^{75} + 1974 q^{76} - 6041 q^{78} + 22 q^{79} - 804 q^{80} + 795 q^{81} + 8043 q^{82} + 6349 q^{83} + 3094 q^{85} + 1745 q^{86} + 9508 q^{87} + 1299 q^{88} + 2253 q^{89} + 11156 q^{90} + 1284 q^{92} - 3430 q^{93} + 2738 q^{94} - 3290 q^{95} + 3031 q^{96} - 770 q^{97} + 5384 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.93571 −1.39148 −0.695742 0.718292i \(-0.744924\pi\)
−0.695742 + 0.718292i \(0.744924\pi\)
\(3\) −3.09696 −0.596009 −0.298005 0.954564i \(-0.596321\pi\)
−0.298005 + 0.954564i \(0.596321\pi\)
\(4\) 7.48982 0.936227
\(5\) −18.2977 −1.63659 −0.818297 0.574795i \(-0.805082\pi\)
−0.818297 + 0.574795i \(0.805082\pi\)
\(6\) 12.1887 0.829337
\(7\) 0 0
\(8\) 2.00794 0.0887390
\(9\) −17.4089 −0.644773
\(10\) 72.0144 2.27729
\(11\) 11.1264 0.304977 0.152489 0.988305i \(-0.451271\pi\)
0.152489 + 0.988305i \(0.451271\pi\)
\(12\) −23.1956 −0.558000
\(13\) −32.1274 −0.685425 −0.342713 0.939440i \(-0.611346\pi\)
−0.342713 + 0.939440i \(0.611346\pi\)
\(14\) 0 0
\(15\) 56.6671 0.975425
\(16\) −67.8212 −1.05971
\(17\) 68.2593 0.973842 0.486921 0.873446i \(-0.338120\pi\)
0.486921 + 0.873446i \(0.338120\pi\)
\(18\) 68.5163 0.897191
\(19\) 113.492 1.37036 0.685182 0.728372i \(-0.259722\pi\)
0.685182 + 0.728372i \(0.259722\pi\)
\(20\) −137.046 −1.53222
\(21\) 0 0
\(22\) −43.7905 −0.424371
\(23\) 151.295 1.37161 0.685807 0.727784i \(-0.259449\pi\)
0.685807 + 0.727784i \(0.259449\pi\)
\(24\) −6.21849 −0.0528893
\(25\) 209.805 1.67844
\(26\) 126.444 0.953758
\(27\) 137.532 0.980300
\(28\) 0 0
\(29\) −183.747 −1.17658 −0.588291 0.808649i \(-0.700199\pi\)
−0.588291 + 0.808649i \(0.700199\pi\)
\(30\) −223.025 −1.35729
\(31\) 167.796 0.972162 0.486081 0.873914i \(-0.338426\pi\)
0.486081 + 0.873914i \(0.338426\pi\)
\(32\) 250.861 1.38582
\(33\) −34.4581 −0.181769
\(34\) −268.649 −1.35508
\(35\) 0 0
\(36\) −130.389 −0.603654
\(37\) 255.519 1.13533 0.567663 0.823261i \(-0.307848\pi\)
0.567663 + 0.823261i \(0.307848\pi\)
\(38\) −446.673 −1.90684
\(39\) 99.4970 0.408520
\(40\) −36.7406 −0.145230
\(41\) −238.493 −0.908447 −0.454223 0.890888i \(-0.650083\pi\)
−0.454223 + 0.890888i \(0.650083\pi\)
\(42\) 0 0
\(43\) −90.2895 −0.320210 −0.160105 0.987100i \(-0.551183\pi\)
−0.160105 + 0.987100i \(0.551183\pi\)
\(44\) 83.3350 0.285528
\(45\) 318.542 1.05523
\(46\) −595.452 −1.90858
\(47\) 353.761 1.09790 0.548950 0.835855i \(-0.315028\pi\)
0.548950 + 0.835855i \(0.315028\pi\)
\(48\) 210.039 0.631595
\(49\) 0 0
\(50\) −825.732 −2.33552
\(51\) −211.396 −0.580419
\(52\) −240.628 −0.641714
\(53\) 231.242 0.599311 0.299656 0.954047i \(-0.403128\pi\)
0.299656 + 0.954047i \(0.403128\pi\)
\(54\) −541.287 −1.36407
\(55\) −203.588 −0.499124
\(56\) 0 0
\(57\) −351.481 −0.816750
\(58\) 723.174 1.63720
\(59\) 238.752 0.526827 0.263414 0.964683i \(-0.415152\pi\)
0.263414 + 0.964683i \(0.415152\pi\)
\(60\) 424.426 0.913220
\(61\) 33.1087 0.0694940 0.0347470 0.999396i \(-0.488937\pi\)
0.0347470 + 0.999396i \(0.488937\pi\)
\(62\) −660.396 −1.35275
\(63\) 0 0
\(64\) −444.747 −0.868646
\(65\) 587.856 1.12176
\(66\) 135.617 0.252929
\(67\) −505.936 −0.922537 −0.461268 0.887261i \(-0.652605\pi\)
−0.461268 + 0.887261i \(0.652605\pi\)
\(68\) 511.249 0.911737
\(69\) −468.553 −0.817494
\(70\) 0 0
\(71\) 683.159 1.14192 0.570958 0.820979i \(-0.306572\pi\)
0.570958 + 0.820979i \(0.306572\pi\)
\(72\) −34.9559 −0.0572165
\(73\) 587.218 0.941489 0.470745 0.882269i \(-0.343985\pi\)
0.470745 + 0.882269i \(0.343985\pi\)
\(74\) −1005.65 −1.57979
\(75\) −649.757 −1.00037
\(76\) 850.037 1.28297
\(77\) 0 0
\(78\) −391.592 −0.568449
\(79\) −50.1378 −0.0714043 −0.0357022 0.999362i \(-0.511367\pi\)
−0.0357022 + 0.999362i \(0.511367\pi\)
\(80\) 1240.97 1.73431
\(81\) 44.1082 0.0605050
\(82\) 938.639 1.26409
\(83\) 559.144 0.739446 0.369723 0.929142i \(-0.379453\pi\)
0.369723 + 0.929142i \(0.379453\pi\)
\(84\) 0 0
\(85\) −1248.99 −1.59378
\(86\) 355.353 0.445566
\(87\) 569.055 0.701254
\(88\) 22.3412 0.0270634
\(89\) −1171.00 −1.39468 −0.697338 0.716743i \(-0.745632\pi\)
−0.697338 + 0.716743i \(0.745632\pi\)
\(90\) −1253.69 −1.46834
\(91\) 0 0
\(92\) 1133.17 1.28414
\(93\) −519.656 −0.579418
\(94\) −1392.30 −1.52771
\(95\) −2076.65 −2.24273
\(96\) −776.905 −0.825964
\(97\) 5.56045 0.00582039 0.00291019 0.999996i \(-0.499074\pi\)
0.00291019 + 0.999996i \(0.499074\pi\)
\(98\) 0 0
\(99\) −193.699 −0.196641
\(100\) 1571.40 1.57140
\(101\) 1560.22 1.53710 0.768552 0.639787i \(-0.220977\pi\)
0.768552 + 0.639787i \(0.220977\pi\)
\(102\) 831.993 0.807643
\(103\) 958.221 0.916663 0.458332 0.888781i \(-0.348447\pi\)
0.458332 + 0.888781i \(0.348447\pi\)
\(104\) −64.5097 −0.0608240
\(105\) 0 0
\(106\) −910.100 −0.833932
\(107\) −1596.71 −1.44262 −0.721308 0.692614i \(-0.756459\pi\)
−0.721308 + 0.692614i \(0.756459\pi\)
\(108\) 1030.09 0.917783
\(109\) −1383.90 −1.21609 −0.608044 0.793904i \(-0.708045\pi\)
−0.608044 + 0.793904i \(0.708045\pi\)
\(110\) 801.264 0.694523
\(111\) −791.330 −0.676664
\(112\) 0 0
\(113\) 2107.11 1.75416 0.877080 0.480345i \(-0.159489\pi\)
0.877080 + 0.480345i \(0.159489\pi\)
\(114\) 1383.33 1.13649
\(115\) −2768.34 −2.24477
\(116\) −1376.23 −1.10155
\(117\) 559.301 0.441944
\(118\) −939.657 −0.733071
\(119\) 0 0
\(120\) 113.784 0.0865583
\(121\) −1207.20 −0.906989
\(122\) −130.306 −0.0966998
\(123\) 738.602 0.541443
\(124\) 1256.76 0.910165
\(125\) −1551.74 −1.11033
\(126\) 0 0
\(127\) −2051.74 −1.43356 −0.716781 0.697299i \(-0.754385\pi\)
−0.716781 + 0.697299i \(0.754385\pi\)
\(128\) −256.493 −0.177117
\(129\) 279.622 0.190848
\(130\) −2313.63 −1.56092
\(131\) 158.468 0.105691 0.0528453 0.998603i \(-0.483171\pi\)
0.0528453 + 0.998603i \(0.483171\pi\)
\(132\) −258.085 −0.170177
\(133\) 0 0
\(134\) 1991.22 1.28369
\(135\) −2516.52 −1.60435
\(136\) 137.060 0.0864178
\(137\) −70.9378 −0.0442381 −0.0221191 0.999755i \(-0.507041\pi\)
−0.0221191 + 0.999755i \(0.507041\pi\)
\(138\) 1844.09 1.13753
\(139\) 1374.54 0.838753 0.419377 0.907812i \(-0.362249\pi\)
0.419377 + 0.907812i \(0.362249\pi\)
\(140\) 0 0
\(141\) −1095.58 −0.654358
\(142\) −2688.72 −1.58896
\(143\) −357.464 −0.209039
\(144\) 1180.69 0.683270
\(145\) 3362.14 1.92559
\(146\) −2311.12 −1.31007
\(147\) 0 0
\(148\) 1913.79 1.06292
\(149\) 349.364 0.192087 0.0960436 0.995377i \(-0.469381\pi\)
0.0960436 + 0.995377i \(0.469381\pi\)
\(150\) 2557.26 1.39199
\(151\) −1660.64 −0.894975 −0.447488 0.894290i \(-0.647681\pi\)
−0.447488 + 0.894290i \(0.647681\pi\)
\(152\) 227.885 0.121605
\(153\) −1188.32 −0.627907
\(154\) 0 0
\(155\) −3070.28 −1.59104
\(156\) 745.215 0.382467
\(157\) 3076.18 1.56373 0.781867 0.623446i \(-0.214268\pi\)
0.781867 + 0.623446i \(0.214268\pi\)
\(158\) 197.328 0.0993580
\(159\) −716.145 −0.357195
\(160\) −4590.18 −2.26803
\(161\) 0 0
\(162\) −173.597 −0.0841918
\(163\) −2772.40 −1.33222 −0.666108 0.745855i \(-0.732041\pi\)
−0.666108 + 0.745855i \(0.732041\pi\)
\(164\) −1786.27 −0.850513
\(165\) 630.503 0.297483
\(166\) −2200.63 −1.02893
\(167\) −593.286 −0.274909 −0.137455 0.990508i \(-0.543892\pi\)
−0.137455 + 0.990508i \(0.543892\pi\)
\(168\) 0 0
\(169\) −1164.83 −0.530192
\(170\) 4915.65 2.21772
\(171\) −1975.77 −0.883574
\(172\) −676.251 −0.299789
\(173\) −1622.53 −0.713058 −0.356529 0.934284i \(-0.616040\pi\)
−0.356529 + 0.934284i \(0.616040\pi\)
\(174\) −2239.64 −0.975784
\(175\) 0 0
\(176\) −754.609 −0.323186
\(177\) −739.403 −0.313994
\(178\) 4608.73 1.94067
\(179\) 2025.46 0.845756 0.422878 0.906187i \(-0.361020\pi\)
0.422878 + 0.906187i \(0.361020\pi\)
\(180\) 2385.82 0.987936
\(181\) −2765.94 −1.13586 −0.567930 0.823077i \(-0.692255\pi\)
−0.567930 + 0.823077i \(0.692255\pi\)
\(182\) 0 0
\(183\) −102.536 −0.0414191
\(184\) 303.790 0.121716
\(185\) −4675.40 −1.85807
\(186\) 2045.22 0.806250
\(187\) 759.483 0.297000
\(188\) 2649.60 1.02788
\(189\) 0 0
\(190\) 8173.08 3.12072
\(191\) 976.430 0.369906 0.184953 0.982747i \(-0.440787\pi\)
0.184953 + 0.982747i \(0.440787\pi\)
\(192\) 1377.36 0.517721
\(193\) 4578.51 1.70761 0.853805 0.520593i \(-0.174289\pi\)
0.853805 + 0.520593i \(0.174289\pi\)
\(194\) −21.8843 −0.00809898
\(195\) −1820.57 −0.668581
\(196\) 0 0
\(197\) 1085.93 0.392737 0.196369 0.980530i \(-0.437085\pi\)
0.196369 + 0.980530i \(0.437085\pi\)
\(198\) 762.343 0.273623
\(199\) −2662.01 −0.948267 −0.474133 0.880453i \(-0.657239\pi\)
−0.474133 + 0.880453i \(0.657239\pi\)
\(200\) 421.275 0.148943
\(201\) 1566.86 0.549840
\(202\) −6140.57 −2.13886
\(203\) 0 0
\(204\) −1583.32 −0.543404
\(205\) 4363.87 1.48676
\(206\) −3771.28 −1.27552
\(207\) −2633.87 −0.884379
\(208\) 2178.92 0.726349
\(209\) 1262.77 0.417930
\(210\) 0 0
\(211\) 3338.26 1.08917 0.544586 0.838705i \(-0.316687\pi\)
0.544586 + 0.838705i \(0.316687\pi\)
\(212\) 1731.96 0.561091
\(213\) −2115.71 −0.680593
\(214\) 6284.19 2.00738
\(215\) 1652.09 0.524053
\(216\) 276.156 0.0869909
\(217\) 0 0
\(218\) 5446.63 1.69217
\(219\) −1818.59 −0.561136
\(220\) −1524.84 −0.467293
\(221\) −2192.99 −0.667496
\(222\) 3114.45 0.941568
\(223\) −272.956 −0.0819663 −0.0409832 0.999160i \(-0.513049\pi\)
−0.0409832 + 0.999160i \(0.513049\pi\)
\(224\) 0 0
\(225\) −3652.47 −1.08221
\(226\) −8292.96 −2.44088
\(227\) 3637.99 1.06371 0.531855 0.846836i \(-0.321495\pi\)
0.531855 + 0.846836i \(0.321495\pi\)
\(228\) −2632.53 −0.764664
\(229\) −853.825 −0.246386 −0.123193 0.992383i \(-0.539313\pi\)
−0.123193 + 0.992383i \(0.539313\pi\)
\(230\) 10895.4 3.12357
\(231\) 0 0
\(232\) −368.951 −0.104409
\(233\) −6233.09 −1.75255 −0.876273 0.481816i \(-0.839977\pi\)
−0.876273 + 0.481816i \(0.839977\pi\)
\(234\) −2201.25 −0.614958
\(235\) −6473.00 −1.79682
\(236\) 1788.21 0.493230
\(237\) 155.275 0.0425577
\(238\) 0 0
\(239\) 4372.77 1.18348 0.591739 0.806130i \(-0.298442\pi\)
0.591739 + 0.806130i \(0.298442\pi\)
\(240\) −3843.23 −1.03366
\(241\) 374.956 0.100220 0.0501101 0.998744i \(-0.484043\pi\)
0.0501101 + 0.998744i \(0.484043\pi\)
\(242\) 4751.20 1.26206
\(243\) −3849.97 −1.01636
\(244\) 247.978 0.0650621
\(245\) 0 0
\(246\) −2906.92 −0.753409
\(247\) −3646.21 −0.939283
\(248\) 336.923 0.0862687
\(249\) −1731.64 −0.440717
\(250\) 6107.18 1.54501
\(251\) −5177.11 −1.30190 −0.650949 0.759122i \(-0.725629\pi\)
−0.650949 + 0.759122i \(0.725629\pi\)
\(252\) 0 0
\(253\) 1683.37 0.418311
\(254\) 8075.04 1.99478
\(255\) 3868.05 0.949910
\(256\) 4567.46 1.11510
\(257\) 2579.54 0.626099 0.313049 0.949737i \(-0.398649\pi\)
0.313049 + 0.949737i \(0.398649\pi\)
\(258\) −1100.51 −0.265562
\(259\) 0 0
\(260\) 4402.94 1.05023
\(261\) 3198.82 0.758629
\(262\) −623.686 −0.147067
\(263\) −3988.24 −0.935078 −0.467539 0.883973i \(-0.654859\pi\)
−0.467539 + 0.883973i \(0.654859\pi\)
\(264\) −69.1897 −0.0161300
\(265\) −4231.19 −0.980829
\(266\) 0 0
\(267\) 3626.54 0.831239
\(268\) −3789.37 −0.863704
\(269\) 3146.82 0.713252 0.356626 0.934247i \(-0.383927\pi\)
0.356626 + 0.934247i \(0.383927\pi\)
\(270\) 9904.30 2.23243
\(271\) 2115.95 0.474298 0.237149 0.971473i \(-0.423787\pi\)
0.237149 + 0.971473i \(0.423787\pi\)
\(272\) −4629.42 −1.03199
\(273\) 0 0
\(274\) 279.190 0.0615566
\(275\) 2334.39 0.511886
\(276\) −3509.37 −0.765360
\(277\) −3176.01 −0.688910 −0.344455 0.938803i \(-0.611936\pi\)
−0.344455 + 0.938803i \(0.611936\pi\)
\(278\) −5409.78 −1.16711
\(279\) −2921.14 −0.626824
\(280\) 0 0
\(281\) 1518.75 0.322424 0.161212 0.986920i \(-0.448460\pi\)
0.161212 + 0.986920i \(0.448460\pi\)
\(282\) 4311.89 0.910529
\(283\) 1518.90 0.319044 0.159522 0.987194i \(-0.449005\pi\)
0.159522 + 0.987194i \(0.449005\pi\)
\(284\) 5116.74 1.06909
\(285\) 6431.28 1.33669
\(286\) 1406.87 0.290875
\(287\) 0 0
\(288\) −4367.21 −0.893542
\(289\) −253.671 −0.0516326
\(290\) −13232.4 −2.67942
\(291\) −17.2205 −0.00346901
\(292\) 4398.16 0.881448
\(293\) −6408.29 −1.27774 −0.638868 0.769317i \(-0.720597\pi\)
−0.638868 + 0.769317i \(0.720597\pi\)
\(294\) 0 0
\(295\) −4368.60 −0.862202
\(296\) 513.065 0.100748
\(297\) 1530.25 0.298969
\(298\) −1374.99 −0.267286
\(299\) −4860.70 −0.940139
\(300\) −4866.56 −0.936570
\(301\) 0 0
\(302\) 6535.81 1.24534
\(303\) −4831.93 −0.916129
\(304\) −7697.19 −1.45218
\(305\) −605.812 −0.113733
\(306\) 4676.87 0.873722
\(307\) −4645.18 −0.863565 −0.431783 0.901978i \(-0.642115\pi\)
−0.431783 + 0.901978i \(0.642115\pi\)
\(308\) 0 0
\(309\) −2967.57 −0.546340
\(310\) 12083.7 2.21390
\(311\) −829.604 −0.151262 −0.0756311 0.997136i \(-0.524097\pi\)
−0.0756311 + 0.997136i \(0.524097\pi\)
\(312\) 199.784 0.0362517
\(313\) 7156.11 1.29229 0.646146 0.763214i \(-0.276380\pi\)
0.646146 + 0.763214i \(0.276380\pi\)
\(314\) −12107.0 −2.17591
\(315\) 0 0
\(316\) −375.523 −0.0668507
\(317\) 3114.62 0.551844 0.275922 0.961180i \(-0.411017\pi\)
0.275922 + 0.961180i \(0.411017\pi\)
\(318\) 2818.54 0.497031
\(319\) −2044.45 −0.358831
\(320\) 8137.84 1.42162
\(321\) 4944.94 0.859813
\(322\) 0 0
\(323\) 7746.91 1.33452
\(324\) 330.362 0.0566465
\(325\) −6740.49 −1.15045
\(326\) 10911.4 1.85376
\(327\) 4285.87 0.724799
\(328\) −478.878 −0.0806147
\(329\) 0 0
\(330\) −2481.48 −0.413942
\(331\) −8372.51 −1.39032 −0.695158 0.718857i \(-0.744666\pi\)
−0.695158 + 0.718857i \(0.744666\pi\)
\(332\) 4187.88 0.692289
\(333\) −4448.29 −0.732027
\(334\) 2335.00 0.382532
\(335\) 9257.46 1.50982
\(336\) 0 0
\(337\) 4752.53 0.768210 0.384105 0.923290i \(-0.374510\pi\)
0.384105 + 0.923290i \(0.374510\pi\)
\(338\) 4584.44 0.737753
\(339\) −6525.62 −1.04550
\(340\) −9354.68 −1.49214
\(341\) 1866.97 0.296487
\(342\) 7776.07 1.22948
\(343\) 0 0
\(344\) −181.295 −0.0284151
\(345\) 8573.43 1.33791
\(346\) 6385.82 0.992208
\(347\) −5903.14 −0.913248 −0.456624 0.889660i \(-0.650941\pi\)
−0.456624 + 0.889660i \(0.650941\pi\)
\(348\) 4262.12 0.656533
\(349\) 446.879 0.0685412 0.0342706 0.999413i \(-0.489089\pi\)
0.0342706 + 0.999413i \(0.489089\pi\)
\(350\) 0 0
\(351\) −4418.55 −0.671923
\(352\) 2791.19 0.422645
\(353\) 7681.47 1.15820 0.579098 0.815258i \(-0.303405\pi\)
0.579098 + 0.815258i \(0.303405\pi\)
\(354\) 2910.08 0.436917
\(355\) −12500.2 −1.86885
\(356\) −8770.60 −1.30573
\(357\) 0 0
\(358\) −7971.64 −1.17686
\(359\) 9406.07 1.38282 0.691411 0.722461i \(-0.256989\pi\)
0.691411 + 0.722461i \(0.256989\pi\)
\(360\) 639.612 0.0936402
\(361\) 6021.51 0.877900
\(362\) 10885.9 1.58053
\(363\) 3738.65 0.540574
\(364\) 0 0
\(365\) −10744.7 −1.54084
\(366\) 403.552 0.0576340
\(367\) −445.233 −0.0633268 −0.0316634 0.999499i \(-0.510080\pi\)
−0.0316634 + 0.999499i \(0.510080\pi\)
\(368\) −10261.0 −1.45351
\(369\) 4151.89 0.585742
\(370\) 18401.0 2.58547
\(371\) 0 0
\(372\) −3892.13 −0.542467
\(373\) 9545.30 1.32503 0.662516 0.749048i \(-0.269489\pi\)
0.662516 + 0.749048i \(0.269489\pi\)
\(374\) −2989.11 −0.413270
\(375\) 4805.66 0.661768
\(376\) 710.328 0.0974266
\(377\) 5903.30 0.806460
\(378\) 0 0
\(379\) 321.340 0.0435518 0.0217759 0.999763i \(-0.493068\pi\)
0.0217759 + 0.999763i \(0.493068\pi\)
\(380\) −15553.7 −2.09971
\(381\) 6354.14 0.854416
\(382\) −3842.95 −0.514718
\(383\) 4423.96 0.590219 0.295110 0.955463i \(-0.404644\pi\)
0.295110 + 0.955463i \(0.404644\pi\)
\(384\) 794.348 0.105563
\(385\) 0 0
\(386\) −18019.7 −2.37611
\(387\) 1571.84 0.206462
\(388\) 41.6467 0.00544921
\(389\) −9517.64 −1.24052 −0.620262 0.784395i \(-0.712974\pi\)
−0.620262 + 0.784395i \(0.712974\pi\)
\(390\) 7165.22 0.930320
\(391\) 10327.3 1.33573
\(392\) 0 0
\(393\) −490.770 −0.0629925
\(394\) −4273.90 −0.546488
\(395\) 917.405 0.116860
\(396\) −1450.77 −0.184101
\(397\) −1484.81 −0.187710 −0.0938548 0.995586i \(-0.529919\pi\)
−0.0938548 + 0.995586i \(0.529919\pi\)
\(398\) 10476.9 1.31950
\(399\) 0 0
\(400\) −14229.2 −1.77865
\(401\) 6186.84 0.770464 0.385232 0.922820i \(-0.374121\pi\)
0.385232 + 0.922820i \(0.374121\pi\)
\(402\) −6166.72 −0.765094
\(403\) −5390.84 −0.666345
\(404\) 11685.8 1.43908
\(405\) −807.077 −0.0990222
\(406\) 0 0
\(407\) 2843.02 0.346248
\(408\) −424.469 −0.0515058
\(409\) 10738.0 1.29819 0.649093 0.760709i \(-0.275149\pi\)
0.649093 + 0.760709i \(0.275149\pi\)
\(410\) −17174.9 −2.06880
\(411\) 219.691 0.0263663
\(412\) 7176.90 0.858205
\(413\) 0 0
\(414\) 10366.1 1.23060
\(415\) −10231.0 −1.21017
\(416\) −8059.51 −0.949879
\(417\) −4256.88 −0.499905
\(418\) −4969.88 −0.581543
\(419\) 4920.15 0.573663 0.286832 0.957981i \(-0.407398\pi\)
0.286832 + 0.957981i \(0.407398\pi\)
\(420\) 0 0
\(421\) −11804.0 −1.36648 −0.683242 0.730192i \(-0.739431\pi\)
−0.683242 + 0.730192i \(0.739431\pi\)
\(422\) −13138.4 −1.51557
\(423\) −6158.57 −0.707896
\(424\) 464.318 0.0531823
\(425\) 14321.1 1.63454
\(426\) 8326.83 0.947034
\(427\) 0 0
\(428\) −11959.1 −1.35062
\(429\) 1107.05 0.124589
\(430\) −6502.14 −0.729212
\(431\) 2901.97 0.324323 0.162161 0.986764i \(-0.448153\pi\)
0.162161 + 0.986764i \(0.448153\pi\)
\(432\) −9327.60 −1.03883
\(433\) 398.338 0.0442099 0.0221049 0.999756i \(-0.492963\pi\)
0.0221049 + 0.999756i \(0.492963\pi\)
\(434\) 0 0
\(435\) −10412.4 −1.14767
\(436\) −10365.2 −1.13853
\(437\) 17170.8 1.87961
\(438\) 7157.44 0.780812
\(439\) −4977.64 −0.541161 −0.270580 0.962697i \(-0.587216\pi\)
−0.270580 + 0.962697i \(0.587216\pi\)
\(440\) −408.792 −0.0442918
\(441\) 0 0
\(442\) 8630.98 0.928810
\(443\) −2201.59 −0.236119 −0.118059 0.993007i \(-0.537667\pi\)
−0.118059 + 0.993007i \(0.537667\pi\)
\(444\) −5926.92 −0.633512
\(445\) 21426.6 2.28252
\(446\) 1074.28 0.114055
\(447\) −1081.96 −0.114486
\(448\) 0 0
\(449\) 18314.1 1.92494 0.962468 0.271395i \(-0.0874851\pi\)
0.962468 + 0.271395i \(0.0874851\pi\)
\(450\) 14375.1 1.50588
\(451\) −2653.58 −0.277056
\(452\) 15781.8 1.64229
\(453\) 5142.94 0.533414
\(454\) −14318.1 −1.48013
\(455\) 0 0
\(456\) −705.750 −0.0724776
\(457\) −8747.89 −0.895425 −0.447712 0.894178i \(-0.647761\pi\)
−0.447712 + 0.894178i \(0.647761\pi\)
\(458\) 3360.41 0.342842
\(459\) 9387.85 0.954657
\(460\) −20734.4 −2.10162
\(461\) 9307.86 0.940370 0.470185 0.882568i \(-0.344187\pi\)
0.470185 + 0.882568i \(0.344187\pi\)
\(462\) 0 0
\(463\) −14225.1 −1.42785 −0.713927 0.700220i \(-0.753085\pi\)
−0.713927 + 0.700220i \(0.753085\pi\)
\(464\) 12461.9 1.24683
\(465\) 9508.50 0.948272
\(466\) 24531.6 2.43864
\(467\) 5884.52 0.583090 0.291545 0.956557i \(-0.405831\pi\)
0.291545 + 0.956557i \(0.405831\pi\)
\(468\) 4189.06 0.413760
\(469\) 0 0
\(470\) 25475.8 2.50024
\(471\) −9526.80 −0.931999
\(472\) 479.398 0.0467501
\(473\) −1004.60 −0.0976567
\(474\) −611.115 −0.0592183
\(475\) 23811.3 2.30008
\(476\) 0 0
\(477\) −4025.66 −0.386420
\(478\) −17210.0 −1.64679
\(479\) 12489.8 1.19138 0.595692 0.803213i \(-0.296878\pi\)
0.595692 + 0.803213i \(0.296878\pi\)
\(480\) 14215.6 1.35177
\(481\) −8209.15 −0.778181
\(482\) −1475.72 −0.139455
\(483\) 0 0
\(484\) −9041.72 −0.849147
\(485\) −101.743 −0.00952562
\(486\) 15152.4 1.41425
\(487\) 8170.07 0.760208 0.380104 0.924944i \(-0.375888\pi\)
0.380104 + 0.924944i \(0.375888\pi\)
\(488\) 66.4801 0.00616683
\(489\) 8586.00 0.794013
\(490\) 0 0
\(491\) 5894.06 0.541741 0.270871 0.962616i \(-0.412688\pi\)
0.270871 + 0.962616i \(0.412688\pi\)
\(492\) 5531.99 0.506913
\(493\) −12542.4 −1.14581
\(494\) 14350.4 1.30700
\(495\) 3544.24 0.321822
\(496\) −11380.1 −1.03021
\(497\) 0 0
\(498\) 6815.25 0.613250
\(499\) 7089.14 0.635979 0.317989 0.948094i \(-0.396992\pi\)
0.317989 + 0.948094i \(0.396992\pi\)
\(500\) −11622.2 −1.03952
\(501\) 1837.38 0.163849
\(502\) 20375.6 1.81157
\(503\) −2916.01 −0.258486 −0.129243 0.991613i \(-0.541255\pi\)
−0.129243 + 0.991613i \(0.541255\pi\)
\(504\) 0 0
\(505\) −28548.4 −2.51562
\(506\) −6625.26 −0.582073
\(507\) 3607.43 0.315999
\(508\) −15367.1 −1.34214
\(509\) 11495.4 1.00104 0.500518 0.865726i \(-0.333143\pi\)
0.500518 + 0.865726i \(0.333143\pi\)
\(510\) −15223.5 −1.32178
\(511\) 0 0
\(512\) −15924.2 −1.37453
\(513\) 15608.9 1.34337
\(514\) −10152.3 −0.871206
\(515\) −17533.2 −1.50021
\(516\) 2094.32 0.178677
\(517\) 3936.10 0.334834
\(518\) 0 0
\(519\) 5024.92 0.424989
\(520\) 1180.38 0.0995442
\(521\) 16479.2 1.38574 0.692868 0.721064i \(-0.256347\pi\)
0.692868 + 0.721064i \(0.256347\pi\)
\(522\) −12589.6 −1.05562
\(523\) 12363.5 1.03369 0.516844 0.856080i \(-0.327107\pi\)
0.516844 + 0.856080i \(0.327107\pi\)
\(524\) 1186.90 0.0989503
\(525\) 0 0
\(526\) 15696.6 1.30115
\(527\) 11453.6 0.946732
\(528\) 2336.99 0.192622
\(529\) 10723.1 0.881324
\(530\) 16652.7 1.36481
\(531\) −4156.39 −0.339684
\(532\) 0 0
\(533\) 7662.15 0.622673
\(534\) −14273.0 −1.15666
\(535\) 29216.1 2.36098
\(536\) −1015.89 −0.0818650
\(537\) −6272.77 −0.504078
\(538\) −12385.0 −0.992479
\(539\) 0 0
\(540\) −18848.3 −1.50204
\(541\) −5706.02 −0.453458 −0.226729 0.973958i \(-0.572803\pi\)
−0.226729 + 0.973958i \(0.572803\pi\)
\(542\) −8327.76 −0.659978
\(543\) 8565.98 0.676983
\(544\) 17123.6 1.34957
\(545\) 25322.1 1.99024
\(546\) 0 0
\(547\) 6452.32 0.504354 0.252177 0.967681i \(-0.418854\pi\)
0.252177 + 0.967681i \(0.418854\pi\)
\(548\) −531.311 −0.0414169
\(549\) −576.385 −0.0448078
\(550\) −9187.46 −0.712281
\(551\) −20853.8 −1.61235
\(552\) −940.823 −0.0725437
\(553\) 0 0
\(554\) 12499.9 0.958607
\(555\) 14479.5 1.10743
\(556\) 10295.0 0.785263
\(557\) 8462.90 0.643778 0.321889 0.946777i \(-0.395682\pi\)
0.321889 + 0.946777i \(0.395682\pi\)
\(558\) 11496.7 0.872215
\(559\) 2900.76 0.219480
\(560\) 0 0
\(561\) −2352.09 −0.177014
\(562\) −5977.36 −0.448647
\(563\) 16622.0 1.24429 0.622145 0.782902i \(-0.286262\pi\)
0.622145 + 0.782902i \(0.286262\pi\)
\(564\) −8205.70 −0.612628
\(565\) −38555.2 −2.87085
\(566\) −5977.96 −0.443944
\(567\) 0 0
\(568\) 1371.74 0.101333
\(569\) −5553.95 −0.409198 −0.204599 0.978846i \(-0.565589\pi\)
−0.204599 + 0.978846i \(0.565589\pi\)
\(570\) −25311.7 −1.85998
\(571\) 17365.2 1.27270 0.636351 0.771399i \(-0.280443\pi\)
0.636351 + 0.771399i \(0.280443\pi\)
\(572\) −2677.34 −0.195708
\(573\) −3023.96 −0.220467
\(574\) 0 0
\(575\) 31742.4 2.30217
\(576\) 7742.54 0.560080
\(577\) 14165.9 1.02207 0.511035 0.859560i \(-0.329262\pi\)
0.511035 + 0.859560i \(0.329262\pi\)
\(578\) 998.376 0.0718460
\(579\) −14179.5 −1.01775
\(580\) 25181.8 1.80279
\(581\) 0 0
\(582\) 67.7747 0.00482707
\(583\) 2572.90 0.182776
\(584\) 1179.10 0.0835469
\(585\) −10233.9 −0.723283
\(586\) 25221.2 1.77795
\(587\) 13013.6 0.915043 0.457521 0.889199i \(-0.348737\pi\)
0.457521 + 0.889199i \(0.348737\pi\)
\(588\) 0 0
\(589\) 19043.5 1.33222
\(590\) 17193.5 1.19974
\(591\) −3363.07 −0.234075
\(592\) −17329.6 −1.20311
\(593\) 1489.95 0.103179 0.0515894 0.998668i \(-0.483571\pi\)
0.0515894 + 0.998668i \(0.483571\pi\)
\(594\) −6022.60 −0.416011
\(595\) 0 0
\(596\) 2616.67 0.179837
\(597\) 8244.13 0.565176
\(598\) 19130.3 1.30819
\(599\) −11764.0 −0.802446 −0.401223 0.915980i \(-0.631415\pi\)
−0.401223 + 0.915980i \(0.631415\pi\)
\(600\) −1304.67 −0.0887715
\(601\) 11373.3 0.771925 0.385962 0.922515i \(-0.373869\pi\)
0.385962 + 0.922515i \(0.373869\pi\)
\(602\) 0 0
\(603\) 8807.78 0.594827
\(604\) −12437.9 −0.837900
\(605\) 22089.0 1.48437
\(606\) 19017.1 1.27478
\(607\) −20896.4 −1.39730 −0.698648 0.715465i \(-0.746215\pi\)
−0.698648 + 0.715465i \(0.746215\pi\)
\(608\) 28470.8 1.89909
\(609\) 0 0
\(610\) 2384.30 0.158258
\(611\) −11365.4 −0.752528
\(612\) −8900.27 −0.587863
\(613\) −4220.00 −0.278049 −0.139024 0.990289i \(-0.544397\pi\)
−0.139024 + 0.990289i \(0.544397\pi\)
\(614\) 18282.1 1.20164
\(615\) −13514.7 −0.886122
\(616\) 0 0
\(617\) −250.008 −0.0163127 −0.00815634 0.999967i \(-0.502596\pi\)
−0.00815634 + 0.999967i \(0.502596\pi\)
\(618\) 11679.5 0.760223
\(619\) −10844.4 −0.704158 −0.352079 0.935970i \(-0.614525\pi\)
−0.352079 + 0.935970i \(0.614525\pi\)
\(620\) −22995.8 −1.48957
\(621\) 20807.9 1.34459
\(622\) 3265.08 0.210479
\(623\) 0 0
\(624\) −6748.01 −0.432911
\(625\) 2167.54 0.138722
\(626\) −28164.4 −1.79820
\(627\) −3910.73 −0.249090
\(628\) 23040.0 1.46401
\(629\) 17441.5 1.10563
\(630\) 0 0
\(631\) −12729.0 −0.803061 −0.401531 0.915846i \(-0.631522\pi\)
−0.401531 + 0.915846i \(0.631522\pi\)
\(632\) −100.673 −0.00633635
\(633\) −10338.4 −0.649157
\(634\) −12258.2 −0.767882
\(635\) 37542.0 2.34616
\(636\) −5363.80 −0.334416
\(637\) 0 0
\(638\) 8046.35 0.499307
\(639\) −11893.0 −0.736277
\(640\) 4693.23 0.289869
\(641\) −9838.08 −0.606210 −0.303105 0.952957i \(-0.598023\pi\)
−0.303105 + 0.952957i \(0.598023\pi\)
\(642\) −19461.9 −1.19642
\(643\) −16456.6 −1.00931 −0.504655 0.863321i \(-0.668380\pi\)
−0.504655 + 0.863321i \(0.668380\pi\)
\(644\) 0 0
\(645\) −5116.44 −0.312341
\(646\) −30489.6 −1.85696
\(647\) −8370.82 −0.508641 −0.254321 0.967120i \(-0.581852\pi\)
−0.254321 + 0.967120i \(0.581852\pi\)
\(648\) 88.5664 0.00536916
\(649\) 2656.46 0.160670
\(650\) 26528.6 1.60083
\(651\) 0 0
\(652\) −20764.8 −1.24726
\(653\) 9681.16 0.580173 0.290087 0.957000i \(-0.406316\pi\)
0.290087 + 0.957000i \(0.406316\pi\)
\(654\) −16868.0 −1.00855
\(655\) −2899.61 −0.172972
\(656\) 16174.9 0.962687
\(657\) −10222.8 −0.607047
\(658\) 0 0
\(659\) 3978.93 0.235200 0.117600 0.993061i \(-0.462480\pi\)
0.117600 + 0.993061i \(0.462480\pi\)
\(660\) 4722.35 0.278511
\(661\) −23777.7 −1.39916 −0.699581 0.714554i \(-0.746630\pi\)
−0.699581 + 0.714554i \(0.746630\pi\)
\(662\) 32951.8 1.93460
\(663\) 6791.60 0.397834
\(664\) 1122.72 0.0656177
\(665\) 0 0
\(666\) 17507.2 1.01860
\(667\) −27799.9 −1.61382
\(668\) −4443.61 −0.257378
\(669\) 845.333 0.0488527
\(670\) −36434.7 −2.10089
\(671\) 368.382 0.0211941
\(672\) 0 0
\(673\) −6783.00 −0.388507 −0.194254 0.980951i \(-0.562228\pi\)
−0.194254 + 0.980951i \(0.562228\pi\)
\(674\) −18704.6 −1.06895
\(675\) 28855.0 1.64538
\(676\) −8724.38 −0.496380
\(677\) −19979.7 −1.13424 −0.567121 0.823635i \(-0.691943\pi\)
−0.567121 + 0.823635i \(0.691943\pi\)
\(678\) 25682.9 1.45479
\(679\) 0 0
\(680\) −2507.88 −0.141431
\(681\) −11266.7 −0.633981
\(682\) −7347.86 −0.412557
\(683\) 7057.33 0.395375 0.197688 0.980265i \(-0.436657\pi\)
0.197688 + 0.980265i \(0.436657\pi\)
\(684\) −14798.2 −0.827226
\(685\) 1298.00 0.0723998
\(686\) 0 0
\(687\) 2644.26 0.146848
\(688\) 6123.54 0.339328
\(689\) −7429.19 −0.410783
\(690\) −33742.5 −1.86168
\(691\) 9084.49 0.500131 0.250065 0.968229i \(-0.419548\pi\)
0.250065 + 0.968229i \(0.419548\pi\)
\(692\) −12152.5 −0.667584
\(693\) 0 0
\(694\) 23233.0 1.27077
\(695\) −25150.8 −1.37270
\(696\) 1142.63 0.0622286
\(697\) −16279.3 −0.884683
\(698\) −1758.79 −0.0953740
\(699\) 19303.6 1.04453
\(700\) 0 0
\(701\) 15607.4 0.840920 0.420460 0.907311i \(-0.361869\pi\)
0.420460 + 0.907311i \(0.361869\pi\)
\(702\) 17390.1 0.934969
\(703\) 28999.4 1.55581
\(704\) −4948.45 −0.264917
\(705\) 20046.6 1.07092
\(706\) −30232.0 −1.61161
\(707\) 0 0
\(708\) −5537.99 −0.293970
\(709\) −14222.5 −0.753367 −0.376684 0.926342i \(-0.622936\pi\)
−0.376684 + 0.926342i \(0.622936\pi\)
\(710\) 49197.3 2.60048
\(711\) 872.842 0.0460396
\(712\) −2351.30 −0.123762
\(713\) 25386.6 1.33343
\(714\) 0 0
\(715\) 6540.75 0.342112
\(716\) 15170.3 0.791819
\(717\) −13542.3 −0.705363
\(718\) −37019.6 −1.92418
\(719\) −2333.58 −0.121040 −0.0605200 0.998167i \(-0.519276\pi\)
−0.0605200 + 0.998167i \(0.519276\pi\)
\(720\) −21603.9 −1.11824
\(721\) 0 0
\(722\) −23698.9 −1.22158
\(723\) −1161.22 −0.0597321
\(724\) −20716.4 −1.06342
\(725\) −38551.0 −1.97482
\(726\) −14714.2 −0.752200
\(727\) −21602.3 −1.10204 −0.551020 0.834492i \(-0.685761\pi\)
−0.551020 + 0.834492i \(0.685761\pi\)
\(728\) 0 0
\(729\) 10732.3 0.545256
\(730\) 42288.2 2.14405
\(731\) −6163.09 −0.311833
\(732\) −767.977 −0.0387776
\(733\) −33179.7 −1.67192 −0.835961 0.548789i \(-0.815089\pi\)
−0.835961 + 0.548789i \(0.815089\pi\)
\(734\) 1752.31 0.0881183
\(735\) 0 0
\(736\) 37953.9 1.90082
\(737\) −5629.27 −0.281353
\(738\) −16340.6 −0.815050
\(739\) −19573.5 −0.974322 −0.487161 0.873312i \(-0.661968\pi\)
−0.487161 + 0.873312i \(0.661968\pi\)
\(740\) −35017.9 −1.73957
\(741\) 11292.2 0.559821
\(742\) 0 0
\(743\) 27842.0 1.37473 0.687365 0.726312i \(-0.258767\pi\)
0.687365 + 0.726312i \(0.258767\pi\)
\(744\) −1043.44 −0.0514170
\(745\) −6392.55 −0.314369
\(746\) −37567.6 −1.84376
\(747\) −9734.06 −0.476775
\(748\) 5688.39 0.278059
\(749\) 0 0
\(750\) −18913.7 −0.920840
\(751\) −29613.8 −1.43891 −0.719455 0.694539i \(-0.755608\pi\)
−0.719455 + 0.694539i \(0.755608\pi\)
\(752\) −23992.5 −1.16345
\(753\) 16033.3 0.775943
\(754\) −23233.7 −1.12218
\(755\) 30385.9 1.46471
\(756\) 0 0
\(757\) 7371.98 0.353949 0.176974 0.984215i \(-0.443369\pi\)
0.176974 + 0.984215i \(0.443369\pi\)
\(758\) −1264.70 −0.0606016
\(759\) −5213.33 −0.249317
\(760\) −4169.77 −0.199018
\(761\) 24101.3 1.14806 0.574029 0.818835i \(-0.305380\pi\)
0.574029 + 0.818835i \(0.305380\pi\)
\(762\) −25008.1 −1.18891
\(763\) 0 0
\(764\) 7313.28 0.346316
\(765\) 21743.4 1.02763
\(766\) −17411.4 −0.821281
\(767\) −7670.46 −0.361101
\(768\) −14145.2 −0.664611
\(769\) 34245.7 1.60589 0.802947 0.596051i \(-0.203264\pi\)
0.802947 + 0.596051i \(0.203264\pi\)
\(770\) 0 0
\(771\) −7988.73 −0.373161
\(772\) 34292.2 1.59871
\(773\) −21268.3 −0.989609 −0.494804 0.869004i \(-0.664760\pi\)
−0.494804 + 0.869004i \(0.664760\pi\)
\(774\) −6186.30 −0.287289
\(775\) 35204.4 1.63172
\(776\) 11.1650 0.000516496 0
\(777\) 0 0
\(778\) 37458.7 1.72617
\(779\) −27067.1 −1.24490
\(780\) −13635.7 −0.625944
\(781\) 7601.13 0.348259
\(782\) −40645.1 −1.85865
\(783\) −25271.1 −1.15340
\(784\) 0 0
\(785\) −56287.0 −2.55920
\(786\) 1931.53 0.0876531
\(787\) 1773.26 0.0803173 0.0401587 0.999193i \(-0.487214\pi\)
0.0401587 + 0.999193i \(0.487214\pi\)
\(788\) 8133.41 0.367691
\(789\) 12351.4 0.557315
\(790\) −3610.64 −0.162609
\(791\) 0 0
\(792\) −388.935 −0.0174497
\(793\) −1063.70 −0.0476329
\(794\) 5843.80 0.261195
\(795\) 13103.8 0.584583
\(796\) −19938.0 −0.887793
\(797\) 4473.60 0.198825 0.0994123 0.995046i \(-0.468304\pi\)
0.0994123 + 0.995046i \(0.468304\pi\)
\(798\) 0 0
\(799\) 24147.4 1.06918
\(800\) 52631.9 2.32602
\(801\) 20385.8 0.899249
\(802\) −24349.6 −1.07209
\(803\) 6533.66 0.287133
\(804\) 11735.5 0.514776
\(805\) 0 0
\(806\) 21216.8 0.927208
\(807\) −9745.56 −0.425105
\(808\) 3132.82 0.136401
\(809\) −15255.6 −0.662989 −0.331494 0.943457i \(-0.607553\pi\)
−0.331494 + 0.943457i \(0.607553\pi\)
\(810\) 3176.42 0.137788
\(811\) −4911.79 −0.212671 −0.106336 0.994330i \(-0.533912\pi\)
−0.106336 + 0.994330i \(0.533912\pi\)
\(812\) 0 0
\(813\) −6553.00 −0.282686
\(814\) −11189.3 −0.481799
\(815\) 50728.5 2.18030
\(816\) 14337.1 0.615073
\(817\) −10247.2 −0.438804
\(818\) −42261.5 −1.80640
\(819\) 0 0
\(820\) 32684.5 1.39194
\(821\) 22792.2 0.968884 0.484442 0.874823i \(-0.339023\pi\)
0.484442 + 0.874823i \(0.339023\pi\)
\(822\) −864.640 −0.0366883
\(823\) 17358.6 0.735216 0.367608 0.929981i \(-0.380177\pi\)
0.367608 + 0.929981i \(0.380177\pi\)
\(824\) 1924.05 0.0813438
\(825\) −7229.49 −0.305089
\(826\) 0 0
\(827\) −34567.7 −1.45349 −0.726745 0.686907i \(-0.758968\pi\)
−0.726745 + 0.686907i \(0.758968\pi\)
\(828\) −19727.2 −0.827980
\(829\) −568.054 −0.0237990 −0.0118995 0.999929i \(-0.503788\pi\)
−0.0118995 + 0.999929i \(0.503788\pi\)
\(830\) 40266.4 1.68394
\(831\) 9835.96 0.410597
\(832\) 14288.6 0.595392
\(833\) 0 0
\(834\) 16753.8 0.695609
\(835\) 10855.8 0.449915
\(836\) 9457.89 0.391277
\(837\) 23077.3 0.953011
\(838\) −19364.3 −0.798243
\(839\) 28050.8 1.15426 0.577129 0.816653i \(-0.304173\pi\)
0.577129 + 0.816653i \(0.304173\pi\)
\(840\) 0 0
\(841\) 9373.83 0.384347
\(842\) 46457.0 1.90144
\(843\) −4703.50 −0.192167
\(844\) 25003.0 1.01971
\(845\) 21313.7 0.867709
\(846\) 24238.4 0.985026
\(847\) 0 0
\(848\) −15683.1 −0.635094
\(849\) −4703.98 −0.190153
\(850\) −56363.9 −2.27443
\(851\) 38658.6 1.55723
\(852\) −15846.3 −0.637189
\(853\) −8242.71 −0.330862 −0.165431 0.986221i \(-0.552901\pi\)
−0.165431 + 0.986221i \(0.552901\pi\)
\(854\) 0 0
\(855\) 36152.1 1.44605
\(856\) −3206.09 −0.128016
\(857\) −21781.0 −0.868175 −0.434087 0.900871i \(-0.642929\pi\)
−0.434087 + 0.900871i \(0.642929\pi\)
\(858\) −4357.02 −0.173364
\(859\) −46751.1 −1.85696 −0.928480 0.371383i \(-0.878884\pi\)
−0.928480 + 0.371383i \(0.878884\pi\)
\(860\) 12373.8 0.490633
\(861\) 0 0
\(862\) −11421.3 −0.451290
\(863\) −20805.6 −0.820663 −0.410331 0.911936i \(-0.634587\pi\)
−0.410331 + 0.911936i \(0.634587\pi\)
\(864\) 34501.5 1.35852
\(865\) 29688.6 1.16699
\(866\) −1567.74 −0.0615173
\(867\) 785.608 0.0307735
\(868\) 0 0
\(869\) −557.856 −0.0217767
\(870\) 40980.1 1.59696
\(871\) 16254.4 0.632330
\(872\) −2778.78 −0.107914
\(873\) −96.8011 −0.00375283
\(874\) −67579.2 −2.61545
\(875\) 0 0
\(876\) −13620.9 −0.525351
\(877\) 3507.96 0.135069 0.0675345 0.997717i \(-0.478487\pi\)
0.0675345 + 0.997717i \(0.478487\pi\)
\(878\) 19590.5 0.753017
\(879\) 19846.2 0.761542
\(880\) 13807.6 0.528925
\(881\) 29531.8 1.12934 0.564671 0.825316i \(-0.309003\pi\)
0.564671 + 0.825316i \(0.309003\pi\)
\(882\) 0 0
\(883\) −41514.5 −1.58219 −0.791096 0.611692i \(-0.790489\pi\)
−0.791096 + 0.611692i \(0.790489\pi\)
\(884\) −16425.1 −0.624928
\(885\) 13529.4 0.513881
\(886\) 8664.81 0.328555
\(887\) 36859.9 1.39530 0.697652 0.716437i \(-0.254228\pi\)
0.697652 + 0.716437i \(0.254228\pi\)
\(888\) −1588.94 −0.0600466
\(889\) 0 0
\(890\) −84329.1 −3.17609
\(891\) 490.767 0.0184527
\(892\) −2044.39 −0.0767391
\(893\) 40149.1 1.50452
\(894\) 4258.30 0.159305
\(895\) −37061.3 −1.38416
\(896\) 0 0
\(897\) 15053.4 0.560332
\(898\) −72079.0 −2.67852
\(899\) −30831.9 −1.14383
\(900\) −27356.3 −1.01320
\(901\) 15784.4 0.583634
\(902\) 10443.7 0.385518
\(903\) 0 0
\(904\) 4230.94 0.155662
\(905\) 50610.2 1.85894
\(906\) −20241.1 −0.742236
\(907\) −17428.2 −0.638031 −0.319016 0.947749i \(-0.603352\pi\)
−0.319016 + 0.947749i \(0.603352\pi\)
\(908\) 27247.9 0.995874
\(909\) −27161.6 −0.991083
\(910\) 0 0
\(911\) −14994.7 −0.545333 −0.272666 0.962109i \(-0.587906\pi\)
−0.272666 + 0.962109i \(0.587906\pi\)
\(912\) 23837.8 0.865515
\(913\) 6221.28 0.225514
\(914\) 34429.2 1.24597
\(915\) 1876.17 0.0677862
\(916\) −6394.99 −0.230673
\(917\) 0 0
\(918\) −36947.9 −1.32839
\(919\) 24719.2 0.887280 0.443640 0.896205i \(-0.353687\pi\)
0.443640 + 0.896205i \(0.353687\pi\)
\(920\) −5558.65 −0.199199
\(921\) 14385.9 0.514693
\(922\) −36633.1 −1.30851
\(923\) −21948.1 −0.782698
\(924\) 0 0
\(925\) 53609.2 1.90558
\(926\) 55985.9 1.98684
\(927\) −16681.5 −0.591040
\(928\) −46094.9 −1.63054
\(929\) −41255.1 −1.45698 −0.728490 0.685056i \(-0.759778\pi\)
−0.728490 + 0.685056i \(0.759778\pi\)
\(930\) −37422.7 −1.31950
\(931\) 0 0
\(932\) −46684.7 −1.64078
\(933\) 2569.25 0.0901536
\(934\) −23159.8 −0.811361
\(935\) −13896.8 −0.486068
\(936\) 1123.04 0.0392177
\(937\) −30271.6 −1.05542 −0.527711 0.849424i \(-0.676950\pi\)
−0.527711 + 0.849424i \(0.676950\pi\)
\(938\) 0 0
\(939\) −22162.1 −0.770218
\(940\) −48481.6 −1.68223
\(941\) 49515.6 1.71537 0.857685 0.514175i \(-0.171902\pi\)
0.857685 + 0.514175i \(0.171902\pi\)
\(942\) 37494.7 1.29686
\(943\) −36082.7 −1.24604
\(944\) −16192.4 −0.558282
\(945\) 0 0
\(946\) 3953.82 0.135888
\(947\) −48772.3 −1.67359 −0.836794 0.547518i \(-0.815573\pi\)
−0.836794 + 0.547518i \(0.815573\pi\)
\(948\) 1162.98 0.0398436
\(949\) −18865.8 −0.645321
\(950\) −93714.3 −3.20052
\(951\) −9645.84 −0.328904
\(952\) 0 0
\(953\) −43341.2 −1.47320 −0.736599 0.676329i \(-0.763570\pi\)
−0.736599 + 0.676329i \(0.763570\pi\)
\(954\) 15843.8 0.537697
\(955\) −17866.4 −0.605386
\(956\) 32751.3 1.10800
\(957\) 6331.56 0.213867
\(958\) −49156.2 −1.65779
\(959\) 0 0
\(960\) −25202.5 −0.847300
\(961\) −1635.54 −0.0549006
\(962\) 32308.8 1.08283
\(963\) 27796.9 0.930160
\(964\) 2808.35 0.0938288
\(965\) −83776.2 −2.79466
\(966\) 0 0
\(967\) −636.799 −0.0211769 −0.0105885 0.999944i \(-0.503370\pi\)
−0.0105885 + 0.999944i \(0.503370\pi\)
\(968\) −2423.98 −0.0804853
\(969\) −23991.8 −0.795385
\(970\) 400.432 0.0132547
\(971\) −19763.9 −0.653195 −0.326598 0.945163i \(-0.605902\pi\)
−0.326598 + 0.945163i \(0.605902\pi\)
\(972\) −28835.6 −0.951545
\(973\) 0 0
\(974\) −32155.0 −1.05782
\(975\) 20875.0 0.685676
\(976\) −2245.47 −0.0736432
\(977\) 40980.6 1.34195 0.670975 0.741480i \(-0.265876\pi\)
0.670975 + 0.741480i \(0.265876\pi\)
\(978\) −33792.0 −1.10486
\(979\) −13029.1 −0.425344
\(980\) 0 0
\(981\) 24092.1 0.784100
\(982\) −23197.3 −0.753824
\(983\) 9296.84 0.301651 0.150826 0.988560i \(-0.451807\pi\)
0.150826 + 0.988560i \(0.451807\pi\)
\(984\) 1483.06 0.0480471
\(985\) −19870.0 −0.642752
\(986\) 49363.3 1.59437
\(987\) 0 0
\(988\) −27309.5 −0.879382
\(989\) −13660.3 −0.439204
\(990\) −13949.1 −0.447810
\(991\) 6575.47 0.210774 0.105387 0.994431i \(-0.466392\pi\)
0.105387 + 0.994431i \(0.466392\pi\)
\(992\) 42093.4 1.34725
\(993\) 25929.3 0.828641
\(994\) 0 0
\(995\) 48708.6 1.55193
\(996\) −12969.7 −0.412611
\(997\) −5380.51 −0.170915 −0.0854576 0.996342i \(-0.527235\pi\)
−0.0854576 + 0.996342i \(0.527235\pi\)
\(998\) −27900.8 −0.884954
\(999\) 35142.1 1.11296
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 2401.4.a.d.1.7 39
7.6 odd 2 2401.4.a.c.1.7 39
49.22 even 7 49.4.e.a.43.3 yes 78
49.29 even 7 49.4.e.a.8.3 78
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
49.4.e.a.8.3 78 49.29 even 7
49.4.e.a.43.3 yes 78 49.22 even 7
2401.4.a.c.1.7 39 7.6 odd 2
2401.4.a.d.1.7 39 1.1 even 1 trivial