Properties

Label 575.4.a.j.1.1
Level $575$
Weight $4$
Character 575.1
Self dual yes
Analytic conductor $33.926$
Analytic rank $1$
Dimension $5$
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] = [575,4,Mod(1,575)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(575, 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("575.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 575 = 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 575.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: \(33.9260982533\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - x^{4} - 27x^{3} + 7x^{2} + 168x + 92 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 115)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(4.60878\) of defining polynomial
Character \(\chi\) \(=\) 575.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.60878 q^{2} +1.89520 q^{3} +23.4584 q^{4} -10.6297 q^{6} -11.4426 q^{7} -86.7031 q^{8} -23.4082 q^{9} +O(q^{10})\) \(q-5.60878 q^{2} +1.89520 q^{3} +23.4584 q^{4} -10.6297 q^{6} -11.4426 q^{7} -86.7031 q^{8} -23.4082 q^{9} +37.7245 q^{11} +44.4584 q^{12} +8.69346 q^{13} +64.1788 q^{14} +298.631 q^{16} +105.687 q^{17} +131.292 q^{18} -128.279 q^{19} -21.6859 q^{21} -211.588 q^{22} +23.0000 q^{23} -164.319 q^{24} -48.7597 q^{26} -95.5335 q^{27} -268.425 q^{28} -133.383 q^{29} +106.008 q^{31} -981.333 q^{32} +71.4953 q^{33} -592.773 q^{34} -549.121 q^{36} +248.835 q^{37} +719.491 q^{38} +16.4758 q^{39} +134.233 q^{41} +121.631 q^{42} -108.684 q^{43} +884.957 q^{44} -129.002 q^{46} +76.2000 q^{47} +565.965 q^{48} -212.068 q^{49} +200.297 q^{51} +203.935 q^{52} -476.207 q^{53} +535.827 q^{54} +992.105 q^{56} -243.114 q^{57} +748.118 q^{58} +608.000 q^{59} -366.273 q^{61} -594.575 q^{62} +267.850 q^{63} +3115.03 q^{64} -401.001 q^{66} -136.041 q^{67} +2479.24 q^{68} +43.5895 q^{69} -152.874 q^{71} +2029.57 q^{72} -1228.16 q^{73} -1395.66 q^{74} -3009.23 q^{76} -431.664 q^{77} -92.4092 q^{78} -364.637 q^{79} +450.968 q^{81} -752.882 q^{82} +762.744 q^{83} -508.717 q^{84} +609.583 q^{86} -252.788 q^{87} -3270.83 q^{88} +271.222 q^{89} -99.4754 q^{91} +539.544 q^{92} +200.906 q^{93} -427.389 q^{94} -1859.82 q^{96} -574.510 q^{97} +1189.44 q^{98} -883.063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 6 q^{2} - 4 q^{3} + 22 q^{4} + 19 q^{6} + 3 q^{7} - 138 q^{8} + 77 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 6 q^{2} - 4 q^{3} + 22 q^{4} + 19 q^{6} + 3 q^{7} - 138 q^{8} + 77 q^{9} + 23 q^{11} - 47 q^{12} - 132 q^{13} + 93 q^{14} + 282 q^{16} - 23 q^{17} + 15 q^{18} - 161 q^{19} - 60 q^{21} - 193 q^{22} + 115 q^{23} + 105 q^{24} - 257 q^{26} - 577 q^{27} - 17 q^{28} + 401 q^{29} + 32 q^{31} - 670 q^{32} - 189 q^{33} - 663 q^{34} - 659 q^{36} + 38 q^{37} + 875 q^{38} + 335 q^{39} - 12 q^{41} + 798 q^{42} + 566 q^{43} + 47 q^{44} - 138 q^{46} - 919 q^{47} + 773 q^{48} - 738 q^{49} - 993 q^{51} + 305 q^{52} - 1156 q^{53} - 8 q^{54} + 343 q^{56} - 114 q^{57} + 1042 q^{58} + 1324 q^{59} - 1673 q^{61} - 565 q^{62} - 270 q^{63} + 2466 q^{64} - 2781 q^{66} - 558 q^{67} + 2267 q^{68} - 92 q^{69} - 108 q^{71} + 789 q^{72} - 1173 q^{73} + 1458 q^{74} - 3477 q^{76} - 2608 q^{77} - 704 q^{78} + 656 q^{79} - 319 q^{81} - 3505 q^{82} + 82 q^{83} - 718 q^{84} + 112 q^{86} - 2389 q^{87} - 2397 q^{88} + 570 q^{89} - 1589 q^{91} + 506 q^{92} - 911 q^{93} - 948 q^{94} - 5991 q^{96} - 633 q^{97} + 2555 q^{98} + 2021 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.60878 −1.98300 −0.991502 0.130090i \(-0.958473\pi\)
−0.991502 + 0.130090i \(0.958473\pi\)
\(3\) 1.89520 0.364731 0.182365 0.983231i \(-0.441625\pi\)
0.182365 + 0.983231i \(0.441625\pi\)
\(4\) 23.4584 2.93231
\(5\) 0 0
\(6\) −10.6297 −0.723262
\(7\) −11.4426 −0.617840 −0.308920 0.951088i \(-0.599968\pi\)
−0.308920 + 0.951088i \(0.599968\pi\)
\(8\) −86.7031 −3.83177
\(9\) −23.4082 −0.866972
\(10\) 0 0
\(11\) 37.7245 1.03403 0.517016 0.855976i \(-0.327043\pi\)
0.517016 + 0.855976i \(0.327043\pi\)
\(12\) 44.4584 1.06950
\(13\) 8.69346 0.185472 0.0927358 0.995691i \(-0.470439\pi\)
0.0927358 + 0.995691i \(0.470439\pi\)
\(14\) 64.1788 1.22518
\(15\) 0 0
\(16\) 298.631 4.66611
\(17\) 105.687 1.50781 0.753905 0.656983i \(-0.228168\pi\)
0.753905 + 0.656983i \(0.228168\pi\)
\(18\) 131.292 1.71921
\(19\) −128.279 −1.54891 −0.774455 0.632629i \(-0.781976\pi\)
−0.774455 + 0.632629i \(0.781976\pi\)
\(20\) 0 0
\(21\) −21.6859 −0.225345
\(22\) −211.588 −2.05049
\(23\) 23.0000 0.208514
\(24\) −164.319 −1.39756
\(25\) 0 0
\(26\) −48.7597 −0.367791
\(27\) −95.5335 −0.680942
\(28\) −268.425 −1.81170
\(29\) −133.383 −0.854092 −0.427046 0.904230i \(-0.640446\pi\)
−0.427046 + 0.904230i \(0.640446\pi\)
\(30\) 0 0
\(31\) 106.008 0.614179 0.307090 0.951681i \(-0.400645\pi\)
0.307090 + 0.951681i \(0.400645\pi\)
\(32\) −981.333 −5.42115
\(33\) 71.4953 0.377143
\(34\) −592.773 −2.98999
\(35\) 0 0
\(36\) −549.121 −2.54223
\(37\) 248.835 1.10563 0.552814 0.833305i \(-0.313554\pi\)
0.552814 + 0.833305i \(0.313554\pi\)
\(38\) 719.491 3.07150
\(39\) 16.4758 0.0676472
\(40\) 0 0
\(41\) 134.233 0.511308 0.255654 0.966768i \(-0.417709\pi\)
0.255654 + 0.966768i \(0.417709\pi\)
\(42\) 121.631 0.446860
\(43\) −108.684 −0.385444 −0.192722 0.981253i \(-0.561732\pi\)
−0.192722 + 0.981253i \(0.561732\pi\)
\(44\) 884.957 3.03210
\(45\) 0 0
\(46\) −129.002 −0.413485
\(47\) 76.2000 0.236488 0.118244 0.992985i \(-0.462274\pi\)
0.118244 + 0.992985i \(0.462274\pi\)
\(48\) 565.965 1.70187
\(49\) −212.068 −0.618274
\(50\) 0 0
\(51\) 200.297 0.549945
\(52\) 203.935 0.543859
\(53\) −476.207 −1.23419 −0.617095 0.786889i \(-0.711691\pi\)
−0.617095 + 0.786889i \(0.711691\pi\)
\(54\) 535.827 1.35031
\(55\) 0 0
\(56\) 992.105 2.36742
\(57\) −243.114 −0.564935
\(58\) 748.118 1.69367
\(59\) 608.000 1.34161 0.670804 0.741635i \(-0.265949\pi\)
0.670804 + 0.741635i \(0.265949\pi\)
\(60\) 0 0
\(61\) −366.273 −0.768794 −0.384397 0.923168i \(-0.625591\pi\)
−0.384397 + 0.923168i \(0.625591\pi\)
\(62\) −594.575 −1.21792
\(63\) 267.850 0.535650
\(64\) 3115.03 6.08405
\(65\) 0 0
\(66\) −401.001 −0.747877
\(67\) −136.041 −0.248060 −0.124030 0.992278i \(-0.539582\pi\)
−0.124030 + 0.992278i \(0.539582\pi\)
\(68\) 2479.24 4.42136
\(69\) 43.5895 0.0760516
\(70\) 0 0
\(71\) −152.874 −0.255533 −0.127766 0.991804i \(-0.540781\pi\)
−0.127766 + 0.991804i \(0.540781\pi\)
\(72\) 2029.57 3.32204
\(73\) −1228.16 −1.96911 −0.984556 0.175070i \(-0.943985\pi\)
−0.984556 + 0.175070i \(0.943985\pi\)
\(74\) −1395.66 −2.19246
\(75\) 0 0
\(76\) −3009.23 −4.54188
\(77\) −431.664 −0.638867
\(78\) −92.4092 −0.134145
\(79\) −364.637 −0.519302 −0.259651 0.965702i \(-0.583608\pi\)
−0.259651 + 0.965702i \(0.583608\pi\)
\(80\) 0 0
\(81\) 450.968 0.618611
\(82\) −752.882 −1.01393
\(83\) 762.744 1.00870 0.504350 0.863499i \(-0.331732\pi\)
0.504350 + 0.863499i \(0.331732\pi\)
\(84\) −508.717 −0.660781
\(85\) 0 0
\(86\) 609.583 0.764338
\(87\) −252.788 −0.311514
\(88\) −3270.83 −3.96217
\(89\) 271.222 0.323028 0.161514 0.986870i \(-0.448362\pi\)
0.161514 + 0.986870i \(0.448362\pi\)
\(90\) 0 0
\(91\) −99.4754 −0.114592
\(92\) 539.544 0.611428
\(93\) 200.906 0.224010
\(94\) −427.389 −0.468956
\(95\) 0 0
\(96\) −1859.82 −1.97726
\(97\) −574.510 −0.601367 −0.300684 0.953724i \(-0.597215\pi\)
−0.300684 + 0.953724i \(0.597215\pi\)
\(98\) 1189.44 1.22604
\(99\) −883.063 −0.896477
\(100\) 0 0
\(101\) 1372.25 1.35192 0.675958 0.736940i \(-0.263730\pi\)
0.675958 + 0.736940i \(0.263730\pi\)
\(102\) −1123.42 −1.09054
\(103\) 242.428 0.231914 0.115957 0.993254i \(-0.463007\pi\)
0.115957 + 0.993254i \(0.463007\pi\)
\(104\) −753.749 −0.710685
\(105\) 0 0
\(106\) 2670.94 2.44740
\(107\) −650.896 −0.588079 −0.294039 0.955793i \(-0.595000\pi\)
−0.294039 + 0.955793i \(0.595000\pi\)
\(108\) −2241.07 −1.99673
\(109\) −1230.43 −1.08123 −0.540613 0.841271i \(-0.681808\pi\)
−0.540613 + 0.841271i \(0.681808\pi\)
\(110\) 0 0
\(111\) 471.591 0.403256
\(112\) −3417.10 −2.88291
\(113\) −238.959 −0.198932 −0.0994662 0.995041i \(-0.531714\pi\)
−0.0994662 + 0.995041i \(0.531714\pi\)
\(114\) 1363.58 1.12027
\(115\) 0 0
\(116\) −3128.97 −2.50446
\(117\) −203.498 −0.160799
\(118\) −3410.14 −2.66041
\(119\) −1209.33 −0.931586
\(120\) 0 0
\(121\) 92.1354 0.0692227
\(122\) 2054.34 1.52452
\(123\) 254.397 0.186490
\(124\) 2486.78 1.80096
\(125\) 0 0
\(126\) −1502.31 −1.06220
\(127\) −2608.48 −1.82256 −0.911280 0.411788i \(-0.864904\pi\)
−0.911280 + 0.411788i \(0.864904\pi\)
\(128\) −9620.89 −6.64355
\(129\) −205.977 −0.140583
\(130\) 0 0
\(131\) −936.409 −0.624538 −0.312269 0.949994i \(-0.601089\pi\)
−0.312269 + 0.949994i \(0.601089\pi\)
\(132\) 1677.17 1.10590
\(133\) 1467.84 0.956979
\(134\) 763.023 0.491904
\(135\) 0 0
\(136\) −9163.36 −5.77758
\(137\) −415.511 −0.259121 −0.129560 0.991572i \(-0.541357\pi\)
−0.129560 + 0.991572i \(0.541357\pi\)
\(138\) −244.484 −0.150811
\(139\) −949.629 −0.579471 −0.289736 0.957107i \(-0.593567\pi\)
−0.289736 + 0.957107i \(0.593567\pi\)
\(140\) 0 0
\(141\) 144.414 0.0862542
\(142\) 857.439 0.506723
\(143\) 327.956 0.191784
\(144\) −6990.43 −4.04539
\(145\) 0 0
\(146\) 6888.48 3.90476
\(147\) −401.910 −0.225503
\(148\) 5837.28 3.24204
\(149\) 2209.84 1.21502 0.607508 0.794314i \(-0.292169\pi\)
0.607508 + 0.794314i \(0.292169\pi\)
\(150\) 0 0
\(151\) −1384.25 −0.746018 −0.373009 0.927828i \(-0.621674\pi\)
−0.373009 + 0.927828i \(0.621674\pi\)
\(152\) 11122.2 5.93507
\(153\) −2473.94 −1.30723
\(154\) 2421.11 1.26688
\(155\) 0 0
\(156\) 386.497 0.198362
\(157\) −561.399 −0.285379 −0.142690 0.989767i \(-0.545575\pi\)
−0.142690 + 0.989767i \(0.545575\pi\)
\(158\) 2045.17 1.02978
\(159\) −902.506 −0.450147
\(160\) 0 0
\(161\) −263.179 −0.128829
\(162\) −2529.38 −1.22671
\(163\) −2134.47 −1.02567 −0.512836 0.858487i \(-0.671405\pi\)
−0.512836 + 0.858487i \(0.671405\pi\)
\(164\) 3148.89 1.49931
\(165\) 0 0
\(166\) −4278.07 −2.00026
\(167\) 1315.64 0.609623 0.304812 0.952413i \(-0.401406\pi\)
0.304812 + 0.952413i \(0.401406\pi\)
\(168\) 1880.23 0.863471
\(169\) −2121.42 −0.965600
\(170\) 0 0
\(171\) 3002.79 1.34286
\(172\) −2549.55 −1.13024
\(173\) −676.565 −0.297331 −0.148666 0.988888i \(-0.547498\pi\)
−0.148666 + 0.988888i \(0.547498\pi\)
\(174\) 1417.83 0.617733
\(175\) 0 0
\(176\) 11265.7 4.82491
\(177\) 1152.28 0.489325
\(178\) −1521.23 −0.640566
\(179\) −3737.96 −1.56083 −0.780414 0.625263i \(-0.784992\pi\)
−0.780414 + 0.625263i \(0.784992\pi\)
\(180\) 0 0
\(181\) −1873.40 −0.769330 −0.384665 0.923056i \(-0.625683\pi\)
−0.384665 + 0.923056i \(0.625683\pi\)
\(182\) 557.936 0.227236
\(183\) −694.158 −0.280403
\(184\) −1994.17 −0.798979
\(185\) 0 0
\(186\) −1126.84 −0.444213
\(187\) 3986.97 1.55912
\(188\) 1787.53 0.693454
\(189\) 1093.15 0.420713
\(190\) 0 0
\(191\) −5158.92 −1.95438 −0.977190 0.212366i \(-0.931883\pi\)
−0.977190 + 0.212366i \(0.931883\pi\)
\(192\) 5903.60 2.21904
\(193\) 4806.41 1.79261 0.896303 0.443442i \(-0.146243\pi\)
0.896303 + 0.443442i \(0.146243\pi\)
\(194\) 3222.30 1.19251
\(195\) 0 0
\(196\) −4974.78 −1.81297
\(197\) −3202.59 −1.15825 −0.579125 0.815239i \(-0.696606\pi\)
−0.579125 + 0.815239i \(0.696606\pi\)
\(198\) 4952.91 1.77772
\(199\) −2210.46 −0.787415 −0.393707 0.919236i \(-0.628808\pi\)
−0.393707 + 0.919236i \(0.628808\pi\)
\(200\) 0 0
\(201\) −257.824 −0.0904751
\(202\) −7696.62 −2.68085
\(203\) 1526.25 0.527692
\(204\) 4698.65 1.61261
\(205\) 0 0
\(206\) −1359.73 −0.459886
\(207\) −538.389 −0.180776
\(208\) 2596.14 0.865431
\(209\) −4839.27 −1.60162
\(210\) 0 0
\(211\) 153.164 0.0499726 0.0249863 0.999688i \(-0.492046\pi\)
0.0249863 + 0.999688i \(0.492046\pi\)
\(212\) −11171.1 −3.61902
\(213\) −289.727 −0.0932007
\(214\) 3650.73 1.16616
\(215\) 0 0
\(216\) 8283.05 2.60921
\(217\) −1213.00 −0.379465
\(218\) 6901.21 2.14408
\(219\) −2327.60 −0.718195
\(220\) 0 0
\(221\) 918.782 0.279656
\(222\) −2645.05 −0.799659
\(223\) 3068.41 0.921416 0.460708 0.887552i \(-0.347595\pi\)
0.460708 + 0.887552i \(0.347595\pi\)
\(224\) 11229.0 3.34940
\(225\) 0 0
\(226\) 1340.27 0.394484
\(227\) −4540.20 −1.32750 −0.663752 0.747953i \(-0.731037\pi\)
−0.663752 + 0.747953i \(0.731037\pi\)
\(228\) −5703.09 −1.65656
\(229\) 1476.25 0.425996 0.212998 0.977053i \(-0.431677\pi\)
0.212998 + 0.977053i \(0.431677\pi\)
\(230\) 0 0
\(231\) −818.089 −0.233014
\(232\) 11564.7 3.27269
\(233\) 90.7306 0.0255106 0.0127553 0.999919i \(-0.495940\pi\)
0.0127553 + 0.999919i \(0.495940\pi\)
\(234\) 1141.38 0.318864
\(235\) 0 0
\(236\) 14262.7 3.93400
\(237\) −691.059 −0.189405
\(238\) 6782.85 1.84734
\(239\) −1619.16 −0.438221 −0.219111 0.975700i \(-0.570316\pi\)
−0.219111 + 0.975700i \(0.570316\pi\)
\(240\) 0 0
\(241\) −6447.48 −1.72331 −0.861657 0.507491i \(-0.830573\pi\)
−0.861657 + 0.507491i \(0.830573\pi\)
\(242\) −516.768 −0.137269
\(243\) 3434.08 0.906568
\(244\) −8592.19 −2.25434
\(245\) 0 0
\(246\) −1426.86 −0.369810
\(247\) −1115.19 −0.287279
\(248\) −9191.20 −2.35339
\(249\) 1445.55 0.367904
\(250\) 0 0
\(251\) 3428.17 0.862089 0.431044 0.902331i \(-0.358145\pi\)
0.431044 + 0.902331i \(0.358145\pi\)
\(252\) 6283.35 1.57069
\(253\) 867.663 0.215611
\(254\) 14630.4 3.61414
\(255\) 0 0
\(256\) 29041.2 7.09014
\(257\) −2261.08 −0.548803 −0.274402 0.961615i \(-0.588480\pi\)
−0.274402 + 0.961615i \(0.588480\pi\)
\(258\) 1155.28 0.278777
\(259\) −2847.31 −0.683101
\(260\) 0 0
\(261\) 3122.27 0.740474
\(262\) 5252.11 1.23846
\(263\) −5319.64 −1.24724 −0.623618 0.781729i \(-0.714338\pi\)
−0.623618 + 0.781729i \(0.714338\pi\)
\(264\) −6198.86 −1.44513
\(265\) 0 0
\(266\) −8232.81 −1.89769
\(267\) 514.019 0.117818
\(268\) −3191.31 −0.727388
\(269\) −1992.51 −0.451620 −0.225810 0.974171i \(-0.572503\pi\)
−0.225810 + 0.974171i \(0.572503\pi\)
\(270\) 0 0
\(271\) 3950.62 0.885546 0.442773 0.896634i \(-0.353995\pi\)
0.442773 + 0.896634i \(0.353995\pi\)
\(272\) 31561.3 7.03561
\(273\) −188.525 −0.0417951
\(274\) 2330.51 0.513837
\(275\) 0 0
\(276\) 1022.54 0.223007
\(277\) 178.126 0.0386375 0.0193187 0.999813i \(-0.493850\pi\)
0.0193187 + 0.999813i \(0.493850\pi\)
\(278\) 5326.27 1.14909
\(279\) −2481.46 −0.532476
\(280\) 0 0
\(281\) 3523.49 0.748020 0.374010 0.927425i \(-0.377983\pi\)
0.374010 + 0.927425i \(0.377983\pi\)
\(282\) −809.986 −0.171043
\(283\) 699.284 0.146884 0.0734419 0.997300i \(-0.476602\pi\)
0.0734419 + 0.997300i \(0.476602\pi\)
\(284\) −3586.19 −0.749301
\(285\) 0 0
\(286\) −1839.43 −0.380308
\(287\) −1535.96 −0.315906
\(288\) 22971.3 4.69998
\(289\) 6256.67 1.27349
\(290\) 0 0
\(291\) −1088.81 −0.219337
\(292\) −28810.7 −5.77404
\(293\) −8552.97 −1.70536 −0.852678 0.522436i \(-0.825023\pi\)
−0.852678 + 0.522436i \(0.825023\pi\)
\(294\) 2254.23 0.447174
\(295\) 0 0
\(296\) −21574.8 −4.23651
\(297\) −3603.95 −0.704116
\(298\) −12394.5 −2.40938
\(299\) 199.949 0.0386735
\(300\) 0 0
\(301\) 1243.62 0.238143
\(302\) 7763.96 1.47936
\(303\) 2600.67 0.493085
\(304\) −38308.2 −7.22739
\(305\) 0 0
\(306\) 13875.8 2.59224
\(307\) 5621.73 1.04511 0.522555 0.852606i \(-0.324979\pi\)
0.522555 + 0.852606i \(0.324979\pi\)
\(308\) −10126.2 −1.87335
\(309\) 459.448 0.0845861
\(310\) 0 0
\(311\) −6533.62 −1.19128 −0.595639 0.803252i \(-0.703101\pi\)
−0.595639 + 0.803252i \(0.703101\pi\)
\(312\) −1428.50 −0.259208
\(313\) 2713.24 0.489973 0.244987 0.969526i \(-0.421216\pi\)
0.244987 + 0.969526i \(0.421216\pi\)
\(314\) 3148.77 0.565908
\(315\) 0 0
\(316\) −8553.82 −1.52275
\(317\) 7544.32 1.33669 0.668346 0.743851i \(-0.267003\pi\)
0.668346 + 0.743851i \(0.267003\pi\)
\(318\) 5061.96 0.892643
\(319\) −5031.82 −0.883159
\(320\) 0 0
\(321\) −1233.57 −0.214490
\(322\) 1476.11 0.255468
\(323\) −13557.4 −2.33546
\(324\) 10579.0 1.81396
\(325\) 0 0
\(326\) 11971.8 2.03391
\(327\) −2331.90 −0.394356
\(328\) −11638.4 −1.95921
\(329\) −871.923 −0.146111
\(330\) 0 0
\(331\) 5991.64 0.994956 0.497478 0.867477i \(-0.334260\pi\)
0.497478 + 0.867477i \(0.334260\pi\)
\(332\) 17892.8 2.95782
\(333\) −5824.79 −0.958548
\(334\) −7379.13 −1.20889
\(335\) 0 0
\(336\) −6476.08 −1.05149
\(337\) −5665.46 −0.915778 −0.457889 0.889009i \(-0.651394\pi\)
−0.457889 + 0.889009i \(0.651394\pi\)
\(338\) 11898.6 1.91479
\(339\) −452.874 −0.0725567
\(340\) 0 0
\(341\) 3999.09 0.635081
\(342\) −16842.0 −2.66290
\(343\) 6351.40 0.999834
\(344\) 9423.21 1.47693
\(345\) 0 0
\(346\) 3794.71 0.589609
\(347\) −5593.30 −0.865315 −0.432657 0.901558i \(-0.642424\pi\)
−0.432657 + 0.901558i \(0.642424\pi\)
\(348\) −5930.00 −0.913453
\(349\) 4304.61 0.660230 0.330115 0.943941i \(-0.392912\pi\)
0.330115 + 0.943941i \(0.392912\pi\)
\(350\) 0 0
\(351\) −830.516 −0.126295
\(352\) −37020.3 −5.60564
\(353\) −1056.64 −0.159318 −0.0796592 0.996822i \(-0.525383\pi\)
−0.0796592 + 0.996822i \(0.525383\pi\)
\(354\) −6462.88 −0.970334
\(355\) 0 0
\(356\) 6362.45 0.947217
\(357\) −2291.91 −0.339778
\(358\) 20965.4 3.09513
\(359\) 5186.43 0.762477 0.381238 0.924477i \(-0.375498\pi\)
0.381238 + 0.924477i \(0.375498\pi\)
\(360\) 0 0
\(361\) 9596.58 1.39912
\(362\) 10507.5 1.52558
\(363\) 174.615 0.0252476
\(364\) −2333.54 −0.336018
\(365\) 0 0
\(366\) 3893.38 0.556039
\(367\) −178.772 −0.0254274 −0.0127137 0.999919i \(-0.504047\pi\)
−0.0127137 + 0.999919i \(0.504047\pi\)
\(368\) 6868.52 0.972952
\(369\) −3142.15 −0.443289
\(370\) 0 0
\(371\) 5449.03 0.762532
\(372\) 4712.93 0.656866
\(373\) −7463.86 −1.03610 −0.518049 0.855351i \(-0.673341\pi\)
−0.518049 + 0.855351i \(0.673341\pi\)
\(374\) −22362.1 −3.09175
\(375\) 0 0
\(376\) −6606.78 −0.906166
\(377\) −1159.56 −0.158410
\(378\) −6131.23 −0.834276
\(379\) −6075.99 −0.823490 −0.411745 0.911299i \(-0.635081\pi\)
−0.411745 + 0.911299i \(0.635081\pi\)
\(380\) 0 0
\(381\) −4943.58 −0.664743
\(382\) 28935.3 3.87554
\(383\) 580.709 0.0774747 0.0387374 0.999249i \(-0.487666\pi\)
0.0387374 + 0.999249i \(0.487666\pi\)
\(384\) −18233.5 −2.42311
\(385\) 0 0
\(386\) −26958.1 −3.55475
\(387\) 2544.09 0.334169
\(388\) −13477.1 −1.76339
\(389\) 11373.5 1.48241 0.741205 0.671278i \(-0.234255\pi\)
0.741205 + 0.671278i \(0.234255\pi\)
\(390\) 0 0
\(391\) 2430.79 0.314400
\(392\) 18386.9 2.36908
\(393\) −1774.68 −0.227788
\(394\) 17962.6 2.29681
\(395\) 0 0
\(396\) −20715.3 −2.62874
\(397\) −3701.46 −0.467937 −0.233969 0.972244i \(-0.575171\pi\)
−0.233969 + 0.972244i \(0.575171\pi\)
\(398\) 12398.0 1.56145
\(399\) 2781.85 0.349039
\(400\) 0 0
\(401\) −7615.01 −0.948317 −0.474159 0.880439i \(-0.657248\pi\)
−0.474159 + 0.880439i \(0.657248\pi\)
\(402\) 1446.08 0.179413
\(403\) 921.574 0.113913
\(404\) 32190.7 3.96423
\(405\) 0 0
\(406\) −8560.39 −1.04642
\(407\) 9387.17 1.14325
\(408\) −17366.4 −2.10726
\(409\) −15423.6 −1.86466 −0.932330 0.361608i \(-0.882228\pi\)
−0.932330 + 0.361608i \(0.882228\pi\)
\(410\) 0 0
\(411\) −787.475 −0.0945092
\(412\) 5686.98 0.680042
\(413\) −6957.07 −0.828899
\(414\) 3019.71 0.358480
\(415\) 0 0
\(416\) −8531.17 −1.00547
\(417\) −1799.73 −0.211351
\(418\) 27142.4 3.17603
\(419\) 4273.20 0.498233 0.249116 0.968474i \(-0.419860\pi\)
0.249116 + 0.968474i \(0.419860\pi\)
\(420\) 0 0
\(421\) −6076.38 −0.703432 −0.351716 0.936107i \(-0.614402\pi\)
−0.351716 + 0.936107i \(0.614402\pi\)
\(422\) −859.061 −0.0990958
\(423\) −1783.71 −0.205028
\(424\) 41288.6 4.72913
\(425\) 0 0
\(426\) 1625.01 0.184817
\(427\) 4191.10 0.474991
\(428\) −15269.0 −1.72443
\(429\) 621.541 0.0699494
\(430\) 0 0
\(431\) −3386.04 −0.378422 −0.189211 0.981936i \(-0.560593\pi\)
−0.189211 + 0.981936i \(0.560593\pi\)
\(432\) −28529.3 −3.17735
\(433\) −7924.63 −0.879523 −0.439762 0.898114i \(-0.644937\pi\)
−0.439762 + 0.898114i \(0.644937\pi\)
\(434\) 6803.46 0.752480
\(435\) 0 0
\(436\) −28863.9 −3.17049
\(437\) −2950.42 −0.322970
\(438\) 13055.0 1.42418
\(439\) 13530.9 1.47106 0.735530 0.677492i \(-0.236933\pi\)
0.735530 + 0.677492i \(0.236933\pi\)
\(440\) 0 0
\(441\) 4964.13 0.536026
\(442\) −5153.25 −0.554559
\(443\) −996.052 −0.106826 −0.0534129 0.998573i \(-0.517010\pi\)
−0.0534129 + 0.998573i \(0.517010\pi\)
\(444\) 11062.8 1.18247
\(445\) 0 0
\(446\) −17210.0 −1.82717
\(447\) 4188.08 0.443153
\(448\) −35644.0 −3.75897
\(449\) −5079.36 −0.533875 −0.266938 0.963714i \(-0.586012\pi\)
−0.266938 + 0.963714i \(0.586012\pi\)
\(450\) 0 0
\(451\) 5063.85 0.528709
\(452\) −5605.60 −0.583331
\(453\) −2623.43 −0.272096
\(454\) 25465.0 2.63245
\(455\) 0 0
\(456\) 21078.8 2.16470
\(457\) 11190.9 1.14549 0.572747 0.819732i \(-0.305878\pi\)
0.572747 + 0.819732i \(0.305878\pi\)
\(458\) −8279.94 −0.844752
\(459\) −10096.6 −1.02673
\(460\) 0 0
\(461\) 2426.07 0.245105 0.122553 0.992462i \(-0.460892\pi\)
0.122553 + 0.992462i \(0.460892\pi\)
\(462\) 4588.48 0.462068
\(463\) 16349.2 1.64106 0.820531 0.571602i \(-0.193678\pi\)
0.820531 + 0.571602i \(0.193678\pi\)
\(464\) −39832.4 −3.98529
\(465\) 0 0
\(466\) −508.889 −0.0505876
\(467\) 2880.80 0.285455 0.142728 0.989762i \(-0.454413\pi\)
0.142728 + 0.989762i \(0.454413\pi\)
\(468\) −4773.76 −0.471511
\(469\) 1556.65 0.153261
\(470\) 0 0
\(471\) −1063.96 −0.104087
\(472\) −52715.4 −5.14073
\(473\) −4100.03 −0.398562
\(474\) 3876.00 0.375592
\(475\) 0 0
\(476\) −28368.9 −2.73169
\(477\) 11147.2 1.07001
\(478\) 9081.53 0.868994
\(479\) 7850.31 0.748831 0.374415 0.927261i \(-0.377843\pi\)
0.374415 + 0.927261i \(0.377843\pi\)
\(480\) 0 0
\(481\) 2163.24 0.205063
\(482\) 36162.5 3.41734
\(483\) −498.775 −0.0469877
\(484\) 2161.35 0.202982
\(485\) 0 0
\(486\) −19261.0 −1.79773
\(487\) 11262.4 1.04794 0.523971 0.851736i \(-0.324450\pi\)
0.523971 + 0.851736i \(0.324450\pi\)
\(488\) 31757.0 2.94584
\(489\) −4045.24 −0.374094
\(490\) 0 0
\(491\) 15810.7 1.45321 0.726607 0.687054i \(-0.241096\pi\)
0.726607 + 0.687054i \(0.241096\pi\)
\(492\) 5967.76 0.546844
\(493\) −14096.8 −1.28781
\(494\) 6254.86 0.569675
\(495\) 0 0
\(496\) 31657.2 2.86583
\(497\) 1749.27 0.157878
\(498\) −8107.78 −0.729555
\(499\) −10470.4 −0.939322 −0.469661 0.882847i \(-0.655624\pi\)
−0.469661 + 0.882847i \(0.655624\pi\)
\(500\) 0 0
\(501\) 2493.39 0.222348
\(502\) −19227.9 −1.70953
\(503\) 5425.35 0.480923 0.240462 0.970659i \(-0.422701\pi\)
0.240462 + 0.970659i \(0.422701\pi\)
\(504\) −23223.4 −2.05249
\(505\) 0 0
\(506\) −4866.53 −0.427557
\(507\) −4020.51 −0.352184
\(508\) −61190.9 −5.34430
\(509\) 8098.38 0.705215 0.352608 0.935771i \(-0.385295\pi\)
0.352608 + 0.935771i \(0.385295\pi\)
\(510\) 0 0
\(511\) 14053.3 1.21660
\(512\) −85918.7 −7.41622
\(513\) 12255.0 1.05472
\(514\) 12681.9 1.08828
\(515\) 0 0
\(516\) −4831.90 −0.412233
\(517\) 2874.60 0.244536
\(518\) 15969.9 1.35459
\(519\) −1282.22 −0.108446
\(520\) 0 0
\(521\) 14691.8 1.23543 0.617717 0.786400i \(-0.288058\pi\)
0.617717 + 0.786400i \(0.288058\pi\)
\(522\) −17512.1 −1.46836
\(523\) 19263.6 1.61059 0.805297 0.592872i \(-0.202006\pi\)
0.805297 + 0.592872i \(0.202006\pi\)
\(524\) −21966.7 −1.83134
\(525\) 0 0
\(526\) 29836.7 2.47327
\(527\) 11203.6 0.926066
\(528\) 21350.7 1.75979
\(529\) 529.000 0.0434783
\(530\) 0 0
\(531\) −14232.2 −1.16314
\(532\) 34433.3 2.80615
\(533\) 1166.95 0.0948331
\(534\) −2883.02 −0.233634
\(535\) 0 0
\(536\) 11795.2 0.950510
\(537\) −7084.17 −0.569282
\(538\) 11175.6 0.895564
\(539\) −8000.15 −0.639315
\(540\) 0 0
\(541\) −18737.4 −1.48906 −0.744531 0.667588i \(-0.767327\pi\)
−0.744531 + 0.667588i \(0.767327\pi\)
\(542\) −22158.2 −1.75604
\(543\) −3550.46 −0.280598
\(544\) −103714. −8.17407
\(545\) 0 0
\(546\) 1057.40 0.0828799
\(547\) 14180.2 1.10841 0.554207 0.832379i \(-0.313022\pi\)
0.554207 + 0.832379i \(0.313022\pi\)
\(548\) −9747.25 −0.759821
\(549\) 8573.80 0.666522
\(550\) 0 0
\(551\) 17110.3 1.32291
\(552\) −3779.34 −0.291412
\(553\) 4172.38 0.320846
\(554\) −999.073 −0.0766183
\(555\) 0 0
\(556\) −22276.8 −1.69919
\(557\) −15154.2 −1.15279 −0.576397 0.817170i \(-0.695542\pi\)
−0.576397 + 0.817170i \(0.695542\pi\)
\(558\) 13917.9 1.05590
\(559\) −944.837 −0.0714890
\(560\) 0 0
\(561\) 7556.09 0.568660
\(562\) −19762.5 −1.48333
\(563\) −14444.7 −1.08130 −0.540651 0.841247i \(-0.681822\pi\)
−0.540651 + 0.841247i \(0.681822\pi\)
\(564\) 3387.73 0.252924
\(565\) 0 0
\(566\) −3922.13 −0.291271
\(567\) −5160.22 −0.382203
\(568\) 13254.7 0.979144
\(569\) −8851.15 −0.652125 −0.326063 0.945348i \(-0.605722\pi\)
−0.326063 + 0.945348i \(0.605722\pi\)
\(570\) 0 0
\(571\) −22318.9 −1.63576 −0.817879 0.575391i \(-0.804850\pi\)
−0.817879 + 0.575391i \(0.804850\pi\)
\(572\) 7693.34 0.562368
\(573\) −9777.17 −0.712822
\(574\) 8614.89 0.626444
\(575\) 0 0
\(576\) −72917.4 −5.27470
\(577\) 4530.99 0.326911 0.163455 0.986551i \(-0.447736\pi\)
0.163455 + 0.986551i \(0.447736\pi\)
\(578\) −35092.3 −2.52534
\(579\) 9109.09 0.653818
\(580\) 0 0
\(581\) −8727.75 −0.623215
\(582\) 6106.89 0.434946
\(583\) −17964.7 −1.27619
\(584\) 106485. 7.54519
\(585\) 0 0
\(586\) 47971.7 3.38173
\(587\) 5092.89 0.358103 0.179051 0.983840i \(-0.442697\pi\)
0.179051 + 0.983840i \(0.442697\pi\)
\(588\) −9428.19 −0.661245
\(589\) −13598.6 −0.951309
\(590\) 0 0
\(591\) −6069.54 −0.422449
\(592\) 74309.9 5.15898
\(593\) −4193.92 −0.290427 −0.145214 0.989400i \(-0.546387\pi\)
−0.145214 + 0.989400i \(0.546387\pi\)
\(594\) 20213.8 1.39626
\(595\) 0 0
\(596\) 51839.5 3.56280
\(597\) −4189.26 −0.287194
\(598\) −1121.47 −0.0766897
\(599\) 17663.0 1.20483 0.602414 0.798184i \(-0.294206\pi\)
0.602414 + 0.798184i \(0.294206\pi\)
\(600\) 0 0
\(601\) −15817.7 −1.07357 −0.536785 0.843719i \(-0.680361\pi\)
−0.536785 + 0.843719i \(0.680361\pi\)
\(602\) −6975.19 −0.472239
\(603\) 3184.47 0.215061
\(604\) −32472.4 −2.18755
\(605\) 0 0
\(606\) −14586.6 −0.977790
\(607\) 740.284 0.0495011 0.0247506 0.999694i \(-0.492121\pi\)
0.0247506 + 0.999694i \(0.492121\pi\)
\(608\) 125885. 8.39687
\(609\) 2892.54 0.192466
\(610\) 0 0
\(611\) 662.441 0.0438617
\(612\) −58034.7 −3.83319
\(613\) 12412.1 0.817815 0.408908 0.912576i \(-0.365910\pi\)
0.408908 + 0.912576i \(0.365910\pi\)
\(614\) −31531.0 −2.07246
\(615\) 0 0
\(616\) 37426.6 2.44799
\(617\) 27047.9 1.76484 0.882422 0.470459i \(-0.155911\pi\)
0.882422 + 0.470459i \(0.155911\pi\)
\(618\) −2576.95 −0.167735
\(619\) 193.644 0.0125738 0.00628691 0.999980i \(-0.497999\pi\)
0.00628691 + 0.999980i \(0.497999\pi\)
\(620\) 0 0
\(621\) −2197.27 −0.141986
\(622\) 36645.6 2.36231
\(623\) −3103.48 −0.199580
\(624\) 4920.19 0.315649
\(625\) 0 0
\(626\) −15218.0 −0.971619
\(627\) −9171.36 −0.584161
\(628\) −13169.6 −0.836819
\(629\) 26298.5 1.66708
\(630\) 0 0
\(631\) 11459.7 0.722982 0.361491 0.932376i \(-0.382268\pi\)
0.361491 + 0.932376i \(0.382268\pi\)
\(632\) 31615.2 1.98985
\(633\) 290.275 0.0182265
\(634\) −42314.4 −2.65066
\(635\) 0 0
\(636\) −21171.4 −1.31997
\(637\) −1843.60 −0.114672
\(638\) 28222.4 1.75131
\(639\) 3578.52 0.221540
\(640\) 0 0
\(641\) 2261.29 0.139338 0.0696689 0.997570i \(-0.477806\pi\)
0.0696689 + 0.997570i \(0.477806\pi\)
\(642\) 6918.85 0.425335
\(643\) −10224.8 −0.627101 −0.313551 0.949572i \(-0.601519\pi\)
−0.313551 + 0.949572i \(0.601519\pi\)
\(644\) −6173.77 −0.377765
\(645\) 0 0
\(646\) 76040.6 4.63123
\(647\) 16733.4 1.01678 0.508390 0.861127i \(-0.330241\pi\)
0.508390 + 0.861127i \(0.330241\pi\)
\(648\) −39100.3 −2.37038
\(649\) 22936.5 1.38727
\(650\) 0 0
\(651\) −2298.87 −0.138402
\(652\) −50071.3 −3.00758
\(653\) 9106.08 0.545710 0.272855 0.962055i \(-0.412032\pi\)
0.272855 + 0.962055i \(0.412032\pi\)
\(654\) 13079.1 0.782010
\(655\) 0 0
\(656\) 40086.0 2.38582
\(657\) 28749.0 1.70716
\(658\) 4890.43 0.289740
\(659\) −19951.5 −1.17936 −0.589680 0.807637i \(-0.700746\pi\)
−0.589680 + 0.807637i \(0.700746\pi\)
\(660\) 0 0
\(661\) 16531.2 0.972750 0.486375 0.873750i \(-0.338319\pi\)
0.486375 + 0.873750i \(0.338319\pi\)
\(662\) −33605.8 −1.97300
\(663\) 1741.27 0.101999
\(664\) −66132.3 −3.86511
\(665\) 0 0
\(666\) 32670.0 1.90080
\(667\) −3067.82 −0.178091
\(668\) 30862.8 1.78760
\(669\) 5815.24 0.336069
\(670\) 0 0
\(671\) −13817.4 −0.794957
\(672\) 21281.1 1.22163
\(673\) 10268.9 0.588169 0.294084 0.955779i \(-0.404985\pi\)
0.294084 + 0.955779i \(0.404985\pi\)
\(674\) 31776.3 1.81599
\(675\) 0 0
\(676\) −49765.3 −2.83144
\(677\) −4729.79 −0.268509 −0.134254 0.990947i \(-0.542864\pi\)
−0.134254 + 0.990947i \(0.542864\pi\)
\(678\) 2540.07 0.143880
\(679\) 6573.86 0.371549
\(680\) 0 0
\(681\) −8604.56 −0.484182
\(682\) −22430.0 −1.25937
\(683\) −11551.0 −0.647123 −0.323561 0.946207i \(-0.604880\pi\)
−0.323561 + 0.946207i \(0.604880\pi\)
\(684\) 70440.8 3.93768
\(685\) 0 0
\(686\) −35623.6 −1.98268
\(687\) 2797.77 0.155374
\(688\) −32456.3 −1.79853
\(689\) −4139.89 −0.228907
\(690\) 0 0
\(691\) 26575.2 1.46305 0.731526 0.681813i \(-0.238808\pi\)
0.731526 + 0.681813i \(0.238808\pi\)
\(692\) −15871.2 −0.871866
\(693\) 10104.5 0.553879
\(694\) 31371.6 1.71592
\(695\) 0 0
\(696\) 21917.5 1.19365
\(697\) 14186.6 0.770955
\(698\) −24143.6 −1.30924
\(699\) 171.952 0.00930448
\(700\) 0 0
\(701\) 5886.27 0.317149 0.158574 0.987347i \(-0.449310\pi\)
0.158574 + 0.987347i \(0.449310\pi\)
\(702\) 4658.18 0.250444
\(703\) −31920.4 −1.71252
\(704\) 117513. 6.29110
\(705\) 0 0
\(706\) 5926.48 0.315929
\(707\) −15702.0 −0.835268
\(708\) 27030.7 1.43485
\(709\) −2588.26 −0.137100 −0.0685501 0.997648i \(-0.521837\pi\)
−0.0685501 + 0.997648i \(0.521837\pi\)
\(710\) 0 0
\(711\) 8535.51 0.450220
\(712\) −23515.8 −1.23777
\(713\) 2438.18 0.128065
\(714\) 12854.8 0.673781
\(715\) 0 0
\(716\) −87686.8 −4.57683
\(717\) −3068.63 −0.159833
\(718\) −29089.5 −1.51199
\(719\) 1170.46 0.0607106 0.0303553 0.999539i \(-0.490336\pi\)
0.0303553 + 0.999539i \(0.490336\pi\)
\(720\) 0 0
\(721\) −2774.00 −0.143286
\(722\) −53825.1 −2.77447
\(723\) −12219.2 −0.628545
\(724\) −43947.0 −2.25591
\(725\) 0 0
\(726\) −979.376 −0.0500662
\(727\) 3135.70 0.159968 0.0799838 0.996796i \(-0.474513\pi\)
0.0799838 + 0.996796i \(0.474513\pi\)
\(728\) 8624.82 0.439089
\(729\) −5667.88 −0.287958
\(730\) 0 0
\(731\) −11486.4 −0.581177
\(732\) −16283.9 −0.822226
\(733\) 25792.4 1.29968 0.649839 0.760072i \(-0.274836\pi\)
0.649839 + 0.760072i \(0.274836\pi\)
\(734\) 1002.70 0.0504225
\(735\) 0 0
\(736\) −22570.7 −1.13039
\(737\) −5132.07 −0.256502
\(738\) 17623.6 0.879044
\(739\) −809.931 −0.0403164 −0.0201582 0.999797i \(-0.506417\pi\)
−0.0201582 + 0.999797i \(0.506417\pi\)
\(740\) 0 0
\(741\) −2113.50 −0.104779
\(742\) −30562.4 −1.51210
\(743\) −1825.32 −0.0901270 −0.0450635 0.998984i \(-0.514349\pi\)
−0.0450635 + 0.998984i \(0.514349\pi\)
\(744\) −17419.1 −0.858355
\(745\) 0 0
\(746\) 41863.2 2.05459
\(747\) −17854.5 −0.874514
\(748\) 93528.2 4.57183
\(749\) 7447.91 0.363339
\(750\) 0 0
\(751\) 4310.27 0.209433 0.104716 0.994502i \(-0.466606\pi\)
0.104716 + 0.994502i \(0.466606\pi\)
\(752\) 22755.7 1.10348
\(753\) 6497.06 0.314430
\(754\) 6503.73 0.314127
\(755\) 0 0
\(756\) 25643.5 1.23366
\(757\) −19302.2 −0.926750 −0.463375 0.886162i \(-0.653362\pi\)
−0.463375 + 0.886162i \(0.653362\pi\)
\(758\) 34078.9 1.63298
\(759\) 1644.39 0.0786398
\(760\) 0 0
\(761\) −30144.8 −1.43594 −0.717968 0.696076i \(-0.754927\pi\)
−0.717968 + 0.696076i \(0.754927\pi\)
\(762\) 27727.5 1.31819
\(763\) 14079.3 0.668025
\(764\) −121020. −5.73084
\(765\) 0 0
\(766\) −3257.07 −0.153633
\(767\) 5285.62 0.248830
\(768\) 55038.8 2.58599
\(769\) 37297.7 1.74901 0.874506 0.485015i \(-0.161186\pi\)
0.874506 + 0.485015i \(0.161186\pi\)
\(770\) 0 0
\(771\) −4285.19 −0.200165
\(772\) 112751. 5.25647
\(773\) 13602.8 0.632933 0.316467 0.948604i \(-0.397503\pi\)
0.316467 + 0.948604i \(0.397503\pi\)
\(774\) −14269.3 −0.662659
\(775\) 0 0
\(776\) 49811.8 2.30430
\(777\) −5396.21 −0.249148
\(778\) −63791.3 −2.93963
\(779\) −17219.3 −0.791970
\(780\) 0 0
\(781\) −5767.10 −0.264229
\(782\) −13633.8 −0.623457
\(783\) 12742.6 0.581587
\(784\) −63330.1 −2.88493
\(785\) 0 0
\(786\) 9953.79 0.451705
\(787\) −14129.9 −0.639997 −0.319998 0.947418i \(-0.603682\pi\)
−0.319998 + 0.947418i \(0.603682\pi\)
\(788\) −75127.8 −3.39634
\(789\) −10081.8 −0.454905
\(790\) 0 0
\(791\) 2734.30 0.122908
\(792\) 76564.3 3.43509
\(793\) −3184.18 −0.142589
\(794\) 20760.7 0.927922
\(795\) 0 0
\(796\) −51854.0 −2.30894
\(797\) −16171.3 −0.718715 −0.359357 0.933200i \(-0.617004\pi\)
−0.359357 + 0.933200i \(0.617004\pi\)
\(798\) −15602.8 −0.692147
\(799\) 8053.32 0.356578
\(800\) 0 0
\(801\) −6348.83 −0.280056
\(802\) 42710.9 1.88052
\(803\) −46331.7 −2.03613
\(804\) −6048.15 −0.265301
\(805\) 0 0
\(806\) −5168.91 −0.225890
\(807\) −3776.20 −0.164720
\(808\) −118978. −5.18023
\(809\) −41744.9 −1.81418 −0.907090 0.420937i \(-0.861701\pi\)
−0.907090 + 0.420937i \(0.861701\pi\)
\(810\) 0 0
\(811\) −12210.2 −0.528679 −0.264340 0.964430i \(-0.585154\pi\)
−0.264340 + 0.964430i \(0.585154\pi\)
\(812\) 35803.4 1.54736
\(813\) 7487.19 0.322986
\(814\) −52650.6 −2.26708
\(815\) 0 0
\(816\) 59814.9 2.56610
\(817\) 13941.9 0.597019
\(818\) 86507.4 3.69763
\(819\) 2328.54 0.0993478
\(820\) 0 0
\(821\) −22326.2 −0.949074 −0.474537 0.880236i \(-0.657385\pi\)
−0.474537 + 0.880236i \(0.657385\pi\)
\(822\) 4416.78 0.187412
\(823\) 29128.6 1.23373 0.616864 0.787069i \(-0.288403\pi\)
0.616864 + 0.787069i \(0.288403\pi\)
\(824\) −21019.2 −0.888641
\(825\) 0 0
\(826\) 39020.7 1.64371
\(827\) 13540.8 0.569357 0.284679 0.958623i \(-0.408113\pi\)
0.284679 + 0.958623i \(0.408113\pi\)
\(828\) −12629.8 −0.530091
\(829\) 93.8298 0.00393105 0.00196553 0.999998i \(-0.499374\pi\)
0.00196553 + 0.999998i \(0.499374\pi\)
\(830\) 0 0
\(831\) 337.585 0.0140923
\(832\) 27080.4 1.12842
\(833\) −22412.7 −0.932239
\(834\) 10094.3 0.419110
\(835\) 0 0
\(836\) −113522. −4.69645
\(837\) −10127.3 −0.418220
\(838\) −23967.4 −0.987997
\(839\) −33750.6 −1.38880 −0.694398 0.719591i \(-0.744329\pi\)
−0.694398 + 0.719591i \(0.744329\pi\)
\(840\) 0 0
\(841\) −6597.88 −0.270527
\(842\) 34081.1 1.39491
\(843\) 6677.70 0.272826
\(844\) 3592.98 0.146535
\(845\) 0 0
\(846\) 10004.4 0.406571
\(847\) −1054.26 −0.0427686
\(848\) −142210. −5.75887
\(849\) 1325.28 0.0535730
\(850\) 0 0
\(851\) 5723.21 0.230539
\(852\) −6796.54 −0.273293
\(853\) 2680.73 0.107604 0.0538022 0.998552i \(-0.482866\pi\)
0.0538022 + 0.998552i \(0.482866\pi\)
\(854\) −23506.9 −0.941910
\(855\) 0 0
\(856\) 56434.7 2.25338
\(857\) −29267.7 −1.16659 −0.583295 0.812261i \(-0.698237\pi\)
−0.583295 + 0.812261i \(0.698237\pi\)
\(858\) −3486.09 −0.138710
\(859\) 34842.9 1.38396 0.691982 0.721914i \(-0.256738\pi\)
0.691982 + 0.721914i \(0.256738\pi\)
\(860\) 0 0
\(861\) −2910.95 −0.115221
\(862\) 18991.6 0.750412
\(863\) 4041.96 0.159432 0.0797161 0.996818i \(-0.474599\pi\)
0.0797161 + 0.996818i \(0.474599\pi\)
\(864\) 93750.1 3.69149
\(865\) 0 0
\(866\) 44447.6 1.74410
\(867\) 11857.6 0.464482
\(868\) −28455.1 −1.11271
\(869\) −13755.7 −0.536975
\(870\) 0 0
\(871\) −1182.66 −0.0460081
\(872\) 106682. 4.14301
\(873\) 13448.3 0.521368
\(874\) 16548.3 0.640451
\(875\) 0 0
\(876\) −54601.9 −2.10597
\(877\) −34918.5 −1.34448 −0.672242 0.740331i \(-0.734669\pi\)
−0.672242 + 0.740331i \(0.734669\pi\)
\(878\) −75891.9 −2.91712
\(879\) −16209.5 −0.621996
\(880\) 0 0
\(881\) 2473.77 0.0946008 0.0473004 0.998881i \(-0.484938\pi\)
0.0473004 + 0.998881i \(0.484938\pi\)
\(882\) −27842.8 −1.06294
\(883\) −16956.8 −0.646252 −0.323126 0.946356i \(-0.604734\pi\)
−0.323126 + 0.946356i \(0.604734\pi\)
\(884\) 21553.2 0.820037
\(885\) 0 0
\(886\) 5586.64 0.211836
\(887\) −582.058 −0.0220334 −0.0110167 0.999939i \(-0.503507\pi\)
−0.0110167 + 0.999939i \(0.503507\pi\)
\(888\) −40888.4 −1.54519
\(889\) 29847.7 1.12605
\(890\) 0 0
\(891\) 17012.5 0.639664
\(892\) 71980.1 2.70188
\(893\) −9774.88 −0.366298
\(894\) −23490.1 −0.878775
\(895\) 0 0
\(896\) 110088. 4.10465
\(897\) 378.943 0.0141054
\(898\) 28489.0 1.05868
\(899\) −14139.7 −0.524566
\(900\) 0 0
\(901\) −50328.7 −1.86092
\(902\) −28402.1 −1.04843
\(903\) 2356.90 0.0868580
\(904\) 20718.5 0.762263
\(905\) 0 0
\(906\) 14714.2 0.539567
\(907\) −26224.8 −0.960065 −0.480033 0.877251i \(-0.659375\pi\)
−0.480033 + 0.877251i \(0.659375\pi\)
\(908\) −106506. −3.89265
\(909\) −32121.8 −1.17207
\(910\) 0 0
\(911\) −12266.6 −0.446117 −0.223058 0.974805i \(-0.571604\pi\)
−0.223058 + 0.974805i \(0.571604\pi\)
\(912\) −72601.5 −2.63605
\(913\) 28774.1 1.04303
\(914\) −62767.6 −2.27152
\(915\) 0 0
\(916\) 34630.4 1.24915
\(917\) 10714.9 0.385864
\(918\) 56629.7 2.03601
\(919\) 12114.7 0.434850 0.217425 0.976077i \(-0.430234\pi\)
0.217425 + 0.976077i \(0.430234\pi\)
\(920\) 0 0
\(921\) 10654.3 0.381184
\(922\) −13607.3 −0.486045
\(923\) −1329.01 −0.0473941
\(924\) −19191.1 −0.683269
\(925\) 0 0
\(926\) −91699.1 −3.25423
\(927\) −5674.81 −0.201063
\(928\) 130893. 4.63016
\(929\) −2418.31 −0.0854059 −0.0427029 0.999088i \(-0.513597\pi\)
−0.0427029 + 0.999088i \(0.513597\pi\)
\(930\) 0 0
\(931\) 27203.9 0.957650
\(932\) 2128.40 0.0748048
\(933\) −12382.5 −0.434496
\(934\) −16157.8 −0.566059
\(935\) 0 0
\(936\) 17643.9 0.616143
\(937\) −16448.7 −0.573486 −0.286743 0.958008i \(-0.592573\pi\)
−0.286743 + 0.958008i \(0.592573\pi\)
\(938\) −8730.94 −0.303918
\(939\) 5142.13 0.178708
\(940\) 0 0
\(941\) −17373.2 −0.601859 −0.300929 0.953646i \(-0.597297\pi\)
−0.300929 + 0.953646i \(0.597297\pi\)
\(942\) 5967.53 0.206404
\(943\) 3087.35 0.106615
\(944\) 181568. 6.26009
\(945\) 0 0
\(946\) 22996.2 0.790350
\(947\) −18638.9 −0.639579 −0.319790 0.947489i \(-0.603612\pi\)
−0.319790 + 0.947489i \(0.603612\pi\)
\(948\) −16211.2 −0.555395
\(949\) −10676.9 −0.365214
\(950\) 0 0
\(951\) 14298.0 0.487532
\(952\) 104852. 3.56962
\(953\) 31188.1 1.06011 0.530053 0.847965i \(-0.322172\pi\)
0.530053 + 0.847965i \(0.322172\pi\)
\(954\) −62522.0 −2.12183
\(955\) 0 0
\(956\) −37983.0 −1.28500
\(957\) −9536.28 −0.322115
\(958\) −44030.7 −1.48493
\(959\) 4754.51 0.160095
\(960\) 0 0
\(961\) −18553.3 −0.622784
\(962\) −12133.1 −0.406640
\(963\) 15236.3 0.509848
\(964\) −151248. −5.05328
\(965\) 0 0
\(966\) 2797.52 0.0931768
\(967\) −43197.8 −1.43655 −0.718277 0.695757i \(-0.755069\pi\)
−0.718277 + 0.695757i \(0.755069\pi\)
\(968\) −7988.42 −0.265246
\(969\) −25693.9 −0.851815
\(970\) 0 0
\(971\) 13497.0 0.446074 0.223037 0.974810i \(-0.428403\pi\)
0.223037 + 0.974810i \(0.428403\pi\)
\(972\) 80558.1 2.65834
\(973\) 10866.2 0.358021
\(974\) −63168.4 −2.07808
\(975\) 0 0
\(976\) −109380. −3.58728
\(977\) 34955.4 1.14465 0.572325 0.820027i \(-0.306042\pi\)
0.572325 + 0.820027i \(0.306042\pi\)
\(978\) 22688.8 0.741830
\(979\) 10231.7 0.334021
\(980\) 0 0
\(981\) 28802.2 0.937393
\(982\) −88678.9 −2.88173
\(983\) 27521.6 0.892984 0.446492 0.894788i \(-0.352673\pi\)
0.446492 + 0.894788i \(0.352673\pi\)
\(984\) −22057.0 −0.714585
\(985\) 0 0
\(986\) 79066.1 2.55373
\(987\) −1652.46 −0.0532913
\(988\) −26160.6 −0.842389
\(989\) −2499.73 −0.0803707
\(990\) 0 0
\(991\) 24567.9 0.787513 0.393756 0.919215i \(-0.371175\pi\)
0.393756 + 0.919215i \(0.371175\pi\)
\(992\) −104029. −3.32956
\(993\) 11355.3 0.362891
\(994\) −9811.29 −0.313074
\(995\) 0 0
\(996\) 33910.4 1.07881
\(997\) −2293.84 −0.0728652 −0.0364326 0.999336i \(-0.511599\pi\)
−0.0364326 + 0.999336i \(0.511599\pi\)
\(998\) 58726.5 1.86268
\(999\) −23772.1 −0.752868
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 575.4.a.j.1.1 5
5.2 odd 4 575.4.b.i.24.1 10
5.3 odd 4 575.4.b.i.24.10 10
5.4 even 2 115.4.a.e.1.5 5
15.14 odd 2 1035.4.a.k.1.1 5
20.19 odd 2 1840.4.a.n.1.3 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.4.a.e.1.5 5 5.4 even 2
575.4.a.j.1.1 5 1.1 even 1 trivial
575.4.b.i.24.1 10 5.2 odd 4
575.4.b.i.24.10 10 5.3 odd 4
1035.4.a.k.1.1 5 15.14 odd 2
1840.4.a.n.1.3 5 20.19 odd 2