Properties

Label 2254.4.a.l.1.2
Level $2254$
Weight $4$
Character 2254.1
Self dual yes
Analytic conductor $132.990$
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] = [2254,4,Mod(1,2254)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2254, 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("2254.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2254.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: \(132.990305153\)
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: \( x^{5} - 92x^{3} - 28x^{2} + 1593x - 1782 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 322)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-6.17693\) of defining polynomial
Character \(\chi\) \(=\) 2254.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} -7.17693 q^{3} +4.00000 q^{4} -18.7050 q^{5} -14.3539 q^{6} +8.00000 q^{8} +24.5083 q^{9} -37.4099 q^{10} -36.8949 q^{11} -28.7077 q^{12} -22.7900 q^{13} +134.244 q^{15} +16.0000 q^{16} -66.6941 q^{17} +49.0166 q^{18} +106.301 q^{19} -74.8199 q^{20} -73.7897 q^{22} +23.0000 q^{23} -57.4154 q^{24} +224.876 q^{25} -45.5800 q^{26} +17.8829 q^{27} -199.773 q^{29} +268.488 q^{30} +262.034 q^{31} +32.0000 q^{32} +264.792 q^{33} -133.388 q^{34} +98.0331 q^{36} +202.174 q^{37} +212.601 q^{38} +163.562 q^{39} -149.640 q^{40} -44.4679 q^{41} -18.2027 q^{43} -147.579 q^{44} -458.426 q^{45} +46.0000 q^{46} +306.525 q^{47} -114.831 q^{48} +449.751 q^{50} +478.659 q^{51} -91.1600 q^{52} +300.565 q^{53} +35.7658 q^{54} +690.117 q^{55} -762.913 q^{57} -399.547 q^{58} -255.485 q^{59} +536.977 q^{60} -598.006 q^{61} +524.068 q^{62} +64.0000 q^{64} +426.286 q^{65} +529.584 q^{66} -636.773 q^{67} -266.776 q^{68} -165.069 q^{69} +320.916 q^{71} +196.066 q^{72} +24.5948 q^{73} +404.348 q^{74} -1613.92 q^{75} +425.203 q^{76} +327.124 q^{78} +1121.21 q^{79} -299.279 q^{80} -790.068 q^{81} -88.9358 q^{82} +767.685 q^{83} +1247.51 q^{85} -36.4055 q^{86} +1433.76 q^{87} -295.159 q^{88} +807.439 q^{89} -916.853 q^{90} +92.0000 q^{92} -1880.60 q^{93} +613.051 q^{94} -1988.35 q^{95} -229.662 q^{96} -1170.29 q^{97} -904.230 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + 10 q^{2} - 5 q^{3} + 20 q^{4} - 22 q^{5} - 10 q^{6} + 40 q^{8} + 54 q^{9} - 44 q^{10} + 42 q^{11} - 20 q^{12} - 107 q^{13} + 122 q^{15} + 80 q^{16} - 218 q^{17} + 108 q^{18} - 194 q^{19} - 88 q^{20}+ \cdots - 2616 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) −7.17693 −1.38120 −0.690600 0.723237i \(-0.742654\pi\)
−0.690600 + 0.723237i \(0.742654\pi\)
\(4\) 4.00000 0.500000
\(5\) −18.7050 −1.67302 −0.836511 0.547949i \(-0.815409\pi\)
−0.836511 + 0.547949i \(0.815409\pi\)
\(6\) −14.3539 −0.976656
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 24.5083 0.907714
\(10\) −37.4099 −1.18301
\(11\) −36.8949 −1.01129 −0.505646 0.862741i \(-0.668746\pi\)
−0.505646 + 0.862741i \(0.668746\pi\)
\(12\) −28.7077 −0.690600
\(13\) −22.7900 −0.486216 −0.243108 0.969999i \(-0.578167\pi\)
−0.243108 + 0.969999i \(0.578167\pi\)
\(14\) 0 0
\(15\) 134.244 2.31078
\(16\) 16.0000 0.250000
\(17\) −66.6941 −0.951511 −0.475756 0.879577i \(-0.657825\pi\)
−0.475756 + 0.879577i \(0.657825\pi\)
\(18\) 49.0166 0.641851
\(19\) 106.301 1.28353 0.641765 0.766901i \(-0.278203\pi\)
0.641765 + 0.766901i \(0.278203\pi\)
\(20\) −74.8199 −0.836511
\(21\) 0 0
\(22\) −73.7897 −0.715092
\(23\) 23.0000 0.208514
\(24\) −57.4154 −0.488328
\(25\) 224.876 1.79901
\(26\) −45.5800 −0.343807
\(27\) 17.8829 0.127465
\(28\) 0 0
\(29\) −199.773 −1.27921 −0.639603 0.768705i \(-0.720901\pi\)
−0.639603 + 0.768705i \(0.720901\pi\)
\(30\) 268.488 1.63397
\(31\) 262.034 1.51815 0.759075 0.651003i \(-0.225651\pi\)
0.759075 + 0.651003i \(0.225651\pi\)
\(32\) 32.0000 0.176777
\(33\) 264.792 1.39680
\(34\) −133.388 −0.672820
\(35\) 0 0
\(36\) 98.0331 0.453857
\(37\) 202.174 0.898302 0.449151 0.893456i \(-0.351726\pi\)
0.449151 + 0.893456i \(0.351726\pi\)
\(38\) 212.601 0.907593
\(39\) 163.562 0.671562
\(40\) −149.640 −0.591503
\(41\) −44.4679 −0.169383 −0.0846917 0.996407i \(-0.526991\pi\)
−0.0846917 + 0.996407i \(0.526991\pi\)
\(42\) 0 0
\(43\) −18.2027 −0.0645556 −0.0322778 0.999479i \(-0.510276\pi\)
−0.0322778 + 0.999479i \(0.510276\pi\)
\(44\) −147.579 −0.505646
\(45\) −458.426 −1.51863
\(46\) 46.0000 0.147442
\(47\) 306.525 0.951305 0.475652 0.879633i \(-0.342212\pi\)
0.475652 + 0.879633i \(0.342212\pi\)
\(48\) −114.831 −0.345300
\(49\) 0 0
\(50\) 449.751 1.27209
\(51\) 478.659 1.31423
\(52\) −91.1600 −0.243108
\(53\) 300.565 0.778977 0.389488 0.921031i \(-0.372652\pi\)
0.389488 + 0.921031i \(0.372652\pi\)
\(54\) 35.7658 0.0901317
\(55\) 690.117 1.69192
\(56\) 0 0
\(57\) −762.913 −1.77281
\(58\) −399.547 −0.904535
\(59\) −255.485 −0.563750 −0.281875 0.959451i \(-0.590956\pi\)
−0.281875 + 0.959451i \(0.590956\pi\)
\(60\) 536.977 1.15539
\(61\) −598.006 −1.25519 −0.627597 0.778538i \(-0.715961\pi\)
−0.627597 + 0.778538i \(0.715961\pi\)
\(62\) 524.068 1.07349
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 426.286 0.813451
\(66\) 529.584 0.987685
\(67\) −636.773 −1.16111 −0.580553 0.814222i \(-0.697164\pi\)
−0.580553 + 0.814222i \(0.697164\pi\)
\(68\) −266.776 −0.475756
\(69\) −165.069 −0.288000
\(70\) 0 0
\(71\) 320.916 0.536418 0.268209 0.963361i \(-0.413568\pi\)
0.268209 + 0.963361i \(0.413568\pi\)
\(72\) 196.066 0.320925
\(73\) 24.5948 0.0394330 0.0197165 0.999806i \(-0.493724\pi\)
0.0197165 + 0.999806i \(0.493724\pi\)
\(74\) 404.348 0.635196
\(75\) −1613.92 −2.48479
\(76\) 425.203 0.641765
\(77\) 0 0
\(78\) 327.124 0.474866
\(79\) 1121.21 1.59678 0.798390 0.602141i \(-0.205685\pi\)
0.798390 + 0.602141i \(0.205685\pi\)
\(80\) −299.279 −0.418256
\(81\) −790.068 −1.08377
\(82\) −88.9358 −0.119772
\(83\) 767.685 1.01523 0.507617 0.861583i \(-0.330527\pi\)
0.507617 + 0.861583i \(0.330527\pi\)
\(84\) 0 0
\(85\) 1247.51 1.59190
\(86\) −36.4055 −0.0456477
\(87\) 1433.76 1.76684
\(88\) −295.159 −0.357546
\(89\) 807.439 0.961667 0.480833 0.876812i \(-0.340334\pi\)
0.480833 + 0.876812i \(0.340334\pi\)
\(90\) −916.853 −1.07383
\(91\) 0 0
\(92\) 92.0000 0.104257
\(93\) −1880.60 −2.09687
\(94\) 613.051 0.672674
\(95\) −1988.35 −2.14737
\(96\) −229.662 −0.244164
\(97\) −1170.29 −1.22500 −0.612500 0.790471i \(-0.709836\pi\)
−0.612500 + 0.790471i \(0.709836\pi\)
\(98\) 0 0
\(99\) −904.230 −0.917965
\(100\) 899.503 0.899503
\(101\) 554.631 0.546414 0.273207 0.961955i \(-0.411916\pi\)
0.273207 + 0.961955i \(0.411916\pi\)
\(102\) 957.317 0.929299
\(103\) 1018.33 0.974166 0.487083 0.873356i \(-0.338061\pi\)
0.487083 + 0.873356i \(0.338061\pi\)
\(104\) −182.320 −0.171903
\(105\) 0 0
\(106\) 601.130 0.550820
\(107\) 1451.75 1.31164 0.655821 0.754916i \(-0.272322\pi\)
0.655821 + 0.754916i \(0.272322\pi\)
\(108\) 71.5317 0.0637327
\(109\) 1719.61 1.51109 0.755544 0.655098i \(-0.227372\pi\)
0.755544 + 0.655098i \(0.227372\pi\)
\(110\) 1380.23 1.19637
\(111\) −1450.99 −1.24074
\(112\) 0 0
\(113\) −2162.47 −1.80025 −0.900126 0.435630i \(-0.856525\pi\)
−0.900126 + 0.435630i \(0.856525\pi\)
\(114\) −1525.83 −1.25357
\(115\) −430.214 −0.348849
\(116\) −799.093 −0.639603
\(117\) −558.544 −0.441345
\(118\) −510.969 −0.398631
\(119\) 0 0
\(120\) 1073.95 0.816984
\(121\) 30.2313 0.0227132
\(122\) −1196.01 −0.887556
\(123\) 319.143 0.233952
\(124\) 1048.14 0.759075
\(125\) −1868.17 −1.33675
\(126\) 0 0
\(127\) 1462.69 1.02199 0.510994 0.859584i \(-0.329278\pi\)
0.510994 + 0.859584i \(0.329278\pi\)
\(128\) 128.000 0.0883883
\(129\) 130.640 0.0891642
\(130\) 852.573 0.575197
\(131\) −1970.02 −1.31390 −0.656952 0.753932i \(-0.728155\pi\)
−0.656952 + 0.753932i \(0.728155\pi\)
\(132\) 1059.17 0.698399
\(133\) 0 0
\(134\) −1273.55 −0.821027
\(135\) −334.499 −0.213253
\(136\) −533.553 −0.336410
\(137\) −2064.12 −1.28722 −0.643611 0.765353i \(-0.722565\pi\)
−0.643611 + 0.765353i \(0.722565\pi\)
\(138\) −330.139 −0.203647
\(139\) −9.19537 −0.00561108 −0.00280554 0.999996i \(-0.500893\pi\)
−0.00280554 + 0.999996i \(0.500893\pi\)
\(140\) 0 0
\(141\) −2199.91 −1.31394
\(142\) 641.831 0.379305
\(143\) 840.834 0.491707
\(144\) 392.132 0.226928
\(145\) 3736.75 2.14014
\(146\) 49.1897 0.0278833
\(147\) 0 0
\(148\) 808.696 0.449151
\(149\) −619.044 −0.340363 −0.170181 0.985413i \(-0.554435\pi\)
−0.170181 + 0.985413i \(0.554435\pi\)
\(150\) −3227.83 −1.75701
\(151\) 162.870 0.0877758 0.0438879 0.999036i \(-0.486026\pi\)
0.0438879 + 0.999036i \(0.486026\pi\)
\(152\) 850.406 0.453796
\(153\) −1634.56 −0.863700
\(154\) 0 0
\(155\) −4901.33 −2.53990
\(156\) 654.249 0.335781
\(157\) 1320.45 0.671234 0.335617 0.941999i \(-0.391055\pi\)
0.335617 + 0.941999i \(0.391055\pi\)
\(158\) 2242.41 1.12909
\(159\) −2157.13 −1.07592
\(160\) −598.559 −0.295751
\(161\) 0 0
\(162\) −1580.14 −0.766341
\(163\) −2193.25 −1.05392 −0.526960 0.849890i \(-0.676668\pi\)
−0.526960 + 0.849890i \(0.676668\pi\)
\(164\) −177.872 −0.0846917
\(165\) −4952.92 −2.33687
\(166\) 1535.37 0.717878
\(167\) −2117.18 −0.981030 −0.490515 0.871433i \(-0.663191\pi\)
−0.490515 + 0.871433i \(0.663191\pi\)
\(168\) 0 0
\(169\) −1677.62 −0.763594
\(170\) 2495.02 1.12564
\(171\) 2605.25 1.16508
\(172\) −72.8109 −0.0322778
\(173\) 2576.00 1.13208 0.566040 0.824378i \(-0.308475\pi\)
0.566040 + 0.824378i \(0.308475\pi\)
\(174\) 2867.52 1.24934
\(175\) 0 0
\(176\) −590.318 −0.252823
\(177\) 1833.59 0.778652
\(178\) 1614.88 0.680001
\(179\) −3008.14 −1.25608 −0.628042 0.778179i \(-0.716144\pi\)
−0.628042 + 0.778179i \(0.716144\pi\)
\(180\) −1833.71 −0.759313
\(181\) −202.379 −0.0831090 −0.0415545 0.999136i \(-0.513231\pi\)
−0.0415545 + 0.999136i \(0.513231\pi\)
\(182\) 0 0
\(183\) 4291.85 1.73367
\(184\) 184.000 0.0737210
\(185\) −3781.66 −1.50288
\(186\) −3761.19 −1.48271
\(187\) 2460.67 0.962257
\(188\) 1226.10 0.475652
\(189\) 0 0
\(190\) −3976.70 −1.51842
\(191\) 4260.13 1.61389 0.806943 0.590629i \(-0.201120\pi\)
0.806943 + 0.590629i \(0.201120\pi\)
\(192\) −459.323 −0.172650
\(193\) 2071.29 0.772510 0.386255 0.922392i \(-0.373768\pi\)
0.386255 + 0.922392i \(0.373768\pi\)
\(194\) −2340.58 −0.866206
\(195\) −3059.43 −1.12354
\(196\) 0 0
\(197\) −4143.04 −1.49837 −0.749187 0.662359i \(-0.769555\pi\)
−0.749187 + 0.662359i \(0.769555\pi\)
\(198\) −1808.46 −0.649099
\(199\) −1113.48 −0.396647 −0.198323 0.980137i \(-0.563550\pi\)
−0.198323 + 0.980137i \(0.563550\pi\)
\(200\) 1799.01 0.636045
\(201\) 4570.07 1.60372
\(202\) 1109.26 0.386373
\(203\) 0 0
\(204\) 1914.63 0.657114
\(205\) 831.770 0.283382
\(206\) 2036.66 0.688840
\(207\) 563.690 0.189271
\(208\) −364.640 −0.121554
\(209\) −3921.95 −1.29802
\(210\) 0 0
\(211\) 1213.02 0.395772 0.197886 0.980225i \(-0.436592\pi\)
0.197886 + 0.980225i \(0.436592\pi\)
\(212\) 1202.26 0.389488
\(213\) −2303.19 −0.740901
\(214\) 2903.50 0.927471
\(215\) 340.481 0.108003
\(216\) 143.063 0.0450659
\(217\) 0 0
\(218\) 3439.22 1.06850
\(219\) −176.515 −0.0544649
\(220\) 2760.47 0.845958
\(221\) 1519.96 0.462640
\(222\) −2901.97 −0.877332
\(223\) 3263.55 0.980016 0.490008 0.871718i \(-0.336994\pi\)
0.490008 + 0.871718i \(0.336994\pi\)
\(224\) 0 0
\(225\) 5511.32 1.63298
\(226\) −4324.95 −1.27297
\(227\) −6282.29 −1.83687 −0.918436 0.395569i \(-0.870547\pi\)
−0.918436 + 0.395569i \(0.870547\pi\)
\(228\) −3051.65 −0.886406
\(229\) 2034.66 0.587136 0.293568 0.955938i \(-0.405157\pi\)
0.293568 + 0.955938i \(0.405157\pi\)
\(230\) −860.428 −0.246674
\(231\) 0 0
\(232\) −1598.19 −0.452268
\(233\) 1687.13 0.474368 0.237184 0.971465i \(-0.423776\pi\)
0.237184 + 0.971465i \(0.423776\pi\)
\(234\) −1117.09 −0.312078
\(235\) −5733.55 −1.59155
\(236\) −1021.94 −0.281875
\(237\) −8046.82 −2.20547
\(238\) 0 0
\(239\) −6511.95 −1.76244 −0.881220 0.472707i \(-0.843277\pi\)
−0.881220 + 0.472707i \(0.843277\pi\)
\(240\) 2147.91 0.577695
\(241\) −3163.26 −0.845492 −0.422746 0.906248i \(-0.638934\pi\)
−0.422746 + 0.906248i \(0.638934\pi\)
\(242\) 60.4625 0.0160607
\(243\) 5187.42 1.36944
\(244\) −2392.02 −0.627597
\(245\) 0 0
\(246\) 638.286 0.165429
\(247\) −2422.60 −0.624073
\(248\) 2096.27 0.536747
\(249\) −5509.62 −1.40224
\(250\) −3736.34 −0.945228
\(251\) −518.424 −0.130369 −0.0651845 0.997873i \(-0.520764\pi\)
−0.0651845 + 0.997873i \(0.520764\pi\)
\(252\) 0 0
\(253\) −848.582 −0.210869
\(254\) 2925.37 0.722654
\(255\) −8953.29 −2.19873
\(256\) 256.000 0.0625000
\(257\) −5445.71 −1.32177 −0.660884 0.750488i \(-0.729818\pi\)
−0.660884 + 0.750488i \(0.729818\pi\)
\(258\) 261.279 0.0630486
\(259\) 0 0
\(260\) 1705.15 0.406726
\(261\) −4896.10 −1.16115
\(262\) −3940.04 −0.929071
\(263\) 5094.98 1.19456 0.597281 0.802032i \(-0.296248\pi\)
0.597281 + 0.802032i \(0.296248\pi\)
\(264\) 2118.33 0.493843
\(265\) −5622.05 −1.30325
\(266\) 0 0
\(267\) −5794.93 −1.32825
\(268\) −2547.09 −0.580553
\(269\) −7694.70 −1.74407 −0.872034 0.489446i \(-0.837199\pi\)
−0.872034 + 0.489446i \(0.837199\pi\)
\(270\) −668.999 −0.150792
\(271\) 898.571 0.201418 0.100709 0.994916i \(-0.467889\pi\)
0.100709 + 0.994916i \(0.467889\pi\)
\(272\) −1067.11 −0.237878
\(273\) 0 0
\(274\) −4128.24 −0.910204
\(275\) −8296.76 −1.81932
\(276\) −660.277 −0.144000
\(277\) −3660.31 −0.793959 −0.396979 0.917828i \(-0.629942\pi\)
−0.396979 + 0.917828i \(0.629942\pi\)
\(278\) −18.3907 −0.00396764
\(279\) 6422.00 1.37805
\(280\) 0 0
\(281\) 3392.36 0.720183 0.360092 0.932917i \(-0.382745\pi\)
0.360092 + 0.932917i \(0.382745\pi\)
\(282\) −4399.82 −0.929097
\(283\) −8150.68 −1.71204 −0.856021 0.516942i \(-0.827070\pi\)
−0.856021 + 0.516942i \(0.827070\pi\)
\(284\) 1283.66 0.268209
\(285\) 14270.3 2.96595
\(286\) 1681.67 0.347689
\(287\) 0 0
\(288\) 784.265 0.160463
\(289\) −464.898 −0.0946261
\(290\) 7473.51 1.51331
\(291\) 8399.09 1.69197
\(292\) 98.3794 0.0197165
\(293\) −6020.89 −1.20049 −0.600246 0.799816i \(-0.704931\pi\)
−0.600246 + 0.799816i \(0.704931\pi\)
\(294\) 0 0
\(295\) 4778.83 0.943167
\(296\) 1617.39 0.317598
\(297\) −659.788 −0.128905
\(298\) −1238.09 −0.240673
\(299\) −524.170 −0.101383
\(300\) −6455.67 −1.24239
\(301\) 0 0
\(302\) 325.739 0.0620669
\(303\) −3980.54 −0.754707
\(304\) 1700.81 0.320882
\(305\) 11185.7 2.09997
\(306\) −3269.11 −0.610728
\(307\) −2860.72 −0.531824 −0.265912 0.963997i \(-0.585673\pi\)
−0.265912 + 0.963997i \(0.585673\pi\)
\(308\) 0 0
\(309\) −7308.49 −1.34552
\(310\) −9802.67 −1.79598
\(311\) −1380.64 −0.251732 −0.125866 0.992047i \(-0.540171\pi\)
−0.125866 + 0.992047i \(0.540171\pi\)
\(312\) 1308.50 0.237433
\(313\) −298.973 −0.0539902 −0.0269951 0.999636i \(-0.508594\pi\)
−0.0269951 + 0.999636i \(0.508594\pi\)
\(314\) 2640.91 0.474634
\(315\) 0 0
\(316\) 4484.83 0.798390
\(317\) −2343.58 −0.415232 −0.207616 0.978210i \(-0.566570\pi\)
−0.207616 + 0.978210i \(0.566570\pi\)
\(318\) −4314.26 −0.760792
\(319\) 7370.61 1.29365
\(320\) −1197.12 −0.209128
\(321\) −10419.1 −1.81164
\(322\) 0 0
\(323\) −7089.63 −1.22129
\(324\) −3160.27 −0.541885
\(325\) −5124.92 −0.874706
\(326\) −4386.51 −0.745234
\(327\) −12341.5 −2.08712
\(328\) −355.743 −0.0598861
\(329\) 0 0
\(330\) −9905.84 −1.65242
\(331\) 1886.83 0.313322 0.156661 0.987652i \(-0.449927\pi\)
0.156661 + 0.987652i \(0.449927\pi\)
\(332\) 3070.74 0.507617
\(333\) 4954.93 0.815402
\(334\) −4234.35 −0.693693
\(335\) 11910.8 1.94256
\(336\) 0 0
\(337\) 10943.8 1.76898 0.884488 0.466564i \(-0.154508\pi\)
0.884488 + 0.466564i \(0.154508\pi\)
\(338\) −3355.23 −0.539942
\(339\) 15519.9 2.48651
\(340\) 4990.04 0.795950
\(341\) −9667.70 −1.53529
\(342\) 5210.50 0.823834
\(343\) 0 0
\(344\) −145.622 −0.0228238
\(345\) 3087.62 0.481831
\(346\) 5152.00 0.800501
\(347\) 10567.0 1.63477 0.817385 0.576091i \(-0.195423\pi\)
0.817385 + 0.576091i \(0.195423\pi\)
\(348\) 5735.03 0.883420
\(349\) −1332.92 −0.204440 −0.102220 0.994762i \(-0.532595\pi\)
−0.102220 + 0.994762i \(0.532595\pi\)
\(350\) 0 0
\(351\) −407.552 −0.0619758
\(352\) −1180.64 −0.178773
\(353\) 3880.43 0.585083 0.292541 0.956253i \(-0.405499\pi\)
0.292541 + 0.956253i \(0.405499\pi\)
\(354\) 3667.19 0.550590
\(355\) −6002.72 −0.897440
\(356\) 3229.76 0.480833
\(357\) 0 0
\(358\) −6016.29 −0.888186
\(359\) −12612.1 −1.85415 −0.927073 0.374880i \(-0.877684\pi\)
−0.927073 + 0.374880i \(0.877684\pi\)
\(360\) −3667.41 −0.536915
\(361\) 4440.85 0.647448
\(362\) −404.758 −0.0587669
\(363\) −216.968 −0.0313715
\(364\) 0 0
\(365\) −460.046 −0.0659723
\(366\) 8583.69 1.22589
\(367\) 5092.93 0.724384 0.362192 0.932104i \(-0.382029\pi\)
0.362192 + 0.932104i \(0.382029\pi\)
\(368\) 368.000 0.0521286
\(369\) −1089.83 −0.153752
\(370\) −7563.31 −1.06270
\(371\) 0 0
\(372\) −7522.39 −1.04843
\(373\) −12578.8 −1.74612 −0.873062 0.487609i \(-0.837869\pi\)
−0.873062 + 0.487609i \(0.837869\pi\)
\(374\) 4921.34 0.680418
\(375\) 13407.7 1.84633
\(376\) 2452.20 0.336337
\(377\) 4552.84 0.621971
\(378\) 0 0
\(379\) 3831.85 0.519338 0.259669 0.965698i \(-0.416387\pi\)
0.259669 + 0.965698i \(0.416387\pi\)
\(380\) −7953.41 −1.07369
\(381\) −10497.6 −1.41157
\(382\) 8520.27 1.14119
\(383\) 7165.67 0.956002 0.478001 0.878359i \(-0.341362\pi\)
0.478001 + 0.878359i \(0.341362\pi\)
\(384\) −918.647 −0.122082
\(385\) 0 0
\(386\) 4142.57 0.546247
\(387\) −446.118 −0.0585980
\(388\) −4681.16 −0.612500
\(389\) 10808.2 1.40873 0.704364 0.709839i \(-0.251232\pi\)
0.704364 + 0.709839i \(0.251232\pi\)
\(390\) −6118.85 −0.794462
\(391\) −1533.96 −0.198404
\(392\) 0 0
\(393\) 14138.7 1.81477
\(394\) −8286.08 −1.05951
\(395\) −20972.1 −2.67145
\(396\) −3616.92 −0.458982
\(397\) 12829.0 1.62183 0.810917 0.585162i \(-0.198969\pi\)
0.810917 + 0.585162i \(0.198969\pi\)
\(398\) −2226.97 −0.280472
\(399\) 0 0
\(400\) 3598.01 0.449751
\(401\) 10168.2 1.26628 0.633139 0.774038i \(-0.281766\pi\)
0.633139 + 0.774038i \(0.281766\pi\)
\(402\) 9140.14 1.13400
\(403\) −5971.75 −0.738149
\(404\) 2218.52 0.273207
\(405\) 14778.2 1.81317
\(406\) 0 0
\(407\) −7459.18 −0.908447
\(408\) 3829.27 0.464650
\(409\) −1594.36 −0.192753 −0.0963766 0.995345i \(-0.530725\pi\)
−0.0963766 + 0.995345i \(0.530725\pi\)
\(410\) 1663.54 0.200382
\(411\) 14814.0 1.77791
\(412\) 4073.32 0.487083
\(413\) 0 0
\(414\) 1127.38 0.133835
\(415\) −14359.5 −1.69851
\(416\) −729.280 −0.0859517
\(417\) 65.9945 0.00775003
\(418\) −7843.90 −0.917842
\(419\) −8355.45 −0.974201 −0.487101 0.873346i \(-0.661945\pi\)
−0.487101 + 0.873346i \(0.661945\pi\)
\(420\) 0 0
\(421\) −1727.23 −0.199952 −0.0999762 0.994990i \(-0.531877\pi\)
−0.0999762 + 0.994990i \(0.531877\pi\)
\(422\) 2426.04 0.279853
\(423\) 7512.41 0.863513
\(424\) 2404.52 0.275410
\(425\) −14997.9 −1.71177
\(426\) −4606.38 −0.523896
\(427\) 0 0
\(428\) 5806.99 0.655821
\(429\) −6034.61 −0.679146
\(430\) 680.963 0.0763696
\(431\) 5240.54 0.585680 0.292840 0.956161i \(-0.405400\pi\)
0.292840 + 0.956161i \(0.405400\pi\)
\(432\) 286.127 0.0318664
\(433\) 6074.43 0.674177 0.337088 0.941473i \(-0.390558\pi\)
0.337088 + 0.941473i \(0.390558\pi\)
\(434\) 0 0
\(435\) −26818.4 −2.95596
\(436\) 6878.44 0.755544
\(437\) 2444.92 0.267634
\(438\) −353.031 −0.0385125
\(439\) 10981.3 1.19388 0.596938 0.802288i \(-0.296384\pi\)
0.596938 + 0.802288i \(0.296384\pi\)
\(440\) 5520.94 0.598183
\(441\) 0 0
\(442\) 3039.92 0.327136
\(443\) 4102.85 0.440028 0.220014 0.975497i \(-0.429390\pi\)
0.220014 + 0.975497i \(0.429390\pi\)
\(444\) −5803.95 −0.620368
\(445\) −15103.1 −1.60889
\(446\) 6527.10 0.692976
\(447\) 4442.83 0.470109
\(448\) 0 0
\(449\) 16448.6 1.72886 0.864429 0.502754i \(-0.167680\pi\)
0.864429 + 0.502754i \(0.167680\pi\)
\(450\) 11022.6 1.15469
\(451\) 1640.64 0.171296
\(452\) −8649.89 −0.900126
\(453\) −1168.90 −0.121236
\(454\) −12564.6 −1.29886
\(455\) 0 0
\(456\) −6103.30 −0.626783
\(457\) 14213.7 1.45490 0.727452 0.686159i \(-0.240704\pi\)
0.727452 + 0.686159i \(0.240704\pi\)
\(458\) 4069.32 0.415168
\(459\) −1192.68 −0.121285
\(460\) −1720.86 −0.174425
\(461\) 6087.14 0.614982 0.307491 0.951551i \(-0.400511\pi\)
0.307491 + 0.951551i \(0.400511\pi\)
\(462\) 0 0
\(463\) 5359.06 0.537919 0.268959 0.963151i \(-0.413320\pi\)
0.268959 + 0.963151i \(0.413320\pi\)
\(464\) −3196.37 −0.319801
\(465\) 35176.5 3.50811
\(466\) 3374.27 0.335429
\(467\) 17780.9 1.76188 0.880942 0.473224i \(-0.156910\pi\)
0.880942 + 0.473224i \(0.156910\pi\)
\(468\) −2234.18 −0.220673
\(469\) 0 0
\(470\) −11467.1 −1.12540
\(471\) −9476.80 −0.927108
\(472\) −2043.88 −0.199316
\(473\) 671.587 0.0652846
\(474\) −16093.6 −1.55950
\(475\) 23904.5 2.30908
\(476\) 0 0
\(477\) 7366.33 0.707088
\(478\) −13023.9 −1.24623
\(479\) 12340.2 1.17711 0.588555 0.808457i \(-0.299697\pi\)
0.588555 + 0.808457i \(0.299697\pi\)
\(480\) 4295.81 0.408492
\(481\) −4607.55 −0.436769
\(482\) −6326.52 −0.597853
\(483\) 0 0
\(484\) 120.925 0.0113566
\(485\) 21890.2 2.04945
\(486\) 10374.8 0.968338
\(487\) −14345.9 −1.33486 −0.667428 0.744674i \(-0.732605\pi\)
−0.667428 + 0.744674i \(0.732605\pi\)
\(488\) −4784.05 −0.443778
\(489\) 15740.8 1.45567
\(490\) 0 0
\(491\) −839.846 −0.0771929 −0.0385964 0.999255i \(-0.512289\pi\)
−0.0385964 + 0.999255i \(0.512289\pi\)
\(492\) 1276.57 0.116976
\(493\) 13323.7 1.21718
\(494\) −4845.19 −0.441286
\(495\) 16913.6 1.53578
\(496\) 4192.54 0.379538
\(497\) 0 0
\(498\) −11019.2 −0.991534
\(499\) −10473.4 −0.939587 −0.469794 0.882776i \(-0.655672\pi\)
−0.469794 + 0.882776i \(0.655672\pi\)
\(500\) −7472.69 −0.668377
\(501\) 15194.8 1.35500
\(502\) −1036.85 −0.0921849
\(503\) −21797.3 −1.93219 −0.966097 0.258180i \(-0.916877\pi\)
−0.966097 + 0.258180i \(0.916877\pi\)
\(504\) 0 0
\(505\) −10374.3 −0.914163
\(506\) −1697.16 −0.149107
\(507\) 12040.1 1.05468
\(508\) 5850.74 0.510994
\(509\) −18466.3 −1.60806 −0.804031 0.594587i \(-0.797316\pi\)
−0.804031 + 0.594587i \(0.797316\pi\)
\(510\) −17906.6 −1.55474
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 1900.97 0.163606
\(514\) −10891.4 −0.934631
\(515\) −19047.8 −1.62980
\(516\) 522.559 0.0445821
\(517\) −11309.2 −0.962048
\(518\) 0 0
\(519\) −18487.8 −1.56363
\(520\) 3410.29 0.287598
\(521\) −970.557 −0.0816139 −0.0408070 0.999167i \(-0.512993\pi\)
−0.0408070 + 0.999167i \(0.512993\pi\)
\(522\) −9792.20 −0.821059
\(523\) −2501.73 −0.209164 −0.104582 0.994516i \(-0.533350\pi\)
−0.104582 + 0.994516i \(0.533350\pi\)
\(524\) −7880.08 −0.656952
\(525\) 0 0
\(526\) 10190.0 0.844683
\(527\) −17476.1 −1.44454
\(528\) 4236.67 0.349199
\(529\) 529.000 0.0434783
\(530\) −11244.1 −0.921534
\(531\) −6261.49 −0.511724
\(532\) 0 0
\(533\) 1013.42 0.0823570
\(534\) −11589.9 −0.939218
\(535\) −27154.9 −2.19441
\(536\) −5094.18 −0.410513
\(537\) 21589.2 1.73490
\(538\) −15389.4 −1.23324
\(539\) 0 0
\(540\) −1338.00 −0.106626
\(541\) −5519.57 −0.438641 −0.219321 0.975653i \(-0.570384\pi\)
−0.219321 + 0.975653i \(0.570384\pi\)
\(542\) 1797.14 0.142424
\(543\) 1452.46 0.114790
\(544\) −2134.21 −0.168205
\(545\) −32165.2 −2.52809
\(546\) 0 0
\(547\) −15172.9 −1.18601 −0.593004 0.805199i \(-0.702058\pi\)
−0.593004 + 0.805199i \(0.702058\pi\)
\(548\) −8256.47 −0.643611
\(549\) −14656.1 −1.13936
\(550\) −16593.5 −1.28645
\(551\) −21236.1 −1.64190
\(552\) −1320.55 −0.101823
\(553\) 0 0
\(554\) −7320.61 −0.561413
\(555\) 27140.7 2.07578
\(556\) −36.7815 −0.00280554
\(557\) −2907.15 −0.221149 −0.110574 0.993868i \(-0.535269\pi\)
−0.110574 + 0.993868i \(0.535269\pi\)
\(558\) 12844.0 0.974426
\(559\) 414.840 0.0313880
\(560\) 0 0
\(561\) −17660.0 −1.32907
\(562\) 6784.73 0.509246
\(563\) −1318.69 −0.0987141 −0.0493570 0.998781i \(-0.515717\pi\)
−0.0493570 + 0.998781i \(0.515717\pi\)
\(564\) −8799.64 −0.656971
\(565\) 40449.0 3.01186
\(566\) −16301.4 −1.21060
\(567\) 0 0
\(568\) 2567.33 0.189652
\(569\) −2920.60 −0.215181 −0.107591 0.994195i \(-0.534314\pi\)
−0.107591 + 0.994195i \(0.534314\pi\)
\(570\) 28540.5 2.09725
\(571\) 11200.3 0.820873 0.410436 0.911889i \(-0.365376\pi\)
0.410436 + 0.911889i \(0.365376\pi\)
\(572\) 3363.34 0.245854
\(573\) −30574.7 −2.22910
\(574\) 0 0
\(575\) 5172.14 0.375119
\(576\) 1568.53 0.113464
\(577\) 3416.96 0.246534 0.123267 0.992374i \(-0.460663\pi\)
0.123267 + 0.992374i \(0.460663\pi\)
\(578\) −929.796 −0.0669108
\(579\) −14865.5 −1.06699
\(580\) 14947.0 1.07007
\(581\) 0 0
\(582\) 16798.2 1.19640
\(583\) −11089.3 −0.787773
\(584\) 196.759 0.0139417
\(585\) 10447.5 0.738381
\(586\) −12041.8 −0.848876
\(587\) 16614.4 1.16823 0.584114 0.811671i \(-0.301442\pi\)
0.584114 + 0.811671i \(0.301442\pi\)
\(588\) 0 0
\(589\) 27854.4 1.94859
\(590\) 9557.66 0.666920
\(591\) 29734.3 2.06955
\(592\) 3234.78 0.224576
\(593\) 16559.0 1.14671 0.573354 0.819308i \(-0.305642\pi\)
0.573354 + 0.819308i \(0.305642\pi\)
\(594\) −1319.58 −0.0911496
\(595\) 0 0
\(596\) −2476.18 −0.170181
\(597\) 7991.39 0.547849
\(598\) −1048.34 −0.0716887
\(599\) 10995.8 0.750043 0.375021 0.927016i \(-0.377635\pi\)
0.375021 + 0.927016i \(0.377635\pi\)
\(600\) −12911.3 −0.878505
\(601\) −9311.94 −0.632016 −0.316008 0.948756i \(-0.602343\pi\)
−0.316008 + 0.948756i \(0.602343\pi\)
\(602\) 0 0
\(603\) −15606.2 −1.05395
\(604\) 651.479 0.0438879
\(605\) −565.475 −0.0379997
\(606\) −7961.09 −0.533659
\(607\) 19247.2 1.28702 0.643510 0.765438i \(-0.277477\pi\)
0.643510 + 0.765438i \(0.277477\pi\)
\(608\) 3401.62 0.226898
\(609\) 0 0
\(610\) 22371.4 1.48490
\(611\) −6985.72 −0.462540
\(612\) −6538.23 −0.431850
\(613\) −10419.4 −0.686517 −0.343259 0.939241i \(-0.611531\pi\)
−0.343259 + 0.939241i \(0.611531\pi\)
\(614\) −5721.44 −0.376057
\(615\) −5969.56 −0.391408
\(616\) 0 0
\(617\) 15890.0 1.03681 0.518403 0.855137i \(-0.326527\pi\)
0.518403 + 0.855137i \(0.326527\pi\)
\(618\) −14617.0 −0.951425
\(619\) 2325.59 0.151007 0.0755035 0.997146i \(-0.475944\pi\)
0.0755035 + 0.997146i \(0.475944\pi\)
\(620\) −19605.3 −1.26995
\(621\) 411.307 0.0265784
\(622\) −2761.28 −0.178002
\(623\) 0 0
\(624\) 2617.00 0.167891
\(625\) 6834.62 0.437416
\(626\) −597.945 −0.0381768
\(627\) 28147.6 1.79283
\(628\) 5281.82 0.335617
\(629\) −13483.8 −0.854745
\(630\) 0 0
\(631\) 25002.0 1.57736 0.788678 0.614806i \(-0.210766\pi\)
0.788678 + 0.614806i \(0.210766\pi\)
\(632\) 8969.65 0.564547
\(633\) −8705.77 −0.546640
\(634\) −4687.15 −0.293613
\(635\) −27359.5 −1.70981
\(636\) −8628.53 −0.537961
\(637\) 0 0
\(638\) 14741.2 0.914750
\(639\) 7865.09 0.486914
\(640\) −2394.24 −0.147876
\(641\) −23855.1 −1.46992 −0.734960 0.678110i \(-0.762799\pi\)
−0.734960 + 0.678110i \(0.762799\pi\)
\(642\) −20838.2 −1.28102
\(643\) −28805.3 −1.76667 −0.883337 0.468738i \(-0.844709\pi\)
−0.883337 + 0.468738i \(0.844709\pi\)
\(644\) 0 0
\(645\) −2443.61 −0.149174
\(646\) −14179.3 −0.863585
\(647\) −32498.4 −1.97472 −0.987360 0.158492i \(-0.949337\pi\)
−0.987360 + 0.158492i \(0.949337\pi\)
\(648\) −6320.54 −0.383170
\(649\) 9426.07 0.570116
\(650\) −10249.8 −0.618510
\(651\) 0 0
\(652\) −8773.02 −0.526960
\(653\) 16341.1 0.979290 0.489645 0.871922i \(-0.337126\pi\)
0.489645 + 0.871922i \(0.337126\pi\)
\(654\) −24683.0 −1.47581
\(655\) 36849.2 2.19819
\(656\) −711.486 −0.0423458
\(657\) 602.777 0.0357939
\(658\) 0 0
\(659\) 5445.43 0.321887 0.160944 0.986964i \(-0.448546\pi\)
0.160944 + 0.986964i \(0.448546\pi\)
\(660\) −19811.7 −1.16844
\(661\) −17006.6 −1.00073 −0.500363 0.865816i \(-0.666800\pi\)
−0.500363 + 0.865816i \(0.666800\pi\)
\(662\) 3773.66 0.221552
\(663\) −10908.6 −0.638999
\(664\) 6141.48 0.358939
\(665\) 0 0
\(666\) 9909.87 0.576576
\(667\) −4594.79 −0.266733
\(668\) −8468.70 −0.490515
\(669\) −23422.3 −1.35360
\(670\) 23821.6 1.37360
\(671\) 22063.4 1.26937
\(672\) 0 0
\(673\) −20763.5 −1.18926 −0.594631 0.803999i \(-0.702702\pi\)
−0.594631 + 0.803999i \(0.702702\pi\)
\(674\) 21887.5 1.25085
\(675\) 4021.43 0.229311
\(676\) −6710.46 −0.381797
\(677\) 18958.9 1.07629 0.538146 0.842851i \(-0.319125\pi\)
0.538146 + 0.842851i \(0.319125\pi\)
\(678\) 31039.8 1.75823
\(679\) 0 0
\(680\) 9980.08 0.562822
\(681\) 45087.5 2.53709
\(682\) −19335.4 −1.08562
\(683\) 22546.4 1.26312 0.631562 0.775325i \(-0.282414\pi\)
0.631562 + 0.775325i \(0.282414\pi\)
\(684\) 10421.0 0.582539
\(685\) 38609.3 2.15355
\(686\) 0 0
\(687\) −14602.6 −0.810952
\(688\) −291.244 −0.0161389
\(689\) −6849.88 −0.378751
\(690\) 6175.23 0.340706
\(691\) −27690.6 −1.52446 −0.762228 0.647309i \(-0.775894\pi\)
−0.762228 + 0.647309i \(0.775894\pi\)
\(692\) 10304.0 0.566040
\(693\) 0 0
\(694\) 21134.0 1.15596
\(695\) 171.999 0.00938747
\(696\) 11470.1 0.624672
\(697\) 2965.75 0.161170
\(698\) −2665.84 −0.144561
\(699\) −12108.4 −0.655198
\(700\) 0 0
\(701\) 2135.07 0.115036 0.0575182 0.998344i \(-0.481681\pi\)
0.0575182 + 0.998344i \(0.481681\pi\)
\(702\) −815.104 −0.0438235
\(703\) 21491.2 1.15300
\(704\) −2361.27 −0.126412
\(705\) 41149.2 2.19826
\(706\) 7760.85 0.413716
\(707\) 0 0
\(708\) 7334.37 0.389326
\(709\) −18765.6 −0.994016 −0.497008 0.867746i \(-0.665568\pi\)
−0.497008 + 0.867746i \(0.665568\pi\)
\(710\) −12005.4 −0.634586
\(711\) 27478.8 1.44942
\(712\) 6459.51 0.340001
\(713\) 6026.78 0.316556
\(714\) 0 0
\(715\) −15727.8 −0.822637
\(716\) −12032.6 −0.628042
\(717\) 46735.8 2.43428
\(718\) −25224.1 −1.31108
\(719\) −24563.0 −1.27405 −0.637027 0.770842i \(-0.719836\pi\)
−0.637027 + 0.770842i \(0.719836\pi\)
\(720\) −7334.82 −0.379657
\(721\) 0 0
\(722\) 8881.70 0.457815
\(723\) 22702.5 1.16779
\(724\) −809.517 −0.0415545
\(725\) −44924.2 −2.30130
\(726\) −433.935 −0.0221830
\(727\) −1895.61 −0.0967045 −0.0483522 0.998830i \(-0.515397\pi\)
−0.0483522 + 0.998830i \(0.515397\pi\)
\(728\) 0 0
\(729\) −15897.9 −0.807697
\(730\) −920.091 −0.0466495
\(731\) 1214.01 0.0614254
\(732\) 17167.4 0.866837
\(733\) 8040.15 0.405143 0.202571 0.979268i \(-0.435070\pi\)
0.202571 + 0.979268i \(0.435070\pi\)
\(734\) 10185.9 0.512217
\(735\) 0 0
\(736\) 736.000 0.0368605
\(737\) 23493.6 1.17422
\(738\) −2179.66 −0.108719
\(739\) 7025.86 0.349730 0.174865 0.984592i \(-0.444051\pi\)
0.174865 + 0.984592i \(0.444051\pi\)
\(740\) −15126.6 −0.751440
\(741\) 17386.8 0.861970
\(742\) 0 0
\(743\) 35267.7 1.74138 0.870691 0.491830i \(-0.163672\pi\)
0.870691 + 0.491830i \(0.163672\pi\)
\(744\) −15044.8 −0.741355
\(745\) 11579.2 0.569435
\(746\) −25157.5 −1.23470
\(747\) 18814.6 0.921542
\(748\) 9842.68 0.481128
\(749\) 0 0
\(750\) 26815.5 1.30555
\(751\) −26262.0 −1.27605 −0.638026 0.770015i \(-0.720249\pi\)
−0.638026 + 0.770015i \(0.720249\pi\)
\(752\) 4904.41 0.237826
\(753\) 3720.69 0.180066
\(754\) 9105.67 0.439800
\(755\) −3046.47 −0.146851
\(756\) 0 0
\(757\) 20312.0 0.975234 0.487617 0.873058i \(-0.337866\pi\)
0.487617 + 0.873058i \(0.337866\pi\)
\(758\) 7663.70 0.367227
\(759\) 6090.21 0.291252
\(760\) −15906.8 −0.759212
\(761\) −5976.37 −0.284682 −0.142341 0.989818i \(-0.545463\pi\)
−0.142341 + 0.989818i \(0.545463\pi\)
\(762\) −20995.2 −0.998130
\(763\) 0 0
\(764\) 17040.5 0.806943
\(765\) 30574.3 1.44499
\(766\) 14331.3 0.675995
\(767\) 5822.50 0.274104
\(768\) −1837.29 −0.0863250
\(769\) −20927.5 −0.981360 −0.490680 0.871340i \(-0.663252\pi\)
−0.490680 + 0.871340i \(0.663252\pi\)
\(770\) 0 0
\(771\) 39083.5 1.82563
\(772\) 8285.15 0.386255
\(773\) −15071.3 −0.701262 −0.350631 0.936514i \(-0.614033\pi\)
−0.350631 + 0.936514i \(0.614033\pi\)
\(774\) −892.235 −0.0414350
\(775\) 58925.0 2.73116
\(776\) −9362.33 −0.433103
\(777\) 0 0
\(778\) 21616.3 0.996121
\(779\) −4726.97 −0.217409
\(780\) −12237.7 −0.561769
\(781\) −11840.1 −0.542476
\(782\) −3067.93 −0.140293
\(783\) −3572.53 −0.163055
\(784\) 0 0
\(785\) −24699.0 −1.12299
\(786\) 28277.4 1.28323
\(787\) 9818.43 0.444713 0.222357 0.974965i \(-0.428625\pi\)
0.222357 + 0.974965i \(0.428625\pi\)
\(788\) −16572.2 −0.749187
\(789\) −36566.3 −1.64993
\(790\) −41944.3 −1.88900
\(791\) 0 0
\(792\) −7233.84 −0.324550
\(793\) 13628.6 0.610296
\(794\) 25658.0 1.14681
\(795\) 40349.1 1.80004
\(796\) −4453.93 −0.198323
\(797\) 25841.3 1.14849 0.574244 0.818684i \(-0.305296\pi\)
0.574244 + 0.818684i \(0.305296\pi\)
\(798\) 0 0
\(799\) −20443.4 −0.905177
\(800\) 7196.02 0.318022
\(801\) 19788.9 0.872918
\(802\) 20336.5 0.895393
\(803\) −907.423 −0.0398783
\(804\) 18280.3 0.801861
\(805\) 0 0
\(806\) −11943.5 −0.521950
\(807\) 55224.3 2.40891
\(808\) 4437.05 0.193187
\(809\) −44965.3 −1.95414 −0.977068 0.212926i \(-0.931701\pi\)
−0.977068 + 0.212926i \(0.931701\pi\)
\(810\) 29556.4 1.28211
\(811\) 23927.0 1.03599 0.517997 0.855382i \(-0.326678\pi\)
0.517997 + 0.855382i \(0.326678\pi\)
\(812\) 0 0
\(813\) −6448.98 −0.278199
\(814\) −14918.4 −0.642369
\(815\) 41024.8 1.76323
\(816\) 7658.54 0.328557
\(817\) −1934.96 −0.0828590
\(818\) −3188.72 −0.136297
\(819\) 0 0
\(820\) 3327.08 0.141691
\(821\) −45775.0 −1.94587 −0.972934 0.231082i \(-0.925773\pi\)
−0.972934 + 0.231082i \(0.925773\pi\)
\(822\) 29628.0 1.25717
\(823\) 187.951 0.00796060 0.00398030 0.999992i \(-0.498733\pi\)
0.00398030 + 0.999992i \(0.498733\pi\)
\(824\) 8146.65 0.344420
\(825\) 59545.2 2.51285
\(826\) 0 0
\(827\) −11598.2 −0.487676 −0.243838 0.969816i \(-0.578406\pi\)
−0.243838 + 0.969816i \(0.578406\pi\)
\(828\) 2254.76 0.0946357
\(829\) 4238.86 0.177590 0.0887948 0.996050i \(-0.471698\pi\)
0.0887948 + 0.996050i \(0.471698\pi\)
\(830\) −28719.0 −1.20103
\(831\) 26269.8 1.09662
\(832\) −1458.56 −0.0607770
\(833\) 0 0
\(834\) 131.989 0.00548010
\(835\) 39601.7 1.64129
\(836\) −15687.8 −0.649012
\(837\) 4685.93 0.193512
\(838\) −16710.9 −0.688864
\(839\) 30548.4 1.25703 0.628514 0.777798i \(-0.283663\pi\)
0.628514 + 0.777798i \(0.283663\pi\)
\(840\) 0 0
\(841\) 15520.4 0.636368
\(842\) −3454.46 −0.141388
\(843\) −24346.7 −0.994717
\(844\) 4852.09 0.197886
\(845\) 31379.7 1.27751
\(846\) 15024.8 0.610596
\(847\) 0 0
\(848\) 4809.04 0.194744
\(849\) 58496.8 2.36467
\(850\) −29995.8 −1.21041
\(851\) 4650.00 0.187309
\(852\) −9212.75 −0.370450
\(853\) −7956.01 −0.319354 −0.159677 0.987169i \(-0.551045\pi\)
−0.159677 + 0.987169i \(0.551045\pi\)
\(854\) 0 0
\(855\) −48731.1 −1.94920
\(856\) 11614.0 0.463736
\(857\) −32534.3 −1.29679 −0.648396 0.761303i \(-0.724560\pi\)
−0.648396 + 0.761303i \(0.724560\pi\)
\(858\) −12069.2 −0.480229
\(859\) 818.271 0.0325018 0.0162509 0.999868i \(-0.494827\pi\)
0.0162509 + 0.999868i \(0.494827\pi\)
\(860\) 1361.93 0.0540015
\(861\) 0 0
\(862\) 10481.1 0.414138
\(863\) −20161.0 −0.795238 −0.397619 0.917551i \(-0.630163\pi\)
−0.397619 + 0.917551i \(0.630163\pi\)
\(864\) 572.253 0.0225329
\(865\) −48184.0 −1.89400
\(866\) 12148.9 0.476715
\(867\) 3336.54 0.130698
\(868\) 0 0
\(869\) −41366.8 −1.61481
\(870\) −53636.8 −2.09018
\(871\) 14512.1 0.564549
\(872\) 13756.9 0.534250
\(873\) −28681.8 −1.11195
\(874\) 4889.83 0.189246
\(875\) 0 0
\(876\) −706.061 −0.0272324
\(877\) −33048.9 −1.27250 −0.636250 0.771483i \(-0.719515\pi\)
−0.636250 + 0.771483i \(0.719515\pi\)
\(878\) 21962.7 0.844197
\(879\) 43211.5 1.65812
\(880\) 11041.9 0.422979
\(881\) −15531.2 −0.593938 −0.296969 0.954887i \(-0.595976\pi\)
−0.296969 + 0.954887i \(0.595976\pi\)
\(882\) 0 0
\(883\) −22079.1 −0.841474 −0.420737 0.907183i \(-0.638228\pi\)
−0.420737 + 0.907183i \(0.638228\pi\)
\(884\) 6079.84 0.231320
\(885\) −34297.3 −1.30270
\(886\) 8205.70 0.311147
\(887\) −8427.81 −0.319028 −0.159514 0.987196i \(-0.550993\pi\)
−0.159514 + 0.987196i \(0.550993\pi\)
\(888\) −11607.9 −0.438666
\(889\) 0 0
\(890\) −30206.2 −1.13766
\(891\) 29149.4 1.09601
\(892\) 13054.2 0.490008
\(893\) 32583.9 1.22103
\(894\) 8885.67 0.332417
\(895\) 56267.2 2.10146
\(896\) 0 0
\(897\) 3761.93 0.140030
\(898\) 32897.2 1.22249
\(899\) −52347.4 −1.94203
\(900\) 22045.3 0.816491
\(901\) −20045.9 −0.741205
\(902\) 3281.27 0.121125
\(903\) 0 0
\(904\) −17299.8 −0.636485
\(905\) 3785.50 0.139043
\(906\) −2337.81 −0.0857268
\(907\) −28182.9 −1.03175 −0.515876 0.856663i \(-0.672533\pi\)
−0.515876 + 0.856663i \(0.672533\pi\)
\(908\) −25129.1 −0.918436
\(909\) 13593.0 0.495988
\(910\) 0 0
\(911\) −48586.1 −1.76699 −0.883496 0.468439i \(-0.844816\pi\)
−0.883496 + 0.468439i \(0.844816\pi\)
\(912\) −12206.6 −0.443203
\(913\) −28323.6 −1.02670
\(914\) 28427.5 1.02877
\(915\) −80278.8 −2.90048
\(916\) 8138.64 0.293568
\(917\) 0 0
\(918\) −2385.37 −0.0857614
\(919\) −48873.3 −1.75428 −0.877139 0.480236i \(-0.840551\pi\)
−0.877139 + 0.480236i \(0.840551\pi\)
\(920\) −3441.71 −0.123337
\(921\) 20531.2 0.734556
\(922\) 12174.3 0.434858
\(923\) −7313.67 −0.260815
\(924\) 0 0
\(925\) 45464.0 1.61605
\(926\) 10718.1 0.380366
\(927\) 24957.5 0.884264
\(928\) −6392.75 −0.226134
\(929\) −36236.5 −1.27974 −0.639872 0.768482i \(-0.721012\pi\)
−0.639872 + 0.768482i \(0.721012\pi\)
\(930\) 70353.0 2.48061
\(931\) 0 0
\(932\) 6748.53 0.237184
\(933\) 9908.74 0.347693
\(934\) 35561.7 1.24584
\(935\) −46026.7 −1.60988
\(936\) −4468.35 −0.156039
\(937\) 37238.1 1.29831 0.649154 0.760657i \(-0.275123\pi\)
0.649154 + 0.760657i \(0.275123\pi\)
\(938\) 0 0
\(939\) 2145.70 0.0745713
\(940\) −22934.2 −0.795777
\(941\) 7961.47 0.275809 0.137905 0.990446i \(-0.455963\pi\)
0.137905 + 0.990446i \(0.455963\pi\)
\(942\) −18953.6 −0.655565
\(943\) −1022.76 −0.0353189
\(944\) −4087.75 −0.140938
\(945\) 0 0
\(946\) 1343.17 0.0461632
\(947\) 5376.57 0.184493 0.0922465 0.995736i \(-0.470595\pi\)
0.0922465 + 0.995736i \(0.470595\pi\)
\(948\) −32187.3 −1.10274
\(949\) −560.517 −0.0191730
\(950\) 47808.9 1.63276
\(951\) 16819.7 0.573518
\(952\) 0 0
\(953\) −19459.6 −0.661448 −0.330724 0.943728i \(-0.607293\pi\)
−0.330724 + 0.943728i \(0.607293\pi\)
\(954\) 14732.7 0.499987
\(955\) −79685.6 −2.70007
\(956\) −26047.8 −0.881220
\(957\) −52898.3 −1.78679
\(958\) 24680.3 0.832343
\(959\) 0 0
\(960\) 8591.63 0.288847
\(961\) 38870.7 1.30478
\(962\) −9215.09 −0.308842
\(963\) 35579.8 1.19060
\(964\) −12653.0 −0.422746
\(965\) −38743.4 −1.29243
\(966\) 0 0
\(967\) −7286.78 −0.242324 −0.121162 0.992633i \(-0.538662\pi\)
−0.121162 + 0.992633i \(0.538662\pi\)
\(968\) 241.850 0.00803033
\(969\) 50881.8 1.68685
\(970\) 43780.5 1.44918
\(971\) 1401.06 0.0463050 0.0231525 0.999732i \(-0.492630\pi\)
0.0231525 + 0.999732i \(0.492630\pi\)
\(972\) 20749.7 0.684718
\(973\) 0 0
\(974\) −28691.8 −0.943886
\(975\) 36781.2 1.20814
\(976\) −9568.10 −0.313799
\(977\) 28822.9 0.943833 0.471917 0.881643i \(-0.343562\pi\)
0.471917 + 0.881643i \(0.343562\pi\)
\(978\) 31481.7 1.02932
\(979\) −29790.4 −0.972527
\(980\) 0 0
\(981\) 42144.6 1.37164
\(982\) −1679.69 −0.0545836
\(983\) −8699.13 −0.282257 −0.141129 0.989991i \(-0.545073\pi\)
−0.141129 + 0.989991i \(0.545073\pi\)
\(984\) 2553.14 0.0827146
\(985\) 77495.5 2.50681
\(986\) 26647.4 0.860676
\(987\) 0 0
\(988\) −9690.38 −0.312037
\(989\) −418.663 −0.0134608
\(990\) 33827.2 1.08596
\(991\) 40870.4 1.31008 0.655041 0.755593i \(-0.272651\pi\)
0.655041 + 0.755593i \(0.272651\pi\)
\(992\) 8385.08 0.268374
\(993\) −13541.6 −0.432760
\(994\) 0 0
\(995\) 20827.7 0.663599
\(996\) −22038.5 −0.701120
\(997\) 36867.5 1.17112 0.585560 0.810629i \(-0.300875\pi\)
0.585560 + 0.810629i \(0.300875\pi\)
\(998\) −20946.8 −0.664389
\(999\) 3615.46 0.114503
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 2254.4.a.l.1.2 5
7.6 odd 2 322.4.a.h.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
322.4.a.h.1.4 5 7.6 odd 2
2254.4.a.l.1.2 5 1.1 even 1 trivial