Properties

Label 175.4.a.d.1.2
Level $175$
Weight $4$
Character 175.1
Self dual yes
Analytic conductor $10.325$
Analytic rank $1$
Dimension $2$
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] = [175,4,Mod(1,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, 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("175.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 175.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: \(10.3253342510\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{41}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.70156\) of defining polynomial
Character \(\chi\) \(=\) 175.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.70156 q^{2} -0.701562 q^{3} -0.701562 q^{4} -1.89531 q^{6} -7.00000 q^{7} -23.5078 q^{8} -26.5078 q^{9} +O(q^{10})\) \(q+2.70156 q^{2} -0.701562 q^{3} -0.701562 q^{4} -1.89531 q^{6} -7.00000 q^{7} -23.5078 q^{8} -26.5078 q^{9} +4.01562 q^{11} +0.492189 q^{12} -51.6125 q^{13} -18.9109 q^{14} -57.8953 q^{16} +67.5078 q^{17} -71.6125 q^{18} -50.9109 q^{19} +4.91093 q^{21} +10.8485 q^{22} -0.507811 q^{23} +16.4922 q^{24} -139.434 q^{26} +37.5391 q^{27} +4.91093 q^{28} -120.058 q^{29} -292.303 q^{31} +31.6547 q^{32} -2.81721 q^{33} +182.377 q^{34} +18.5969 q^{36} +144.989 q^{37} -137.539 q^{38} +36.2094 q^{39} -57.2047 q^{41} +13.2672 q^{42} +283.020 q^{43} -2.81721 q^{44} -1.37188 q^{46} +233.769 q^{47} +40.6172 q^{48} +49.0000 q^{49} -47.3609 q^{51} +36.2094 q^{52} +406.334 q^{53} +101.414 q^{54} +164.555 q^{56} +35.7172 q^{57} -324.344 q^{58} -577.328 q^{59} +322.116 q^{61} -789.675 q^{62} +185.555 q^{63} +548.680 q^{64} -7.61086 q^{66} -985.459 q^{67} -47.3609 q^{68} +0.356261 q^{69} +1033.57 q^{71} +623.141 q^{72} -692.720 q^{73} +391.697 q^{74} +35.7172 q^{76} -28.1093 q^{77} +97.8219 q^{78} -428.236 q^{79} +689.375 q^{81} -154.542 q^{82} +537.592 q^{83} -3.44533 q^{84} +764.597 q^{86} +84.2280 q^{87} -94.3985 q^{88} -802.073 q^{89} +361.287 q^{91} +0.356261 q^{92} +205.069 q^{93} +631.541 q^{94} -22.2077 q^{96} -1752.82 q^{97} +132.377 q^{98} -106.445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} + 5 q^{3} + 5 q^{4} - 23 q^{6} - 14 q^{7} - 15 q^{8} - 21 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{2} + 5 q^{3} + 5 q^{4} - 23 q^{6} - 14 q^{7} - 15 q^{8} - 21 q^{9} - 56 q^{11} + 33 q^{12} - 52 q^{13} + 7 q^{14} - 135 q^{16} + 103 q^{17} - 92 q^{18} - 57 q^{19} - 35 q^{21} + 233 q^{22} + 31 q^{23} + 65 q^{24} - 138 q^{26} - 85 q^{27} - 35 q^{28} - 413 q^{29} - 162 q^{31} + 249 q^{32} - 345 q^{33} + 51 q^{34} + 50 q^{36} - 75 q^{37} - 115 q^{38} + 34 q^{39} - 505 q^{41} + 161 q^{42} + 73 q^{43} - 345 q^{44} - 118 q^{46} - 224 q^{47} - 399 q^{48} + 98 q^{49} + 155 q^{51} + 34 q^{52} + 262 q^{53} + 555 q^{54} + 105 q^{56} + q^{57} + 760 q^{58} + 190 q^{59} + 990 q^{61} - 1272 q^{62} + 147 q^{63} + 361 q^{64} + 1259 q^{66} - 908 q^{67} + 155 q^{68} + 180 q^{69} + 127 q^{71} + 670 q^{72} + 337 q^{73} + 1206 q^{74} + q^{76} + 392 q^{77} + 106 q^{78} - 1119 q^{79} - 158 q^{81} + 1503 q^{82} + 1517 q^{83} - 231 q^{84} + 1542 q^{86} - 1586 q^{87} - 605 q^{88} - 1713 q^{89} + 364 q^{91} + 180 q^{92} + 948 q^{93} + 2326 q^{94} + 1217 q^{96} - 1764 q^{97} - 49 q^{98} - 437 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.70156 0.955146 0.477573 0.878592i \(-0.341517\pi\)
0.477573 + 0.878592i \(0.341517\pi\)
\(3\) −0.701562 −0.135016 −0.0675078 0.997719i \(-0.521505\pi\)
−0.0675078 + 0.997719i \(0.521505\pi\)
\(4\) −0.701562 −0.0876953
\(5\) 0 0
\(6\) −1.89531 −0.128960
\(7\) −7.00000 −0.377964
\(8\) −23.5078 −1.03891
\(9\) −26.5078 −0.981771
\(10\) 0 0
\(11\) 4.01562 0.110069 0.0550343 0.998484i \(-0.482473\pi\)
0.0550343 + 0.998484i \(0.482473\pi\)
\(12\) 0.492189 0.0118402
\(13\) −51.6125 −1.10113 −0.550567 0.834791i \(-0.685588\pi\)
−0.550567 + 0.834791i \(0.685588\pi\)
\(14\) −18.9109 −0.361011
\(15\) 0 0
\(16\) −57.8953 −0.904614
\(17\) 67.5078 0.963121 0.481560 0.876413i \(-0.340070\pi\)
0.481560 + 0.876413i \(0.340070\pi\)
\(18\) −71.6125 −0.937735
\(19\) −50.9109 −0.614725 −0.307362 0.951593i \(-0.599446\pi\)
−0.307362 + 0.951593i \(0.599446\pi\)
\(20\) 0 0
\(21\) 4.91093 0.0510311
\(22\) 10.8485 0.105132
\(23\) −0.507811 −0.00460373 −0.00230187 0.999997i \(-0.500733\pi\)
−0.00230187 + 0.999997i \(0.500733\pi\)
\(24\) 16.4922 0.140269
\(25\) 0 0
\(26\) −139.434 −1.05174
\(27\) 37.5391 0.267570
\(28\) 4.91093 0.0331457
\(29\) −120.058 −0.768765 −0.384382 0.923174i \(-0.625586\pi\)
−0.384382 + 0.923174i \(0.625586\pi\)
\(30\) 0 0
\(31\) −292.303 −1.69352 −0.846761 0.531973i \(-0.821451\pi\)
−0.846761 + 0.531973i \(0.821451\pi\)
\(32\) 31.6547 0.174869
\(33\) −2.81721 −0.0148610
\(34\) 182.377 0.919921
\(35\) 0 0
\(36\) 18.5969 0.0860966
\(37\) 144.989 0.644218 0.322109 0.946703i \(-0.395608\pi\)
0.322109 + 0.946703i \(0.395608\pi\)
\(38\) −137.539 −0.587152
\(39\) 36.2094 0.148670
\(40\) 0 0
\(41\) −57.2047 −0.217899 −0.108950 0.994047i \(-0.534749\pi\)
−0.108950 + 0.994047i \(0.534749\pi\)
\(42\) 13.2672 0.0487422
\(43\) 283.020 1.00373 0.501863 0.864947i \(-0.332648\pi\)
0.501863 + 0.864947i \(0.332648\pi\)
\(44\) −2.81721 −0.00965250
\(45\) 0 0
\(46\) −1.37188 −0.00439724
\(47\) 233.769 0.725504 0.362752 0.931886i \(-0.381837\pi\)
0.362752 + 0.931886i \(0.381837\pi\)
\(48\) 40.6172 0.122137
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) −47.3609 −0.130036
\(52\) 36.2094 0.0965642
\(53\) 406.334 1.05310 0.526550 0.850144i \(-0.323485\pi\)
0.526550 + 0.850144i \(0.323485\pi\)
\(54\) 101.414 0.255569
\(55\) 0 0
\(56\) 164.555 0.392670
\(57\) 35.7172 0.0829975
\(58\) −324.344 −0.734283
\(59\) −577.328 −1.27393 −0.636964 0.770894i \(-0.719810\pi\)
−0.636964 + 0.770894i \(0.719810\pi\)
\(60\) 0 0
\(61\) 322.116 0.676110 0.338055 0.941126i \(-0.390231\pi\)
0.338055 + 0.941126i \(0.390231\pi\)
\(62\) −789.675 −1.61756
\(63\) 185.555 0.371074
\(64\) 548.680 1.07164
\(65\) 0 0
\(66\) −7.61086 −0.0141944
\(67\) −985.459 −1.79691 −0.898455 0.439065i \(-0.855310\pi\)
−0.898455 + 0.439065i \(0.855310\pi\)
\(68\) −47.3609 −0.0844611
\(69\) 0.356261 0.000621576 0
\(70\) 0 0
\(71\) 1033.57 1.72764 0.863821 0.503799i \(-0.168065\pi\)
0.863821 + 0.503799i \(0.168065\pi\)
\(72\) 623.141 1.01997
\(73\) −692.720 −1.11064 −0.555320 0.831637i \(-0.687404\pi\)
−0.555320 + 0.831637i \(0.687404\pi\)
\(74\) 391.697 0.615322
\(75\) 0 0
\(76\) 35.7172 0.0539084
\(77\) −28.1093 −0.0416020
\(78\) 97.8219 0.142002
\(79\) −428.236 −0.609877 −0.304939 0.952372i \(-0.598636\pi\)
−0.304939 + 0.952372i \(0.598636\pi\)
\(80\) 0 0
\(81\) 689.375 0.945645
\(82\) −154.542 −0.208126
\(83\) 537.592 0.710945 0.355472 0.934687i \(-0.384320\pi\)
0.355472 + 0.934687i \(0.384320\pi\)
\(84\) −3.44533 −0.00447519
\(85\) 0 0
\(86\) 764.597 0.958705
\(87\) 84.2280 0.103795
\(88\) −94.3985 −0.114351
\(89\) −802.073 −0.955277 −0.477638 0.878557i \(-0.658507\pi\)
−0.477638 + 0.878557i \(0.658507\pi\)
\(90\) 0 0
\(91\) 361.287 0.416189
\(92\) 0.356261 0.000403725 0
\(93\) 205.069 0.228652
\(94\) 631.541 0.692962
\(95\) 0 0
\(96\) −22.2077 −0.0236101
\(97\) −1752.82 −1.83477 −0.917384 0.398004i \(-0.869703\pi\)
−0.917384 + 0.398004i \(0.869703\pi\)
\(98\) 132.377 0.136449
\(99\) −106.445 −0.108062
\(100\) 0 0
\(101\) −1987.85 −1.95840 −0.979200 0.202896i \(-0.934965\pi\)
−0.979200 + 0.202896i \(0.934965\pi\)
\(102\) −127.948 −0.124204
\(103\) 389.122 0.372246 0.186123 0.982526i \(-0.440408\pi\)
0.186123 + 0.982526i \(0.440408\pi\)
\(104\) 1213.30 1.14398
\(105\) 0 0
\(106\) 1097.74 1.00586
\(107\) 508.595 0.459512 0.229756 0.973248i \(-0.426207\pi\)
0.229756 + 0.973248i \(0.426207\pi\)
\(108\) −26.3360 −0.0234646
\(109\) 344.130 0.302400 0.151200 0.988503i \(-0.451686\pi\)
0.151200 + 0.988503i \(0.451686\pi\)
\(110\) 0 0
\(111\) −101.719 −0.0869795
\(112\) 405.267 0.341912
\(113\) 1218.12 1.01408 0.507040 0.861923i \(-0.330740\pi\)
0.507040 + 0.861923i \(0.330740\pi\)
\(114\) 96.4922 0.0792748
\(115\) 0 0
\(116\) 84.2280 0.0674170
\(117\) 1368.13 1.08106
\(118\) −1559.69 −1.21679
\(119\) −472.555 −0.364025
\(120\) 0 0
\(121\) −1314.87 −0.987885
\(122\) 870.215 0.645784
\(123\) 40.1327 0.0294198
\(124\) 205.069 0.148514
\(125\) 0 0
\(126\) 501.287 0.354430
\(127\) 281.652 0.196792 0.0983958 0.995147i \(-0.468629\pi\)
0.0983958 + 0.995147i \(0.468629\pi\)
\(128\) 1229.05 0.848704
\(129\) −198.556 −0.135519
\(130\) 0 0
\(131\) −699.706 −0.466669 −0.233334 0.972397i \(-0.574964\pi\)
−0.233334 + 0.972397i \(0.574964\pi\)
\(132\) 1.97645 0.00130324
\(133\) 356.377 0.232344
\(134\) −2662.28 −1.71631
\(135\) 0 0
\(136\) −1586.96 −1.00059
\(137\) −1588.77 −0.990789 −0.495394 0.868668i \(-0.664976\pi\)
−0.495394 + 0.868668i \(0.664976\pi\)
\(138\) 0.962460 0.000593696 0
\(139\) 2564.09 1.56463 0.782315 0.622884i \(-0.214039\pi\)
0.782315 + 0.622884i \(0.214039\pi\)
\(140\) 0 0
\(141\) −164.003 −0.0979544
\(142\) 2792.26 1.65015
\(143\) −207.256 −0.121200
\(144\) 1534.68 0.888124
\(145\) 0 0
\(146\) −1871.43 −1.06082
\(147\) −34.3765 −0.0192880
\(148\) −101.719 −0.0564948
\(149\) −3386.03 −1.86171 −0.930854 0.365390i \(-0.880935\pi\)
−0.930854 + 0.365390i \(0.880935\pi\)
\(150\) 0 0
\(151\) −2301.98 −1.24061 −0.620306 0.784360i \(-0.712992\pi\)
−0.620306 + 0.784360i \(0.712992\pi\)
\(152\) 1196.80 0.638643
\(153\) −1789.48 −0.945564
\(154\) −75.9392 −0.0397360
\(155\) 0 0
\(156\) −25.4031 −0.0130377
\(157\) −587.325 −0.298558 −0.149279 0.988795i \(-0.547695\pi\)
−0.149279 + 0.988795i \(0.547695\pi\)
\(158\) −1156.91 −0.582522
\(159\) −285.069 −0.142185
\(160\) 0 0
\(161\) 3.55467 0.00174005
\(162\) 1862.39 0.903229
\(163\) −914.189 −0.439293 −0.219647 0.975579i \(-0.570490\pi\)
−0.219647 + 0.975579i \(0.570490\pi\)
\(164\) 40.1327 0.0191087
\(165\) 0 0
\(166\) 1452.34 0.679056
\(167\) −3316.66 −1.53683 −0.768416 0.639951i \(-0.778955\pi\)
−0.768416 + 0.639951i \(0.778955\pi\)
\(168\) −115.445 −0.0530167
\(169\) 466.850 0.212494
\(170\) 0 0
\(171\) 1349.54 0.603519
\(172\) −198.556 −0.0880220
\(173\) −1542.16 −0.677737 −0.338868 0.940834i \(-0.610044\pi\)
−0.338868 + 0.940834i \(0.610044\pi\)
\(174\) 227.547 0.0991397
\(175\) 0 0
\(176\) −232.486 −0.0995697
\(177\) 405.031 0.172000
\(178\) −2166.85 −0.912429
\(179\) −550.755 −0.229974 −0.114987 0.993367i \(-0.536683\pi\)
−0.114987 + 0.993367i \(0.536683\pi\)
\(180\) 0 0
\(181\) −3562.15 −1.46283 −0.731416 0.681931i \(-0.761140\pi\)
−0.731416 + 0.681931i \(0.761140\pi\)
\(182\) 976.041 0.397522
\(183\) −225.984 −0.0912854
\(184\) 11.9375 0.00478285
\(185\) 0 0
\(186\) 554.006 0.218396
\(187\) 271.086 0.106009
\(188\) −164.003 −0.0636232
\(189\) −262.773 −0.101132
\(190\) 0 0
\(191\) 3436.00 1.30168 0.650838 0.759217i \(-0.274418\pi\)
0.650838 + 0.759217i \(0.274418\pi\)
\(192\) −384.933 −0.144688
\(193\) −1047.12 −0.390534 −0.195267 0.980750i \(-0.562557\pi\)
−0.195267 + 0.980750i \(0.562557\pi\)
\(194\) −4735.37 −1.75247
\(195\) 0 0
\(196\) −34.3765 −0.0125279
\(197\) 3205.61 1.15934 0.579670 0.814851i \(-0.303181\pi\)
0.579670 + 0.814851i \(0.303181\pi\)
\(198\) −287.569 −0.103215
\(199\) 22.0532 0.00785581 0.00392791 0.999992i \(-0.498750\pi\)
0.00392791 + 0.999992i \(0.498750\pi\)
\(200\) 0 0
\(201\) 691.361 0.242611
\(202\) −5370.30 −1.87056
\(203\) 840.405 0.290566
\(204\) 33.2266 0.0114036
\(205\) 0 0
\(206\) 1051.24 0.355549
\(207\) 13.4609 0.00451981
\(208\) 2988.12 0.996101
\(209\) −204.439 −0.0676619
\(210\) 0 0
\(211\) 2362.52 0.770819 0.385410 0.922746i \(-0.374060\pi\)
0.385410 + 0.922746i \(0.374060\pi\)
\(212\) −285.069 −0.0923519
\(213\) −725.116 −0.233259
\(214\) 1374.00 0.438901
\(215\) 0 0
\(216\) −882.461 −0.277981
\(217\) 2046.12 0.640091
\(218\) 929.688 0.288837
\(219\) 485.986 0.149954
\(220\) 0 0
\(221\) −3484.25 −1.06052
\(222\) −274.800 −0.0830781
\(223\) 1428.67 0.429016 0.214508 0.976722i \(-0.431185\pi\)
0.214508 + 0.976722i \(0.431185\pi\)
\(224\) −221.583 −0.0660943
\(225\) 0 0
\(226\) 3290.82 0.968594
\(227\) −5979.38 −1.74831 −0.874153 0.485651i \(-0.838582\pi\)
−0.874153 + 0.485651i \(0.838582\pi\)
\(228\) −25.0578 −0.00727849
\(229\) 6377.77 1.84042 0.920208 0.391430i \(-0.128020\pi\)
0.920208 + 0.391430i \(0.128020\pi\)
\(230\) 0 0
\(231\) 19.7205 0.00561693
\(232\) 2822.30 0.798676
\(233\) 4947.18 1.39099 0.695495 0.718531i \(-0.255185\pi\)
0.695495 + 0.718531i \(0.255185\pi\)
\(234\) 3696.10 1.03257
\(235\) 0 0
\(236\) 405.031 0.111717
\(237\) 300.434 0.0823430
\(238\) −1276.64 −0.347698
\(239\) −348.213 −0.0942427 −0.0471213 0.998889i \(-0.515005\pi\)
−0.0471213 + 0.998889i \(0.515005\pi\)
\(240\) 0 0
\(241\) 4702.23 1.25683 0.628417 0.777876i \(-0.283703\pi\)
0.628417 + 0.777876i \(0.283703\pi\)
\(242\) −3552.22 −0.943575
\(243\) −1497.19 −0.395247
\(244\) −225.984 −0.0592916
\(245\) 0 0
\(246\) 108.421 0.0281003
\(247\) 2627.64 0.676894
\(248\) 6871.41 1.75941
\(249\) −377.154 −0.0959887
\(250\) 0 0
\(251\) −2431.64 −0.611489 −0.305745 0.952114i \(-0.598905\pi\)
−0.305745 + 0.952114i \(0.598905\pi\)
\(252\) −130.178 −0.0325415
\(253\) −2.03917 −0.000506727 0
\(254\) 760.899 0.187965
\(255\) 0 0
\(256\) −1069.07 −0.261003
\(257\) 1631.76 0.396055 0.198028 0.980196i \(-0.436546\pi\)
0.198028 + 0.980196i \(0.436546\pi\)
\(258\) −536.412 −0.129440
\(259\) −1014.92 −0.243491
\(260\) 0 0
\(261\) 3182.47 0.754751
\(262\) −1890.30 −0.445737
\(263\) 3563.67 0.835534 0.417767 0.908554i \(-0.362813\pi\)
0.417767 + 0.908554i \(0.362813\pi\)
\(264\) 66.2264 0.0154392
\(265\) 0 0
\(266\) 962.773 0.221923
\(267\) 562.704 0.128977
\(268\) 691.361 0.157581
\(269\) 791.631 0.179430 0.0897149 0.995967i \(-0.471404\pi\)
0.0897149 + 0.995967i \(0.471404\pi\)
\(270\) 0 0
\(271\) 7823.17 1.75359 0.876796 0.480862i \(-0.159676\pi\)
0.876796 + 0.480862i \(0.159676\pi\)
\(272\) −3908.39 −0.871253
\(273\) −253.466 −0.0561921
\(274\) −4292.17 −0.946348
\(275\) 0 0
\(276\) −0.249939 −5.45093e−5 0
\(277\) 1554.16 0.337114 0.168557 0.985692i \(-0.446089\pi\)
0.168557 + 0.985692i \(0.446089\pi\)
\(278\) 6927.05 1.49445
\(279\) 7748.32 1.66265
\(280\) 0 0
\(281\) −5043.72 −1.07076 −0.535379 0.844612i \(-0.679831\pi\)
−0.535379 + 0.844612i \(0.679831\pi\)
\(282\) −443.065 −0.0935608
\(283\) 5897.15 1.23869 0.619345 0.785119i \(-0.287398\pi\)
0.619345 + 0.785119i \(0.287398\pi\)
\(284\) −725.116 −0.151506
\(285\) 0 0
\(286\) −559.916 −0.115764
\(287\) 400.433 0.0823582
\(288\) −839.097 −0.171681
\(289\) −355.696 −0.0723988
\(290\) 0 0
\(291\) 1229.72 0.247722
\(292\) 485.986 0.0973979
\(293\) −8592.25 −1.71319 −0.856595 0.515990i \(-0.827424\pi\)
−0.856595 + 0.515990i \(0.827424\pi\)
\(294\) −92.8704 −0.0184228
\(295\) 0 0
\(296\) −3408.37 −0.669283
\(297\) 150.743 0.0294511
\(298\) −9147.58 −1.77820
\(299\) 26.2094 0.00506932
\(300\) 0 0
\(301\) −1981.14 −0.379373
\(302\) −6218.94 −1.18497
\(303\) 1394.60 0.264415
\(304\) 2947.50 0.556089
\(305\) 0 0
\(306\) −4834.40 −0.903152
\(307\) 3682.20 0.684542 0.342271 0.939601i \(-0.388804\pi\)
0.342271 + 0.939601i \(0.388804\pi\)
\(308\) 19.7205 0.00364830
\(309\) −272.993 −0.0502590
\(310\) 0 0
\(311\) 6866.18 1.25191 0.625957 0.779858i \(-0.284709\pi\)
0.625957 + 0.779858i \(0.284709\pi\)
\(312\) −851.203 −0.154455
\(313\) −2958.60 −0.534281 −0.267140 0.963658i \(-0.586079\pi\)
−0.267140 + 0.963658i \(0.586079\pi\)
\(314\) −1586.69 −0.285167
\(315\) 0 0
\(316\) 300.434 0.0534834
\(317\) −1585.21 −0.280866 −0.140433 0.990090i \(-0.544849\pi\)
−0.140433 + 0.990090i \(0.544849\pi\)
\(318\) −770.131 −0.135808
\(319\) −482.107 −0.0846169
\(320\) 0 0
\(321\) −356.811 −0.0620413
\(322\) 9.60317 0.00166200
\(323\) −3436.89 −0.592054
\(324\) −483.639 −0.0829286
\(325\) 0 0
\(326\) −2469.74 −0.419589
\(327\) −241.428 −0.0408288
\(328\) 1344.76 0.226377
\(329\) −1636.38 −0.274215
\(330\) 0 0
\(331\) 6045.84 1.00396 0.501978 0.864880i \(-0.332606\pi\)
0.501978 + 0.864880i \(0.332606\pi\)
\(332\) −377.154 −0.0623465
\(333\) −3843.34 −0.632474
\(334\) −8960.16 −1.46790
\(335\) 0 0
\(336\) −284.320 −0.0461635
\(337\) 9205.64 1.48802 0.744010 0.668168i \(-0.232921\pi\)
0.744010 + 0.668168i \(0.232921\pi\)
\(338\) 1261.22 0.202963
\(339\) −854.586 −0.136917
\(340\) 0 0
\(341\) −1173.78 −0.186404
\(342\) 3645.86 0.576449
\(343\) −343.000 −0.0539949
\(344\) −6653.19 −1.04278
\(345\) 0 0
\(346\) −4166.25 −0.647338
\(347\) 3092.28 0.478393 0.239196 0.970971i \(-0.423116\pi\)
0.239196 + 0.970971i \(0.423116\pi\)
\(348\) −59.0912 −0.00910236
\(349\) −5231.61 −0.802412 −0.401206 0.915988i \(-0.631409\pi\)
−0.401206 + 0.915988i \(0.631409\pi\)
\(350\) 0 0
\(351\) −1937.48 −0.294630
\(352\) 127.113 0.0192476
\(353\) −9013.71 −1.35907 −0.679534 0.733644i \(-0.737818\pi\)
−0.679534 + 0.733644i \(0.737818\pi\)
\(354\) 1094.22 0.164285
\(355\) 0 0
\(356\) 562.704 0.0837732
\(357\) 331.526 0.0491491
\(358\) −1487.90 −0.219659
\(359\) −4779.38 −0.702635 −0.351317 0.936256i \(-0.614266\pi\)
−0.351317 + 0.936256i \(0.614266\pi\)
\(360\) 0 0
\(361\) −4267.08 −0.622114
\(362\) −9623.38 −1.39722
\(363\) 922.466 0.133380
\(364\) −253.466 −0.0364978
\(365\) 0 0
\(366\) −610.510 −0.0871909
\(367\) −175.769 −0.0250001 −0.0125001 0.999922i \(-0.503979\pi\)
−0.0125001 + 0.999922i \(0.503979\pi\)
\(368\) 29.3999 0.00416460
\(369\) 1516.37 0.213927
\(370\) 0 0
\(371\) −2844.34 −0.398034
\(372\) −143.868 −0.0200517
\(373\) −7982.98 −1.10816 −0.554079 0.832464i \(-0.686930\pi\)
−0.554079 + 0.832464i \(0.686930\pi\)
\(374\) 732.355 0.101254
\(375\) 0 0
\(376\) −5495.39 −0.753732
\(377\) 6196.48 0.846512
\(378\) −709.899 −0.0965959
\(379\) 12663.1 1.71626 0.858129 0.513434i \(-0.171627\pi\)
0.858129 + 0.513434i \(0.171627\pi\)
\(380\) 0 0
\(381\) −197.596 −0.0265700
\(382\) 9282.56 1.24329
\(383\) −4678.68 −0.624202 −0.312101 0.950049i \(-0.601033\pi\)
−0.312101 + 0.950049i \(0.601033\pi\)
\(384\) −862.258 −0.114588
\(385\) 0 0
\(386\) −2828.85 −0.373017
\(387\) −7502.25 −0.985428
\(388\) 1229.72 0.160900
\(389\) −50.2546 −0.00655015 −0.00327508 0.999995i \(-0.501042\pi\)
−0.00327508 + 0.999995i \(0.501042\pi\)
\(390\) 0 0
\(391\) −34.2812 −0.00443395
\(392\) −1151.88 −0.148415
\(393\) 490.887 0.0630076
\(394\) 8660.15 1.10734
\(395\) 0 0
\(396\) 74.6780 0.00947654
\(397\) 11059.9 1.39819 0.699095 0.715029i \(-0.253587\pi\)
0.699095 + 0.715029i \(0.253587\pi\)
\(398\) 59.5780 0.00750345
\(399\) −250.020 −0.0313701
\(400\) 0 0
\(401\) −13667.8 −1.70209 −0.851046 0.525092i \(-0.824031\pi\)
−0.851046 + 0.525092i \(0.824031\pi\)
\(402\) 1867.75 0.231729
\(403\) 15086.5 1.86479
\(404\) 1394.60 0.171742
\(405\) 0 0
\(406\) 2270.41 0.277533
\(407\) 582.221 0.0709082
\(408\) 1113.35 0.135096
\(409\) −10990.5 −1.32872 −0.664359 0.747414i \(-0.731295\pi\)
−0.664359 + 0.747414i \(0.731295\pi\)
\(410\) 0 0
\(411\) 1114.62 0.133772
\(412\) −272.993 −0.0326442
\(413\) 4041.30 0.481499
\(414\) 36.3656 0.00431708
\(415\) 0 0
\(416\) −1633.78 −0.192554
\(417\) −1798.87 −0.211249
\(418\) −552.305 −0.0646271
\(419\) 1115.39 0.130049 0.0650246 0.997884i \(-0.479287\pi\)
0.0650246 + 0.997884i \(0.479287\pi\)
\(420\) 0 0
\(421\) −2395.26 −0.277287 −0.138643 0.990342i \(-0.544274\pi\)
−0.138643 + 0.990342i \(0.544274\pi\)
\(422\) 6382.50 0.736245
\(423\) −6196.70 −0.712278
\(424\) −9552.03 −1.09407
\(425\) 0 0
\(426\) −1958.95 −0.222796
\(427\) −2254.81 −0.255545
\(428\) −356.811 −0.0402970
\(429\) 145.403 0.0163639
\(430\) 0 0
\(431\) 1684.62 0.188272 0.0941360 0.995559i \(-0.469991\pi\)
0.0941360 + 0.995559i \(0.469991\pi\)
\(432\) −2173.34 −0.242048
\(433\) 13355.7 1.48230 0.741150 0.671340i \(-0.234281\pi\)
0.741150 + 0.671340i \(0.234281\pi\)
\(434\) 5527.72 0.611381
\(435\) 0 0
\(436\) −241.428 −0.0265191
\(437\) 25.8531 0.00283003
\(438\) 1312.92 0.143228
\(439\) 13817.4 1.50220 0.751101 0.660188i \(-0.229523\pi\)
0.751101 + 0.660188i \(0.229523\pi\)
\(440\) 0 0
\(441\) −1298.88 −0.140253
\(442\) −9412.91 −1.01296
\(443\) −6305.19 −0.676227 −0.338114 0.941105i \(-0.609789\pi\)
−0.338114 + 0.941105i \(0.609789\pi\)
\(444\) 71.3621 0.00762769
\(445\) 0 0
\(446\) 3859.63 0.409773
\(447\) 2375.51 0.251360
\(448\) −3840.76 −0.405042
\(449\) 5446.85 0.572501 0.286250 0.958155i \(-0.407591\pi\)
0.286250 + 0.958155i \(0.407591\pi\)
\(450\) 0 0
\(451\) −229.712 −0.0239839
\(452\) −854.586 −0.0889300
\(453\) 1614.98 0.167502
\(454\) −16153.7 −1.66989
\(455\) 0 0
\(456\) −839.633 −0.0862268
\(457\) −1221.02 −0.124982 −0.0624910 0.998046i \(-0.519904\pi\)
−0.0624910 + 0.998046i \(0.519904\pi\)
\(458\) 17230.0 1.75787
\(459\) 2534.18 0.257702
\(460\) 0 0
\(461\) 9967.46 1.00701 0.503504 0.863993i \(-0.332044\pi\)
0.503504 + 0.863993i \(0.332044\pi\)
\(462\) 53.2760 0.00536499
\(463\) 6309.54 0.633324 0.316662 0.948538i \(-0.397438\pi\)
0.316662 + 0.948538i \(0.397438\pi\)
\(464\) 6950.79 0.695436
\(465\) 0 0
\(466\) 13365.1 1.32860
\(467\) −7784.79 −0.771386 −0.385693 0.922627i \(-0.626038\pi\)
−0.385693 + 0.922627i \(0.626038\pi\)
\(468\) −959.831 −0.0948039
\(469\) 6898.22 0.679168
\(470\) 0 0
\(471\) 412.045 0.0403100
\(472\) 13571.7 1.32349
\(473\) 1136.50 0.110479
\(474\) 811.641 0.0786496
\(475\) 0 0
\(476\) 331.526 0.0319233
\(477\) −10771.0 −1.03390
\(478\) −940.718 −0.0900156
\(479\) −4425.28 −0.422122 −0.211061 0.977473i \(-0.567692\pi\)
−0.211061 + 0.977473i \(0.567692\pi\)
\(480\) 0 0
\(481\) −7483.25 −0.709369
\(482\) 12703.4 1.20046
\(483\) −2.49382 −0.000234934 0
\(484\) 922.466 0.0866328
\(485\) 0 0
\(486\) −4044.76 −0.377519
\(487\) −13075.3 −1.21663 −0.608315 0.793695i \(-0.708154\pi\)
−0.608315 + 0.793695i \(0.708154\pi\)
\(488\) −7572.23 −0.702416
\(489\) 641.360 0.0593115
\(490\) 0 0
\(491\) 11455.7 1.05293 0.526463 0.850198i \(-0.323518\pi\)
0.526463 + 0.850198i \(0.323518\pi\)
\(492\) −28.1556 −0.00257998
\(493\) −8104.84 −0.740413
\(494\) 7098.73 0.646533
\(495\) 0 0
\(496\) 16923.0 1.53198
\(497\) −7235.01 −0.652987
\(498\) −1018.91 −0.0916833
\(499\) 5521.10 0.495307 0.247654 0.968849i \(-0.420340\pi\)
0.247654 + 0.968849i \(0.420340\pi\)
\(500\) 0 0
\(501\) 2326.84 0.207496
\(502\) −6569.23 −0.584062
\(503\) 11491.6 1.01866 0.509328 0.860573i \(-0.329894\pi\)
0.509328 + 0.860573i \(0.329894\pi\)
\(504\) −4361.98 −0.385512
\(505\) 0 0
\(506\) −5.50896 −0.000483998 0
\(507\) −327.524 −0.0286901
\(508\) −197.596 −0.0172577
\(509\) −9207.84 −0.801828 −0.400914 0.916116i \(-0.631307\pi\)
−0.400914 + 0.916116i \(0.631307\pi\)
\(510\) 0 0
\(511\) 4849.04 0.419783
\(512\) −12720.6 −1.09800
\(513\) −1911.15 −0.164482
\(514\) 4408.29 0.378291
\(515\) 0 0
\(516\) 139.300 0.0118843
\(517\) 938.727 0.0798552
\(518\) −2741.88 −0.232570
\(519\) 1081.92 0.0915051
\(520\) 0 0
\(521\) −11598.0 −0.975271 −0.487636 0.873047i \(-0.662141\pi\)
−0.487636 + 0.873047i \(0.662141\pi\)
\(522\) 8597.64 0.720898
\(523\) −4596.93 −0.384340 −0.192170 0.981362i \(-0.561552\pi\)
−0.192170 + 0.981362i \(0.561552\pi\)
\(524\) 490.887 0.0409246
\(525\) 0 0
\(526\) 9627.49 0.798058
\(527\) −19732.7 −1.63107
\(528\) 163.103 0.0134435
\(529\) −12166.7 −0.999979
\(530\) 0 0
\(531\) 15303.7 1.25070
\(532\) −250.020 −0.0203755
\(533\) 2952.48 0.239936
\(534\) 1520.18 0.123192
\(535\) 0 0
\(536\) 23166.0 1.86683
\(537\) 386.389 0.0310501
\(538\) 2138.64 0.171382
\(539\) 196.765 0.0157241
\(540\) 0 0
\(541\) −8427.65 −0.669747 −0.334874 0.942263i \(-0.608694\pi\)
−0.334874 + 0.942263i \(0.608694\pi\)
\(542\) 21134.8 1.67494
\(543\) 2499.07 0.197505
\(544\) 2136.94 0.168420
\(545\) 0 0
\(546\) −684.753 −0.0536717
\(547\) −12864.6 −1.00557 −0.502787 0.864410i \(-0.667692\pi\)
−0.502787 + 0.864410i \(0.667692\pi\)
\(548\) 1114.62 0.0868875
\(549\) −8538.58 −0.663785
\(550\) 0 0
\(551\) 6112.26 0.472579
\(552\) −8.37491 −0.000645760 0
\(553\) 2997.65 0.230512
\(554\) 4198.67 0.321993
\(555\) 0 0
\(556\) −1798.87 −0.137211
\(557\) 19219.4 1.46203 0.731016 0.682360i \(-0.239046\pi\)
0.731016 + 0.682360i \(0.239046\pi\)
\(558\) 20932.6 1.58807
\(559\) −14607.4 −1.10524
\(560\) 0 0
\(561\) −190.184 −0.0143129
\(562\) −13625.9 −1.02273
\(563\) −17253.3 −1.29155 −0.645774 0.763529i \(-0.723465\pi\)
−0.645774 + 0.763529i \(0.723465\pi\)
\(564\) 115.058 0.00859013
\(565\) 0 0
\(566\) 15931.5 1.18313
\(567\) −4825.62 −0.357420
\(568\) −24297.0 −1.79486
\(569\) −6242.80 −0.459950 −0.229975 0.973197i \(-0.573864\pi\)
−0.229975 + 0.973197i \(0.573864\pi\)
\(570\) 0 0
\(571\) 5904.17 0.432718 0.216359 0.976314i \(-0.430582\pi\)
0.216359 + 0.976314i \(0.430582\pi\)
\(572\) 145.403 0.0106287
\(573\) −2410.57 −0.175747
\(574\) 1081.79 0.0786642
\(575\) 0 0
\(576\) −14544.3 −1.05210
\(577\) −11390.2 −0.821806 −0.410903 0.911679i \(-0.634786\pi\)
−0.410903 + 0.911679i \(0.634786\pi\)
\(578\) −960.934 −0.0691515
\(579\) 734.617 0.0527282
\(580\) 0 0
\(581\) −3763.15 −0.268712
\(582\) 3322.15 0.236611
\(583\) 1631.68 0.115913
\(584\) 16284.3 1.15385
\(585\) 0 0
\(586\) −23212.5 −1.63635
\(587\) 20459.5 1.43859 0.719295 0.694704i \(-0.244465\pi\)
0.719295 + 0.694704i \(0.244465\pi\)
\(588\) 24.1173 0.00169146
\(589\) 14881.4 1.04105
\(590\) 0 0
\(591\) −2248.93 −0.156529
\(592\) −8394.19 −0.582768
\(593\) −20051.1 −1.38853 −0.694266 0.719719i \(-0.744271\pi\)
−0.694266 + 0.719719i \(0.744271\pi\)
\(594\) 407.241 0.0281301
\(595\) 0 0
\(596\) 2375.51 0.163263
\(597\) −15.4717 −0.00106066
\(598\) 70.8062 0.00484194
\(599\) 10578.4 0.721572 0.360786 0.932649i \(-0.382508\pi\)
0.360786 + 0.932649i \(0.382508\pi\)
\(600\) 0 0
\(601\) −4619.46 −0.313530 −0.156765 0.987636i \(-0.550107\pi\)
−0.156765 + 0.987636i \(0.550107\pi\)
\(602\) −5352.18 −0.362356
\(603\) 26122.4 1.76415
\(604\) 1614.98 0.108796
\(605\) 0 0
\(606\) 3767.60 0.252555
\(607\) −5724.50 −0.382785 −0.191392 0.981514i \(-0.561300\pi\)
−0.191392 + 0.981514i \(0.561300\pi\)
\(608\) −1611.57 −0.107496
\(609\) −589.596 −0.0392309
\(610\) 0 0
\(611\) −12065.4 −0.798876
\(612\) 1255.43 0.0829214
\(613\) 19286.4 1.27075 0.635375 0.772204i \(-0.280846\pi\)
0.635375 + 0.772204i \(0.280846\pi\)
\(614\) 9947.70 0.653838
\(615\) 0 0
\(616\) 660.789 0.0432207
\(617\) −6864.84 −0.447922 −0.223961 0.974598i \(-0.571899\pi\)
−0.223961 + 0.974598i \(0.571899\pi\)
\(618\) −737.508 −0.0480047
\(619\) −17559.4 −1.14018 −0.570090 0.821582i \(-0.693092\pi\)
−0.570090 + 0.821582i \(0.693092\pi\)
\(620\) 0 0
\(621\) −19.0627 −0.00123182
\(622\) 18549.4 1.19576
\(623\) 5614.51 0.361061
\(624\) −2096.35 −0.134489
\(625\) 0 0
\(626\) −7992.84 −0.510317
\(627\) 143.427 0.00913542
\(628\) 412.045 0.0261821
\(629\) 9787.89 0.620459
\(630\) 0 0
\(631\) −24780.6 −1.56339 −0.781694 0.623662i \(-0.785644\pi\)
−0.781694 + 0.623662i \(0.785644\pi\)
\(632\) 10066.9 0.633607
\(633\) −1657.46 −0.104073
\(634\) −4282.55 −0.268268
\(635\) 0 0
\(636\) 199.993 0.0124690
\(637\) −2529.01 −0.157305
\(638\) −1302.44 −0.0808215
\(639\) −27397.8 −1.69615
\(640\) 0 0
\(641\) −21724.3 −1.33863 −0.669313 0.742980i \(-0.733412\pi\)
−0.669313 + 0.742980i \(0.733412\pi\)
\(642\) −963.947 −0.0592585
\(643\) 18736.1 1.14911 0.574555 0.818466i \(-0.305175\pi\)
0.574555 + 0.818466i \(0.305175\pi\)
\(644\) −2.49382 −0.000152594 0
\(645\) 0 0
\(646\) −9284.96 −0.565498
\(647\) 25687.8 1.56088 0.780442 0.625228i \(-0.214994\pi\)
0.780442 + 0.625228i \(0.214994\pi\)
\(648\) −16205.7 −0.982438
\(649\) −2318.33 −0.140219
\(650\) 0 0
\(651\) −1435.48 −0.0864224
\(652\) 641.360 0.0385239
\(653\) −15450.7 −0.925929 −0.462964 0.886377i \(-0.653214\pi\)
−0.462964 + 0.886377i \(0.653214\pi\)
\(654\) −652.234 −0.0389975
\(655\) 0 0
\(656\) 3311.88 0.197115
\(657\) 18362.5 1.09039
\(658\) −4420.78 −0.261915
\(659\) −1402.85 −0.0829246 −0.0414623 0.999140i \(-0.513202\pi\)
−0.0414623 + 0.999140i \(0.513202\pi\)
\(660\) 0 0
\(661\) 6896.75 0.405828 0.202914 0.979197i \(-0.434959\pi\)
0.202914 + 0.979197i \(0.434959\pi\)
\(662\) 16333.2 0.958926
\(663\) 2444.42 0.143187
\(664\) −12637.6 −0.738606
\(665\) 0 0
\(666\) −10383.0 −0.604105
\(667\) 60.9666 0.00353919
\(668\) 2326.84 0.134773
\(669\) −1002.30 −0.0579239
\(670\) 0 0
\(671\) 1293.49 0.0744185
\(672\) 155.454 0.00892377
\(673\) 3869.29 0.221620 0.110810 0.993842i \(-0.464656\pi\)
0.110810 + 0.993842i \(0.464656\pi\)
\(674\) 24869.6 1.42128
\(675\) 0 0
\(676\) −327.524 −0.0186347
\(677\) −711.604 −0.0403976 −0.0201988 0.999796i \(-0.506430\pi\)
−0.0201988 + 0.999796i \(0.506430\pi\)
\(678\) −2308.72 −0.130775
\(679\) 12269.8 0.693477
\(680\) 0 0
\(681\) 4194.91 0.236049
\(682\) −3171.04 −0.178043
\(683\) 13112.0 0.734577 0.367288 0.930107i \(-0.380286\pi\)
0.367288 + 0.930107i \(0.380286\pi\)
\(684\) −946.784 −0.0529257
\(685\) 0 0
\(686\) −926.636 −0.0515731
\(687\) −4474.40 −0.248485
\(688\) −16385.5 −0.907984
\(689\) −20971.9 −1.15960
\(690\) 0 0
\(691\) −12573.5 −0.692211 −0.346105 0.938196i \(-0.612496\pi\)
−0.346105 + 0.938196i \(0.612496\pi\)
\(692\) 1081.92 0.0594343
\(693\) 745.117 0.0408437
\(694\) 8353.98 0.456935
\(695\) 0 0
\(696\) −1980.02 −0.107834
\(697\) −3861.76 −0.209863
\(698\) −14133.5 −0.766421
\(699\) −3470.75 −0.187805
\(700\) 0 0
\(701\) −7489.24 −0.403516 −0.201758 0.979435i \(-0.564665\pi\)
−0.201758 + 0.979435i \(0.564665\pi\)
\(702\) −5234.23 −0.281415
\(703\) −7381.53 −0.396016
\(704\) 2203.29 0.117954
\(705\) 0 0
\(706\) −24351.1 −1.29811
\(707\) 13914.9 0.740206
\(708\) −284.155 −0.0150836
\(709\) 20869.6 1.10547 0.552733 0.833358i \(-0.313585\pi\)
0.552733 + 0.833358i \(0.313585\pi\)
\(710\) 0 0
\(711\) 11351.6 0.598760
\(712\) 18855.0 0.992445
\(713\) 148.435 0.00779652
\(714\) 895.639 0.0469446
\(715\) 0 0
\(716\) 386.389 0.0201676
\(717\) 244.293 0.0127242
\(718\) −12911.8 −0.671119
\(719\) −5889.90 −0.305503 −0.152751 0.988265i \(-0.548813\pi\)
−0.152751 + 0.988265i \(0.548813\pi\)
\(720\) 0 0
\(721\) −2723.85 −0.140696
\(722\) −11527.8 −0.594210
\(723\) −3298.91 −0.169692
\(724\) 2499.07 0.128284
\(725\) 0 0
\(726\) 2492.10 0.127397
\(727\) −24760.2 −1.26314 −0.631571 0.775318i \(-0.717589\pi\)
−0.631571 + 0.775318i \(0.717589\pi\)
\(728\) −8493.08 −0.432382
\(729\) −17562.7 −0.892280
\(730\) 0 0
\(731\) 19106.1 0.966708
\(732\) 158.542 0.00800530
\(733\) 4537.53 0.228646 0.114323 0.993444i \(-0.463530\pi\)
0.114323 + 0.993444i \(0.463530\pi\)
\(734\) −474.850 −0.0238788
\(735\) 0 0
\(736\) −16.0746 −0.000805051 0
\(737\) −3957.23 −0.197784
\(738\) 4096.57 0.204332
\(739\) −24010.0 −1.19516 −0.597579 0.801810i \(-0.703870\pi\)
−0.597579 + 0.801810i \(0.703870\pi\)
\(740\) 0 0
\(741\) −1843.45 −0.0913913
\(742\) −7684.16 −0.380181
\(743\) −25175.4 −1.24306 −0.621532 0.783389i \(-0.713489\pi\)
−0.621532 + 0.783389i \(0.713489\pi\)
\(744\) −4820.72 −0.237549
\(745\) 0 0
\(746\) −21566.5 −1.05845
\(747\) −14250.4 −0.697985
\(748\) −190.184 −0.00929652
\(749\) −3560.17 −0.173679
\(750\) 0 0
\(751\) 24920.0 1.21085 0.605423 0.795904i \(-0.293004\pi\)
0.605423 + 0.795904i \(0.293004\pi\)
\(752\) −13534.1 −0.656301
\(753\) 1705.95 0.0825607
\(754\) 16740.2 0.808543
\(755\) 0 0
\(756\) 184.352 0.00886880
\(757\) 28274.4 1.35753 0.678765 0.734356i \(-0.262516\pi\)
0.678765 + 0.734356i \(0.262516\pi\)
\(758\) 34210.3 1.63928
\(759\) 1.43061 6.84160e−5 0
\(760\) 0 0
\(761\) 12377.9 0.589616 0.294808 0.955557i \(-0.404744\pi\)
0.294808 + 0.955557i \(0.404744\pi\)
\(762\) −533.818 −0.0253782
\(763\) −2408.91 −0.114297
\(764\) −2410.57 −0.114151
\(765\) 0 0
\(766\) −12639.7 −0.596204
\(767\) 29797.3 1.40276
\(768\) 750.019 0.0352396
\(769\) −31845.7 −1.49335 −0.746674 0.665190i \(-0.768350\pi\)
−0.746674 + 0.665190i \(0.768350\pi\)
\(770\) 0 0
\(771\) −1144.78 −0.0534736
\(772\) 734.617 0.0342480
\(773\) −7342.21 −0.341631 −0.170816 0.985303i \(-0.554640\pi\)
−0.170816 + 0.985303i \(0.554640\pi\)
\(774\) −20267.8 −0.941228
\(775\) 0 0
\(776\) 41205.1 1.90615
\(777\) 712.032 0.0328752
\(778\) −135.766 −0.00625636
\(779\) 2912.35 0.133948
\(780\) 0 0
\(781\) 4150.44 0.190159
\(782\) −92.6127 −0.00423507
\(783\) −4506.86 −0.205699
\(784\) −2836.87 −0.129231
\(785\) 0 0
\(786\) 1326.16 0.0601815
\(787\) −36457.4 −1.65129 −0.825646 0.564188i \(-0.809189\pi\)
−0.825646 + 0.564188i \(0.809189\pi\)
\(788\) −2248.93 −0.101669
\(789\) −2500.14 −0.112810
\(790\) 0 0
\(791\) −8526.83 −0.383286
\(792\) 2502.30 0.112267
\(793\) −16625.2 −0.744487
\(794\) 29879.0 1.33548
\(795\) 0 0
\(796\) −15.4717 −0.000688918 0
\(797\) 9358.08 0.415910 0.207955 0.978138i \(-0.433319\pi\)
0.207955 + 0.978138i \(0.433319\pi\)
\(798\) −675.445 −0.0299630
\(799\) 15781.2 0.698747
\(800\) 0 0
\(801\) 21261.2 0.937863
\(802\) −36924.5 −1.62575
\(803\) −2781.70 −0.122247
\(804\) −485.033 −0.0212758
\(805\) 0 0
\(806\) 40757.1 1.78115
\(807\) −555.378 −0.0242258
\(808\) 46730.0 2.03460
\(809\) 28189.6 1.22509 0.612543 0.790437i \(-0.290147\pi\)
0.612543 + 0.790437i \(0.290147\pi\)
\(810\) 0 0
\(811\) −22909.7 −0.991946 −0.495973 0.868338i \(-0.665189\pi\)
−0.495973 + 0.868338i \(0.665189\pi\)
\(812\) −589.596 −0.0254812
\(813\) −5488.44 −0.236763
\(814\) 1572.91 0.0677277
\(815\) 0 0
\(816\) 2741.98 0.117633
\(817\) −14408.8 −0.617015
\(818\) −29691.5 −1.26912
\(819\) −9576.94 −0.408602
\(820\) 0 0
\(821\) 20512.6 0.871980 0.435990 0.899952i \(-0.356398\pi\)
0.435990 + 0.899952i \(0.356398\pi\)
\(822\) 3011.22 0.127772
\(823\) −7882.78 −0.333872 −0.166936 0.985968i \(-0.553387\pi\)
−0.166936 + 0.985968i \(0.553387\pi\)
\(824\) −9147.40 −0.386729
\(825\) 0 0
\(826\) 10917.8 0.459902
\(827\) 19276.5 0.810531 0.405265 0.914199i \(-0.367179\pi\)
0.405265 + 0.914199i \(0.367179\pi\)
\(828\) −9.44369 −0.000396366 0
\(829\) 13771.7 0.576972 0.288486 0.957484i \(-0.406848\pi\)
0.288486 + 0.957484i \(0.406848\pi\)
\(830\) 0 0
\(831\) −1090.34 −0.0455157
\(832\) −28318.7 −1.18002
\(833\) 3307.88 0.137589
\(834\) −4859.76 −0.201774
\(835\) 0 0
\(836\) 143.427 0.00593363
\(837\) −10972.8 −0.453136
\(838\) 3013.31 0.124216
\(839\) 23175.4 0.953640 0.476820 0.879001i \(-0.341789\pi\)
0.476820 + 0.879001i \(0.341789\pi\)
\(840\) 0 0
\(841\) −9975.12 −0.409001
\(842\) −6470.94 −0.264849
\(843\) 3538.48 0.144569
\(844\) −1657.46 −0.0675972
\(845\) 0 0
\(846\) −16740.8 −0.680330
\(847\) 9204.12 0.373385
\(848\) −23524.9 −0.952650
\(849\) −4137.22 −0.167243
\(850\) 0 0
\(851\) −73.6270 −0.00296581
\(852\) 508.714 0.0204557
\(853\) 31431.7 1.26166 0.630832 0.775920i \(-0.282714\pi\)
0.630832 + 0.775920i \(0.282714\pi\)
\(854\) −6091.51 −0.244083
\(855\) 0 0
\(856\) −11956.0 −0.477391
\(857\) −3992.52 −0.159139 −0.0795693 0.996829i \(-0.525354\pi\)
−0.0795693 + 0.996829i \(0.525354\pi\)
\(858\) 392.816 0.0156300
\(859\) 12909.8 0.512778 0.256389 0.966574i \(-0.417467\pi\)
0.256389 + 0.966574i \(0.417467\pi\)
\(860\) 0 0
\(861\) −280.929 −0.0111197
\(862\) 4551.10 0.179827
\(863\) 40128.5 1.58284 0.791419 0.611274i \(-0.209343\pi\)
0.791419 + 0.611274i \(0.209343\pi\)
\(864\) 1188.29 0.0467898
\(865\) 0 0
\(866\) 36081.3 1.41581
\(867\) 249.542 0.00977498
\(868\) −1435.48 −0.0561330
\(869\) −1719.63 −0.0671284
\(870\) 0 0
\(871\) 50862.0 1.97864
\(872\) −8089.73 −0.314166
\(873\) 46463.6 1.80132
\(874\) 69.8438 0.00270309
\(875\) 0 0
\(876\) −340.950 −0.0131502
\(877\) −3222.42 −0.124074 −0.0620372 0.998074i \(-0.519760\pi\)
−0.0620372 + 0.998074i \(0.519760\pi\)
\(878\) 37328.4 1.43482
\(879\) 6028.00 0.231307
\(880\) 0 0
\(881\) −18712.4 −0.715591 −0.357795 0.933800i \(-0.616471\pi\)
−0.357795 + 0.933800i \(0.616471\pi\)
\(882\) −3509.01 −0.133962
\(883\) 17924.0 0.683114 0.341557 0.939861i \(-0.389046\pi\)
0.341557 + 0.939861i \(0.389046\pi\)
\(884\) 2444.42 0.0930029
\(885\) 0 0
\(886\) −17033.9 −0.645896
\(887\) −9873.21 −0.373743 −0.186871 0.982384i \(-0.559835\pi\)
−0.186871 + 0.982384i \(0.559835\pi\)
\(888\) 2391.19 0.0903637
\(889\) −1971.56 −0.0743803
\(890\) 0 0
\(891\) 2768.27 0.104086
\(892\) −1002.30 −0.0376226
\(893\) −11901.4 −0.445985
\(894\) 6417.59 0.240086
\(895\) 0 0
\(896\) −8603.38 −0.320780
\(897\) −18.3875 −0.000684438 0
\(898\) 14715.0 0.546822
\(899\) 35093.3 1.30192
\(900\) 0 0
\(901\) 27430.7 1.01426
\(902\) −620.582 −0.0229081
\(903\) 1389.89 0.0512212
\(904\) −28635.3 −1.05354
\(905\) 0 0
\(906\) 4362.97 0.159989
\(907\) 30129.2 1.10300 0.551502 0.834174i \(-0.314055\pi\)
0.551502 + 0.834174i \(0.314055\pi\)
\(908\) 4194.91 0.153318
\(909\) 52693.5 1.92270
\(910\) 0 0
\(911\) −37831.8 −1.37588 −0.687938 0.725769i \(-0.741484\pi\)
−0.687938 + 0.725769i \(0.741484\pi\)
\(912\) −2067.86 −0.0750807
\(913\) 2158.77 0.0782527
\(914\) −3298.65 −0.119376
\(915\) 0 0
\(916\) −4474.40 −0.161396
\(917\) 4897.94 0.176384
\(918\) 6846.24 0.246143
\(919\) 4771.81 0.171281 0.0856407 0.996326i \(-0.472706\pi\)
0.0856407 + 0.996326i \(0.472706\pi\)
\(920\) 0 0
\(921\) −2583.30 −0.0924240
\(922\) 26927.7 0.961841
\(923\) −53345.3 −1.90236
\(924\) −13.8351 −0.000492578 0
\(925\) 0 0
\(926\) 17045.6 0.604917
\(927\) −10314.8 −0.365460
\(928\) −3800.39 −0.134433
\(929\) −45138.3 −1.59412 −0.797061 0.603899i \(-0.793613\pi\)
−0.797061 + 0.603899i \(0.793613\pi\)
\(930\) 0 0
\(931\) −2494.64 −0.0878178
\(932\) −3470.75 −0.121983
\(933\) −4817.05 −0.169028
\(934\) −21031.1 −0.736786
\(935\) 0 0
\(936\) −32161.8 −1.12312
\(937\) −22634.7 −0.789161 −0.394580 0.918861i \(-0.629110\pi\)
−0.394580 + 0.918861i \(0.629110\pi\)
\(938\) 18636.0 0.648705
\(939\) 2075.64 0.0721363
\(940\) 0 0
\(941\) 11695.3 0.405160 0.202580 0.979266i \(-0.435067\pi\)
0.202580 + 0.979266i \(0.435067\pi\)
\(942\) 1113.16 0.0385020
\(943\) 29.0492 0.00100315
\(944\) 33424.6 1.15241
\(945\) 0 0
\(946\) 3070.33 0.105523
\(947\) 45429.1 1.55887 0.779434 0.626485i \(-0.215507\pi\)
0.779434 + 0.626485i \(0.215507\pi\)
\(948\) −210.773 −0.00722109
\(949\) 35753.0 1.22296
\(950\) 0 0
\(951\) 1112.13 0.0379213
\(952\) 11108.7 0.378189
\(953\) 39025.9 1.32652 0.663259 0.748390i \(-0.269173\pi\)
0.663259 + 0.748390i \(0.269173\pi\)
\(954\) −29098.6 −0.987529
\(955\) 0 0
\(956\) 244.293 0.00826464
\(957\) 338.228 0.0114246
\(958\) −11955.2 −0.403188
\(959\) 11121.4 0.374483
\(960\) 0 0
\(961\) 55650.1 1.86802
\(962\) −20216.5 −0.677552
\(963\) −13481.7 −0.451135
\(964\) −3298.91 −0.110218
\(965\) 0 0
\(966\) −6.73722 −0.000224396 0
\(967\) 12986.1 0.431857 0.215929 0.976409i \(-0.430722\pi\)
0.215929 + 0.976409i \(0.430722\pi\)
\(968\) 30909.8 1.02632
\(969\) 2411.19 0.0799366
\(970\) 0 0
\(971\) −15044.2 −0.497210 −0.248605 0.968605i \(-0.579972\pi\)
−0.248605 + 0.968605i \(0.579972\pi\)
\(972\) 1050.37 0.0346613
\(973\) −17948.6 −0.591374
\(974\) −35323.8 −1.16206
\(975\) 0 0
\(976\) −18649.0 −0.611618
\(977\) −26593.4 −0.870828 −0.435414 0.900230i \(-0.643398\pi\)
−0.435414 + 0.900230i \(0.643398\pi\)
\(978\) 1732.68 0.0566512
\(979\) −3220.82 −0.105146
\(980\) 0 0
\(981\) −9122.12 −0.296888
\(982\) 30948.2 1.00570
\(983\) −36050.3 −1.16971 −0.584856 0.811137i \(-0.698849\pi\)
−0.584856 + 0.811137i \(0.698849\pi\)
\(984\) −943.431 −0.0305645
\(985\) 0 0
\(986\) −21895.7 −0.707203
\(987\) 1148.02 0.0370233
\(988\) −1843.45 −0.0593604
\(989\) −143.721 −0.00462088
\(990\) 0 0
\(991\) −54789.8 −1.75626 −0.878131 0.478420i \(-0.841210\pi\)
−0.878131 + 0.478420i \(0.841210\pi\)
\(992\) −9252.77 −0.296145
\(993\) −4241.53 −0.135550
\(994\) −19545.8 −0.623699
\(995\) 0 0
\(996\) 264.597 0.00841775
\(997\) −23309.0 −0.740426 −0.370213 0.928947i \(-0.620715\pi\)
−0.370213 + 0.928947i \(0.620715\pi\)
\(998\) 14915.6 0.473091
\(999\) 5442.75 0.172373
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 175.4.a.d.1.2 2
3.2 odd 2 1575.4.a.v.1.1 2
5.2 odd 4 175.4.b.d.99.3 4
5.3 odd 4 175.4.b.d.99.2 4
5.4 even 2 175.4.a.e.1.1 yes 2
7.6 odd 2 1225.4.a.r.1.2 2
15.14 odd 2 1575.4.a.s.1.2 2
35.34 odd 2 1225.4.a.t.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.4.a.d.1.2 2 1.1 even 1 trivial
175.4.a.e.1.1 yes 2 5.4 even 2
175.4.b.d.99.2 4 5.3 odd 4
175.4.b.d.99.3 4 5.2 odd 4
1225.4.a.r.1.2 2 7.6 odd 2
1225.4.a.t.1.1 2 35.34 odd 2
1575.4.a.s.1.2 2 15.14 odd 2
1575.4.a.v.1.1 2 3.2 odd 2