Properties

Label 1849.4.a.d.1.4
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $0$
Dimension $10$
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] = [1849,4,Mod(1,1849)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1849.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.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: \(109.094531601\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} - 59x^{8} + 42x^{7} + 1187x^{6} - 541x^{5} - 9389x^{4} + 2180x^{3} + 22676x^{2} - 320x - 768 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(2.14781\) of defining polynomial
Character \(\chi\) \(=\) 1849.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.14781 q^{2} +6.84883 q^{3} -3.38692 q^{4} -17.1363 q^{5} -14.7100 q^{6} +22.9786 q^{7} +24.4569 q^{8} +19.9064 q^{9} +O(q^{10})\) \(q-2.14781 q^{2} +6.84883 q^{3} -3.38692 q^{4} -17.1363 q^{5} -14.7100 q^{6} +22.9786 q^{7} +24.4569 q^{8} +19.9064 q^{9} +36.8056 q^{10} -49.3031 q^{11} -23.1964 q^{12} +15.4223 q^{13} -49.3537 q^{14} -117.364 q^{15} -25.4334 q^{16} +71.6119 q^{17} -42.7552 q^{18} -59.6425 q^{19} +58.0394 q^{20} +157.377 q^{21} +105.894 q^{22} +161.135 q^{23} +167.501 q^{24} +168.654 q^{25} -33.1241 q^{26} -48.5826 q^{27} -77.8267 q^{28} -7.84331 q^{29} +252.075 q^{30} -208.323 q^{31} -141.029 q^{32} -337.668 q^{33} -153.809 q^{34} -393.769 q^{35} -67.4215 q^{36} -25.8568 q^{37} +128.101 q^{38} +105.625 q^{39} -419.102 q^{40} +383.496 q^{41} -338.015 q^{42} +166.986 q^{44} -341.123 q^{45} -346.087 q^{46} -577.020 q^{47} -174.189 q^{48} +185.017 q^{49} -362.237 q^{50} +490.458 q^{51} -52.2341 q^{52} +134.370 q^{53} +104.346 q^{54} +844.874 q^{55} +561.986 q^{56} -408.481 q^{57} +16.8459 q^{58} +532.562 q^{59} +397.502 q^{60} +253.789 q^{61} +447.439 q^{62} +457.422 q^{63} +506.371 q^{64} -264.282 q^{65} +725.247 q^{66} -690.488 q^{67} -242.544 q^{68} +1103.59 q^{69} +845.741 q^{70} -636.819 q^{71} +486.850 q^{72} +475.895 q^{73} +55.5354 q^{74} +1155.08 q^{75} +202.004 q^{76} -1132.92 q^{77} -226.861 q^{78} +146.424 q^{79} +435.836 q^{80} -870.208 q^{81} -823.677 q^{82} -783.374 q^{83} -533.022 q^{84} -1227.17 q^{85} -53.7175 q^{87} -1205.80 q^{88} +1056.24 q^{89} +732.668 q^{90} +354.383 q^{91} -545.751 q^{92} -1426.77 q^{93} +1239.33 q^{94} +1022.05 q^{95} -965.885 q^{96} -102.057 q^{97} -397.381 q^{98} -981.449 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - q^{2} + 5 q^{3} + 39 q^{4} + 19 q^{5} - 15 q^{6} + 51 q^{7} - 36 q^{8} + 117 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - q^{2} + 5 q^{3} + 39 q^{4} + 19 q^{5} - 15 q^{6} + 51 q^{7} - 36 q^{8} + 117 q^{9} - 27 q^{10} + 27 q^{11} + 72 q^{12} + 15 q^{13} - 96 q^{14} - 65 q^{15} + 67 q^{16} + 82 q^{17} - 247 q^{18} - 78 q^{19} + 495 q^{20} - 9 q^{21} + 190 q^{22} + 61 q^{23} - 202 q^{24} + 151 q^{25} + 21 q^{26} - 97 q^{27} + 794 q^{28} + 53 q^{29} - 627 q^{30} - 253 q^{31} - 399 q^{32} + 424 q^{33} + 231 q^{34} + 355 q^{35} + 1092 q^{36} + 129 q^{37} + 854 q^{38} + 691 q^{39} - 1345 q^{40} + 391 q^{41} + 31 q^{42} + 377 q^{44} + 944 q^{45} + 40 q^{46} - 334 q^{47} + 2401 q^{48} + 115 q^{49} - 424 q^{50} + 795 q^{51} + 564 q^{52} - 773 q^{53} + 182 q^{54} + 1242 q^{55} + 923 q^{56} + 765 q^{57} - 1328 q^{58} - 1483 q^{59} + 1075 q^{60} - 437 q^{61} - 1509 q^{62} + 2222 q^{63} - 738 q^{64} - 1063 q^{65} - 1483 q^{66} + 642 q^{67} + 1052 q^{68} + 3503 q^{69} - 85 q^{70} + 1545 q^{71} - 3834 q^{72} - 1292 q^{73} + 2232 q^{74} + 82 q^{75} + 252 q^{76} - 1448 q^{77} + 2822 q^{78} + 1405 q^{79} + 3157 q^{80} - 974 q^{81} + 3304 q^{82} - 543 q^{83} + 3652 q^{84} + 973 q^{85} + 1409 q^{87} - 2686 q^{88} + 2196 q^{89} - 742 q^{90} + 3513 q^{91} - 2629 q^{92} + 983 q^{93} + 4939 q^{94} + 149 q^{95} - 3540 q^{96} - 425 q^{97} + 213 q^{98} + 3181 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.14781 −0.759365 −0.379682 0.925117i \(-0.623967\pi\)
−0.379682 + 0.925117i \(0.623967\pi\)
\(3\) 6.84883 1.31806 0.659029 0.752118i \(-0.270968\pi\)
0.659029 + 0.752118i \(0.270968\pi\)
\(4\) −3.38692 −0.423365
\(5\) −17.1363 −1.53272 −0.766360 0.642411i \(-0.777934\pi\)
−0.766360 + 0.642411i \(0.777934\pi\)
\(6\) −14.7100 −1.00089
\(7\) 22.9786 1.24073 0.620364 0.784314i \(-0.286985\pi\)
0.620364 + 0.784314i \(0.286985\pi\)
\(8\) 24.4569 1.08085
\(9\) 19.9064 0.737275
\(10\) 36.8056 1.16389
\(11\) −49.3031 −1.35140 −0.675702 0.737175i \(-0.736159\pi\)
−0.675702 + 0.737175i \(0.736159\pi\)
\(12\) −23.1964 −0.558019
\(13\) 15.4223 0.329029 0.164514 0.986375i \(-0.447394\pi\)
0.164514 + 0.986375i \(0.447394\pi\)
\(14\) −49.3537 −0.942166
\(15\) −117.364 −2.02021
\(16\) −25.4334 −0.397397
\(17\) 71.6119 1.02167 0.510837 0.859678i \(-0.329336\pi\)
0.510837 + 0.859678i \(0.329336\pi\)
\(18\) −42.7552 −0.559861
\(19\) −59.6425 −0.720154 −0.360077 0.932923i \(-0.617250\pi\)
−0.360077 + 0.932923i \(0.617250\pi\)
\(20\) 58.0394 0.648900
\(21\) 157.377 1.63535
\(22\) 105.894 1.02621
\(23\) 161.135 1.46082 0.730412 0.683007i \(-0.239328\pi\)
0.730412 + 0.683007i \(0.239328\pi\)
\(24\) 167.501 1.42463
\(25\) 168.654 1.34923
\(26\) −33.1241 −0.249853
\(27\) −48.5826 −0.346286
\(28\) −77.8267 −0.525281
\(29\) −7.84331 −0.0502230 −0.0251115 0.999685i \(-0.507994\pi\)
−0.0251115 + 0.999685i \(0.507994\pi\)
\(30\) 252.075 1.53408
\(31\) −208.323 −1.20697 −0.603484 0.797375i \(-0.706221\pi\)
−0.603484 + 0.797375i \(0.706221\pi\)
\(32\) −141.029 −0.779084
\(33\) −337.668 −1.78123
\(34\) −153.809 −0.775823
\(35\) −393.769 −1.90169
\(36\) −67.4215 −0.312137
\(37\) −25.8568 −0.114887 −0.0574436 0.998349i \(-0.518295\pi\)
−0.0574436 + 0.998349i \(0.518295\pi\)
\(38\) 128.101 0.546859
\(39\) 105.625 0.433679
\(40\) −419.102 −1.65665
\(41\) 383.496 1.46078 0.730391 0.683029i \(-0.239338\pi\)
0.730391 + 0.683029i \(0.239338\pi\)
\(42\) −338.015 −1.24183
\(43\) 0 0
\(44\) 166.986 0.572137
\(45\) −341.123 −1.13004
\(46\) −346.087 −1.10930
\(47\) −577.020 −1.79079 −0.895394 0.445276i \(-0.853106\pi\)
−0.895394 + 0.445276i \(0.853106\pi\)
\(48\) −174.189 −0.523792
\(49\) 185.017 0.539408
\(50\) −362.237 −1.02456
\(51\) 490.458 1.34662
\(52\) −52.2341 −0.139299
\(53\) 134.370 0.348247 0.174124 0.984724i \(-0.444291\pi\)
0.174124 + 0.984724i \(0.444291\pi\)
\(54\) 104.346 0.262958
\(55\) 844.874 2.07132
\(56\) 561.986 1.34105
\(57\) −408.481 −0.949204
\(58\) 16.8459 0.0381375
\(59\) 532.562 1.17515 0.587573 0.809171i \(-0.300084\pi\)
0.587573 + 0.809171i \(0.300084\pi\)
\(60\) 397.502 0.855288
\(61\) 253.789 0.532694 0.266347 0.963877i \(-0.414183\pi\)
0.266347 + 0.963877i \(0.414183\pi\)
\(62\) 447.439 0.916529
\(63\) 457.422 0.914759
\(64\) 506.371 0.989006
\(65\) −264.282 −0.504309
\(66\) 725.247 1.35260
\(67\) −690.488 −1.25905 −0.629527 0.776979i \(-0.716751\pi\)
−0.629527 + 0.776979i \(0.716751\pi\)
\(68\) −242.544 −0.432541
\(69\) 1103.59 1.92545
\(70\) 845.741 1.44408
\(71\) −636.819 −1.06446 −0.532229 0.846600i \(-0.678646\pi\)
−0.532229 + 0.846600i \(0.678646\pi\)
\(72\) 486.850 0.796887
\(73\) 475.895 0.763004 0.381502 0.924368i \(-0.375407\pi\)
0.381502 + 0.924368i \(0.375407\pi\)
\(74\) 55.5354 0.0872413
\(75\) 1155.08 1.77837
\(76\) 202.004 0.304888
\(77\) −1132.92 −1.67673
\(78\) −226.861 −0.329321
\(79\) 146.424 0.208531 0.104266 0.994549i \(-0.466751\pi\)
0.104266 + 0.994549i \(0.466751\pi\)
\(80\) 435.836 0.609099
\(81\) −870.208 −1.19370
\(82\) −823.677 −1.10927
\(83\) −783.374 −1.03598 −0.517991 0.855386i \(-0.673320\pi\)
−0.517991 + 0.855386i \(0.673320\pi\)
\(84\) −533.022 −0.692351
\(85\) −1227.17 −1.56594
\(86\) 0 0
\(87\) −53.7175 −0.0661967
\(88\) −1205.80 −1.46067
\(89\) 1056.24 1.25799 0.628997 0.777407i \(-0.283466\pi\)
0.628997 + 0.777407i \(0.283466\pi\)
\(90\) 732.668 0.858111
\(91\) 354.383 0.408236
\(92\) −545.751 −0.618462
\(93\) −1426.77 −1.59085
\(94\) 1239.33 1.35986
\(95\) 1022.05 1.10379
\(96\) −965.885 −1.02688
\(97\) −102.057 −0.106828 −0.0534140 0.998572i \(-0.517010\pi\)
−0.0534140 + 0.998572i \(0.517010\pi\)
\(98\) −397.381 −0.409608
\(99\) −981.449 −0.996357
\(100\) −571.218 −0.571218
\(101\) 1135.10 1.11828 0.559140 0.829073i \(-0.311131\pi\)
0.559140 + 0.829073i \(0.311131\pi\)
\(102\) −1053.41 −1.02258
\(103\) 759.720 0.726772 0.363386 0.931639i \(-0.381621\pi\)
0.363386 + 0.931639i \(0.381621\pi\)
\(104\) 377.182 0.355632
\(105\) −2696.86 −2.50654
\(106\) −288.600 −0.264447
\(107\) −587.456 −0.530761 −0.265381 0.964144i \(-0.585498\pi\)
−0.265381 + 0.964144i \(0.585498\pi\)
\(108\) 164.545 0.146605
\(109\) 591.336 0.519630 0.259815 0.965658i \(-0.416338\pi\)
0.259815 + 0.965658i \(0.416338\pi\)
\(110\) −1814.63 −1.57289
\(111\) −177.089 −0.151428
\(112\) −584.425 −0.493062
\(113\) −904.939 −0.753359 −0.376679 0.926344i \(-0.622934\pi\)
−0.376679 + 0.926344i \(0.622934\pi\)
\(114\) 877.339 0.720792
\(115\) −2761.26 −2.23903
\(116\) 26.5647 0.0212626
\(117\) 307.003 0.242585
\(118\) −1143.84 −0.892365
\(119\) 1645.54 1.26762
\(120\) −2870.36 −2.18355
\(121\) 1099.79 0.826292
\(122\) −545.090 −0.404509
\(123\) 2626.50 1.92539
\(124\) 705.575 0.510988
\(125\) −748.071 −0.535276
\(126\) −982.456 −0.694636
\(127\) 1437.81 1.00461 0.502303 0.864692i \(-0.332486\pi\)
0.502303 + 0.864692i \(0.332486\pi\)
\(128\) 40.6460 0.0280674
\(129\) 0 0
\(130\) 567.626 0.382955
\(131\) 839.267 0.559749 0.279874 0.960037i \(-0.409707\pi\)
0.279874 + 0.960037i \(0.409707\pi\)
\(132\) 1143.66 0.754109
\(133\) −1370.50 −0.893516
\(134\) 1483.04 0.956081
\(135\) 832.528 0.530760
\(136\) 1751.41 1.10428
\(137\) 1329.77 0.829272 0.414636 0.909987i \(-0.363909\pi\)
0.414636 + 0.909987i \(0.363909\pi\)
\(138\) −2370.29 −1.46212
\(139\) −2130.67 −1.30015 −0.650075 0.759870i \(-0.725263\pi\)
−0.650075 + 0.759870i \(0.725263\pi\)
\(140\) 1333.67 0.805109
\(141\) −3951.91 −2.36036
\(142\) 1367.77 0.808312
\(143\) −760.367 −0.444651
\(144\) −506.289 −0.292991
\(145\) 134.406 0.0769778
\(146\) −1022.13 −0.579398
\(147\) 1267.15 0.710971
\(148\) 87.5748 0.0486392
\(149\) −336.440 −0.184981 −0.0924906 0.995714i \(-0.529483\pi\)
−0.0924906 + 0.995714i \(0.529483\pi\)
\(150\) −2480.90 −1.35043
\(151\) 1200.49 0.646982 0.323491 0.946231i \(-0.395143\pi\)
0.323491 + 0.946231i \(0.395143\pi\)
\(152\) −1458.67 −0.778381
\(153\) 1425.54 0.753255
\(154\) 2433.29 1.27325
\(155\) 3569.90 1.84994
\(156\) −357.742 −0.183604
\(157\) −1592.21 −0.809378 −0.404689 0.914454i \(-0.632620\pi\)
−0.404689 + 0.914454i \(0.632620\pi\)
\(158\) −314.490 −0.158351
\(159\) 920.275 0.459010
\(160\) 2416.73 1.19412
\(161\) 3702.66 1.81249
\(162\) 1869.04 0.906454
\(163\) 3945.38 1.89587 0.947933 0.318469i \(-0.103169\pi\)
0.947933 + 0.318469i \(0.103169\pi\)
\(164\) −1298.87 −0.618444
\(165\) 5786.40 2.73012
\(166\) 1682.54 0.786688
\(167\) 2058.29 0.953746 0.476873 0.878972i \(-0.341770\pi\)
0.476873 + 0.878972i \(0.341770\pi\)
\(168\) 3848.95 1.76758
\(169\) −1959.15 −0.891740
\(170\) 2635.72 1.18912
\(171\) −1187.27 −0.530952
\(172\) 0 0
\(173\) 1201.75 0.528134 0.264067 0.964504i \(-0.414936\pi\)
0.264067 + 0.964504i \(0.414936\pi\)
\(174\) 115.375 0.0502675
\(175\) 3875.44 1.67403
\(176\) 1253.95 0.537044
\(177\) 3647.42 1.54891
\(178\) −2268.61 −0.955277
\(179\) 3664.67 1.53023 0.765113 0.643896i \(-0.222683\pi\)
0.765113 + 0.643896i \(0.222683\pi\)
\(180\) 1155.36 0.478418
\(181\) 185.832 0.0763138 0.0381569 0.999272i \(-0.487851\pi\)
0.0381569 + 0.999272i \(0.487851\pi\)
\(182\) −761.147 −0.310000
\(183\) 1738.16 0.702121
\(184\) 3940.86 1.57894
\(185\) 443.090 0.176090
\(186\) 3064.43 1.20804
\(187\) −3530.69 −1.38069
\(188\) 1954.32 0.758157
\(189\) −1116.36 −0.429647
\(190\) −2195.17 −0.838183
\(191\) 1326.38 0.502478 0.251239 0.967925i \(-0.419162\pi\)
0.251239 + 0.967925i \(0.419162\pi\)
\(192\) 3468.05 1.30357
\(193\) −1507.87 −0.562378 −0.281189 0.959652i \(-0.590729\pi\)
−0.281189 + 0.959652i \(0.590729\pi\)
\(194\) 219.199 0.0811214
\(195\) −1810.02 −0.664709
\(196\) −626.638 −0.228367
\(197\) 407.216 0.147274 0.0736369 0.997285i \(-0.476539\pi\)
0.0736369 + 0.997285i \(0.476539\pi\)
\(198\) 2107.96 0.756598
\(199\) 394.575 0.140556 0.0702782 0.997527i \(-0.477611\pi\)
0.0702782 + 0.997527i \(0.477611\pi\)
\(200\) 4124.76 1.45832
\(201\) −4729.03 −1.65950
\(202\) −2437.97 −0.849183
\(203\) −180.228 −0.0623131
\(204\) −1661.14 −0.570113
\(205\) −6571.72 −2.23897
\(206\) −1631.73 −0.551885
\(207\) 3207.62 1.07703
\(208\) −392.242 −0.130755
\(209\) 2940.56 0.973218
\(210\) 5792.34 1.90338
\(211\) 3347.80 1.09229 0.546143 0.837692i \(-0.316096\pi\)
0.546143 + 0.837692i \(0.316096\pi\)
\(212\) −455.099 −0.147436
\(213\) −4361.47 −1.40302
\(214\) 1261.74 0.403042
\(215\) 0 0
\(216\) −1188.18 −0.374285
\(217\) −4786.99 −1.49752
\(218\) −1270.08 −0.394589
\(219\) 3259.32 1.00568
\(220\) −2861.52 −0.876926
\(221\) 1104.42 0.336160
\(222\) 380.352 0.114989
\(223\) −820.804 −0.246480 −0.123240 0.992377i \(-0.539329\pi\)
−0.123240 + 0.992377i \(0.539329\pi\)
\(224\) −3240.66 −0.966632
\(225\) 3357.30 0.994756
\(226\) 1943.64 0.572074
\(227\) −2225.27 −0.650646 −0.325323 0.945603i \(-0.605473\pi\)
−0.325323 + 0.945603i \(0.605473\pi\)
\(228\) 1383.49 0.401860
\(229\) −2109.88 −0.608842 −0.304421 0.952538i \(-0.598463\pi\)
−0.304421 + 0.952538i \(0.598463\pi\)
\(230\) 5930.66 1.70024
\(231\) −7759.15 −2.21002
\(232\) −191.823 −0.0542837
\(233\) 2118.94 0.595779 0.297890 0.954600i \(-0.403717\pi\)
0.297890 + 0.954600i \(0.403717\pi\)
\(234\) −659.383 −0.184210
\(235\) 9888.01 2.74478
\(236\) −1803.74 −0.497516
\(237\) 1002.83 0.274856
\(238\) −3534.31 −0.962586
\(239\) 2706.53 0.732513 0.366257 0.930514i \(-0.380639\pi\)
0.366257 + 0.930514i \(0.380639\pi\)
\(240\) 2984.96 0.802827
\(241\) −965.679 −0.258111 −0.129056 0.991637i \(-0.541195\pi\)
−0.129056 + 0.991637i \(0.541195\pi\)
\(242\) −2362.15 −0.627457
\(243\) −4648.17 −1.22708
\(244\) −859.562 −0.225524
\(245\) −3170.51 −0.826762
\(246\) −5641.22 −1.46208
\(247\) −919.824 −0.236951
\(248\) −5094.95 −1.30455
\(249\) −5365.19 −1.36548
\(250\) 1606.71 0.406470
\(251\) 6103.02 1.53474 0.767369 0.641205i \(-0.221565\pi\)
0.767369 + 0.641205i \(0.221565\pi\)
\(252\) −1549.25 −0.387277
\(253\) −7944.45 −1.97416
\(254\) −3088.14 −0.762862
\(255\) −8404.65 −2.06400
\(256\) −4138.27 −1.01032
\(257\) 6760.71 1.64094 0.820469 0.571691i \(-0.193712\pi\)
0.820469 + 0.571691i \(0.193712\pi\)
\(258\) 0 0
\(259\) −594.153 −0.142544
\(260\) 895.101 0.213507
\(261\) −156.132 −0.0370281
\(262\) −1802.59 −0.425054
\(263\) 7838.17 1.83773 0.918864 0.394574i \(-0.129108\pi\)
0.918864 + 0.394574i \(0.129108\pi\)
\(264\) −8258.33 −1.92525
\(265\) −2302.60 −0.533766
\(266\) 2943.57 0.678504
\(267\) 7234.02 1.65811
\(268\) 2338.63 0.533039
\(269\) −3952.54 −0.895876 −0.447938 0.894065i \(-0.647842\pi\)
−0.447938 + 0.894065i \(0.647842\pi\)
\(270\) −1788.11 −0.403040
\(271\) −583.263 −0.130741 −0.0653703 0.997861i \(-0.520823\pi\)
−0.0653703 + 0.997861i \(0.520823\pi\)
\(272\) −1821.34 −0.406010
\(273\) 2427.11 0.538078
\(274\) −2856.10 −0.629720
\(275\) −8315.17 −1.82336
\(276\) −3737.75 −0.815168
\(277\) 3050.70 0.661729 0.330864 0.943678i \(-0.392660\pi\)
0.330864 + 0.943678i \(0.392660\pi\)
\(278\) 4576.27 0.987288
\(279\) −4146.98 −0.889867
\(280\) −9630.39 −2.05545
\(281\) 6333.07 1.34448 0.672241 0.740332i \(-0.265332\pi\)
0.672241 + 0.740332i \(0.265332\pi\)
\(282\) 8487.94 1.79237
\(283\) 7840.90 1.64697 0.823486 0.567337i \(-0.192026\pi\)
0.823486 + 0.567337i \(0.192026\pi\)
\(284\) 2156.86 0.450654
\(285\) 6999.87 1.45486
\(286\) 1633.12 0.337652
\(287\) 8812.22 1.81243
\(288\) −2807.39 −0.574399
\(289\) 215.269 0.0438163
\(290\) −288.677 −0.0584542
\(291\) −698.971 −0.140805
\(292\) −1611.82 −0.323029
\(293\) 7168.90 1.42939 0.714696 0.699435i \(-0.246565\pi\)
0.714696 + 0.699435i \(0.246565\pi\)
\(294\) −2721.59 −0.539886
\(295\) −9126.16 −1.80117
\(296\) −632.377 −0.124176
\(297\) 2395.27 0.467972
\(298\) 722.608 0.140468
\(299\) 2485.07 0.480653
\(300\) −3912.17 −0.752898
\(301\) 0 0
\(302\) −2578.42 −0.491295
\(303\) 7774.08 1.47396
\(304\) 1516.91 0.286187
\(305\) −4349.01 −0.816471
\(306\) −3061.78 −0.571995
\(307\) 697.459 0.129662 0.0648308 0.997896i \(-0.479349\pi\)
0.0648308 + 0.997896i \(0.479349\pi\)
\(308\) 3837.10 0.709867
\(309\) 5203.19 0.957927
\(310\) −7667.46 −1.40478
\(311\) 2348.86 0.428269 0.214135 0.976804i \(-0.431307\pi\)
0.214135 + 0.976804i \(0.431307\pi\)
\(312\) 2583.25 0.468743
\(313\) 9405.55 1.69851 0.849254 0.527985i \(-0.177052\pi\)
0.849254 + 0.527985i \(0.177052\pi\)
\(314\) 3419.77 0.614613
\(315\) −7838.54 −1.40207
\(316\) −495.926 −0.0882848
\(317\) −6357.40 −1.12640 −0.563198 0.826322i \(-0.690429\pi\)
−0.563198 + 0.826322i \(0.690429\pi\)
\(318\) −1976.57 −0.348556
\(319\) 386.699 0.0678715
\(320\) −8677.35 −1.51587
\(321\) −4023.38 −0.699574
\(322\) −7952.60 −1.37634
\(323\) −4271.11 −0.735762
\(324\) 2947.32 0.505371
\(325\) 2601.03 0.443936
\(326\) −8473.93 −1.43965
\(327\) 4049.96 0.684902
\(328\) 9379.14 1.57889
\(329\) −13259.1 −2.22188
\(330\) −12428.1 −2.07316
\(331\) 6083.41 1.01019 0.505097 0.863062i \(-0.331457\pi\)
0.505097 + 0.863062i \(0.331457\pi\)
\(332\) 2653.22 0.438598
\(333\) −514.716 −0.0847035
\(334\) −4420.82 −0.724241
\(335\) 11832.4 1.92978
\(336\) −4002.62 −0.649884
\(337\) −3365.71 −0.544041 −0.272020 0.962291i \(-0.587692\pi\)
−0.272020 + 0.962291i \(0.587692\pi\)
\(338\) 4207.88 0.677156
\(339\) −6197.77 −0.992970
\(340\) 4156.31 0.662964
\(341\) 10271.0 1.63110
\(342\) 2550.03 0.403186
\(343\) −3630.23 −0.571470
\(344\) 0 0
\(345\) −18911.4 −2.95118
\(346\) −2581.12 −0.401046
\(347\) 2220.51 0.343524 0.171762 0.985138i \(-0.445054\pi\)
0.171762 + 0.985138i \(0.445054\pi\)
\(348\) 181.937 0.0280254
\(349\) −3836.59 −0.588447 −0.294223 0.955737i \(-0.595061\pi\)
−0.294223 + 0.955737i \(0.595061\pi\)
\(350\) −8323.70 −1.27120
\(351\) −749.255 −0.113938
\(352\) 6953.18 1.05286
\(353\) −3271.92 −0.493334 −0.246667 0.969100i \(-0.579335\pi\)
−0.246667 + 0.969100i \(0.579335\pi\)
\(354\) −7833.96 −1.17619
\(355\) 10912.8 1.63152
\(356\) −3577.41 −0.532591
\(357\) 11270.0 1.67080
\(358\) −7871.02 −1.16200
\(359\) −1270.02 −0.186711 −0.0933555 0.995633i \(-0.529759\pi\)
−0.0933555 + 0.995633i \(0.529759\pi\)
\(360\) −8342.83 −1.22140
\(361\) −3301.78 −0.481379
\(362\) −399.132 −0.0579500
\(363\) 7532.30 1.08910
\(364\) −1200.27 −0.172833
\(365\) −8155.10 −1.16947
\(366\) −3733.23 −0.533166
\(367\) −7336.15 −1.04344 −0.521722 0.853115i \(-0.674710\pi\)
−0.521722 + 0.853115i \(0.674710\pi\)
\(368\) −4098.21 −0.580527
\(369\) 7634.04 1.07700
\(370\) −951.673 −0.133717
\(371\) 3087.63 0.432080
\(372\) 4832.36 0.673511
\(373\) 10341.7 1.43558 0.717791 0.696259i \(-0.245154\pi\)
0.717791 + 0.696259i \(0.245154\pi\)
\(374\) 7583.24 1.04845
\(375\) −5123.41 −0.705525
\(376\) −14112.1 −1.93558
\(377\) −120.962 −0.0165248
\(378\) 2397.73 0.326259
\(379\) −2889.02 −0.391555 −0.195777 0.980648i \(-0.562723\pi\)
−0.195777 + 0.980648i \(0.562723\pi\)
\(380\) −3461.61 −0.467308
\(381\) 9847.30 1.32413
\(382\) −2848.81 −0.381564
\(383\) 1083.65 0.144575 0.0722874 0.997384i \(-0.476970\pi\)
0.0722874 + 0.997384i \(0.476970\pi\)
\(384\) 278.377 0.0369945
\(385\) 19414.0 2.56995
\(386\) 3238.62 0.427050
\(387\) 0 0
\(388\) 345.659 0.0452272
\(389\) 683.935 0.0891436 0.0445718 0.999006i \(-0.485808\pi\)
0.0445718 + 0.999006i \(0.485808\pi\)
\(390\) 3887.57 0.504756
\(391\) 11539.2 1.49248
\(392\) 4524.95 0.583021
\(393\) 5748.00 0.737781
\(394\) −874.622 −0.111835
\(395\) −2509.17 −0.319620
\(396\) 3324.09 0.421823
\(397\) −11007.5 −1.39156 −0.695779 0.718256i \(-0.744941\pi\)
−0.695779 + 0.718256i \(0.744941\pi\)
\(398\) −847.472 −0.106734
\(399\) −9386.33 −1.17770
\(400\) −4289.45 −0.536181
\(401\) 6198.42 0.771906 0.385953 0.922519i \(-0.373873\pi\)
0.385953 + 0.922519i \(0.373873\pi\)
\(402\) 10157.1 1.26017
\(403\) −3212.83 −0.397127
\(404\) −3844.48 −0.473441
\(405\) 14912.2 1.82961
\(406\) 387.096 0.0473184
\(407\) 1274.82 0.155259
\(408\) 11995.1 1.45550
\(409\) 5803.79 0.701660 0.350830 0.936439i \(-0.385899\pi\)
0.350830 + 0.936439i \(0.385899\pi\)
\(410\) 14114.8 1.70020
\(411\) 9107.39 1.09303
\(412\) −2573.11 −0.307690
\(413\) 12237.5 1.45804
\(414\) −6889.36 −0.817858
\(415\) 13424.2 1.58787
\(416\) −2174.99 −0.256341
\(417\) −14592.6 −1.71367
\(418\) −6315.75 −0.739028
\(419\) 6575.42 0.766660 0.383330 0.923612i \(-0.374777\pi\)
0.383330 + 0.923612i \(0.374777\pi\)
\(420\) 9134.04 1.06118
\(421\) −12514.9 −1.44878 −0.724391 0.689390i \(-0.757879\pi\)
−0.724391 + 0.689390i \(0.757879\pi\)
\(422\) −7190.44 −0.829444
\(423\) −11486.4 −1.32030
\(424\) 3286.27 0.376404
\(425\) 12077.6 1.37847
\(426\) 9367.59 1.06540
\(427\) 5831.72 0.660929
\(428\) 1989.66 0.224706
\(429\) −5207.62 −0.586075
\(430\) 0 0
\(431\) 8400.34 0.938818 0.469409 0.882981i \(-0.344467\pi\)
0.469409 + 0.882981i \(0.344467\pi\)
\(432\) 1235.62 0.137613
\(433\) 2423.78 0.269005 0.134503 0.990913i \(-0.457056\pi\)
0.134503 + 0.990913i \(0.457056\pi\)
\(434\) 10281.5 1.13716
\(435\) 920.521 0.101461
\(436\) −2002.81 −0.219993
\(437\) −9610.48 −1.05202
\(438\) −7000.40 −0.763680
\(439\) 813.778 0.0884727 0.0442363 0.999021i \(-0.485915\pi\)
0.0442363 + 0.999021i \(0.485915\pi\)
\(440\) 20663.0 2.23880
\(441\) 3683.03 0.397692
\(442\) −2372.08 −0.255268
\(443\) 6180.97 0.662904 0.331452 0.943472i \(-0.392461\pi\)
0.331452 + 0.943472i \(0.392461\pi\)
\(444\) 599.785 0.0641093
\(445\) −18100.1 −1.92815
\(446\) 1762.93 0.187169
\(447\) −2304.22 −0.243816
\(448\) 11635.7 1.22709
\(449\) −5792.95 −0.608878 −0.304439 0.952532i \(-0.598469\pi\)
−0.304439 + 0.952532i \(0.598469\pi\)
\(450\) −7210.84 −0.755383
\(451\) −18907.6 −1.97411
\(452\) 3064.96 0.318946
\(453\) 8221.93 0.852759
\(454\) 4779.46 0.494078
\(455\) −6072.83 −0.625711
\(456\) −9990.19 −1.02595
\(457\) 1579.20 0.161646 0.0808228 0.996728i \(-0.474245\pi\)
0.0808228 + 0.996728i \(0.474245\pi\)
\(458\) 4531.62 0.462333
\(459\) −3479.09 −0.353791
\(460\) 9352.17 0.947929
\(461\) −3027.25 −0.305842 −0.152921 0.988238i \(-0.548868\pi\)
−0.152921 + 0.988238i \(0.548868\pi\)
\(462\) 16665.2 1.67821
\(463\) 1731.83 0.173834 0.0869168 0.996216i \(-0.472299\pi\)
0.0869168 + 0.996216i \(0.472299\pi\)
\(464\) 199.482 0.0199585
\(465\) 24449.6 2.43833
\(466\) −4551.08 −0.452414
\(467\) −4012.33 −0.397577 −0.198788 0.980042i \(-0.563701\pi\)
−0.198788 + 0.980042i \(0.563701\pi\)
\(468\) −1039.79 −0.102702
\(469\) −15866.5 −1.56214
\(470\) −21237.5 −2.08429
\(471\) −10904.8 −1.06681
\(472\) 13024.8 1.27016
\(473\) 0 0
\(474\) −2153.89 −0.208716
\(475\) −10058.9 −0.971655
\(476\) −5573.32 −0.536666
\(477\) 2674.82 0.256754
\(478\) −5813.10 −0.556245
\(479\) 5871.47 0.560072 0.280036 0.959990i \(-0.409654\pi\)
0.280036 + 0.959990i \(0.409654\pi\)
\(480\) 16551.7 1.57392
\(481\) −398.771 −0.0378012
\(482\) 2074.09 0.196001
\(483\) 25358.9 2.38896
\(484\) −3724.92 −0.349823
\(485\) 1748.88 0.163737
\(486\) 9983.38 0.931801
\(487\) 7302.93 0.679522 0.339761 0.940512i \(-0.389654\pi\)
0.339761 + 0.940512i \(0.389654\pi\)
\(488\) 6206.89 0.575764
\(489\) 27021.2 2.49886
\(490\) 6809.66 0.627814
\(491\) 41.1543 0.00378262 0.00189131 0.999998i \(-0.499398\pi\)
0.00189131 + 0.999998i \(0.499398\pi\)
\(492\) −8895.74 −0.815145
\(493\) −561.674 −0.0513115
\(494\) 1975.61 0.179933
\(495\) 16818.4 1.52714
\(496\) 5298.38 0.479645
\(497\) −14633.2 −1.32070
\(498\) 11523.4 1.03690
\(499\) 6119.14 0.548959 0.274479 0.961593i \(-0.411495\pi\)
0.274479 + 0.961593i \(0.411495\pi\)
\(500\) 2533.66 0.226617
\(501\) 14096.9 1.25709
\(502\) −13108.1 −1.16543
\(503\) −13276.4 −1.17687 −0.588435 0.808545i \(-0.700256\pi\)
−0.588435 + 0.808545i \(0.700256\pi\)
\(504\) 11187.1 0.988720
\(505\) −19451.4 −1.71401
\(506\) 17063.2 1.49911
\(507\) −13417.9 −1.17536
\(508\) −4869.74 −0.425315
\(509\) 22154.6 1.92924 0.964622 0.263637i \(-0.0849220\pi\)
0.964622 + 0.263637i \(0.0849220\pi\)
\(510\) 18051.6 1.56733
\(511\) 10935.4 0.946681
\(512\) 8563.04 0.739134
\(513\) 2897.59 0.249379
\(514\) −14520.7 −1.24607
\(515\) −13018.8 −1.11394
\(516\) 0 0
\(517\) 28448.9 2.42008
\(518\) 1276.13 0.108243
\(519\) 8230.56 0.696111
\(520\) −6463.52 −0.545084
\(521\) 866.938 0.0729006 0.0364503 0.999335i \(-0.488395\pi\)
0.0364503 + 0.999335i \(0.488395\pi\)
\(522\) 335.342 0.0281179
\(523\) −19705.6 −1.64755 −0.823773 0.566920i \(-0.808135\pi\)
−0.823773 + 0.566920i \(0.808135\pi\)
\(524\) −2842.53 −0.236978
\(525\) 26542.2 2.20647
\(526\) −16834.9 −1.39551
\(527\) −14918.4 −1.23313
\(528\) 8588.06 0.707855
\(529\) 13797.5 1.13401
\(530\) 4945.55 0.405323
\(531\) 10601.4 0.866406
\(532\) 4641.78 0.378283
\(533\) 5914.39 0.480639
\(534\) −15537.3 −1.25911
\(535\) 10066.8 0.813509
\(536\) −16887.2 −1.36085
\(537\) 25098.7 2.01693
\(538\) 8489.30 0.680297
\(539\) −9121.91 −0.728958
\(540\) −2819.71 −0.224705
\(541\) −8302.80 −0.659825 −0.329912 0.944012i \(-0.607019\pi\)
−0.329912 + 0.944012i \(0.607019\pi\)
\(542\) 1252.74 0.0992799
\(543\) 1272.73 0.100586
\(544\) −10099.4 −0.795969
\(545\) −10133.3 −0.796448
\(546\) −5212.96 −0.408598
\(547\) −10861.2 −0.848977 −0.424489 0.905433i \(-0.639546\pi\)
−0.424489 + 0.905433i \(0.639546\pi\)
\(548\) −4503.84 −0.351085
\(549\) 5052.03 0.392742
\(550\) 17859.4 1.38459
\(551\) 467.794 0.0361682
\(552\) 26990.3 2.08113
\(553\) 3364.62 0.258731
\(554\) −6552.32 −0.502494
\(555\) 3034.65 0.232097
\(556\) 7216.40 0.550438
\(557\) 16029.1 1.21934 0.609670 0.792655i \(-0.291302\pi\)
0.609670 + 0.792655i \(0.291302\pi\)
\(558\) 8906.91 0.675734
\(559\) 0 0
\(560\) 10014.9 0.755726
\(561\) −24181.1 −1.81983
\(562\) −13602.2 −1.02095
\(563\) 23819.0 1.78304 0.891518 0.452985i \(-0.149641\pi\)
0.891518 + 0.452985i \(0.149641\pi\)
\(564\) 13384.8 0.999294
\(565\) 15507.3 1.15469
\(566\) −16840.7 −1.25065
\(567\) −19996.2 −1.48106
\(568\) −15574.6 −1.15052
\(569\) −6026.59 −0.444021 −0.222010 0.975044i \(-0.571262\pi\)
−0.222010 + 0.975044i \(0.571262\pi\)
\(570\) −15034.4 −1.10477
\(571\) 17370.8 1.27311 0.636554 0.771232i \(-0.280359\pi\)
0.636554 + 0.771232i \(0.280359\pi\)
\(572\) 2575.30 0.188250
\(573\) 9084.13 0.662295
\(574\) −18927.0 −1.37630
\(575\) 27176.1 1.97099
\(576\) 10080.0 0.729170
\(577\) 4746.69 0.342474 0.171237 0.985230i \(-0.445224\pi\)
0.171237 + 0.985230i \(0.445224\pi\)
\(578\) −462.357 −0.0332725
\(579\) −10327.1 −0.741246
\(580\) −455.221 −0.0325897
\(581\) −18000.9 −1.28537
\(582\) 1501.25 0.106923
\(583\) −6624.84 −0.470623
\(584\) 11638.9 0.824695
\(585\) −5260.91 −0.371815
\(586\) −15397.4 −1.08543
\(587\) 1574.61 0.110718 0.0553588 0.998467i \(-0.482370\pi\)
0.0553588 + 0.998467i \(0.482370\pi\)
\(588\) −4291.73 −0.301000
\(589\) 12424.9 0.869202
\(590\) 19601.2 1.36775
\(591\) 2788.95 0.194115
\(592\) 657.626 0.0456559
\(593\) 6250.28 0.432830 0.216415 0.976301i \(-0.430564\pi\)
0.216415 + 0.976301i \(0.430564\pi\)
\(594\) −5144.59 −0.355362
\(595\) −28198.6 −1.94291
\(596\) 1139.49 0.0783146
\(597\) 2702.38 0.185261
\(598\) −5337.45 −0.364991
\(599\) −566.197 −0.0386213 −0.0193107 0.999814i \(-0.506147\pi\)
−0.0193107 + 0.999814i \(0.506147\pi\)
\(600\) 28249.8 1.92215
\(601\) −6295.44 −0.427282 −0.213641 0.976912i \(-0.568532\pi\)
−0.213641 + 0.976912i \(0.568532\pi\)
\(602\) 0 0
\(603\) −13745.2 −0.928269
\(604\) −4065.95 −0.273909
\(605\) −18846.5 −1.26648
\(606\) −16697.2 −1.11927
\(607\) 22657.5 1.51506 0.757528 0.652803i \(-0.226407\pi\)
0.757528 + 0.652803i \(0.226407\pi\)
\(608\) 8411.33 0.561060
\(609\) −1234.35 −0.0821322
\(610\) 9340.84 0.619999
\(611\) −8898.97 −0.589221
\(612\) −4828.18 −0.318902
\(613\) 3576.79 0.235669 0.117835 0.993033i \(-0.462405\pi\)
0.117835 + 0.993033i \(0.462405\pi\)
\(614\) −1498.01 −0.0984605
\(615\) −45008.6 −2.95109
\(616\) −27707.7 −1.81229
\(617\) 5025.02 0.327877 0.163938 0.986471i \(-0.447580\pi\)
0.163938 + 0.986471i \(0.447580\pi\)
\(618\) −11175.5 −0.727416
\(619\) −4767.52 −0.309569 −0.154784 0.987948i \(-0.549468\pi\)
−0.154784 + 0.987948i \(0.549468\pi\)
\(620\) −12091.0 −0.783202
\(621\) −7828.35 −0.505863
\(622\) −5044.91 −0.325213
\(623\) 24271.0 1.56083
\(624\) −2686.40 −0.172343
\(625\) −8262.56 −0.528804
\(626\) −20201.3 −1.28979
\(627\) 20139.4 1.28276
\(628\) 5392.69 0.342662
\(629\) −1851.65 −0.117377
\(630\) 16835.7 1.06468
\(631\) 26994.4 1.70306 0.851531 0.524305i \(-0.175675\pi\)
0.851531 + 0.524305i \(0.175675\pi\)
\(632\) 3581.07 0.225392
\(633\) 22928.5 1.43970
\(634\) 13654.5 0.855345
\(635\) −24638.8 −1.53978
\(636\) −3116.90 −0.194329
\(637\) 2853.39 0.177481
\(638\) −830.556 −0.0515392
\(639\) −12676.8 −0.784799
\(640\) −696.523 −0.0430195
\(641\) 2266.00 0.139628 0.0698141 0.997560i \(-0.477759\pi\)
0.0698141 + 0.997560i \(0.477759\pi\)
\(642\) 8641.45 0.531232
\(643\) −32171.8 −1.97314 −0.986572 0.163329i \(-0.947777\pi\)
−0.986572 + 0.163329i \(0.947777\pi\)
\(644\) −12540.6 −0.767343
\(645\) 0 0
\(646\) 9173.53 0.558712
\(647\) 18687.3 1.13551 0.567753 0.823199i \(-0.307813\pi\)
0.567753 + 0.823199i \(0.307813\pi\)
\(648\) −21282.6 −1.29022
\(649\) −26256.9 −1.58810
\(650\) −5586.52 −0.337110
\(651\) −32785.2 −1.97382
\(652\) −13362.7 −0.802644
\(653\) 11503.4 0.689376 0.344688 0.938717i \(-0.387985\pi\)
0.344688 + 0.938717i \(0.387985\pi\)
\(654\) −8698.53 −0.520091
\(655\) −14382.0 −0.857939
\(656\) −9753.62 −0.580511
\(657\) 9473.37 0.562544
\(658\) 28478.0 1.68722
\(659\) 14603.7 0.863245 0.431623 0.902054i \(-0.357941\pi\)
0.431623 + 0.902054i \(0.357941\pi\)
\(660\) −19598.1 −1.15584
\(661\) 5556.15 0.326943 0.163471 0.986548i \(-0.447731\pi\)
0.163471 + 0.986548i \(0.447731\pi\)
\(662\) −13066.0 −0.767106
\(663\) 7563.98 0.443078
\(664\) −19158.9 −1.11974
\(665\) 23485.4 1.36951
\(666\) 1105.51 0.0643209
\(667\) −1263.83 −0.0733669
\(668\) −6971.28 −0.403783
\(669\) −5621.55 −0.324875
\(670\) −25413.8 −1.46540
\(671\) −12512.6 −0.719885
\(672\) −22194.7 −1.27408
\(673\) −3729.99 −0.213641 −0.106821 0.994278i \(-0.534067\pi\)
−0.106821 + 0.994278i \(0.534067\pi\)
\(674\) 7228.89 0.413125
\(675\) −8193.65 −0.467221
\(676\) 6635.49 0.377531
\(677\) −30830.0 −1.75021 −0.875105 0.483933i \(-0.839208\pi\)
−0.875105 + 0.483933i \(0.839208\pi\)
\(678\) 13311.6 0.754027
\(679\) −2345.13 −0.132545
\(680\) −30012.7 −1.69255
\(681\) −15240.5 −0.857589
\(682\) −22060.1 −1.23860
\(683\) −18270.9 −1.02360 −0.511798 0.859106i \(-0.671020\pi\)
−0.511798 + 0.859106i \(0.671020\pi\)
\(684\) 4021.18 0.224786
\(685\) −22787.5 −1.27104
\(686\) 7797.04 0.433954
\(687\) −14450.2 −0.802489
\(688\) 0 0
\(689\) 2072.29 0.114583
\(690\) 40618.1 2.24102
\(691\) 20487.0 1.12788 0.563939 0.825817i \(-0.309285\pi\)
0.563939 + 0.825817i \(0.309285\pi\)
\(692\) −4070.22 −0.223593
\(693\) −22552.3 −1.23621
\(694\) −4769.22 −0.260860
\(695\) 36511.8 1.99277
\(696\) −1313.76 −0.0715490
\(697\) 27462.9 1.49244
\(698\) 8240.26 0.446846
\(699\) 14512.3 0.785271
\(700\) −13125.8 −0.708726
\(701\) −22050.4 −1.18806 −0.594030 0.804443i \(-0.702464\pi\)
−0.594030 + 0.804443i \(0.702464\pi\)
\(702\) 1609.26 0.0865206
\(703\) 1542.16 0.0827365
\(704\) −24965.7 −1.33655
\(705\) 67721.3 3.61777
\(706\) 7027.46 0.374620
\(707\) 26082.9 1.38748
\(708\) −12353.5 −0.655754
\(709\) 24913.2 1.31966 0.659828 0.751417i \(-0.270629\pi\)
0.659828 + 0.751417i \(0.270629\pi\)
\(710\) −23438.5 −1.23892
\(711\) 2914.77 0.153745
\(712\) 25832.4 1.35971
\(713\) −33568.2 −1.76317
\(714\) −24205.9 −1.26874
\(715\) 13029.9 0.681526
\(716\) −12412.0 −0.647844
\(717\) 18536.5 0.965495
\(718\) 2727.77 0.141782
\(719\) −3253.23 −0.168741 −0.0843706 0.996434i \(-0.526888\pi\)
−0.0843706 + 0.996434i \(0.526888\pi\)
\(720\) 8675.93 0.449074
\(721\) 17457.3 0.901726
\(722\) 7091.58 0.365542
\(723\) −6613.77 −0.340206
\(724\) −629.399 −0.0323086
\(725\) −1322.81 −0.0677625
\(726\) −16177.9 −0.827025
\(727\) −17101.1 −0.872412 −0.436206 0.899847i \(-0.643678\pi\)
−0.436206 + 0.899847i \(0.643678\pi\)
\(728\) 8667.12 0.441243
\(729\) −8338.92 −0.423661
\(730\) 17515.6 0.888056
\(731\) 0 0
\(732\) −5886.99 −0.297253
\(733\) 3820.21 0.192500 0.0962501 0.995357i \(-0.469315\pi\)
0.0962501 + 0.995357i \(0.469315\pi\)
\(734\) 15756.6 0.792355
\(735\) −21714.3 −1.08972
\(736\) −22724.7 −1.13810
\(737\) 34043.2 1.70149
\(738\) −16396.5 −0.817835
\(739\) 22213.3 1.10572 0.552861 0.833274i \(-0.313536\pi\)
0.552861 + 0.833274i \(0.313536\pi\)
\(740\) −1500.71 −0.0745504
\(741\) −6299.71 −0.312315
\(742\) −6631.64 −0.328107
\(743\) −12549.4 −0.619642 −0.309821 0.950795i \(-0.600269\pi\)
−0.309821 + 0.950795i \(0.600269\pi\)
\(744\) −34894.4 −1.71948
\(745\) 5765.34 0.283525
\(746\) −22211.9 −1.09013
\(747\) −15594.2 −0.763804
\(748\) 11958.2 0.584537
\(749\) −13498.9 −0.658531
\(750\) 11004.1 0.535751
\(751\) 4953.67 0.240695 0.120348 0.992732i \(-0.461599\pi\)
0.120348 + 0.992732i \(0.461599\pi\)
\(752\) 14675.6 0.711654
\(753\) 41798.6 2.02287
\(754\) 259.803 0.0125484
\(755\) −20572.0 −0.991643
\(756\) 3781.03 0.181898
\(757\) −22003.1 −1.05643 −0.528215 0.849111i \(-0.677138\pi\)
−0.528215 + 0.849111i \(0.677138\pi\)
\(758\) 6205.07 0.297333
\(759\) −54410.2 −2.60206
\(760\) 24996.3 1.19304
\(761\) −6198.26 −0.295252 −0.147626 0.989043i \(-0.547163\pi\)
−0.147626 + 0.989043i \(0.547163\pi\)
\(762\) −21150.1 −1.00550
\(763\) 13588.1 0.644720
\(764\) −4492.34 −0.212732
\(765\) −24428.5 −1.15453
\(766\) −2327.48 −0.109785
\(767\) 8213.32 0.386657
\(768\) −28342.3 −1.33166
\(769\) 12952.5 0.607386 0.303693 0.952770i \(-0.401780\pi\)
0.303693 + 0.952770i \(0.401780\pi\)
\(770\) −41697.7 −1.95153
\(771\) 46302.9 2.16285
\(772\) 5107.04 0.238091
\(773\) −4395.08 −0.204502 −0.102251 0.994759i \(-0.532604\pi\)
−0.102251 + 0.994759i \(0.532604\pi\)
\(774\) 0 0
\(775\) −35134.6 −1.62848
\(776\) −2496.00 −0.115465
\(777\) −4069.25 −0.187881
\(778\) −1468.96 −0.0676925
\(779\) −22872.7 −1.05199
\(780\) 6130.39 0.281414
\(781\) 31397.2 1.43851
\(782\) −24784.0 −1.13334
\(783\) 381.048 0.0173915
\(784\) −4705.61 −0.214359
\(785\) 27284.7 1.24055
\(786\) −12345.6 −0.560245
\(787\) −34887.0 −1.58016 −0.790080 0.613003i \(-0.789961\pi\)
−0.790080 + 0.613003i \(0.789961\pi\)
\(788\) −1379.21 −0.0623506
\(789\) 53682.3 2.42223
\(790\) 5389.21 0.242708
\(791\) −20794.3 −0.934714
\(792\) −24003.2 −1.07692
\(793\) 3914.01 0.175272
\(794\) 23641.9 1.05670
\(795\) −15770.1 −0.703534
\(796\) −1336.39 −0.0595066
\(797\) 30402.7 1.35122 0.675609 0.737260i \(-0.263881\pi\)
0.675609 + 0.737260i \(0.263881\pi\)
\(798\) 20160.0 0.894308
\(799\) −41321.5 −1.82960
\(800\) −23785.2 −1.05117
\(801\) 21026.0 0.927488
\(802\) −13313.0 −0.586158
\(803\) −23463.1 −1.03113
\(804\) 16016.9 0.702576
\(805\) −63450.0 −2.77804
\(806\) 6900.53 0.301564
\(807\) −27070.3 −1.18082
\(808\) 27761.0 1.20870
\(809\) −7885.52 −0.342695 −0.171347 0.985211i \(-0.554812\pi\)
−0.171347 + 0.985211i \(0.554812\pi\)
\(810\) −32028.5 −1.38934
\(811\) −26413.9 −1.14367 −0.571836 0.820368i \(-0.693769\pi\)
−0.571836 + 0.820368i \(0.693769\pi\)
\(812\) 610.419 0.0263812
\(813\) −3994.67 −0.172324
\(814\) −2738.07 −0.117898
\(815\) −67609.4 −2.90583
\(816\) −12474.0 −0.535145
\(817\) 0 0
\(818\) −12465.4 −0.532816
\(819\) 7054.50 0.300982
\(820\) 22257.9 0.947902
\(821\) −30441.2 −1.29404 −0.647019 0.762474i \(-0.723985\pi\)
−0.647019 + 0.762474i \(0.723985\pi\)
\(822\) −19560.9 −0.830007
\(823\) 8533.72 0.361442 0.180721 0.983534i \(-0.442157\pi\)
0.180721 + 0.983534i \(0.442157\pi\)
\(824\) 18580.4 0.785534
\(825\) −56949.1 −2.40329
\(826\) −26283.9 −1.10718
\(827\) −23457.2 −0.986321 −0.493160 0.869938i \(-0.664158\pi\)
−0.493160 + 0.869938i \(0.664158\pi\)
\(828\) −10864.0 −0.455977
\(829\) 12755.8 0.534413 0.267206 0.963639i \(-0.413899\pi\)
0.267206 + 0.963639i \(0.413899\pi\)
\(830\) −28832.5 −1.20577
\(831\) 20893.7 0.872197
\(832\) 7809.41 0.325412
\(833\) 13249.4 0.551099
\(834\) 31342.1 1.30130
\(835\) −35271.6 −1.46183
\(836\) −9959.43 −0.412027
\(837\) 10120.9 0.417956
\(838\) −14122.7 −0.582174
\(839\) −3046.67 −0.125367 −0.0626834 0.998033i \(-0.519966\pi\)
−0.0626834 + 0.998033i \(0.519966\pi\)
\(840\) −65956.9 −2.70920
\(841\) −24327.5 −0.997478
\(842\) 26879.5 1.10015
\(843\) 43374.1 1.77210
\(844\) −11338.7 −0.462436
\(845\) 33572.7 1.36679
\(846\) 24670.6 1.00259
\(847\) 25271.8 1.02520
\(848\) −3417.48 −0.138392
\(849\) 53700.9 2.17080
\(850\) −25940.5 −1.04677
\(851\) −4166.43 −0.167830
\(852\) 14771.9 0.593988
\(853\) −30583.2 −1.22761 −0.613804 0.789459i \(-0.710361\pi\)
−0.613804 + 0.789459i \(0.710361\pi\)
\(854\) −12525.4 −0.501886
\(855\) 20345.4 0.813800
\(856\) −14367.4 −0.573675
\(857\) −6042.11 −0.240834 −0.120417 0.992723i \(-0.538423\pi\)
−0.120417 + 0.992723i \(0.538423\pi\)
\(858\) 11185.0 0.445045
\(859\) 29736.6 1.18114 0.590570 0.806987i \(-0.298903\pi\)
0.590570 + 0.806987i \(0.298903\pi\)
\(860\) 0 0
\(861\) 60353.3 2.38889
\(862\) −18042.3 −0.712905
\(863\) −33937.7 −1.33865 −0.669324 0.742971i \(-0.733416\pi\)
−0.669324 + 0.742971i \(0.733416\pi\)
\(864\) 6851.57 0.269786
\(865\) −20593.6 −0.809482
\(866\) −5205.81 −0.204273
\(867\) 1474.34 0.0577524
\(868\) 16213.1 0.633997
\(869\) −7219.14 −0.281810
\(870\) −1977.10 −0.0770460
\(871\) −10648.9 −0.414265
\(872\) 14462.2 0.561644
\(873\) −2031.59 −0.0787617
\(874\) 20641.5 0.798865
\(875\) −17189.6 −0.664132
\(876\) −11039.1 −0.425771
\(877\) −42501.2 −1.63645 −0.818224 0.574900i \(-0.805041\pi\)
−0.818224 + 0.574900i \(0.805041\pi\)
\(878\) −1747.84 −0.0671830
\(879\) 49098.6 1.88402
\(880\) −21488.0 −0.823138
\(881\) −29766.2 −1.13831 −0.569154 0.822231i \(-0.692729\pi\)
−0.569154 + 0.822231i \(0.692729\pi\)
\(882\) −7910.44 −0.301994
\(883\) −32939.0 −1.25536 −0.627682 0.778470i \(-0.715996\pi\)
−0.627682 + 0.778470i \(0.715996\pi\)
\(884\) −3740.58 −0.142318
\(885\) −62503.5 −2.37405
\(886\) −13275.5 −0.503386
\(887\) −11353.9 −0.429793 −0.214896 0.976637i \(-0.568941\pi\)
−0.214896 + 0.976637i \(0.568941\pi\)
\(888\) −4331.04 −0.163671
\(889\) 33038.9 1.24644
\(890\) 38875.6 1.46417
\(891\) 42903.9 1.61317
\(892\) 2780.00 0.104351
\(893\) 34414.9 1.28964
\(894\) 4949.02 0.185145
\(895\) −62799.1 −2.34541
\(896\) 933.988 0.0348241
\(897\) 17019.8 0.633529
\(898\) 12442.2 0.462361
\(899\) 1633.94 0.0606175
\(900\) −11370.9 −0.421145
\(901\) 9622.48 0.355795
\(902\) 40609.8 1.49907
\(903\) 0 0
\(904\) −22132.0 −0.814270
\(905\) −3184.48 −0.116968
\(906\) −17659.1 −0.647555
\(907\) −23589.4 −0.863588 −0.431794 0.901972i \(-0.642119\pi\)
−0.431794 + 0.901972i \(0.642119\pi\)
\(908\) 7536.82 0.275461
\(909\) 22595.7 0.824480
\(910\) 13043.3 0.475143
\(911\) −34818.1 −1.26627 −0.633137 0.774040i \(-0.718233\pi\)
−0.633137 + 0.774040i \(0.718233\pi\)
\(912\) 10389.1 0.377211
\(913\) 38622.8 1.40003
\(914\) −3391.83 −0.122748
\(915\) −29785.6 −1.07616
\(916\) 7146.00 0.257762
\(917\) 19285.2 0.694497
\(918\) 7472.43 0.268657
\(919\) 3187.72 0.114421 0.0572106 0.998362i \(-0.481779\pi\)
0.0572106 + 0.998362i \(0.481779\pi\)
\(920\) −67532.0 −2.42007
\(921\) 4776.78 0.170901
\(922\) 6501.95 0.232246
\(923\) −9821.22 −0.350238
\(924\) 26279.6 0.935645
\(925\) −4360.85 −0.155010
\(926\) −3719.64 −0.132003
\(927\) 15123.3 0.535831
\(928\) 1106.14 0.0391279
\(929\) −45524.5 −1.60776 −0.803881 0.594790i \(-0.797235\pi\)
−0.803881 + 0.594790i \(0.797235\pi\)
\(930\) −52513.1 −1.85158
\(931\) −11034.9 −0.388457
\(932\) −7176.69 −0.252232
\(933\) 16087.0 0.564484
\(934\) 8617.71 0.301906
\(935\) 60503.1 2.11622
\(936\) 7508.35 0.262199
\(937\) 4059.73 0.141543 0.0707714 0.997493i \(-0.477454\pi\)
0.0707714 + 0.997493i \(0.477454\pi\)
\(938\) 34078.1 1.18624
\(939\) 64417.0 2.23873
\(940\) −33489.9 −1.16204
\(941\) −54046.4 −1.87233 −0.936165 0.351562i \(-0.885651\pi\)
−0.936165 + 0.351562i \(0.885651\pi\)
\(942\) 23421.4 0.810095
\(943\) 61794.6 2.13395
\(944\) −13544.9 −0.467000
\(945\) 19130.3 0.658529
\(946\) 0 0
\(947\) 31268.1 1.07294 0.536472 0.843918i \(-0.319757\pi\)
0.536472 + 0.843918i \(0.319757\pi\)
\(948\) −3396.51 −0.116364
\(949\) 7339.39 0.251050
\(950\) 21604.7 0.737841
\(951\) −43540.8 −1.48465
\(952\) 40244.9 1.37011
\(953\) −11116.2 −0.377849 −0.188924 0.981992i \(-0.560500\pi\)
−0.188924 + 0.981992i \(0.560500\pi\)
\(954\) −5745.00 −0.194970
\(955\) −22729.3 −0.770159
\(956\) −9166.79 −0.310120
\(957\) 2648.44 0.0894585
\(958\) −12610.8 −0.425299
\(959\) 30556.4 1.02890
\(960\) −59429.6 −1.99800
\(961\) 13607.7 0.456771
\(962\) 856.483 0.0287049
\(963\) −11694.1 −0.391317
\(964\) 3270.68 0.109275
\(965\) 25839.4 0.861968
\(966\) −54466.0 −1.81409
\(967\) 11030.9 0.366835 0.183417 0.983035i \(-0.441284\pi\)
0.183417 + 0.983035i \(0.441284\pi\)
\(968\) 26897.6 0.893101
\(969\) −29252.1 −0.969776
\(970\) −3756.27 −0.124336
\(971\) 856.625 0.0283114 0.0141557 0.999900i \(-0.495494\pi\)
0.0141557 + 0.999900i \(0.495494\pi\)
\(972\) 15743.0 0.519502
\(973\) −48959.8 −1.61313
\(974\) −15685.3 −0.516005
\(975\) 17814.0 0.585134
\(976\) −6454.72 −0.211691
\(977\) 37169.2 1.21714 0.608572 0.793499i \(-0.291743\pi\)
0.608572 + 0.793499i \(0.291743\pi\)
\(978\) −58036.5 −1.89755
\(979\) −52076.0 −1.70006
\(980\) 10738.3 0.350022
\(981\) 11771.4 0.383110
\(982\) −88.3915 −0.00287239
\(983\) −18476.9 −0.599513 −0.299757 0.954016i \(-0.596905\pi\)
−0.299757 + 0.954016i \(0.596905\pi\)
\(984\) 64236.1 2.08107
\(985\) −6978.19 −0.225730
\(986\) 1206.37 0.0389641
\(987\) −90809.4 −2.92857
\(988\) 3115.37 0.100317
\(989\) 0 0
\(990\) −36122.8 −1.15965
\(991\) 38302.6 1.22777 0.613886 0.789395i \(-0.289606\pi\)
0.613886 + 0.789395i \(0.289606\pi\)
\(992\) 29379.7 0.940329
\(993\) 41664.2 1.33149
\(994\) 31429.4 1.00290
\(995\) −6761.58 −0.215434
\(996\) 18171.5 0.578098
\(997\) 53758.0 1.70765 0.853827 0.520557i \(-0.174276\pi\)
0.853827 + 0.520557i \(0.174276\pi\)
\(998\) −13142.7 −0.416860
\(999\) 1256.19 0.0397839
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 1849.4.a.d.1.4 10
43.6 even 3 43.4.c.a.36.4 yes 20
43.36 even 3 43.4.c.a.6.4 20
43.42 odd 2 1849.4.a.f.1.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.4.c.a.6.4 20 43.36 even 3
43.4.c.a.36.4 yes 20 43.6 even 3
1849.4.a.d.1.4 10 1.1 even 1 trivial
1849.4.a.f.1.7 10 43.42 odd 2